100 doors: Difference between revisions
(100 doors in Asymptote) |
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print "Door $a is ${(doors[a]) ? 'open.': 'closed.'}" |
print "Door $a is ${(doors[a]) ? 'open.': 'closed.'}" |
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</lang> |
</lang> |
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=={{header|Asymptote}}== |
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<lang Asymptote>for(int i = 1; i < 100; ++i) { |
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if (i % i^2 < 11) { |
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write("Door ", i^2, suffix=none); |
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write(" is open"); |
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} |
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}</lang> |
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=={{header|ATS}}== |
=={{header|ATS}}== |
Revision as of 00:57, 13 June 2022
You are encouraged to solve this task according to the task description, using any language you may know.
There are 100 doors in a row that are all initially closed.
You make 100 passes by the doors.
The first time through, visit every door and toggle the door (if the door is closed, open it; if it is open, close it).
The second time, only visit every 2nd door (door #2, #4, #6, ...), and toggle it.
The third time, visit every 3rd door (door #3, #6, #9, ...), etc, until you only visit the 100th door.
- Task
Answer the question: what state are the doors in after the last pass? Which are open, which are closed?
Alternate:
As noted in this page's discussion page, the only doors that remain open are those whose numbers are perfect squares.
Opening only those doors is an optimization that may also be expressed;
however, as should be obvious, this defeats the intent of comparing implementations across programming languages.
11l
<lang 11l>V doors = [0B] * 100 L(i) 100
L(j) (i .< 100).step(i + 1) doors[j] = !doors[j] print(‘Door ’(i + 1)‘: ’(I doors[i] {‘open’} E ‘close’))</lang>
360 Assembly
<lang 360asm>* 100 doors 13/08/2015 HUNDOOR CSECT
USING HUNDOOR,R12 LR R12,R15 LA R6,0 LA R8,1 step 1 LA R9,100
LOOPI BXH R6,R8,ELOOPI do ipass=1 to 100 (R6)
LR R7,R6 SR R7,R6 LR R10,R6 step ipass LA R11,100
LOOPJ BXH R7,R10,ELOOPJ do idoor=ipass to 100 by ipass (R7)
LA R5,DOORS-1 AR R5,R7 XI 0(R5),X'01' doors(idoor)=not(doors(idoor))
NEXTJ B LOOPJ ELOOPJ B LOOPI ELOOPI LA R10,BUFFER R10 address of the buffer
LA R5,DOORS R5 address of doors item LA R6,1 idoor=1 (R6) LA R9,100 loop counter
LOOPN CLI 0(R5),X'01' if doors(idoor)=1
BNE NEXTN XDECO R6,XDEC idoor to decimal MVC 0(4,R10),XDEC+8 move decimal to buffer LA R10,4(R10)
NEXTN LA R6,1(R6) idoor=idoor+1
LA R5,1(R5) BCT R9,LOOPN loop
ELOOPN XPRNT BUFFER,80 RETURN XR R15,R15
BR R14
DOORS DC 100X'00' BUFFER DC CL80' ' XDEC DS CL12
YREGS END HUNDOOR</lang>
- Output:
1 4 9 16 25 36 49 64 81 100
4DOS Batch
<lang 4DOS Batch> @echo off set doors=%@repeat[C,100] do step = 1 to 100
do door = %step to 100 by %step set doors=%@left[%@eval[%door-1],%doors]%@if[%@instr[%@eval[%door-1],1,%doors]==C,O,C]%@right[%@eval[100-%door],%doors] enddo
enddo </lang>
The SET line consists of three functions: <lang> %@left[n,string] ^: Return n leftmost chars in string %@right[n,string] ^: Return n rightmost chars in string %@if[condition,true-val,false-val] ^: Evaluate condition; return true-val if true, false-val if false </lang>
Here @IF is used to toggle between C and O.
6502 Assembly
unoptimized Based on BASIC QB64 unoptimized version <lang 6502asm>; 100 DOORS in 6502 assembly language for: http://www.6502asm.com/beta/index.html
- Written for the original MOS Technology, Inc. NMOS version of the 6502, but should work with any version.
- Based on BASIC QB64 unoptimized version
- http://rosettacode.org/wiki/100_doors#BASIC
- Notes
- Doors array[1..100] is at $0201..$0264. On the specified emulator, this is in video memory, so tbe results will
- be directly shown as pixels in the display.
- $0200 (door 0) is cleared for display purposes but is not involved in the open/close loops.
- Y register holds Stride
- X register holds Index
- Zero Page address $01 used to add Stride to Index (via A) because there's no add-to-X or add-Y-to-A instruction.
; First, zero door array LDA #00 LDX #100
Z_LOOP:
STA 200,X DEX BNE Z_LOOP STA 200,X
; Now do doors repeated open/close LDY #01 ; Initial value of Stride
S_LOOP:
CPY #101 BCS S_DONE TYA ; Initial value of Index
I_LOOP:
CMP #101 BCS I_DONE TAX ; Use as Door array index INC $200,X ; Toggle bit 0 to reverse state of door STY 01 ; Add stride (Y) to index (X, via A) ADC 01 BCC I_LOOP
I_DONE:
INY BNE S_LOOP
S_DONE:
; Finally, format array values for output: 0 for closed, 1 for open LDX #100
C_LOOP:
LDA $200,X AND #$01 STA $200,X DEX BNE C_LOOP</lang>
48. bytes of code; the specified emulator does not report cycles.
optimized Largely inspired by the optimized C implementation - makes use of the fact that finally only the doors whose numbers are squares of integers are open, as well as the fact that
.
<lang 6502asm> ;assumes memory at $02xx is initially set to 0 and stack pointer is initialized
;the 1 to 100 door byte array will be at $0200-$0263 (decimal 512 to 611) ;Zero-page location $01 will hold delta ;At end, closed doors = $00, open doors = $01
start: ldx #0 ;initialize index - first door will be at $200 + $0
stx $1 inc $1 ;start out with a delta of 1 (0+1=1)
openloop: inc $200,X ;open X'th door
inc $1 ;add 2 to delta inc $1 txa ;add delta to X by transferring X to A, adding delta to A, then transferring back to X clc ; clear carry before adding (6502 has no add-without-carry instruction) adc $1 tax cpx #$64 ;check to see if we're at or past the 100th door (at $200 + $63) bmi openloop ;jump back to openloop if less than 100</lang>
22. bytes of code; the specified emulator does not report cycles.
68000 Assembly
Some of the macro code is derived from the examples included with EASy68K. <lang 68000devpac>*-----------------------------------------------------------
- Title : 100Doors.X68
- Written by : G. A. Tippery
- Date : 2014-01-17
- Description: Solves "100 Doors" problem, see: http://rosettacode.org/wiki/100_doors
- Notes : Translated from C "Unoptimized" version, http://rosettacode.org/wiki/100_doors#unoptimized
- : No optimizations done relative to C version; "for("-equivalent loops could be optimized.
- -----------------------------------------------------------
- System-specific general console I/O macros (Sim68K, in this case)
PUTS MACRO
** Print a null-terminated string w/o CRLF ** ** Usage: PUTS stringaddress ** Returns with D0, A1 modified MOVEQ #14,D0 ; task number 14 (display null string) LEA \1,A1 ; address of string TRAP #15 ; display it ENDM
PRINTN MACRO
** Print decimal integer from number in register ** Usage: PRINTN register ** Returns with D0,D1 modified IFNC '\1','D1' ;if some register other than D1 MOVE.L \1,D1 ;put number to display in D1 ENDC MOVE.B #3,D0 TRAP #15 ;display number in D1
- Generic constants
CR EQU 13 ;ASCII Carriage Return LF EQU 10 ;ASCII Line Feed
- Definitions specific to this program
- Register usage:
- D3 == pass (index)
- D4 == door (index)
- A2 == Doors array pointer
SIZE EQU 100 ;Define a symbolic constant for # of doors
ORG $1000 ;Specify load address for program -- actual address system-specific
START: ; Execution starts here
LEA Doors,A2 ; make A2 point to Doors byte array MOVEQ #0,D3
PassLoop:
CMP #SIZE,D3 BCC ExitPassLoop ; Branch on Carry Clear - being used as Branch on Higher or Equal MOVE D3,D4
DoorLoop:
CMP #SIZE,D4 BCC ExitDoorLoop NOT.B 0(A2,D4) ADD D3,D4 ADDQ #1,D4 BRA DoorLoop
ExitDoorLoop:
ADDQ #1,D3 BRA PassLoop
ExitPassLoop:
- $28 = 40. bytes of code to this point. 32626 cycles so far.
- At this point, the result exists as the 100 bytes starting at address Doors.
- To get output, we must use methods specific to the particular hardware, OS, or
- emulator system that the code is running on. I use macros to "hide" some of the
- system-specific details; equivalent macros would be written for another system.
MOVEQ #0,D4
PrintLoop:
CMP #SIZE,D4 BCC ExitPrintLoop PUTS DoorMsg1 MOVE D4,D1 ADDQ #1,D1 ; Convert index to 1-based instead of 0-based PRINTN D1 PUTS DoorMsg2 TST.B 0(A2,D4) ; Is this door open (!= 0)? BNE ItsOpen PUTS DoorMsgC BRA Next
ItsOpen:
PUTS DoorMsgO
Next:
ADDQ #1,D4 BRA PrintLoop
ExitPrintLoop:
- What to do at end of program is also system-specific
SIMHALT ;Halt simulator
- $78 = 120. bytes of code to this point, but this will depend on how the I/O macros are actually written.
- Cycle count is nearly meaningless, as the I/O hardware and routines will dominate the timing.
- Data memory usage
ORG $2000
Doors DCB.B SIZE,0 ;Reserve 100 bytes, prefilled with zeros
DoorMsg1 DC.B 'Door ',0 DoorMsg2 DC.B ' is ',0 DoorMsgC DC.B 'closed',CR,LF,0 DoorMsgO DC.B 'open',CR,LF,0
END START ;last line of source
</lang>
8080 Assembly
<lang 8080asm>page: equ 2 ; Store doors in page 2 doors: equ 100 ; 100 doors puts: equ 9 ; CP/M string output org 100h xra a ; Set all doors to zero lxi h,256*page mvi c,doors zero: mov m,a inx h dcr c jnz zero mvi m,'$' ; CP/M string terminator (for easier output later) mov d,a ; D=0 so that DE=E=pass counter mov e,a ; E=0, first pass mvi a,doors-1 ; Last pass and door pass: mov l,e ; L=door counter, start at first door in pass door: inr m ; Incrementing always toggles the low bit dad d ; Go to next door in pass inr l cmp l ; Was this the last door? jnc door ; If not, do the next door inr e ; Next pass cmp e ; Was this the last pass? jnc pass ; If not, do the next pass lxi h,256*page mvi c,doors ; Door counter lxi d,130h ; D=1 (low bit), E=30h (ascii 0) char: mov a,m ; Get door ana d ; Low bit gives door status ora e ; ASCII 0 or 1 mov m,a ; Write character back inx h ; Next door dcr c ; Any doors left? jnz char ; If so, next door lxi d,256*page mvi c,puts ; CP/M system call to print the string jmp 5</lang>
- Output:
1001000010000001000000001000000000010000000000001000000000000001000000000000000010000000000000000001
8086 Assembly
8th
<lang forth> \ Array of doors; init to empty; accessing a non-extant member will return \ 'null', which is treated as 'false', so we don't need to initialize it: [] var, doors
\ given a door number, get the value and toggle it:
- toggle-door \ n --
doors @ over a:@ not rot swap a:! drop ;
\ print which doors are open:
- .doors
( doors @ over a:@ nip if . space else drop then ) 1 100 loop ;
\ iterate over the doors, skipping 'n':
- main-pass \ n --
0 true repeat drop dup toggle-door over n:+ dup 101 < while 2drop drop ;
\ calculate the first 100 doors: ' main-pass 1 100 loop \ print the results: .doors cr bye </lang>
- Output:
1 4 9 16 25 36 49 64 81 100
AArch64 Assembly
unoptimized <lang AArch64 Assembly> /* ARM assembly AARCH64 Raspberry PI 3B */ /* program 100doors64.s */
/*******************************************/ /* Constantes file */ /*******************************************/ /* for this file see task include a file in language AArch64 assembly*/ .include "../includeConstantesARM64.inc"
.equ NBDOORS, 100 /*********************************/ /* Initialized data */ /*********************************/ .data sMessResult: .asciz "The door @ is open.\n"
/*********************************/ /* UnInitialized data */ /*********************************/ .bss stTableDoors: .skip 8 * NBDOORS sZoneConv: .skip 24 /*********************************/ /* code section */ /*********************************/ .text .global main main: // entry of program
// display first line ldr x3,qAdrstTableDoors // table address mov x5,1
1:
mov x4,x5
2: // begin loop
ldr x2,[x3,x4,lsl #3] // read doors index x4 cmp x2,#0 cset x2,eq //moveq x2,#1 // if x2 = 0 1 -> x2 //movne x2,#0 // if x2 = 1 0 -> x2 str x2,[x3,x4,lsl #3] // store value of doors add x4,x4,x5 // increment x4 with x5 value cmp x4,NBDOORS // number of doors ? ble 2b // no -> loop add x5,x5,#1 // increment the increment !! cmp x5,NBDOORS // number of doors ? ble 1b // no -> loop // loop display state doors mov x4,#0
3:
ldr x2,[x3,x4,lsl #3] // read state doors x4 index cmp x2,#0 beq 4f mov x0,x4 // open -> display message ldr x1,qAdrsZoneConv // display value index bl conversion10 // call function ldr x0,qAdrsMessResult ldr x1,qAdrsZoneConv bl strInsertAtCharInc // insert result at first @ character bl affichageMess // display message
4:
add x4,x4,1 cmp x4,NBDOORS ble 3b // loop
100: // standard end of the program
mov x0,0 // return code mov x8,EXIT // request to exit program svc 0 // perform the system call
qAdrstTableDoors: .quad stTableDoors qAdrsMessResult: .quad sMessResult qAdrsZoneConv: .quad sZoneConv /***********************************************/ /* File Include fonctions */ /********************************************************/ /* for this file see task include a file in language AArch64 assembly */ .include "../includeARM64.inc" </lang> optimized <lang AArch64 Assembly> /* ARM assembly AARCH64 Raspberry PI 3B */ /* program 100doors64_1.s */
/*******************************************/ /* Constantes file */ /*******************************************/ /* for this file see task include a file in language AArch64 assembly*/ .include "../includeConstantesARM64.inc"
.equ NBDOORS, 100 /*********************************/ /* Initialized data */ /*********************************/ .data sMessResult: .asciz "The door @ is open.\n"
/*********************************/ /* UnInitialized data */ /*********************************/ .bss sZoneConv: .skip 24 /*********************************/ /* code section */ /*********************************/ .text .global main main: // entry of program
mov x5,3 mov x4,1
1:
mov x0,x4 ldr x1,qAdrsZoneConv // display value index bl conversion10 // call function ldr x0,qAdrsMessResult ldr x1,qAdrsZoneConv bl strInsertAtCharInc // insert result at first @ character bl affichageMess // display message add x4,x4,x5 add x5,x5,2 cmp x4,NBDOORS ble 1b // loop
100: // standard end of the program
mov x0,0 // return code mov x8,EXIT // request to exit program svc 0 // perform the system call
qAdrsMessResult: .quad sMessResult qAdrsZoneConv: .quad sZoneConv /***********************************************/ /* File Include fonctions */ /********************************************************/ /* for this file see task include a file in language AArch64 assembly */ .include "../includeARM64.inc" </lang>
ABAP
unoptimized <lang ABAP>form open_doors_unopt.
data: lv_door type i, lv_count type i value 1. data: lt_doors type standard table of c initial size 100. field-symbols: <wa_door> type c. do 100 times. append initial line to lt_doors assigning <wa_door>. <wa_door> = 'X'. enddo.
while lv_count < 100. lv_count = lv_count + 1. lv_door = lv_count. while lv_door < 100. read table lt_doors index lv_door assigning <wa_door>. if <wa_door> = ' '. <wa_door> = 'X'. else. <wa_door> = ' '. endif. add lv_count to lv_door. endwhile. endwhile.
loop at lt_doors assigning <wa_door>. if <wa_door> = 'X'. write : / 'Door', (4) sy-tabix right-justified, 'is open' no-gap. endif. endloop.
endform.</lang>
unoptimized / functional <lang ABAP> cl_demo_output=>display( REDUCE stringtab( INIT list TYPE stringtab
aux TYPE i FOR door = 1 WHILE door <= 100 FOR pass = 1 WHILE pass <= 100 NEXT aux = COND #( WHEN pass = 1 THEN 1 WHEN door MOD pass = 0 THEN aux + 1 ELSE aux ) list = COND #( WHEN pass = 100 THEN COND #( WHEN aux MOD 2 <> 0 THEN VALUE #( BASE list ( CONV #( door ) ) ) ELSE list ) ELSE list ) ) ).
</lang>
optimized
Using <lang ABAP>form open_doors_opt.
data: lv_square type i value 1, lv_inc type i value 3. data: lt_doors type standard table of c initial size 100. field-symbols: <wa_door> type c. do 100 times. append initial line to lt_doors assigning <wa_door>. if sy-index = lv_square. <wa_door> = 'X'. add: lv_inc to lv_square, 2 to lv_inc. write : / 'Door', (4) sy-index right-justified, 'is open' no-gap. endif. enddo.
endform.</lang>
ultra-optimized / imperative
<lang ABAP>
DO 10 TIMES.
DATA(val) = sy-index * sy-index. WRITE: / val.
ENDDO. </lang>
ultra-optimized / functional <lang ABAP> cl_demo_output=>display( REDUCE stringtab( INIT list TYPE stringtab
FOR i = 1 WHILE i <= 10 NEXT list = VALUE #( BASE list ( i * i ) ) ) ).
</lang>
ACL2
<lang lisp>(defun rep (n x)
(if (zp n) nil (cons x (rep (- n 1) x))))
(defun toggle-every-r (n i bs)
(if (endp bs) nil (cons (if (zp i) (not (first bs)) (first bs)) (toggle-every-r n (mod (1- i) n) (rest bs)))))
(defun toggle-every (n bs)
(toggle-every-r n (1- n) bs))
(defun 100-doors (i doors)
(if (zp i) doors (100-doors (1- i) (toggle-every i doors))))</lang>
Action!
<lang Action!>DEFINE COUNT="100"
PROC Main()
BYTE ARRAY doors(COUNT+1) BYTE door,pass
FOR door=1 TO COUNT DO doors(door)=0 OD PrintE("Following doors are open:") FOR pass=1 TO COUNT DO FOR door=pass TO COUNT STEP pass DO doors(door)==!$FF OD IF doors(pass)=$FF THEN PrintB(pass) Put(32) FI OD
RETURN</lang>
- Output:
Screenshot from Atari 8-bit computer
Following doors are open: 1 4 9 16 25 36 49 64 81 100
ActionScript
unoptimized <lang actionscript>package {
import flash.display.Sprite;
public class Doors extends Sprite { public function Doors() {
// Initialize the array var doors:Array = new Array(100); for (var i:Number = 0; i < 100; i++) { doors[i] = false;
// Do the work for (var pass:Number = 0; pass < 100; pass++) { for (var j:Number = pass; j < 100; j += (pass+1)) { doors[j] = !doors[j]; } } trace(doors); } }
}</lang>
Acurity Architect
Using #HASH-OFF, OPTION OICC ="^" , CICC ="^"
<lang acurity architect> VAR sStatus: SHORT VAR sArray: SHORT VAR sCount: SHORT VAR sDoor: SHORT VAR sPass: SHORT VAR zIndex: STRING VAR zState: STRING // SET sStatus = GET_UNUSED_ARRAY_HANDLE(sArray) SET sStatus = INIT_SORTED_ARRAY(sArray, 0, 0, 1) // DO sCount = 1 TO 100
DO sPass = 1 TO 100 SET sDoor = sCount * sPass IF sDoor <= 100 SET zIndex = REPEAT("0", 3 - LENGTH(STR(sDoor))) + STR(sDoor) SET sStatus = READ_ARRAY_REC("=", sArray, zIndex) SET zState = "OPEN" IF GET_STRING_SAY(sArray, 1) = "OPEN" SET zState = "CLOSE" ENDIF // SET sStatus = ADD_ARRAY_REC(sArray, zIndex) SET sStatus = PUT_STRING_SAY(sArray, 1, zState) ELSE BREAK ENDIF ENDDO
ENDDO // SET zIndex = "" SET sStatus = READ_ARRAY_REC(">=", sArray, zIndex) DO WHILE sStatus = 0
>>Door: ^zIndex^ State: ^GET_STRING_SAY(sArray, 1)^ SET sStatus = READ_ARRAY_REC("+", sArray, zIndex)
ENDDO </lang>
- Output:
Door: 001 State: OPEN Door: 002 State: CLOSE Door: 003 State: CLOSE Door: 004 State: OPEN Door: 005 State: CLOSE Door: 006 State: CLOSE Door: 007 State: CLOSE Door: 008 State: CLOSE Door: 009 State: OPEN Door: 010 State: CLOSE Door: 011 State: CLOSE Door: 012 State: CLOSE Door: 013 State: CLOSE Door: 014 State: CLOSE Door: 015 State: CLOSE Door: 016 State: OPEN Door: 017 State: CLOSE Door: 018 State: CLOSE Door: 019 State: CLOSE Door: 020 State: CLOSE Door: 021 State: CLOSE Door: 022 State: CLOSE Door: 023 State: CLOSE Door: 024 State: CLOSE Door: 025 State: OPEN Door: 026 State: CLOSE Door: 027 State: CLOSE Door: 028 State: CLOSE Door: 029 State: CLOSE Door: 030 State: CLOSE Door: 031 State: CLOSE Door: 032 State: CLOSE Door: 033 State: CLOSE Door: 034 State: CLOSE Door: 035 State: CLOSE Door: 036 State: OPEN Door: 037 State: CLOSE Door: 038 State: CLOSE Door: 039 State: CLOSE Door: 040 State: CLOSE Door: 041 State: CLOSE Door: 042 State: CLOSE Door: 043 State: CLOSE Door: 044 State: CLOSE Door: 045 State: CLOSE Door: 046 State: CLOSE Door: 047 State: CLOSE Door: 048 State: CLOSE Door: 049 State: OPEN Door: 050 State: CLOSE Door: 051 State: CLOSE Door: 052 State: CLOSE Door: 053 State: CLOSE Door: 054 State: CLOSE Door: 055 State: CLOSE Door: 056 State: CLOSE Door: 057 State: CLOSE Door: 058 State: CLOSE Door: 059 State: CLOSE Door: 060 State: CLOSE Door: 061 State: CLOSE Door: 062 State: CLOSE Door: 063 State: CLOSE Door: 064 State: OPEN Door: 065 State: CLOSE Door: 066 State: CLOSE Door: 067 State: CLOSE Door: 068 State: CLOSE Door: 069 State: CLOSE Door: 070 State: CLOSE Door: 071 State: CLOSE Door: 072 State: CLOSE Door: 073 State: CLOSE Door: 074 State: CLOSE Door: 075 State: CLOSE Door: 076 State: CLOSE Door: 077 State: CLOSE Door: 078 State: CLOSE Door: 079 State: CLOSE Door: 080 State: CLOSE Door: 081 State: OPEN Door: 082 State: CLOSE Door: 083 State: CLOSE Door: 084 State: CLOSE Door: 085 State: CLOSE Door: 086 State: CLOSE Door: 087 State: CLOSE Door: 088 State: CLOSE Door: 089 State: CLOSE Door: 090 State: CLOSE Door: 091 State: CLOSE Door: 092 State: CLOSE Door: 093 State: CLOSE Door: 094 State: CLOSE Door: 095 State: CLOSE Door: 096 State: CLOSE Door: 097 State: CLOSE Door: 098 State: CLOSE Door: 099 State: CLOSE Door: 100 State: OPEN
Ada
unoptimized <lang ada>with Ada.Text_Io; use Ada.Text_Io;
procedure Doors is type Door_State is (Closed, Open); type Door_List is array(Positive range 1..100) of Door_State; The_Doors : Door_List := (others => Closed); begin for I in 1..100 loop for J in The_Doors'range loop if J mod I = 0 then if The_Doors(J) = Closed then The_Doors(J) := Open; else The_Doors(J) := Closed; end if; end if; end loop; end loop; for I in The_Doors'range loop Put_Line(Integer'Image(I) & " is " & Door_State'Image(The_Doors(I))); end loop; end Doors;</lang>
optimized <lang ada>with Ada.Text_Io; use Ada.Text_Io;
with Ada.Numerics.Elementary_Functions; use Ada.Numerics.Elementary_Functions; procedure Doors_Optimized is Num : Float; begin for I in 1..100 loop Num := Sqrt(Float(I)); Put(Integer'Image(I) & " is "); if Float'Floor(Num) = Num then Put_Line("Opened"); else Put_Line("Closed"); end if; end loop; end Doors_Optimized;</lang>
Agena
Translation of Algol W. Tested with Agena 2.9.5 Win32 <lang agena># find the first few squares via the unoptimised door flipping method scope
local doorMax := 100; local door; create register door( doorMax );
# set all doors to closed for i to doorMax do door[ i ] := false od;
# repeatedly flip the doors for i to doorMax do for j from i to doorMax by i do door[ j ] := not door[ j ] od od;
# display the results for i to doorMax do if door[ i ] then write( " ", i ) fi od; print()
epocs</lang>
Aikido
<lang aikido> var doors = new int [100]
foreach pass 100 {
for (var door = pass ; door < 100 ; door += pass+1) { doors[door] = !doors[door] }
}
var d = 1 foreach door doors {
println ("door " + d++ + " is " + (door ? "open" : "closed"))
}
</lang>
ALGOL 60
<lang algol60> begin
comment - 100 doors problem in ALGOL-60;
boolean array doors[1:100]; integer i, j; boolean open, closed;
open := true; closed := not true;
outstring(1,"100 Doors Problem\n");
comment - all doors are initially closed; for i := 1 step 1 until 100 do
doors[i] := closed;
comment
cycle through at increasing intervals and flip each door encountered;
for i := 1 step 1 until 100 do
for j := i step i until 100 do doors[j] := not doors[j];
comment - show which doors are open; outstring(1,"The open doors are:"); for i := 1 step 1 until 100 do
if doors[i] then outinteger(1,i);
end </lang>
- Output:
100 Doors Problem The open doors are: 1 4 9 16 25 36 49 64 81 100
ALGOL 68
unoptimized <lang algol68># declare some constants # INT limit = 100;
PROC doors = VOID: (
MODE DOORSTATE = BOOL; BOOL closed = FALSE; BOOL open = NOT closed; MODE DOORLIST = [limit]DOORSTATE;
DOORLIST the doors; FOR i FROM LWB the doors TO UPB the doors DO the doors[i]:=closed OD;
FOR i FROM LWB the doors TO UPB the doors DO FOR j FROM LWB the doors TO UPB the doors DO IF j MOD i = 0 THEN the doors[j] := NOT the doors[j] FI OD OD; FOR i FROM LWB the doors TO UPB the doors DO printf(($g" is "gl$,i,(the doors[i]|"opened"|"closed"))) OD
); doors;</lang> optimized <lang algol68>PROC doors optimised = ( INT limit )VOID:
FOR i TO limit DO REAL num := sqrt(i); printf(($g" is "gl$,i,(ENTIER num = num |"opened"|"closed") )) OD
doors optimised(limit)</lang>
ALGOL W
<lang algolw>begin
% find the first few squares via the unoptimised door flipping method %
integer doorMax; doorMax := 100;
begin % need to start a new block so the array can have variable bounds %
% array of doors - door( i ) is true if open, false if closed % logical array door( 1 :: doorMax );
% set all doors to closed % for i := 1 until doorMax do door( i ) := false;
% repeatedly flip the doors % for i := 1 until doorMax do begin for j := i step i until doorMax do begin door( j ) := not door( j ) end end;
% display the results % i_w := 1; % set integer field width % s_w := 1; % and separator width % for i := 1 until doorMax do if door( i ) then writeon( i )
end
end.</lang>
- Output:
1 4 9 16 25 36 49 64 81 100
ALGOL-M
<lang Algol> BEGIN
INTEGER ARRAY DOORS[1:100]; INTEGER I, J, OPEN, CLOSED;
OPEN := 1; CLOSED := 0;
% ALL DOORS ARE INITIALLY CLOSED % FOR I := 1 STEP 1 UNTIL 100 DO
BEGIN DOORS[I] := CLOSED; END;
% PASS THROUGH AT INCREASING INTERVALS AND FLIP % FOR I := 1 STEP 1 UNTIL 100 DO
BEGIN FOR J := I STEP I UNTIL 100 DO BEGIN DOORS[J] := 1 - DOORS[J]; END; END;
% SHOW RESULTS % WRITE("THE OPEN DOORS ARE:"); WRITE(""); FOR I := 1 STEP 1 UNTIL 100 DO
BEGIN IF DOORS[I] = OPEN THEN WRITEON(I); END;
END </lang>
- Output:
THE OPEN DOORS ARE: 1 4 9 16 25 36 49 64 81 100
AmigaE
<lang amigae>PROC main()
DEF t[100]: ARRAY, pass, door FOR door := 0 TO 99 DO t[door] := FALSE FOR pass := 0 TO 99 door := pass WHILE door <= 99 t[door] := Not(t[door]) door := door + pass + 1 ENDWHILE ENDFOR FOR door := 0 TO 99 DO WriteF('\d is \s\n', door+1, IF t[door] THEN 'open' ELSE 'closed')
ENDPROC</lang>
APL
<lang APL>doors←{100⍴((⍵-1)⍴0),1} ≠⌿⊃doors¨ ⍳100</lang>
- Output:
1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
optimized Note that ⎕IO = 1
2|+/[1]0=D∘.|D←⍳100
The idea is that the n:th door will be flipped the same number of times as there are divisors for n. So first we make D all ints 1..100 (D←⍳100).
The next step is to find the remainders of every such int when divided by every other (D∘.|D).
This results in a 100×100 matrix which we turn into a binary one by testing if the values are equal to zero i.e. divisors.
Next: sum along axis 1, i.e. the columns. This tells us the number of divisors. Finally calculate the remainder of these when divided by 2, i.e. find which n have an odd number of divisors, i.e. will be flipped an odd number of times and thus end up open.
<lang APL> ⍝⍝ Also works with GNU APL after introduction of ⍝⍝ the ⍸ function with SVN r1368, Dec 03 2020 ⍸≠⌿0=(⍳100)∘.|⍳100</lang>
- Output:
1 4 9 16 25 36 49 64 81 100
AppleScript
Iteration
<lang AppleScript>set is_open to {} repeat 100 times
set end of is_open to false
end repeat with pass from 1 to 100
repeat with door from pass to 100 by pass set item door of is_open to not item door of is_open end
end set open_doors to {} repeat with door from 1 to 100
if item door of is_open then set end of open_doors to door end
end set text item delimiters to ", " display dialog "Open doors: " & open_doors</lang>
Functional composition
<lang AppleScript>-- FINAL DOOR STATES ---------------------------------------------------------
-- finalDoors :: Int -> [(Int, Bool)] on finalDoors(n)
-- toggledCorridor :: [(Int, Bool)] -> (Int, Bool) -> Int -> [(Int, Bool)] script toggledCorridor on |λ|(a, _, k) -- perhapsToggled :: Bool -> Int -> Bool script perhapsToggled on |λ|(x, i) if i mod k = 0 then {i, not item 2 of x} else {i, item 2 of x} end if end |λ| end script map(perhapsToggled, a) end |λ| end script set xs to enumFromTo(1, n) foldl(toggledCorridor, ¬ zip(xs, replicate(n, {false})), xs)
end finalDoors
-- TEST ---------------------------------------------------------------------- on run
-- isOpenAtEnd :: (Int, Bool) -> Bool script isOpenAtEnd on |λ|(door) (item 2 of door) end |λ| end script -- doorNumber :: (Int, Bool) -> Int script doorNumber on |λ|(door) (item 1 of door) end |λ| end script map(doorNumber, filter(isOpenAtEnd, finalDoors(100))) --> {1, 4, 9, 16, 25, 36, 49, 64, 81, 100}
end run
-- GENERIC FUNCTIONS ---------------------------------------------------------
-- enumFromTo :: Int -> Int -> [Int] on enumFromTo(m, n)
if n < m then set d to -1 else set d to 1 end if set lst to {} repeat with i from m to n by d set end of lst to i end repeat return lst
end enumFromTo
-- filter :: (a -> Bool) -> [a] -> [a] on filter(f, xs)
tell mReturn(f) set lst to {} set lng to length of xs repeat with i from 1 to lng set v to item i of xs if |λ|(v, i, xs) then set end of lst to v end repeat return lst end tell
end filter
-- foldl :: (a -> b -> a) -> a -> [b] -> a on foldl(f, startValue, xs)
tell mReturn(f) set v to startValue set lng to length of xs repeat with i from 1 to lng set v to |λ|(v, item i of xs, i, xs) end repeat return v end tell
end foldl
-- map :: (a -> b) -> [a] -> [b] on map(f, xs)
tell mReturn(f) set lng to length of xs set lst to {} repeat with i from 1 to lng set end of lst to |λ|(item i of xs, i, xs) end repeat return lst end tell
end map
-- min :: Ord a => a -> a -> a on min(x, y)
if y < x then y else x end if
end min
-- Lift 2nd class handler function into 1st class script wrapper -- mReturn :: Handler -> Script on mReturn(f)
if class of f is script then f else script property |λ| : f end script end if
end mReturn
-- replicate :: Int -> a -> [a] on replicate(n, a)
set out to {} if n < 1 then return out set dbl to {a} repeat while (n > 1) if (n mod 2) > 0 then set out to out & dbl set n to (n div 2) set dbl to (dbl & dbl) end repeat return out & dbl
end replicate
-- zip :: [a] -> [b] -> [(a, b)] on zip(xs, ys)
set lng to min(length of xs, length of ys) set lst to {} repeat with i from 1 to lng set end of lst to {item i of xs, item i of ys} end repeat return lst
end zip</lang>
- Output:
<lang AppleScript>{1, 4, 9, 16, 25, 36, 49, 64, 81, 100}</lang>
Odd numbers of integer factors
The question of which doors are flipped an odd number of times reduces to the question of which numbers in the range have an odd number of integer factors (for an AppleScript implementation of integerFactors(n) see Factors of An Integer). Using map from the functional composition example above:
<lang AppleScript>map(factorCountMod2, enumFromTo(1, 100))
on factorCountMod2(n)
{n, (length of integerFactors(n)) mod 2 = 1}
end factorCountMod2</lang>
This, on inspection, and further reflection, then collapses to the even simpler question of which numbers are perfect squares, since all other numbers have an even number of integer factors (n factors below the square root, plus n paired cofactors above the square root). Using map and enumFromTo from the functional composition example above:
<lang AppleScript>-- perfectSquaresUpTo :: Int -> [Int] on perfectSquaresUpTo(n)
script squared -- (Int -> Int) on |λ|(x) x * x end |λ| end script set realRoot to n ^ (1 / 2) set intRoot to realRoot as integer set blnNotPerfectSquare to not (intRoot = realRoot) map(squared, enumFromTo(1, intRoot - (blnNotPerfectSquare as integer)))
end perfectSquaresUpTo
on run
perfectSquaresUpTo(100)
end run</lang>
- Output:
<lang AppleScript>{1, 4, 9, 16, 25, 36, 49, 64, 81, 100}</lang>
Arbre
<lang Arbre> openshut(n):
for x in [1..n] x%n==0
pass(n):
if n==100 openshut(n) else openshut(n) xor pass(n+1)
100doors():
pass(1) -> io
</lang>
Argile
<lang Argile>use std, array
close all doors for each pass from 1 to 100
for (door = pass) (door <= 100) (door += pass) toggle door
let int pass, door.
.: close all doors :. {memset doors 0 size of doors} .:toggle <int door>:. { !!(doors[door - 1]) }
let doors be an array of 100 bool
for each door from 1 to 100
printf "#%.3d %s\n" door (doors[door - 1]) ? "[ ]", "[X]"</lang>
ARM Assembly
unoptimized <lang ARM Assembly>
/* ARM assembly Raspberry PI */ /* program 100doors.s */
/************************************/ /* Constantes */ /************************************/ .equ STDOUT, 1 @ Linux output console .equ EXIT, 1 @ Linux syscall .equ WRITE, 4 @ Linux syscall .equ NBDOORS, 100 /*********************************/ /* Initialized data */ /*********************************/ .data sMessResult: .ascii "The door " sMessValeur: .fill 11, 1, ' ' @ size => 11
.asciz "is open.\n"
/*********************************/ /* UnInitialized data */ /*********************************/ .bss stTableDoors: .skip 4 * NBDOORS /*********************************/ /* code section */ /*********************************/ .text .global main main: @ entry of program
push {fp,lr} @ saves 2 registers @ display first line ldr r3,iAdrstTableDoors @ table address mov r5,#1
1:
mov r4,r5
2: @ begin loop
ldr r2,[r3,r4,lsl #2] @ read doors index r4 cmp r2,#0 moveq r2,#1 @ if r2 = 0 1 -> r2 movne r2,#0 @ if r2 = 1 0 -> r2 str r2,[r3,r4,lsl #2] @ store value of doors add r4,r5 @ increment r4 with r5 value cmp r4,#NBDOORS @ number of doors ? ble 2b @ no -> loop add r5,#1 @ increment the increment !! cmp r5,#NBDOORS @ number of doors ? ble 1b @ no -> loop
@ loop display state doors mov r4,#0
3:
ldr r2,[r3,r4,lsl #2] @ read state doors r4 index cmp r2,#0 beq 4f mov r0,r4 @ open -> display message ldr r1,iAdrsMessValeur @ display value index bl conversion10 @ call function ldr r0,iAdrsMessResult bl affichageMess @ display message
4:
add r4,#1 cmp r4,#NBDOORS ble 3b @ loop
100: @ standard end of the program
mov r0, #0 @ return code pop {fp,lr} @restaur 2 registers mov r7, #EXIT @ request to exit program svc #0 @ perform the system call
iAdrsMessValeur: .int sMessValeur iAdrstTableDoors: .int stTableDoors iAdrsMessResult: .int sMessResult
/******************************************************************/ /* display text with size calculation */ /******************************************************************/ /* r0 contains the address of the message */ affichageMess:
push {r0,r1,r2,r7,lr} @ save registres mov r2,#0 @ counter length
1: @ loop length calculation
ldrb r1,[r0,r2] @ read octet start position + index cmp r1,#0 @ if 0 its over addne r2,r2,#1 @ else add 1 in the length bne 1b @ and loop @ so here r2 contains the length of the message mov r1,r0 @ address message in r1 mov r0,#STDOUT @ code to write to the standard output Linux mov r7, #WRITE @ code call system "write" svc #0 @ call systeme pop {r0,r1,r2,r7,lr} @ restaur des 2 registres */ bx lr @ return
/******************************************************************/ /* Converting a register to a decimal unsigned */ /******************************************************************/ /* r0 contains value and r1 address area */ /* r0 return size of result (no zero final in area) */ /* area size => 11 bytes */ .equ LGZONECAL, 10 conversion10:
push {r1-r4,lr} @ save registers mov r3,r1 mov r2,#LGZONECAL
1: @ start loop
bl divisionpar10U @unsigned r0 <- dividende. quotient ->r0 reste -> r1 add r1,#48 @ digit strb r1,[r3,r2] @ store digit on area cmp r0,#0 @ stop if quotient = 0 subne r2,#1 @ else previous position bne 1b @ and loop // and move digit from left of area mov r4,#0
2:
ldrb r1,[r3,r2] strb r1,[r3,r4] add r2,#1 add r4,#1 cmp r2,#LGZONECAL ble 2b // and move spaces in end on area mov r0,r4 @ result length mov r1,#' ' @ space
3:
strb r1,[r3,r4] @ store space in area add r4,#1 @ next position cmp r4,#LGZONECAL ble 3b @ loop if r4 <= area size
100:
pop {r1-r4,lr} @ restaur registres bx lr @return
/***************************************************/ /* division par 10 unsigned */ /***************************************************/ /* r0 dividende */ /* r0 quotient */ /* r1 remainder */ divisionpar10U:
push {r2,r3,r4, lr} mov r4,r0 @ save value //mov r3,#0xCCCD @ r3 <- magic_number lower @ for Raspberry pi 3 //movt r3,#0xCCCC @ r3 <- magic_number upper @ for Raspberry pi 3 ldr r3,iMagicNumber @ for Raspberry pi 1 2 umull r1, r2, r3, r0 @ r1<- Lower32Bits(r1*r0) r2<- Upper32Bits(r1*r0) mov r0, r2, LSR #3 @ r2 <- r2 >> shift 3 add r2,r0,r0, lsl #2 @ r2 <- r0 * 5 sub r1,r4,r2, lsl #1 @ r1 <- r4 - (r2 * 2) = r4 - (r0 * 10) pop {r2,r3,r4,lr} bx lr @ leave function
iMagicNumber: .int 0xCCCCCCCD </lang> optimized <lang ARM Assembly> /*********************************************/ /* optimized version */ /*********************************************/ /* ARM assembly Raspberry PI */ /* program 100doors.s */
/************************************/ /* Constantes */ /************************************/ .equ STDOUT, 1 @ Linux output console .equ EXIT, 1 @ Linux syscall .equ WRITE, 4 @ Linux syscall .equ NBDOORS, 100 /*********************************/ /* Initialized data */ /*********************************/ .data sMessResult: .ascii "The door " sMessValeur: .fill 11, 1, ' ' @ size => 11
.asciz "is open.\n"
/*********************************/ /* UnInitialized data */ /*********************************/ .bss /*********************************/ /* code section */ /*********************************/ .text .global main main: @ entry of program
push {fp,lr} @ saves 2 registers @ display first line mov r5,#3 @ start value of increment mov r4,#1 @ start doors @ loop display state doors
1:
mov r0,r4 @ open -> display message ldr r1,iAdrsMessValeur @ display value index bl conversion10 @ call function ldr r0,iAdrsMessResult bl affichageMess @ display message add r4,r5 @ add increment add r5,#2 @ new increment cmp r4,#NBDOORS ble 1b @ loop
100: @ standard end of the program
mov r0, #0 @ return code pop {fp,lr} @ restaur 2 registers mov r7, #EXIT @ request to exit program svc #0 @ perform the system call
iAdrsMessValeur: .int sMessValeur iAdrsMessResult: .int sMessResult
/******************************************************************/ /* display text with size calculation */ /******************************************************************/ /* r0 contains the address of the message */ affichageMess:
push {r0,r1,r2,r7,lr} @ save registres mov r2,#0 @ counter length
1: @ loop length calculation
ldrb r1,[r0,r2] @ read octet start position + index cmp r1,#0 @ if 0 its over addne r2,r2,#1 @ else add 1 in the length bne 1b @ and loop @ so here r2 contains the length of the message mov r1,r0 @ address message in r1 mov r0,#STDOUT @ code to write to the standard output Linux mov r7, #WRITE @ code call system "write" svc #0 @ call systeme pop {r0,r1,r2,r7,lr} @ restaur des 2 registres */ bx lr @ return
/******************************************************************/ /* Converting a register to a decimal unsigned */ /******************************************************************/ /* r0 contains value and r1 address area */ /* r0 return size of result (no zero final in area) */ /* area size => 11 bytes */ .equ LGZONECAL, 10 conversion10:
push {r1-r4,lr} @ save registers mov r3,r1 mov r2,#LGZONECAL
1: @ start loop
bl divisionpar10U @ unsigned r0 <- dividende. quotient ->r0 reste -> r1 add r1,#48 @ digit strb r1,[r3,r2] @ store digit on area cmp r0,#0 @ stop if quotient = 0 subne r2,#1 @ else previous position bne 1b @ and loop @ and move digit from left of area mov r4,#0
2:
ldrb r1,[r3,r2] strb r1,[r3,r4] add r2,#1 add r4,#1 cmp r2,#LGZONECAL ble 2b @ and move spaces in end on area mov r0,r4 @ result length mov r1,#' ' @ space
3:
strb r1,[r3,r4] @ store space in area add r4,#1 @ next position cmp r4,#LGZONECAL ble 3b @ loop if r4 <= area size
100:
pop {r1-r4,lr} @ restaur registres bx lr @return
/***************************************************/ /* division par 10 unsigned */ /***************************************************/ /* r0 dividende */ /* r0 quotient */ /* r1 remainder */ divisionpar10U:
push {r2,r3,r4, lr} mov r4,r0 @ save value //mov r3,#0xCCCD @ r3 <- magic_number lower @ for raspberry 3 //movt r3,#0xCCCC @ r3 <- magic_number upper @ for raspberry 3 ldr r3,iMagicNumber @ for raspberry 1 2 umull r1, r2, r3, r0 @ r1<- Lower32Bits(r1*r0) r2<- Upper32Bits(r1*r0) mov r0, r2, LSR #3 @ r2 <- r2 >> shift 3 add r2,r0,r0, lsl #2 @ r2 <- r0 * 5 sub r1,r4,r2, lsl #1 @ r1 <- r4 - (r2 * 2) = r4 - (r0 * 10) pop {r2,r3,r4,lr} bx lr @ leave function
iMagicNumber: .int 0xCCCCCCCD </lang>
Arturo
<lang rebol>isOpen: map 1..101 => false
loop 1..100 'pass -> loop (range.step:pass pass 100) 'door [ isOpen\[door]: not? isOpen\[door] ]
loop 1..100 'x -> if isOpen\[x] [ print ["Door" x "is open."] ]</lang>
- Output:
Door 1 is open. Door 4 is open. Door 9 is open. Door 16 is open. Door 25 is open. Door 36 is open. Door 49 is open. Door 64 is open. Door 81 is open. Door 100 is open.
Astro
<lang python>var doors = falses(100)
for a in 1..100: for b in a..a..100:
doors[b] = not doors[b]
for a in 1..100:
print "Door $a is ${(doors[a]) ? 'open.': 'closed.'}"
</lang>
Asymptote
<lang Asymptote>for(int i = 1; i < 100; ++i) {
if (i % i^2 < 11) { write("Door ", i^2, suffix=none); write(" is open"); } }</lang>
ATS
<lang ATS>
- include "share/atspre_staload.hats"
implement main0((*void*)) = let // var A = @[bool][100](false) val A = $UNSAFE.cast{arrayref(bool,100)}(addr@A) // fnx loop (
pass: intGte(0)
) : void =
if pass < 100 then loop2 (pass, pass) // end of [if]
and loop2 (
pass: natLt(100), door: intGte(0)
) : void =
if door < 100 then (A[door] := ~A[door]; loop2(pass, door+pass+1)) else loop(pass+1) // end of [if]
// fun loop3 (
door: intGte(0)
) : void =
if door < 100 then ( println!("door #", door+1, " is ", (if A[door] then "open" else "closed"): string, "."); loop3(door+1) ) (* end of [then] *) // end of [if]
// in
loop(0); loop3 (0)
end // end of [main0] </lang>
AutoHotkey
Standard Approach
<lang autohotkey>Loop, 100
Door%A_Index% := "closed"
Loop, 100 {
x := A_Index, y := A_Index While (x <= 100) { CurrentDoor := Door%x% If CurrentDoor contains closed { Door%x% := "open" x += y } else if CurrentDoor contains open { Door%x% := "closed" x += y } }
}
Loop, 100 {
CurrentDoor := Door%A_Index% If CurrentDoor contains open Res .= "Door " A_Index " is open`n"
} MsgBox % Res</lang>
Alternative Approach
Making use of the identity:
<lang autohotkey>increment := 3, square := 1 Loop, 100
If (A_Index = square) outstring .= "`nDoor " A_Index " is open" ,square += increment, increment += 2
MsgBox,, Succesfull, % SubStr(outstring, 2)</lang>
Optimized
<lang autohotkey>While (Door := A_Index ** 2) <= 100
Result .= "Door " Door " is open`n"
MsgBox, %Result%</lang>
AutoIt
<lang AutoIt>
- include <array.au3>
$doors = 100
- door array, 0 = closed, 1 = open
Local $door[$doors +1]
For $ii = 1 To $doors For $i = $ii To $doors Step $ii $door[$i] = Not $door[$i] next Next
- display to screen
For $i = 1 To $doors ConsoleWrite (Number($door[$i])& " ") If Mod($i,10) = 0 Then ConsoleWrite(@CRLF) Next </lang>
AWK
unoptimized <lang awk>BEGIN {
for(i=1; i <= 100; i++) { doors[i] = 0 # close the doors } for(i=1; i <= 100; i++) { for(j=i; j <= 100; j += i) { doors[j] = (doors[j]+1) % 2 } } for(i=1; i <= 100; i++) { print i, doors[i] ? "open" : "close" }
}</lang> optimized <lang awk>BEGIN {
for(i=1; i <= 100; i++) { doors[i] = 0 # close the doors } for(i=1; i <= 100; i++) { if ( int(sqrt(i)) == sqrt(i) ) { doors[i] = 1 } } for(i=1; i <= 100; i++) { print i, doors[i] ? "open" : "close" }
}</lang>
Axiom
Unoptimized:<lang Axiom>(open,closed,change,open?) := (true,false,not,test); doors := bits(100,closed); for i in 1..#doors repeat
for j in i..#doors by i repeat doors.j := change doors.j
[i for i in 1..#doors | open? doors.i] </lang>Optimized:<lang Axiom>[i for i in 1..100 | perfectSquare? i] -- or [i^2 for i in 1..sqrt(100)::Integer]</lang>
B
<lang B>main() {
auto doors[100]; /* != 0 means open */ auto pass, door;
door = 0; while( door<100 ) doors[door++] = 0;
pass = 0; while( pass<100 ) { door = pass; while( door<100 ) { doors[door] = !doors[door]; door =+ pass+1; } ++pass; }
door = 0; while( door<100 ) { printf("door #%d is %s.*n", door+1, doors[door] ? "open" : "closed"); ++door; }
return(0);
}</lang>
BaCon
<lang qbasic> OPTION BASE 1
DECLARE doors[100]
FOR size = 1 TO 100
FOR pass = 0 TO 100 STEP size
doors[pass] = NOT(doors[pass])
NEXT
NEXT
FOR which = 1 TO 100
IF doors[which] THEN PRINT which
NEXT </lang>
- Output:
1 4 9 16 25 36 49 64 81 100
BASIC
Applesoft BASIC
Based on the Sinclair ZX81 BASIC implementation. <lang basic>
100 : 110 REM 100 DOORS PROBLEM 120 : 130 DIM D(100) 140 FOR P = 1 TO 100 150 FOR T = P TO 100 STEP P 160 D(T) = NOT D(T): NEXT T 170 NEXT P 180 FOR I = 1 TO 100 190 IF D(I) THEN PRINT I;" "; 200 NEXT I
</lang>
- Output:
]RUN 1 4 9 16 25 36 49 64 81 100
BASIC256
<lang BASIC256># 100 doors problem dim d(100)
- simple solution
print "simple solution" gosub initialize for t = 1 to 100
for j = t to 100 step t d[j-1] = not d[j-1] next j
next t gosub showopen
- more optimized solution
print "more optimized solution" gosub initialize for t = 1 to 10
d[t^2-1] = true
next t gosub showopen end
initialize: for t = 1 to d[?]
d[t-1] = false # closed
next t return
showopen: for t = 1 to d[?]
print d[t-1]+ " "; if t%10 = 0 then print
next t return</lang>
ultra optimizado: portado desde la versión Julia
<lang basic>
for i = 1 to 10 : if i % i^2 < 11 then print "La puerta "; int(i^2); " esta abierta" : end if : next i : end
</lang>
Commodore BASIC
Based on the Sinclair ZX81 BASIC implementation. <lang gwbasic>10 DIM D(100) 20 FOR I=1 TO 100 30 FOR J=I TO 100 STEP I 40 D(J) = NOT D(J) 50 NEXT J 60 NEXT I 70 FOR I=1 TO 100 80 IF D(I) THEN PRINT I, 90 NEXT I</lang>
IS-BASIC
<lang IS-BASIC>100 PROGRAM "100doors.bas" 110 NUMERIC D(1 TO 100) 120 FOR I=1 TO 100 130 LET D(I)=0 140 NEXT 150 FOR I=1 TO 100 160 FOR J=I TO 100 STEP I 170 LET D(J)=NOT D(J) 180 NEXT 190 NEXT 200 FOR I=1 TO 100 210 IF D(I) THEN PRINT I 220 NEXT</lang> Optimized: <lang IS-BASIC>100 PROGRAM "100doors.bas" 110 LET NR=1:LET D=3 120 DO 130 PRINT NR 140 LET NR=NR+D:LET D=D+2 150 LOOP WHILE NR<=100</lang>
QBasic
unoptimized <lang qbasic>REM "100 Doors" program for QB64 BASIC (http://www.qb64.net/), a QuickBASIC-like compiler. REM Author: G. A. Tippery REM Date: 12-Feb-2014 REM REM Unoptimized (naive) version, per specifications at http://rosettacode.org/wiki/100_doors
DEFINT A-Z CONST N = 100 DIM door(N)
FOR stride = 1 TO N
FOR index = stride TO N STEP stride LET door(index) = NOT (door(index)) NEXT index
NEXT stride
PRINT "Open doors:" FOR index = 1 TO N
IF door(index) THEN PRINT index
NEXT index
END</lang>
unoptimized <lang qbasic>DIM doors(0 TO 99) FOR pass = 0 TO 99 FOR door = pass TO 99 STEP pass + 1 PRINT doors(door) PRINT NOT doors(door) doors(door) = NOT doors(door) NEXT door NEXT pass FOR i = 0 TO 99 PRINT "Door #"; i + 1; " is "; IF NOT doors(i) THEN PRINT "closed" ELSE PRINT "open" END IF NEXT i</lang> optimized <lang qbasic>DIM doors(0 TO 99) FOR door = 0 TO 99 IF INT(SQR(door)) = SQR(door) THEN doors(door) = -1 NEXT door FOR i = 0 TO 99 PRINT "Door #"; i + 1; " is "; IF NOT doors(i) THEN PRINT "closed" ELSE PRINT "open" END IF NEXT i</lang>
Sinclair ZX81 BASIC
Works with only 1k of RAM, although it doesn't leave too much to play with. <lang basic>10 DIM D(100) 20 FOR I=1 TO 100 30 FOR J=I TO 100 STEP I 40 LET D(J)=NOT D(J) 50 NEXT J 60 NEXT I 70 FOR I=1 TO 100 80 IF D(I) THEN PRINT I, 90 NEXT I</lang>
MSX Basic
Based on the Sinclair ZX81 BASIC implementation. <lang basic> 10 DIM D(100) 20 FOR I=1 TO 100 30 FOR J=i TO 100 STEP I 40 D(J)=NOT D(J) 50 NEXT J 60 NEXT I 70 FOR I=1 TO 100 80 IF D(I) THEN PRINT I; 90 NEXT I 100 END </lang>
- Output:
]RUN 1 4 9 16 25 36 49 64 81 100
Batch File
unoptimized <lang dos> @echo off setlocal enableDelayedExpansion
- 0 = closed
- 1 = open
- SET /A treats undefined variable as 0
- Negation operator ! must be escaped because delayed expansion is enabled
for /l %%p in (1 1 100) do for /l %%d in (%%p %%p 100) do set /a "door%%d=^!door%%d" for /l %%d in (1 1 100) do if !door%%d!==1 (
echo door %%d is open
) else echo door %%d is closed </lang>
optimized <lang dos> @echo off setlocal enableDelayedExpansion set /a square=1, incr=3 for /l %%d in (1 1 100) do (
if %%d neq !square! (echo door %%d is closed) else ( echo door %%d is open set /a square+=incr, incr+=2 )
) </lang>
BBC BASIC
<lang bbcbasic>DIM doors%(100) FOR pass% = 1 TO 100
FOR door% = pass% TO 100 STEP pass% doors%(door%) = NOT doors%(door%) NEXT door%
NEXT pass% FOR door% = 1 TO 100
IF doors%(door%) PRINT "Door " ; door% " is open"
NEXT door%</lang>
bc
<lang bc>/* 0 means door is closed, 1 means door is open */ for (i = 0; i < 100; i++) {
for (j = i; j < 100; j += (i + 1)) { d[j] = 1 - d[j] /* Toggle door */ }
}
"Open doors: " for (i = 0; i < 100; i++) {
if (d[i] == 1) (i + 1)
}</lang>
BCPL
<lang BCPL>get "libhdr"
let start() be $( let doors = vec 100
// close all doors for n = 1 to 100 do doors!n := 0
// make 100 passes for pass = 1 to 100 do $( let n = pass while n <= 100 do $( doors!n := ~doors!n n := n + pass $) $) // report which doors are open for n = 1 to 100 do if doors!n then writef("Door %N is open.*N", n)
$)</lang>
- Output:
Door 1 is open. Door 4 is open. Door 9 is open. Door 16 is open. Door 25 is open. Door 36 is open. Door 49 is open. Door 64 is open. Door 81 is open. Door 100 is open.
Befunge
Befunge-93
Unoptimized
Requires an interpreter with working read-write memory support. Padding the code page with extra blank lines can sometimes help. <lang befunge>>"d">:00p1-:>:::9%\9/9+g2%!\:9v $.v_^#!$::$_^#`"c":+g00p+9/9\%<
- <_@#`$:\*:+55:+1p27g1g+9/9\%9
</lang>
Optimized
Just calculates the first 10 perfect squares. <lang befunge>1+:::*.9`#@_ </lang>
Befunge-98
<lang befunge>108p0>:18p;;>:9g!18g9p08g]
- `!0\|+relet|-1`*aap81::+]
- +1<r]!g9;>$08g1+
- 08paa[
- `#@_^._aa</lang>
BlitzMax
optimized <lang BlitzMax>Graphics 640,480 i=1 While ((i*i)<=100) a$=i*i DrawText a$,10,20*i Print i*i i=i+1 Wend Flip WaitKey </lang>
BlooP
The currently available BlooP interpreters don't really allow iterating over cells with any level of ease, so instead I loop over each door in turn, running it through all 100 cycles and toggling it when it is a multiple of the step number. <lang BlooP> DEFINE PROCEDURE DIVIDE [A,B]: BLOCK 0: BEGIN
IF A < B, THEN: QUIT BLOCK 0; CELL(0) <= 1; OUTPUT <= 1; LOOP AT MOST A TIMES: BLOCK 2: BEGIN IF OUTPUT * B = A, THEN: QUIT BLOCK 0; OUTPUT <= OUTPUT + 1; IF OUTPUT * B > A, THEN: BLOCK 3: BEGIN OUTPUT <= CELL(0); QUIT BLOCK 0; BLOCK 3: END; CELL(0) <= OUTPUT; BLOCK 2: END;
BLOCK 0: END.
DEFINE PROCEDURE MINUS [A,B]: BLOCK 0: BEGIN
IF A < B, THEN: QUIT BLOCK 0; LOOP AT MOST A TIMES: BLOCK 1: BEGIN IF OUTPUT + B = A, THEN: QUIT BLOCK 0; OUTPUT <= OUTPUT + 1; BLOCK 1: END;
BLOCK 0: END.
DEFINE PROCEDURE MODULUS [A,B]: BLOCK 0: BEGIN
CELL(0) <= DIVIDE[A,B]; OUTPUT <= MINUS[A,CELL(0) * B];
BLOCK 0: END.
DEFINE PROCEDURE TOGGLE [DOOR]: BLOCK 0: BEGIN
IF DOOR = 1, THEN: QUIT BLOCK 0; OUTPUT <= 1;
BLOCK 0: END.
DEFINE PROCEDURE NUMBERS [DOOR, COUNT]: BLOCK 0: BEGIN
CELL(0) <= 1; /*each number*/ OUTPUT <= 0; /*current door state*/ LOOP COUNT TIMES: BLOCK 1: BEGIN
IF MODULUS[DOOR, CELL(0)] = 0, THEN: OUTPUT <= TOGGLE[OUTPUT]; CELL(0) <= CELL(0) + 1;
BLOCK 1: END;
BLOCK 0: END.
DEFINE PROCEDURE DOORS [COUNT]: BLOCK 0: BEGIN
CELL(0) <= 1; /*each door*/ LOOP COUNT TIMES: BLOCK 1: BEGIN
CELL(1) <= NUMBERS[CELL(0), COUNT]; /*iterate over the states of this door to get its final state*/ IF CELL(1) = 1, THEN: /*door state = open*/ PRINT[CELL(0), ' ']; CELL(0) <= CELL(0) + 1;
BLOCK 1: END;
BLOCK 0: END.
DOORS[100]; </lang>
- Output:
> 1 > 4 > 9 > 16 > 25 > 36 > 49 > 64 > 81 > 100
Bracmat
Bracmat is not really at home in tasks that involve addressing things by index number. Here are four solutions that each do the task, but none should win a price for cleanliness.
Solution 1. Use an indexable array. Local variables are stored in stacks. Each stack corresponds to one variable name and vice versa. Stacks can also be used as arrays, but because of how local variables are implemented, arrays cannot be declared as local variables. <lang bracmat>( 100doors-tbl = door step
. tbl$(doors.101) { Create an array. Indexing is 0-based. Add one extra for addressing element nr. 100 } & 0:?step & whl ' ( 1+!step:~>100:?step { ~> means 'not greater than', i.e. 'less than or equal' } & 0:?door & whl ' ( !step+!door:~>100:?door & 1+-1*!(!door$doors):?doors { <number>$<variable> sets the current index, which stays the same until explicitly changed. } ) ) & 0:?door & whl ' ( 1+!door:~>100:?door & out $ ( door !door is ( !(!door$doors):1&open | closed ) ) ) & tbl$(doors.0) { clean up the array }
)</lang>
Solution 2. Use one variable for each door. In Bracmat, a variable name can be any non-empty string, even a number, so we use the numbers 1 .. 100 as variable names, but also as door numbers. When used as variable an extra level of indirection is needed. See the occurrences of ?!
and !!
in the following code.
<lang bracmat>( 100doors-var
= step door
. 0:?door & whl ' ( 1+!door:~>100:?door & closed:?!door { this creates a variable and assigns a value 'closed' to it } ) & 0:?step & whl ' ( 1+!step:~>100:?step & 0:?door & whl ' ( !step+!door:~>100:?door & ( !!door:closed&open | closed ) : ?!door ) ) & 0:?door & whl ' ( 1+!door:~>100:?door & out$(door !door is !!door) ) & 0:?door & whl ' ( 1+!door:~>100:?door & tbl$(!door.0) { cleanup the variable } )
)</lang>
Solution 3. Use a list and a dedicated positioning pattern to address the right door in the list. Create a new list by concatenating the skipped elements with the toggled elements. This solution is computationally unfavourable because of the many concatenations. <lang bracmat>( 100doors-list = doors door doorIndex step
. :?doors & 0:?door & whl ' ( 1+!door:~>100:?door & closed !doors:?doors ) & 0:?skip & whl ' ( :?ndoors & whl ' ( !doors:?skipped [!skip %?door ?doors { the [<number> pattern only succeeds when the scanning cursor is at position <number> } & !ndoors !skipped ( !door:open&closed | open ) : ?ndoors ) & !ndoors !doors:?doors & 1+!skip:<100:?skip ) & out$!doors
)</lang>
Solution 4. Use a list of objects. Each object can be changed without the need to re-create the whole list. <lang bracmat>( 100doors-obj = doors door doorIndex step
. :?doors & 0:?door & whl ' ( 1+!door:~>100:?door & new$(=closed) !doors:?doors ) & 0:?skip & whl ' ( !doors:?tododoors & whl ' ( !tododoors:? [!skip %?door ?tododoors & ( !(door.):open&closed | open ) : ?(door.) ) & 1+!skip:<100:?skip ) & out$!doors
)</lang>
These four functions are called in the following way: <lang bracmat>100doors-tbl$ & 100doors-var$ & 100doors-list$ & 100doors-obj$;</lang>
Burlesque
Version using square numbers:
<lang burlesque> blsq ) 10ro2?^ {1 4 9 16 25 36 49 64 81 100} </lang>
BQN
<lang bqn>swch ← ≠´{100⥊1«𝕩⥊0}¨1+↕100
¯1↓∾{𝕩∾@+10}¨•Fmt¨⟨swch,/swch⟩</lang>
<lang bqn>"⟨ 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⟩
⟨ 0 3 8 15 24 35 48 63 80 99 ⟩"</lang>
swch
uses an idea similar to the GNU APL solution to generate a boolean array of the correct switches.
The second line then formats the boolean array and the truthy indices into a string for display.
C
unoptimized
<lang c>#include <stdio.h>
int main() {
char is_open[100] = { 0 }; int pass, door;
/* do the 100 passes */ for (pass = 0; pass < 100; ++pass) for (door = pass; door < 100; door += pass+1) is_open[door] = !is_open[door];
/* output the result */ for (door = 0; door < 100; ++door) printf("door #%d is %s.\n", door+1, (is_open[door]? "open" : "closed"));
return 0;
}</lang>
Using defensive programming, pointers, sentinel values and some other standard programming practices,
<lang c>#include <stdio.h>
- define NUM_DOORS 100
int main(int argc, char *argv[]) {
int is_open[NUM_DOORS] = { 0 } ; int * doorptr, * doorlimit = is_open + NUM_DOORS ; int pass ;
/* do the N passes, go backwards because the order is not important */ for ( pass= NUM_DOORS ; ( pass ) ; -- pass ) { for ( doorptr= is_open + ( pass-1 ); ( doorptr < doorlimit ) ; doorptr += pass ) { ( * doorptr ) ^= 1 ; } }
/* output results */ for ( doorptr= is_open ; ( doorptr != doorlimit ) ; ++ doorptr ) { printf("door #%lld is %s\n", ( doorptr - is_open ) + 1, ( * doorptr ) ? "open" : "closed" ) ; }
}</lang>
optimized
This optimized version makes use of the fact that finally only the doors with square index are open, as well as the fact that .
<lang c>#include <stdio.h>
int main() {
int square = 1, increment = 3, door; for (door = 1; door <= 100; ++door) { printf("door #%d", door); if (door == square) { printf(" is open.\n"); square += increment; increment += 2; } else printf(" is closed.\n"); } return 0;
}</lang>
The following ultra-short optimized version demonstrates the flexibility of C loops, but isn't really considered good C style:
<lang c>#include <stdio.h>
int main() {
int door, square, increment; for (door = 1, square = 1, increment = 1; door <= 100; door++ == square && (square += increment += 2)) printf("door #%d is %s.\n", door, (door == square? "open" : "closed")); return 0;
}</lang>
Or really optimize it -- square of an integer is, well, computable:<lang C>#include <stdio.h>
int main() { int i; for (i = 1; i * i <= 100; i++) printf("door %d open\n", i * i);
return 0; }</lang>
C#
Unoptimized with Modulus % Operator
<lang csharp>namespace ConsoleApplication1 {
using System; class Program { static void Main(string[] args) { bool[] doors = new bool[100];
//Close all doors to start. for (int d = 0; d < 100; d++) doors[d] = false;
//For each pass... for (int p = 0; p < 100; p++)//number of passes { //For each door to toggle... for (int d = 0; d < 100; d++)//door number { if ((d + 1) % (p + 1) == 0) { doors[d] = !doors[d]; } } }
//Output the results. Console.WriteLine("Passes Completed!!! Here are the results: \r\n"); for (int d = 0; d < 100; d++) { if (doors[d]) { Console.WriteLine(String.Format("Door #{0}: Open", d + 1)); } else { Console.WriteLine(String.Format("Door #{0}: Closed", d + 1)); } } Console.ReadKey(true); } }
}</lang>
Optimized for Orthogonality
(This version demonstrates a different thought pattern during development, where operation and presentation are separated. It could easily be refactored so that the operations to determine which doors are opened and to display the list of doors would be in separate methods, at which point it would become simple to extract them to separate classes and employ a DI pattern to switch the algorithm or display mechanism being used. It also keeps the calculation clear and concise.) <lang csharp>namespace ConsoleApplication1 {
using System; class Program { static void Main(string[] args) { //Perform the operation. bool[] doors = new bool[100]; int n = 0; int d; while ((d = (++n * n)) <= 100) doors[d - 1] = true;
//Perform the presentation. for (d = 0; d < doors.Length; d++) Console.WriteLine("Door #{0}: {1}", d + 1, doors[d] ? "Open" : "Closed"); Console.ReadKey(true); } }
}</lang>
Unoptimized but Concise
<lang csharp>namespace ConsoleApplication1 {
using System; class Program { static void Main() { bool[] doors = new bool[100];
//The number of passes can be 1-based, but the number of doors must be 0-based. for (int p = 1; p <= 100; p++) for (int d = p - 1; d < 100; d += p) doors[d] = !doors[d]; for (int d = 0; d < 100; d++) Console.WriteLine("Door #{0}: {1}", d + 1, doors[d] ? "Open" : "Closed"); Console.ReadKey(true); } }
}</lang>
Optimized for brevity
<lang csharp>namespace ConsoleApplication1 {
using System; class Program { static void Main() { double n;
//If the current door number is the perfect square of an integer, say it is open, else say it is closed. for (int d = 1; d <= 100; d++) Console.WriteLine("Door #{0}: {1}", d, (n = Math.Sqrt(d)) == (int)n ? "Open" : "Closed"); Console.ReadKey(true); } }
}</lang>
Optimized for Flexibility
This version supports altering the number of doors through console commands. Its main intent is to be flexible and easy to use. <lang csharp> using System; using System.IO; using System.Collections.Generic;
class Program {
static void Main() { Console.Clear(); Console.WriteLine("Input a number of doors to calculate, then press enter"); StartCalculator(); } static void StartCalculator() { //The number to calculate is input here string input = Console.ReadLine(); Console.Clear(); try { //The program attempts to convert the string to an int //Exceptions will be caught on this line int numberOfDoors = Convert.ToInt32(input); //Will call method recursively if input number is less than 1 if (numberOfDoors <= 0) { Console.WriteLine("Please use a number greater than 0"); StartCalculator(); } //The program then starts the calculation process Calculate(numberOfDoors); //After calculation process is finished, restart method is called RestartCalculator(); } catch(FormatException) { //Code will be executed if the number has a decimal or has an unrecognizable symbol Console.WriteLine("Unable to read. Please use a real number without a decimal"); StartCalculator(); } catch (OverflowException) { //Code will be executed if number is too long Console.WriteLine("You number is too long"); StartCalculator(); } } static void Calculate(int numberOfDoors) { //Increases numberOfDoors by 1 since array starts at 0 numberOfDoors++; //Dictionary key represents door number, value represents if the door is open //if value == true, the door is open Dictionary<int, bool> doors = new Dictionary<int, bool>(); //Creates Dictionary size of numberOfDoors, all initialized at false for(int i = 0; i < numberOfDoors; i++) { doors.Add(i, false); } //Creates interval between doors, starting at 0, while less than numberOfDoors for (int doorInterval = 0; doorInterval < numberOfDoors; doorInterval++) { //Will alter every cubby at doorInterval //1 needs to be added since doorInterval will start at 0 and end when equal to numberOfDoors for(int i = 0; i < numberOfDoors; i += doorInterval + 1) { //Changes a false value to true and vice versa doors[i] = doors[i] ? false: true; } } //Writes each door and whether it is open or closed for(int i = 0; i < numberOfDoors; i++) { //Skips over door 0 if (i == 0) continue; //Writes open if door value is true, writes closed if door value is false Console.WriteLine("Door " + (i) + " is " + (doors[i] ? "open" : "closed")); } } static void RestartCalculator() { Console.WriteLine("Press any key to restart"); Console.ReadKey(true); Main(); }
} </lang>
C++
unoptimized <lang cpp>#include <iostream>
int main() {
bool is_open[100] = { false };
// do the 100 passes for (int pass = 0; pass < 100; ++pass) for (int door = pass; door < 100; door += pass+1) is_open[door] = !is_open[door];
// output the result for (int door = 0; door < 100; ++door) std::cout << "door #" << door+1 << (is_open[door]? " is open." : " is closed.") << std::endl; return 0;
}</lang>
optimized This optimized version makes use of the fact that finally only the doors with square index are open, as well as the fact that .
<lang cpp>#include <iostream>
int main() {
int square = 1, increment = 3; for (int door = 1; door <= 100; ++door) { std::cout << "door #" << door; if (door == square) { std::cout << " is open." << std::endl; square += increment; increment += 2; } else std::cout << " is closed." << std::endl; } return 0;
}</lang>
The only calculation that's really needed: <lang cpp>#include <iostream> //compiled with "Dev-C++" , from RaptorOne
int main() {
for(int i=1; i*i<=100; i++) std::cout<<"Door "<<i*i<<" is open!"<<std::endl;
}</lang>
Compile time computation using C++17 to produce fastest runtime. <lang cpp>#include <iostream> // compiled with clang (tags/RELEASE_600/final)
- include <type_traits> // or g++ (GCC) 7.3.1 20180406 -- from hare1039
namespace functional_list // basic building block for template meta programming { struct NIL { using head = NIL; using tail = NIL; friend std::ostream& operator << (std::ostream& os, NIL const) { return os; } };
template <typename H, typename T = NIL> struct list { using head = H; using tail = T; };
template <int i> struct integer { static constexpr int value = i; friend std::ostream& operator << (std::ostream& os, integer const) { os << integer::value; return os;} };
template <typename L, int nTH> constexpr auto at() { if constexpr (nTH == 0) return (typename L::head){}; else if constexpr (not std::is_same_v<typename L::tail, NIL>) return at<typename L::tail, nTH - 1>(); else return NIL{}; } template <typename L, int nTH> using at_t = decltype(at<L, nTH>());
template <typename L, typename elem> constexpr auto prepend() { return list<elem, L>{}; }
template <typename L, typename elem> using prepend_t = decltype(prepend<L, elem>());
template <int Size, typename Dat = integer<0>> constexpr auto gen_list() { if constexpr (Size == 0) return NIL{}; else { using next = decltype(gen_list<Size - 1, Dat>()); return prepend<next, Dat>(); } } template <int Size, typename Dat = integer<0>> using gen_list_t = decltype(gen_list<Size, Dat>());
} namespace fl = functional_list;
constexpr int door_amount = 101; // index from 1 to 100
template <typename L, int current, int moder> constexpr auto construct_loop() { using val_t = fl::at_t<L, current>; if constexpr (std::is_same_v<val_t, fl::NIL>) return fl::NIL{}; else { constexpr int val = val_t::value; using val_add_t = fl::integer<val + 1>; using val_old_t = fl::integer<val>;
if constexpr (current == door_amount) { if constexpr(current % moder == 0) return fl::list<val_add_t>{}; else return fl::list<val_old_t>{}; } else { using sub_list = decltype(construct_loop<L, current + 1, moder>()); if constexpr(current % moder == 0) return fl::prepend<sub_list, val_add_t>(); else return fl::prepend<sub_list, val_old_t>(); } } }
template <int iteration> constexpr auto construct() { if constexpr (iteration == 1) // door index = 1 { using l = fl::gen_list_t<door_amount>; return construct_loop<l, 0, iteration>(); } else { using prev_iter_list = decltype(construct<iteration - 1>()); return construct_loop<prev_iter_list, 0, iteration>(); } }
template <typename L, int pos> constexpr void show_ans() { if constexpr (std::is_same_v<typename L::head, fl::NIL>) return; else { if constexpr (L::head::value % 2 == 1) std::cout << "Door " << pos << " is opened.\n"; show_ans<typename L::tail, pos + 1>(); } }
int main() { using result = decltype(construct<100>()); show_ans<result, 0>(); }</lang>
C1R
<lang c>100_doors</lang>
Caché ObjectScript
<lang>
for i=1:1:100 {
set doors(i) = 0
} for i=1:1:100 {
for door=i:i:100 { Set doors(door)='doors(door) }
} for i = 1:1:100 {
if doors(i)=1 write i_": open",!
}
</lang> Output: <lang> 1: open 4: open 9: open 16: open 25: open 36: open 49: open 64: open 81: open 100: open </lang>
Ceylon
<lang ceylon>shared void run() {
print("Open doors (naive): ``naive()`` Open doors (optimized): ``optimized()``");
}
shared {Integer*} naive(Integer count = 100) {
variable value doors = [ for (_ in 1..count) closed ]; for (step in 1..count) { doors = [for (i->door in doors.indexed) let (index = i+1) if (step == 1 || step.divides(index)) then door.toggle() else door ]; } return doors.indexesWhere((door) => door == opened).map(1.plusInteger);
}
shared {Integer*} optimized(Integer count = 100) =>
{ for (i in 1..count) i*i }.takeWhile(count.notSmallerThan);
shared abstract class Door(shared actual String string) of opened | closed {
shared formal Door toggle();
} object opened extends Door("opened") { toggle() => closed; } object closed extends Door("closed") { toggle() => opened; }</lang>
Output:
Open doors (naive): { 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 } Open doors (optimized): { 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 }
Clarion
<lang clarion>
program
map end
MAX_DOOR_NUMBER equate(100) CRLF equate('<13,10>')
Doors byte,dim(MAX_DOOR_NUMBER) Pass byte DoorNumber byte DisplayString cstring(2000)
ResultWindow window('Result'),at(,,133,291),center,double,auto
prompt('Door states:'),at(8,4),use(?PromptTitle) text,at(8,16,116,266),use(DisplayString),boxed,vscroll,font('Courier New',,,,CHARSET:ANSI),readonly end
code
Doors :=: false loop Pass = 1 to MAX_DOOR_NUMBER loop DoorNumber = Pass to MAX_DOOR_NUMBER by Pass Doors[DoorNumber] = choose(Doors[DoorNumber], false, true) end end
clear(DisplayString) loop DoorNumber = 1 to MAX_DOOR_NUMBER DisplayString = DisplayString & format(DoorNumber, @n3) & ' is ' & choose(Doors[DoorNumber], 'opened', 'closed') & CRLF end open(ResultWindow) accept end close(ResultWindow)
return
</lang>
Clio
Unoptimized
<lang clio>fn visit-doors doors step:
if step > 100: doors else: [1:100] -> * fn index: if index % step: doors[(index - 1)] else: not doors[(index - 1)] -> visit-doors (step + 1)
[1:100] -> * n: false -> visit-doors 1 => doors [1:100] -> * (@eager) fn i:
doors[(i - 1)] -> if = true: #open else: #closed -> print #Door i #is @</lang>
Optimized
<lang clio>[1:100] -> * (@eager) fn i:
i ^ 0.5 -> eq @ (transform i: floor) -> if = true: #open else: #closed -> print #Door i #is @</lang>
CLIPS
Unoptimized
<lang clips>(deffacts initial-state
(door-count 100)
)
(deffunction toggle
(?state) (switch ?state (case "open" then "closed") (case "closed" then "open") )
)
(defrule create-doors-and-visits
(door-count ?count) => (loop-for-count (?num 1 ?count) do (assert (door ?num "closed")) (assert (visit-from ?num ?num)) ) (assert (doors initialized))
)
(defrule visit
(door-count ?max) ?visit <- (visit-from ?num ?step) ?door <- (door ?num ?state) => (retract ?visit) (retract ?door) (assert (door ?num (toggle ?state))) (if (<= (+ ?num ?step) ?max) then (assert (visit-from (+ ?num ?step) ?step)) )
)
(defrule start-printing
(doors initialized) (not (visit-from ? ?)) => (printout t "These doors are open:" crlf) (assert (print-from 1))
)
(defrule print-door
(door-count ?max) ?pf <- (print-from ?num) (door ?num ?state) => (retract ?pf) (if (= 0 (str-compare "open" ?state)) then (printout t ?num " ") ) (if (< ?num ?max) then (assert (print-from (+ ?num 1))) else (printout t crlf "All other doors are closed." crlf) )
)</lang>
Optimized
<lang clips>(deffacts initial-state
(door-count 100)
)
(deffunction is-square
(?num) (= (sqrt ?num) (integer (sqrt ?num)))
)
(defrule check-doors
(door-count ?count) => (printout t "These doors are open:" crlf) (loop-for-count (?num 1 ?count) do (if (is-square ?num) then (printout t ?num " ") ) ) (printout t crlf "All other doors are closed." crlf)
)</lang>
Clojure
Unoptimized / mutable array <lang clojure>(defn doors []
(let [doors (into-array (repeat 100 false))] (doseq [pass (range 1 101) i (range (dec pass) 100 pass) ] (aset doors i (not (aget doors i)))) doors))
(defn open-doors [] (for [[d n] (map vector (doors) (iterate inc 1)) :when d] n))
(defn print-open-doors []
(println "Open doors after 100 passes:" (apply str (interpose ", " (open-doors)))))</lang>
Unoptimized / functional <lang clojure>(defn doors []
(reduce (fn [doors toggle-idx] (update-in doors [toggle-idx] not)) (into [] (repeat 100 false)) (for [pass (range 1 101) i (range (dec pass) 100 pass) ] i)))
(defn open-doors [] (for [[d n] (map vector (doors) (iterate inc 1)) :when d] n))
(defn print-open-doors []
(println "Open doors after 100 passes:" (apply str (interpose ", " (open-doors)))))</lang>
Alternative Unoptimized / functional <lang clojure>(defn open-doors []
(->> (for [step (range 1 101), occ (range step 101 step)] occ) frequencies (filter (comp odd? val)) keys sort))
(defn print-open-doors []
(println "Open doors after 100 passes:" (apply str (interpose ", " (open-doors)))))</lang>
Optimized / functional <lang clojure>(defn doors [] (reduce (fn [doors idx] (assoc doors idx true)) (into [] (repeat 100 false)) (map #(dec (* % %)) (range 1 11))))
(defn open-doors [] (for [[d n] (map vector (doors) (iterate inc 1)) :when d] n))
(defn print-open-doors []
(println "Open doors after 100 passes:" (apply str (interpose ", " (open-doors)))))</lang>
Alternative Optimized / functional
<lang clojure>(defn open-doors [] (->> (iterate inc 1) (map #(* % %)) (take-while #(<= % 100))))
(defn print-open-doors []
(println "Open doors after 100 passes:" (apply str (interpose ", " (open-doors)))))</lang>
CLU
<lang clu>start_up = proc ()
max = 100 po: stream := stream$primary_output() open: array[bool] := array[bool]$fill(1, max, false)
for pass: int in int$from_to(1, max) do for door: int in int$from_to_by(pass, max, pass) do open[door] := ~open[door] end end
for door: int in array[bool]$indexes(open) do if open[door] then stream$putl(po, "Door " || int$unparse(door) || " is open.") end end
end start_up</lang>
- Output:
Door 1 is open. Door 4 is open. Door 9 is open. Door 16 is open. Door 25 is open. Door 36 is open. Door 49 is open. Door 64 is open. Door 81 is open. Door 100 is open.
COBOL
<lang cobol> IDENTIFICATION DIVISION.
PROGRAM-ID. 100Doors.
DATA DIVISION. WORKING-STORAGE SECTION. 01 Current-n PIC 9(3). 01 StepSize PIC 9(3). 01 DoorTable. 02 Doors PIC 9(1) OCCURS 100 TIMES. 88 ClosedDoor VALUE ZERO. 01 Idx PIC 9(3).
PROCEDURE DIVISION. Begin. INITIALIZE DoorTable PERFORM VARYING StepSize FROM 1 BY 1 UNTIL StepSize > 100 PERFORM VARYING Current-n FROM StepSize BY StepSize UNTIL Current-n > 100 SUBTRACT Doors (Current-n) FROM 1 GIVING Doors (Current-n) END-PERFORM END-PERFORM
PERFORM VARYING Idx FROM 1 BY 1 UNTIL Idx > 100 IF ClosedDoor (Idx) DISPLAY Idx " is closed." ELSE DISPLAY Idx " is open." END-IF END-PERFORM
STOP RUN .</lang>
Coco
We use the naive algorithm.
<lang coco>doors = [false] * 100
for pass til doors.length
for i from pass til doors.length by pass + 1 ! = doors[i]
for i til doors.length
console.log 'Door %d is %s.', i + 1, if doors[i] then 'open' else 'closed'</lang>
CoffeeScript
unoptimized: <lang coffeescript>doors = []
for pass in [1..100]
for i in [pass..100] by pass doors[i] = !doors[i]
console.log "Doors #{index for index, open of doors when open} are open"
- matrix output
console.log doors.map (open) -> +open </lang>
optimized:
<lang coffeescript>isInteger = (i) -> Math.floor(i) == i
console.log door for door in [1..100] when isInteger Math.sqrt door</lang>
ultra-optimized: <lang coffeescript>console.log Math.pow(i,2) for i in [1..10]</lang>
ColdFusion
Basic Solution: Returns List of 100 values: 1=open 0=closed <lang coldfusion> doorCount = 1; doorList = ""; // create all doors and set all doors to open while (doorCount LTE 100) { doorList = ListAppend(doorList,"1"); doorCount = doorCount + 1; } loopCount = 2; doorListLen = ListLen(doorList); while (loopCount LTE 100) { loopDoorListCount = 1; while (loopDoorListCount LTE 100) { testDoor = loopDoorListCount / loopCount; if (testDoor EQ Int(testDoor)) { checkOpen = ListGetAt(doorList,loopDoorListCount); if (checkOpen EQ 1) { doorList = ListSetAt(doorList,loopDoorListCount,"0"); } else { doorList = ListSetAt(doorList,loopDoorListCount,"1"); } } loopDoorListCount = loopDoorListCount + 1; } loopCount = loopCount + 1; } </lang>
Squares of Integers Solution: Returns List of 100 values: 1=open 0=closed <lang coldfusion> doorCount = 1; doorList = ""; loopCount = 1; while (loopCount LTE 100) { if (Sqr(loopCount) NEQ Int(Sqr(loopCount))) { doorList = ListAppend(doorList,0); } else { doorList = ListAppend(doorList,1); } loopCount = loopCount + 1; } </lang>
Display only <lang cfm>// Display all doors <cfloop from="1" to="100" index="x">
Door #x# Open: #YesNoFormat(ListGetAt(doorList,x))#
</cfloop>
// Output only open doors <cfloop from="1" to="100" index="x">
<cfif ListGetAt(doorList,x) EQ 1> #x#
</cfif>
</cfloop></lang>
Another Route <lang cfm><Cfparam name="doorlist" default=""> <cfloop from="1" to="100" index="i">
<Cfset doorlist = doorlist & 'c,'>
</cfloop> <cfloop from="1" to="100" index="i">
<Cfloop from="1" to="100" index="door" step="#i#"> <Cfif listgetat(doorlist, door) eq 'c'> <Cfset doorlist = listsetat(doorlist, door, 'O')> <Cfelse> <Cfset doorlist = listsetat(doorlist, door, 'c')> </Cfif> </Cfloop>
</cfloop> <Cfoutput>#doorlist#</Cfoutput></lang>
Comal
<lang comal>0010 DIM doors#(100) 0020 FOR pass#:=1 TO 100 DO 0030 FOR door#:=pass# TO 100 STEP pass# DO doors#(door#):=NOT doors#(door#) 0040 ENDFOR pass# 0050 FOR door#:=1 TO 100 DO 0060 IF doors#(door#) THEN PRINT "Door ",door#," is open." 0070 ENDFOR door# 0080 END</lang>
- Output:
Door 1 is open. Door 4 is open. Door 9 is open. Door 16 is open. Door 25 is open. Door 36 is open. Door 49 is open. Door 64 is open. Door 81 is open. Door 100 is open.
Commodore BASIC
<lang basic> 10 D=100: DIMD(D): P=1 20 PRINT CHR$(147);"PASS: ";P 22 FOR I=P TO D STEP P: D(I)=NOTD(I): NEXT 30 IF P=100 THEN 40 32 P=P+1: GOTO20 40 PRINT: PRINT"THE FOLLOWING DOORS ARE OPEN: " 42 FOR I=1 TO D: IF D(I)=-1 THEN PRINTI; 44 NEXT </lang>
Common Lisp
Unoptimized / functional This is a very unoptimized version of the problem, using recursion and quite considerable list-copying. It emphasizes the functional way of solving this problem.
<lang lisp>(defun visit-door (doors doornum value1 value2)
"visits a door, swapping the value1 to value2 or vice-versa" (let ((d (copy-list doors)) (n (- doornum 1))) (if (eql (nth n d) value1) (setf (nth n d) value2) (setf (nth n d) value1)) d))
(defun visit-every (doors num iter value1 value2)
"visits every 'num' door in the list" (if (> (* iter num) (length doors)) doors (visit-every (visit-door doors (* num iter) value1 value2) num (+ 1 iter) value1 value2)))
(defun do-all-visits (doors cnt value1 value2)
"Visits all doors changing the values accordingly" (if (< cnt 1) doors (do-all-visits (visit-every doors cnt 1 value1 value2) (- cnt 1) value1 value2)))
(defun print-doors (doors)
"Pretty prints the doors list" (format T "~{~A ~A ~A ~A ~A ~A ~A ~A ~A ~A~%~}~%" doors))
(defun start (&optional (size 100))
"Start the program" (let* ((open "_") (shut "#") (doors (make-list size :initial-element shut))) (print-doors (do-all-visits doors size open shut))))</lang>
Unoptimized, imperative This is a version that closely follows the problem description and is still quite short. Of all the presented solutions it might be closest to "idiomatic Common Lisp".
<lang lisp>(define-modify-macro toggle () not)
(defun 100-doors ()
(let ((doors (make-array 100))) (dotimes (i 100) (loop for j from i below 100 by (1+ i)
do (toggle (svref doors j))))
(dotimes (i 100) (format t "door ~a: ~:[closed~;open~]~%" (1+ i) (svref doors i)))))</lang>
Unoptimized, n-doors. <lang lisp>(defun doors (z &optional (w (make-list z)) (n 1))
(if (> n z) w (doors z (toggle w n z) (1+ n))))
(defun toggle (w m z)
(loop for a in w for n from 1 to z collect (if (zerop (mod n m)) (not a) a)))
> (doors 100) (T NIL NIL T NIL NIL NIL NIL T NIL NIL NIL NIL NIL NIL T NIL NIL NIL NIL NIL
NIL NIL NIL T NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL T NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL T NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL T NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL T NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL T)</lang>
Optimized, n-doors. <lang lisp>(defun doors (n)
(loop for a from 1 to n collect (zerop (mod (sqrt a) 1))))
> (doors 100) (T NIL NIL T NIL NIL NIL NIL T NIL NIL NIL NIL NIL NIL T NIL NIL NIL NIL NIL
NIL NIL NIL T NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL T NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL T NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL T NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL T NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL T)</lang>
Optimized This is an optimized version, using the perfect square algorithm.
<lang lisp>(defun 100-doors ()
(let ((doors (make-array 100))) (dotimes (i 10) (setf (svref doors (* i i)) t)) (dotimes (i 100) (format t "door ~a: ~:[closed~;open~]~%" (1+ i) (svref doors i)))))</lang>
Optimized 2 Another optimized version, with finer granular separation of functionality (might be a bit excessive).
<lang lisp>(defun perfect-square-list (n)
"Generates a list of perfect squares from 0 up to n" (loop for i from 1 to (isqrt n) collect (expt i 2)))
(defun print-doors (doors)
"Pretty prints the doors list" (format T "~{~A ~A ~A ~A ~A ~A ~A ~A ~A ~A~%~}~%" doors))
(defun open-door (doors num open)
"Sets door at num to open" (setf (nth (- num 1) doors) open))
(defun visit-all (doors vlist open)
"Visits and opens all the doors indicated in vlist" (dolist (dn vlist doors) (open-door doors dn open)))
(defun start2 (&optional (size 100))
"Start the program" (print-doors (visit-all (make-list size :initial-element '\#) (perfect-square-list size) '_)))</lang>
Optimized (2) This version displays a much more functional solution through the use of MAPCAR.
<lang lisp>(let ((i 0))
(mapcar (lambda (x) (if (zerop (mod (sqrt (incf i)) 1)) "_" "#")) (make-list 100)))</lang>
Component Pascal
BlackBox Component Builder <lang oberon2> MODULE Doors100; IMPORT StdLog;
PROCEDURE Do*; VAR i,j: INTEGER; closed: ARRAY 101 OF BOOLEAN; BEGIN (* initialization of closed to true *) FOR i := 0 TO LEN(closed) - 1 DO closed[i] := TRUE END; (* process *) FOR i := 1 TO LEN(closed) DO; j := 1; WHILE j < LEN(closed) DO IF j MOD i = 0 THEN closed[j] := ~closed[j] END;INC(j) END END; (* print results *) i := 1; WHILE i < LEN(closed) DO IF (i - 1) MOD 10 = 0 THEN StdLog.Ln END; IF closed[i] THEN StdLog.String("C ") ELSE StdLog.String("O ") END; INC(i) END; END Do; END Doors100.
</lang>
Execute: ^Q Doors100.Do
- Output:
O C C O C C C C O C C C C C C O C C C C C C C C O C C C C C C C C C C O C C C C C C C C C C C C O C C C C C C C C C C C C C C O C C C C C C C C C C C C C C C C O C C C C C C C C C C C C C C C C C C O
Coq
Basic solution: <lang coq>Require Import List.
Fixpoint rep {A} (a : A) n :=
match n with | O => nil | S n' => a::(rep a n') end.
Fixpoint flip (l : list bool) (n k : nat) : list bool :=
match l with | nil => nil | cons h t => match k with | O => (negb h) :: (flip t n n) | S k' => h :: (flip t n k') end end.
Definition flipeach l n := flip l n n.
Fixpoint flipwhile l n :=
match n with | O => flipeach l 0 | S n' => flipwhile (flipeach l (S n')) n' end.
Definition prison cells := flipwhile (rep false cells) cells.</lang>
Optimized version ((n+1)^2 = n^2 + 2n + 1): <lang coq>Require Import List.
Fixpoint prisoo' nd n k accu :=
match nd with | O => rev accu | S nd' => let ra := match k with | O => (true, S n, (n + n)) | S k' => (false, n, k') end in prisoo' nd' (snd (fst ra)) (snd ra) ((fst (fst ra))::accu) end.
Definition prisoo cells := prisoo' cells 1 0 nil.</lang>
Unit test: <lang coq>Goal prison 100 = prisoo 100. compute. reflexivity. Qed.</lang>
Full proof at github: <lang coq>Goal forall n, prison n = prisoo n. Abort.</lang>
Cowgol
<lang cowgol>include "cowgol.coh";
var doors: uint8[101]; # one extra so we can start at 1 var pass: @indexof doors; var door: @indexof doors;
MemZero(&doors as [uint8], @bytesof doors);
pass := 1; while pass <= 100 loop
door := pass; while door <= 100 loop doors[door] := 1-doors[door]; door := door + pass; end loop; pass := pass + 1;
end loop;
door := 1; while door <= 100 loop
if doors[door] == 1 then print_i8(door); print(" is open\n"); end if; door := door + 1;
end loop;</lang>
- Output:
1 is open 4 is open 9 is open 16 is open 25 is open 36 is open 49 is open 64 is open 81 is open 100 is open
Crystal
<lang ruby>doors = Array.new(100, false)
1.upto(100) do |i|
i.step(by: i, to: 100) do |j| doors[j - 1] = !doors[j - 1] end
end
doors.each_with_index do |open, i|
puts "Door #{i + 1} is #{open ? "open" : "closed"}"
end</lang>
D
Unoptimized
<lang d>import std.stdio; const N = 101; // #doors + 1 void main() {
bool[N] doors = false; for(auto door=1; door<N; door++ ) { for(auto i=door; i<N; i+=door ) doors[i] = !doors[i]; if (doors[door]) write(door, " "); }
}</lang>
- Output:
1 4 9 16 25 36 49 64 81 100
Optimized
The problem of the 100 doors is an algorithm to find the squares between 1 and 100.
This optimized version prints these squares using an alternative algorithm based on
<lang d>import std.stdio; const N = 101; // #doors + 1 void main() {
for( auto door=1,s=3; door<N; door+=s, s+=2 ) write(door, " ");
}</lang>
- Output:
1 4 9 16 25 36 49 64 81 100
Other proposals
<lang d>import std.stdio, std.algorithm, std.range;
enum DoorState : bool { closed, open } alias Doors = DoorState[];
Doors flipUnoptimized(Doors doors) pure nothrow {
doors[] = DoorState.closed;
foreach (immutable i; 0 .. doors.length) for (ulong j = i; j < doors.length; j += i + 1) if (doors[j] == DoorState.open) doors[j] = DoorState.closed; else doors[j] = DoorState.open; return doors;
}
Doors flipOptimized(Doors doors) pure nothrow {
doors[] = DoorState.closed; for (int i = 1; i ^^ 2 <= doors.length; i++) doors[i ^^ 2 - 1] = DoorState.open; return doors;
}
void main() {
auto doors = new Doors(100);
foreach (const open; [doors.dup.flipUnoptimized, doors.dup.flipOptimized]) iota(1, open.length + 1).filter!(i => open[i - 1]).writeln;
}</lang>
- Output:
[1, 4, 9, 16, 25, 36, 49, 64, 81, 100] [1, 4, 9, 16, 25, 36, 49, 64, 81, 100]
Unoptimized. Demonstrates very basic language syntax/features. Program output allows to see what the code is doing: <lang d> import std.stdio;
void printAllDoors(bool[] doors) {
// Prints the state of all the doors foreach(i, door; doors) { writeln("#: ", i + 1, (door) ? " open" : " closed"); }
} void main() {
bool[100] doors = false; //Create 100 closed doors for(int a = 0; a < 100; ++a) { writefln("Pass #%s; visiting every %s door.", a + 1, a + 1); // Optional
for(int i = a; i < 100; i += (a + 1)) { writefln("Visited door %s", i + 1); //Optional doors[i] = !doors[i]; }
writeln(); // Optional } printAllDoors(doors); // Prints the state of each door
} </lang>
Dafny
The InitializeDoors function demonstrates some of Dafny's advanced features.
<lang dafny> datatype Door = Closed | Open
method InitializeDoors(n:int) returns (doors:array<Door>)
// Precondition: n must be a valid array size. requires n >= 0 // Postcondition: doors is an array, which is not an alias for any other // object, with a length of n, all of whose elements are Closed. The "fresh" // (non-alias) condition is needed to allow doors to be modified by the // remaining code. ensures doors != null && fresh(doors) && doors.Length == n ensures forall j :: 0 <= j < doors.Length ==> doors[j] == Closed;
{
doors := new Door[n]; var i := 0; // Invariant: i is always a valid index inside the loop, and all doors less // than i are Closed. These invariants are needed to ensure the second // postcondition. while i < doors.Length invariant i <= doors.Length invariant forall j :: 0 <= j < i ==> doors[j] == Closed; { doors[i] := Closed; i := i + 1; }
}
method Main () {
var doors := InitializeDoors(100);
var pass := 1; while pass <= doors.Length { var door := pass; while door < doors.Length { doors[door] := if doors[door] == Closed then Open else Closed; door := door + pass; } pass := pass + 1; } var i := 0; while i < doors.Length { print i, " is ", if doors[i] == Closed then "closed\n" else "open\n"; i := i + 1; }
} </lang>
Dart
unoptimized <lang dart>main() {
for (var k = 1, x = new List(101); k <= 100; k++) { for (int i = k; i <= 100; i += k) x[i] = !x[i]; if (x[k]) print("$k open"); }
}</lang>
optimized version (including generating squares without multiplication) <lang dart>main() {
for(int i=1,s=3;i<=100;i+=s,s+=2) print("door $i is open");
}</lang>
comprehensible (not "code golf") version for a pedestrian language <lang dart>import 'dart:io';
final numDoors = 100; final List<bool> doorClosed = List(numDoors);
String stateToString(String message) {
var res = ; for (var i = 0; i < numDoors; i++) { res += (doorClosed[i] ? 'X' : '\u2610'); } return res + " " + message;
}
main() {
for (var i = 0; i < numDoors; i++) { doorClosed[i] = true; } stdout.writeln(stateToString("after initialization")); for (var step = 1; step <= numDoors; step++) { final start = step - 1; for (var i = start; i < numDoors; i += step) { doorClosed[i] = !doorClosed[i]; } stdout.writeln(stateToString("after toggling with step = $step")); }
}</lang>
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX after initialization ☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐ after toggling with step = 1 ☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X☐X after toggling with step = 2 ☐XXX☐☐☐XXX☐☐☐XXX☐☐☐XXX☐☐☐XXX☐☐☐XXX☐☐☐XXX☐☐☐XXX☐☐☐XXX☐☐☐XXX☐☐☐XXX☐☐☐XXX☐☐☐XXX☐☐☐XXX☐☐☐XXX☐☐☐XXX☐☐☐XXX after toggling with step = 3 ☐XX☐☐☐☐☐XX☐X☐XX☐☐☐☐☐XX☐X☐XX☐☐☐☐☐XX☐X☐XX☐☐☐☐☐XX☐X☐XX☐☐☐☐☐XX☐X☐XX☐☐☐☐☐XX☐X☐XX☐☐☐☐☐XX☐X☐XX☐☐☐☐☐XX☐X☐XX☐ after toggling with step = 4 ☐XX☐X☐☐☐X☐☐X☐X☐☐☐☐☐XXX☐XXXX☐☐X☐☐XXXX☐XXX☐☐☐☐☐X☐X☐☐X☐☐☐X☐XX☐☐☐XX☐X☐☐☐X☐☐X☐X☐☐☐☐☐XXX☐XXXX☐☐X☐☐XXXX☐XXX after toggling with step = 5 ☐XX☐XX☐☐X☐☐☐☐X☐☐☐X☐XXX☐☐XXX☐☐☐☐☐XXX☐☐XXX☐X☐☐☐X☐☐☐☐X☐☐XX☐XX☐X☐XX☐XX☐☐X☐☐☐☐X☐☐☐X☐XXX☐☐XXX☐☐☐☐☐XXX☐☐XXX after toggling with step = 6 ☐XX☐XXX☐X☐☐☐☐☐☐☐☐X☐X☐X☐☐XXXX☐☐☐☐XX☐☐☐XXX☐☐☐☐☐X☐☐X☐X☐☐XXXXX☐X☐X☐☐XX☐☐XX☐☐☐X☐☐XX☐XXX☐XXXX☐☐☐X☐XXX☐☐☐XX after toggling with step = 7 ☐XX☐XXXXX☐☐☐☐☐☐X☐X☐X☐X☐XXXXX☐☐☐XXX☐☐☐XX☐☐☐☐☐☐X☐XX☐X☐☐XX☐XX☐X☐X☐XXX☐☐XX☐X☐X☐☐XX☐☐XX☐XXXXX☐☐X☐XXXX☐☐XX after toggling with step = 8 ☐XX☐XXXX☐☐☐☐☐☐☐X☐☐☐X☐X☐XXX☐X☐☐☐XXX☐X☐XX☐☐☐☐☐XX☐XX☐X☐☐☐X☐XX☐X☐XXXXX☐☐XX☐☐☐X☐☐XX☐☐☐X☐XXXXX☐XX☐XXXX☐☐☐X after toggling with step = 9 ☐XX☐XXXX☐X☐☐☐☐☐X☐☐☐☐☐X☐XXX☐X☐X☐XXX☐X☐XXX☐☐☐☐XX☐XXXX☐☐☐X☐XX☐☐☐XXXXX☐☐X☐☐☐☐X☐☐XX☐X☐X☐XXXXX☐☐X☐XXXX☐☐☐☐ after toggling with step = 10 ☐XX☐XXXX☐XX☐☐☐☐X☐☐☐☐☐☐☐XXX☐X☐X☐X☐X☐X☐XXX☐☐☐XXX☐XXXX☐☐☐☐☐XX☐☐☐XXXX☐☐☐X☐☐☐☐X☐☐☐X☐X☐X☐XXXX☐☐☐X☐XXXX☐☐X☐ after toggling with step = 11 ☐XX☐XXXX☐XXX☐☐☐X☐☐☐☐☐☐☐☐XX☐X☐X☐X☐X☐☐☐XXX☐☐☐XXX☐☐XXX☐☐☐☐☐XX☐X☐XXXX☐☐☐X☐☐X☐X☐☐☐X☐X☐X☐☐XXX☐☐☐X☐XXX☐☐☐X☐ after toggling with step = 12 ☐XX☐XXXX☐XXXX☐☐X☐☐☐☐☐☐☐☐X☐☐X☐X☐X☐X☐☐☐X☐X☐☐☐XXX☐☐XXXX☐☐☐☐XX☐X☐XXX☐☐☐☐X☐☐X☐X☐☐☐☐☐X☐X☐☐XXX☐☐☐☐☐XXX☐☐☐X☐ after toggling with step = 13 ☐XX☐XXXX☐XXXXX☐X☐☐☐☐☐☐☐☐X☐☐☐☐X☐X☐X☐☐☐X☐X☐X☐XXX☐☐XXXX☐☐☐XXX☐X☐XXX☐☐☐☐XX☐X☐X☐☐☐☐☐X☐X☐XXXX☐☐☐☐☐XXX☐☐XX☐ after toggling with step = 14 ☐XX☐XXXX☐XXXXXXX☐☐☐☐☐☐☐☐X☐☐☐☐☐☐X☐X☐☐☐X☐X☐X☐X☐X☐☐XXXX☐☐☐XXX☐☐☐XXX☐☐☐☐XX☐X☐XX☐☐☐☐X☐X☐XXXX☐☐X☐☐XXX☐☐XX☐ after toggling with step = 15 ☐XX☐XXXX☐XXXXXX☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐X☐☐☐X☐X☐X☐X☐X☐XXXXX☐☐☐XXX☐☐☐XX☐☐☐☐☐XX☐X☐XX☐☐☐☐☐☐X☐XXXX☐☐X☐☐XXXX☐XX☐ after toggling with step = 16 ☐XX☐XXXX☐XXXXXX☐X☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐X☐X☐X☐X☐X☐XXX☐X☐☐☐XXX☐☐☐XX☐☐☐☐XXX☐X☐XX☐☐☐☐☐☐X☐X☐XX☐☐X☐☐XXXX☐XX☐ after toggling with step = 17 ☐XX☐XXXX☐XXXXXX☐XX☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐X☐X☐X☐X☐X☐X☐XXX☐X☐X☐XXX☐☐☐XX☐☐☐☐XXX☐☐☐XX☐☐☐☐☐☐X☐X☐XX☐☐☐☐☐XXXX☐XX☐ after toggling with step = 18 ☐XX☐XXXX☐XXXXXX☐XXX☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐X☐☐☐X☐X☐X☐X☐XXX☐X☐X☐X☐X☐☐☐XX☐☐☐☐XXX☐☐☐XXX☐☐☐☐☐X☐X☐XX☐☐☐☐☐XX☐X☐XX☐ after toggling with step = 19 ☐XX☐XXXX☐XXXXXX☐XXXX☐☐☐☐X☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐X☐X☐X☐XXX☐X☐X☐X☐X☐X☐XX☐☐☐☐XXX☐☐☐XXX☐☐☐X☐X☐X☐XX☐☐☐☐☐XX☐X☐XXX after toggling with step = 20 ☐XX☐XXXX☐XXXXXX☐XXXXX☐☐☐X☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐X☐X☐XXX☐X☐X☐X☐X☐X☐X☐☐☐☐☐XXX☐☐☐XXX☐☐☐X☐X☐☐☐XX☐☐☐☐☐XX☐X☐XXX after toggling with step = 21 ☐XX☐XXXX☐XXXXXX☐XXXXXX☐☐X☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐X☐XXX☐X☐X☐X☐X☐X☐X☐☐☐X☐XXX☐☐☐XXX☐☐☐X☐X☐☐☐XXX☐☐☐☐XX☐X☐XXX after toggling with step = 22 ☐XX☐XXXX☐XXXXXX☐XXXXXXX☐X☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐XXX☐X☐X☐X☐X☐X☐X☐☐☐X☐X☐X☐☐☐XXX☐☐☐X☐X☐☐☐XXX☐☐☐XXX☐X☐XXX after toggling with step = 23 ☐XX☐XXXX☐XXXXXX☐XXXXXXXXX☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐XX☐X☐X☐X☐X☐X☐X☐☐☐X☐X☐X☐X☐XXX☐☐☐X☐X☐☐☐XXX☐☐☐XXX☐☐☐XXX after toggling with step = 24 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐X☐☐X☐X☐X☐X☐X☐X☐☐☐X☐X☐X☐X☐X☐X☐☐☐X☐X☐☐☐XXX☐☐☐XXX☐☐☐XX☐ after toggling with step = 25 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐X☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐X☐X☐X☐X☐X☐☐☐X☐X☐X☐X☐X☐X☐X☐X☐X☐☐☐XXX☐☐☐XXX☐☐☐XX☐ after toggling with step = 26 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XX☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐X☐X☐X☐X☐☐☐X☐X☐X☐X☐X☐X☐X☐XXX☐☐☐XXX☐☐☐XXX☐☐☐XX☐ after toggling with step = 27 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXX☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐X☐X☐X☐☐☐X☐X☐X☐X☐X☐X☐X☐XXX☐X☐XXX☐☐☐XXX☐☐☐XX☐ after toggling with step = 28 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXX☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐X☐X☐☐☐X☐X☐X☐X☐X☐X☐X☐XXX☐X☐X☐X☐☐☐XXX☐☐☐XX☐ after toggling with step = 29 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXX☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐X☐X☐X☐X☐X☐X☐X☐XXX☐X☐X☐X☐X☐XXX☐☐☐XX☐ after toggling with step = 30 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXX☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐X☐X☐X☐X☐X☐X☐XXX☐X☐X☐X☐X☐X☐X☐☐☐XX☐ after toggling with step = 31 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXX☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐X☐X☐X☐X☐X☐X☐X☐XXX☐X☐X☐X☐X☐X☐X☐X☐XX☐ after toggling with step = 32 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXX☐☐X☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐X☐X☐X☐X☐X☐X☐XXX☐X☐X☐X☐X☐X☐X☐X☐X☐☐ after toggling with step = 33 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXX☐X☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐X☐X☐X☐X☐X☐XXX☐X☐X☐X☐X☐X☐X☐X☐X☐☐ after toggling with step = 34 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXXX☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐X☐X☐X☐X☐XXX☐X☐X☐X☐X☐X☐X☐X☐X☐☐ after toggling with step = 35 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐X☐X☐X☐XXX☐X☐X☐X☐X☐X☐X☐X☐X☐☐ after toggling with step = 36 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐X☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐X☐X☐XXX☐X☐X☐X☐X☐X☐X☐X☐X☐☐ after toggling with step = 37 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XX☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐X☐XXX☐X☐X☐X☐X☐X☐X☐X☐X☐☐ after toggling with step = 38 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXX☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐XXX☐X☐X☐X☐X☐X☐X☐X☐X☐☐ after toggling with step = 39 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXX☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐XX☐X☐X☐X☐X☐X☐X☐X☐X☐☐ after toggling with step = 40 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXX☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐X☐X☐X☐X☐X☐X☐X☐X☐☐ after toggling with step = 41 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXX☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐X☐X☐X☐X☐X☐X☐X☐☐ after toggling with step = 42 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXX☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐X☐X☐X☐X☐X☐X☐☐ after toggling with step = 43 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXX☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐X☐X☐X☐X☐X☐☐ after toggling with step = 44 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXX☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐X☐X☐X☐X☐☐ after toggling with step = 45 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXX☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐X☐X☐X☐☐ after toggling with step = 46 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXX☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐X☐☐ after toggling with step = 47 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXXX☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐ after toggling with step = 48 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐ after toggling with step = 49 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐X☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 50 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XX☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 51 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXX☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 52 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXX☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 53 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXX☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 54 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXX☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 55 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXX☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 56 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXX☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 57 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXX☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 58 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXX☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 59 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXX☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 60 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXX☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 61 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXX☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 62 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXXX☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 63 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 64 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 65 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XX☐☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 66 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXX☐☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 67 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXX☐☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 68 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXX☐☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 69 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXX☐☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 70 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXX☐☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 71 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXX☐☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 72 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXX☐☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 73 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXX☐☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 74 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXX☐☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 75 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXX☐☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 76 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXX☐☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 77 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXX☐☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 78 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXXX☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 79 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXXX☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 80 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXX☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 81 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXX☐X☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 82 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXX☐XX☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 83 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXX☐XXX☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 84 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXX☐XXXX☐☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 85 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXX☐XXXXX☐☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 86 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXX☐XXXXXX☐☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 87 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXX☐XXXXXXX☐☐☐☐☐☐☐☐☐☐☐X after toggling with step = 88 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXX☐XXXXXXXX☐☐☐☐☐☐☐☐☐☐X after toggling with step = 89 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXX☐XXXXXXXXX☐☐☐☐☐☐☐☐☐X after toggling with step = 90 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXX☐XXXXXXXXXX☐☐☐☐☐☐☐☐X after toggling with step = 91 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXX☐XXXXXXXXXXX☐☐☐☐☐☐☐X after toggling with step = 92 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXX☐XXXXXXXXXXXX☐☐☐☐☐☐X after toggling with step = 93 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXX☐XXXXXXXXXXXXX☐☐☐☐☐X after toggling with step = 94 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXX☐XXXXXXXXXXXXXX☐☐☐☐X after toggling with step = 95 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXX☐XXXXXXXXXXXXXXX☐☐☐X after toggling with step = 96 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXX☐☐X after toggling with step = 97 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXXX☐X after toggling with step = 98 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXXXXX after toggling with step = 99 ☐XX☐XXXX☐XXXXXX☐XXXXXXXX☐XXXXXXXXXX☐XXXXXXXXXXXX☐XXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXX☐XXXXXXXXXXXXXXXXXX☐ after toggling with step = 100
Dc
Unoptimized:
<lang Dc>
- NB: This code uses the dc command "r" via register "r".
- You may comment out the unwanted version.
[SxSyLxLy]sr # this should work with every "dc" [r]sr # GNU dc can exchange top 2 stack values by "r"
- Now use "lrx" instead of "r" ...
0k # we work without decimal places [q]sq # useful e.g. as loop termination
- (x)(y)>R == if (y)>(x) eval R
- isle x y --> (x <= y)
[
[1q]S. [ !<. 0 ]x s.L.
]sl
- l: isle
[
100 llx
]sL
- L: isle100
- for initcode condcode incrcode body
- [1] [2] [3] [4]
[
[q]S. 4:. 3:. 2:. 1:. 1;.x [2;.x 0=. 4;.x 3;.x 0;.x]d0:.x Os.L.o
]sf
- f: for
- ----------------------------------------------------------------------------
- for( i=1 ; i<=100 ; ++i ) {
- door[i] = 0;
- }
- [init ...]P []ps-
[1si] [li lLx] [li1+si] [
li 0:d
]lfx
- for( s=1 ; s<=100 ; ++s ) {
- for( i=s ; i<=100 ; i+=s ) {
- door[i] = 1 - door[i]
- }
- }
[1ss] [ls lLx] [ls1+ss] [
#[step ]P lsn [ ...]ps- [lssi] [li lLx] [lils+si] [ 1 li;d - li:d ]lfx
]lfx
- long output:
- for( i=1 ; i<=100 ; ++i ) {
- print "door #", i, " is ", (door[i] ? "open" : "closed")), NL
- }
[
[1si] [li lLx] [li1+si] [ [door #]P li n [ is ]P [closed] [open] li;d 0=r lrx s- n [.]ps- ]lfx
]
- terse output:
- for( i=1 ; i<=100 ; ++i ) {
- if( door[i] ) {
- print i
- }
- print NL
- }
[
[1si] [li lLx] [li1+si] [ [] [ [ ]n lin ] li;d 0=r lrx s- x ]lfx []ps-
]
lrx # comment out for the long output version s- x
- [stack rest...]P []ps- f
</lang> Output:
1 4 9 16 25 36 49 64 81 100
DCL
Adapted from optimized Batch example <lang DCL> $! doors.com $! Excecute by running @doors at prompt. $ square = 1 $ incr = 3 $ count2 = 0 $ d = 1 $ LOOP2: $ count2 = count2 + 1 $ IF (d .NE. square) $ THEN WRITE SYS$OUTPUT "door d' is closed" $ ELSE WRITE SYS$OUTPUT "door d' is open" $ square = incr + square $ incr = incr + 2 $ ENDIF $ d = d + 1 $ IF (count2 .LT. 100) THEN GOTO LOOP2 </lang>
Delphi
- See Pascal
Draco
<lang draco>proc nonrec main() void:
byte DOORS = 100; [DOORS+1] bool door_open; unsigned DOORS i, j;
/* make sure all doors are closed */ for i from 1 upto DOORS do door_open[i] := false od;
/* pass through the doors */ for i from 1 upto DOORS do for j from i by i upto DOORS do door_open[j] := not door_open[j] od od;
/* show the open doors */ for i from 1 upto DOORS do if door_open[i] then writeln("Door ", i, " is open.") fi od
corp</lang>
- Output:
Door 1 is open. Door 4 is open. Door 9 is open. Door 16 is open. Door 25 is open. Door 36 is open. Door 49 is open. Door 64 is open. Door 81 is open. Door 100 is open.
DUP
<lang dup>100[$][0^:1-]# {initialize doors} % [s;[$101<][$$;~\:s;+]#%]d: {function d, switch door state function} 1s:[s;101<][d;!s;1+s:]# {increment step width from 1 to 100, execute function d each time} 1[$101<][$$.' ,;['o,'p,'e,'n,10,]['c,'l,'o,'s,'e,'d,10,]?1+]# {loop through doors, print door number and state}</lang>
Result:
<lang dup>1 open 2 closed 3 closed 4 open 5 closed 6 closed 7 closed 8 closed 9 open 10 closed 11 closed 12 closed ... 94 closed 95 closed 96 closed 97 closed 98 closed 99 closed 100 open</lang>
Compare this solution to the FALSE solution of this problem.
DWScript
Unoptimized <lang delphi>var doors : array [1..100] of Boolean; var i, j : Integer;
for i := 1 to 100 do
for j := i to 100 do if (j mod i) = 0 then doors[j] := not doors[j];F
for i := 1 to 100 do
if doors[i] then PrintLn('Door '+IntToStr(i)+' is open');</lang>
Dyalect
Outputs only open doors to save up space:
<lang Dyalect>var doors = Array.Empty(100, false)
for p in 0..99 {
for d in 0..99 { if (d + 1) % (p + 1) == 0 { doors[d] = !doors[d]; } }
}
for d in doors.Indices() when doors[d] {
print("Door \(d+1): Open")
}</lang>
- Output:
Door 1: Open Door 4: Open Door 9: Open Door 16: Open Door 25: Open Door 36: Open Door 49: Open Door 64: Open Door 81: Open Door 100: Open
Dylan
Unoptimized <lang dylan>define method doors()
let doors = make(<array>, fill: #f, size: 100); for (x from 0 below 100) for (y from x below 100 by x + 1) doors[y] := ~doors[y] end end; for (x from 1 to 100) if (doors[x - 1]) format-out("door %d open\n", x) end end
end</lang>
Déjà Vu
<lang dejavu>local :open-doors [ rep 101 false ]
for i range 1 100: local :j i while <= j 100: set-to open-doors j not open-doors! j set :j + j i
!print\ "Open doors: " for i range 1 100: if open-doors! i: !print\( to-str i " " )</lang>
- Output:
Open doors: 1 4 9 16 25 36 49 64 81 100
E
Graphical
This version animates the changes of the doors (as checkboxes).
<lang e>#!/usr/bin/env rune
var toggles := [] var gets := []
- Set up GUI (and data model)
def frame := <swing:makeJFrame>("100 doors") frame.getContentPane().setLayout(<awt:makeGridLayout>(10, 10)) for i in 1..100 {
def component := <import:javax.swing.makeJCheckBox>(E.toString(i)) toggles with= fn { component.setSelected(!component.isSelected()) } gets with= fn { component.isSelected() } frame.getContentPane().add(component)
}
- Set up termination condition
def done frame.addWindowListener(def _ {
to windowClosing(event) { bind done := true } match _ {}
})
- Open and close doors
def loop(step, i) {
toggles[i] <- () def next := i + step timer.whenPast(timer.now() + 10, fn { if (next >= 100) { if (step >= 100) { # Done. } else { loop <- (step + 1, step) } } else { loop <- (step, i + step) } })
} loop(1, 0)
frame.pack() frame.show() interp.waitAtTop(done)</lang>
EasyLang
<lang>len d[] 101 for p = 1 to 100
i = p while i <= 100 d[i] = 1 - d[i] i += p .
. for i = 1 to 100
if d[i] = 1 print i .
.</lang>
EchoLisp
The result is obviously the same in we run the process backwards. So, we check the state of each door during the 100-th step (opening/closing every door) <lang lisp>
- initial state = closed = #f
(define doors (make-vector 101 #f))
- run pass 100 to 1
(for*
((pass (in-range 100 0 -1)) (door (in-range 0 101 pass))) (when (and (vector-set! doors door (not (vector-ref doors door))) (= pass 1)) (writeln door "is open")))
1 "is open" 4 "is open" 9 "is open" 16 "is open" 25 "is open" 36 "is open" 49 "is open" 64 "is open" 81 "is open" 100 "is open" </lang>
ECL
optimized version
<lang ECL> Doors := RECORD
UNSIGNED1 DoorNumber; STRING6 State;
END;
AllDoors := DATASET([{0,0}],Doors);
Doors OpenThem(AllDoors L,INTEGER Cnt) := TRANSFORM
SELF.DoorNumber := Cnt; SELF.State := IF((CNT * 10) % (SQRT(CNT)*10)<>0,'Closed','Opened');
END;
OpenDoors := NORMALIZE(AllDoors,100,OpenThem(LEFT,COUNTER));
OpenDoors; </lang>
unoptimized version - demonstrating LOOP
<lang ECL> Doors := RECORD
UNSIGNED1 DoorNumber; STRING6 State;
END;
AllDoors := DATASET([{0,'0'}],Doors);
//first build the 100 doors
Doors OpenThem(AllDoors L,INTEGER Cnt) := TRANSFORM
SELF.DoorNumber := Cnt; SELF.State := 'Closed';
END;
ClosedDoors := NORMALIZE(AllDoors,100,OpenThem(LEFT,COUNTER));
//now iterate through them and use door logic
loopBody(DATASET(Doors) ds, UNSIGNED4 c) :=
PROJECT(ds, //ds=original input TRANSFORM(Doors, SELF.State := CASE((COUNTER % c) * 100,
0 => IF(LEFT.STATE = 'Opened','Closed','Opened') ,LEFT.STATE); SELF.DoorNumber := COUNTER; //PROJECT COUNTER
));
g1 := LOOP(ClosedDoors,100,loopBody(ROWS(LEFT),COUNTER));
OUTPUT(g1);
</lang>
unoptimized version - using ITERATE This is a bit more efficient than the LOOP version
<lang ECL> DoorSet := DATASET(100,TRANSFORM({UNSIGNED1 DoorState},SELF.DoorState := 1)); SetDoors := SET(DoorSet,DoorState);
Doors := RECORD
UNSIGNED1 Pass; SET OF UNSIGNED1 DoorSet;
END;
StartDoors := DATASET(100,TRANSFORM(Doors,SELF.Pass := COUNTER,SELF.DoorSet := SetDoors));
Doors XF(Doors L, Doors R) := TRANSFORM
ds := DATASET(L.DoorSet,{UNSIGNED1 DoorState}); NextDoorSet := PROJECT(ds, TRANSFORM({UNSIGNED1 DoorState}, SELF.DoorState := CASE((COUNTER % R.Pass) * 100, 0 => IF(LEFT.DoorState = 1,0,1), LEFT.DoorState))); SELF.DoorSet := IF(L.Pass=0,R.DoorSet,SET(NextDoorSet,DoorState)); SELF.Pass := R.Pass
END;
Res := DATASET(ITERATE(StartDoors,XF(LEFT,RIGHT))[100].DoorSet,{UNSIGNED1 DoorState}); PROJECT(Res,TRANSFORM({STRING20 txt},SELF.Txt := 'Door ' + COUNTER + ' is ' + IF(LEFT.DoorState=1,'Open','Closed'))); </lang>
EDSAC order code
Since there are only 100 doors, we'll keep things simple and use a whole EDSAC location for each door. A single bit would be enough, but that would make the code much longer.
The program works through the array of doors by modifying its own orders (instructions). This would be considered bad practice today, but was quite usual on the EDSAC. <lang edsac> [Hundred doors problem from Rosetta Code website] [EDSAC program, Initial Orders 2]
[Library subroutine M3. Prints header and is then overwritten. Here, the last character sets the teleprinter to figures.]
PFGKIFAFRDLFUFOFE@A6FG@E8FEZPF @&*THE!OPEN!DOORS!ARE@&# ..PZ [blank tape, needed to mark end of header text]
[Library subroutine P6. Prints strictly positive integer. 32 locations; working locations 1, 4, 5]
T56K [define load address for subroutine] GKA3FT25@H29@VFT4DA3@TFH30@S6@T1F V4DU4DAFG26@TFTFO5FA4DF4FS4F L4FT4DA1FS3@G9@EFSFO31@E20@J995FJF!F
T88K [define load address for main program] GK [set @ (theta) for relative addresses]
[The 100 doors are at locations 200..299. Doors are numbered 0..99 internally, and 1..100 for output. The base address and the number of doors can be varied. The value of a door is 0 if open, negative if closed.]
[Constants. Program also uses order 'P 1 F' which is permanently at absolute address 2.] [0] P200F [address of door #0] [1] P100F [number of doors, as an address] [2] UF [makes S order from T, since 'S' = 'T' + 'U'] [3] MF [makes A order from T, since 'A' = 'T' + 'M'] [4] V2047D [all 1's for "closed" (any negative value will do)] [5] &F [line feed] [6] @F [carriage return] [7] K4096F [teleprinter null[
[Variables] [8] PF [pass number; step when toggling doors] [9] PF [door number, as address, 0-based] [10] PF [order referring to door 0]
[Enter with acc = 0] [Part 1 : close all the doors] [11] T8@ [pass := 0 (used in part 2)] T9@ [door number := 0] A16@ [load 'T F' order] A@ [add base address] T10@ [store T order for door #0] [16] TF [clear acc; also serves as constant] A9@ [load door number] A10@ [make T order] T21@ [plant in code] A4@ [load value for "closed"] [21] TF [store in current door] A9@ [load door number] A2F [add 1] U9@ [update door number] S1@ [done all doors yet?] G16@ [if not, loop back]
[Part 2 : 100 passes, toggling the doors] [27] TF [clear acc] A8@ [load pass number] A2F [add 1] T8@ [save updated pass number] S2F [make -1] U9@ [door number := -1] A8@ [add pass number to get first door toggled on this pass] S1@ [gone beyond end?] E50@ [if so, move on to part 3] [36] A1@ [restore acc after test] U9@ [store current door number] A10@ [make T order to load status] U44@ [plant T order for first door in pass] A2@ [convert to S order] T43@ [plant S order] A4@ [load value for "closed"] [43] SF [subtract status; toggles status] [44] TF [update status] A9@ [load door number just toggled] A8@ [add pass number to get next door in pass] S1@ [gone beyond end?] G36@ [no, loop to do next door] E27@ [yes, loop to do next pass]
[Part 3 : Print list of open doors. Header has set teleprinter to figures.] [50] TF [clear acc] T9@ [door nr := 0] A10@ [T order for door 0] A3@ [convert to A order] T10@ [55] TF A9@ [load door number] A10@ [make A order to load value] T59@ [plant in next order] [59] AF [acc := 0 if open, < 0 if closed] G69@ [skip if closed] A9@ [door number as address] A2F [add 1 for 1-based output] RD [shift 1 right, address --> integer] TF [store integer at 0 for printing] [65] A65@ [for return from subroutine] G56F [call subroutine to print door number] O6@ [followed by CRLF] O5@ [69] TF [clear acc] A9@ [load door number] A2F [add 1] U9@ [update door number] S1@ [done all doors yet?] G55@ [if not, loop back] [75] O7@ [output null to flush teleprinter buffer] ZF [stop] E11Z [define relative start address] PF
</lang>
- Output:
THE OPEN DOORS ARE 1 4 9 16 25 36 49 64 81 100
Eero
<lang objc>
- import <Foundation/Foundation.h>
int main()
square := 1, increment = 3
for int door in 1 .. 100 printf("door #%d", door)
if door == square puts(" is open.") square += increment increment += 2 else puts(" is closed.")
return 0
</lang>
Egel
<lang Egel> import "prelude.eg"
using System using List
data open, closed
def toggle =
[ open N -> closed N | closed N -> open N ]
def doors =
[ N -> map [ N -> closed N ] (fromto 1 N) ]
def toggleK =
[ K nil -> nil | K (cons (D N) DD) -> let DOOR = if (N%K) == 0 then toggle (D N) else D N in cons DOOR (toggleK K DD) ]
def toggleEvery =
[ nil DOORS -> DOORS | (cons K KK) DOORS -> toggleEvery KK (toggleK K DOORS) ]
def run =
[ N -> toggleEvery (fromto 1 N) (doors N) ]
def main = run 100 </lang>
EGL
<lang EGL> program OneHundredDoors
function main()
doors boolean[] = new boolean[100]; n int = 100;
for (i int from 1 to n) for (j int from i to n by i) doors[j] = !doors[j]; end end for (i int from 1 to n) if (doors[i]) SysLib.writeStdout( "Door " + i + " is open" ); end end end
end </lang>
Eiffel
This is my first RosettaCode submission, as well as a foray into Eiffel for myself. I've tried to adhere to the description of the problem statement, as well as showcase a few Eiffelisms shown in the documentation.
The replacement code below took the original code and has made improvements in some ways, such as:
- Removal of "magic" many magic numbers and strings.
- Refactor of various code blocks to routines (commands and queries with good CQS).
- Utilization/Demonstration of full, secret, and selective feature exporting.
- Utilization/Demonstration of constants as expanded type constants and once-functions.
- Utilization/Demonstration of static-references (e.g. {APPLICATION}.min_door_count).
- Utilization/Demonstration of "like" keyword type anchoring (e.g. a_index_address: like {DOOR}.address).
- Utilization/Demonstration of semi-strict logical implication (e.g. consistency: is_open implies not Is_closed).
- Utilization/Demonstration of contracts, including require, ensure, and class invariant.
- Utilization/Demonstration of agent and `do_all' call on ITERABLE type.
- Utilization/Demonstration of various forms of across including "loop" and "all".
... as well as other Eiffel-ism's and some coding standards/best-practices.
file: application.e <lang eiffel>note description: "100 Doors problem" date: "08-JUL-2015" revision: "1.1"
class APPLICATION
create make
feature {NONE} -- Initialization
make -- Main application routine. do initialize_closed_doors toggle_doors output_door_states end
feature -- Access
doors: ARRAYED_LIST [DOOR] -- A set of doors (self-initialized to capacity of `max_door_count'). attribute create Result.make (max_door_count) end
feature -- Basic Operations
initialize_closed_doors -- Initialize all `doors'. do across min_door_count |..| max_door_count as ic_address_list loop doors.extend (create {DOOR}.make_closed (ic_address_list.item)) end ensure has_all_closed_doors: across doors as ic_doors_list all not ic_doors_list.item.is_open end end
toggle_doors -- Toggle all `doors'. do across min_door_count |..| max_door_count as ic_addresses_list loop across doors as ic_doors_list loop if is_door_to_toggle (ic_doors_list.item.address, ic_addresses_list.item) then ic_doors_list.item.toggle_door end end end end
output_door_states -- Output the state of all `doors'. do doors.do_all (agent door_state_out) end
feature -- Status Report
is_door_to_toggle (a_door_address, a_index_address: like {DOOR}.address): BOOLEAN -- Is the door at `a_door_address' needing to be toggled, when compared to `a_index_address'? do Result := a_door_address \\ a_index_address = 0 ensure only_modulus_zero: Result = (a_door_address \\ a_index_address = 0) end
feature -- Outputs
door_state_out (a_door: DOOR) -- Output the state of `a_door'. do print ("Door " + a_door.address.out + " is ") if a_door.is_open then print ("open.") else print ("closed.") end io.new_line end
feature {DOOR} -- Constants
min_door_count: INTEGER = 1 -- Minimum number of doors.
max_door_count: INTEGER = 100 -- Maximum number of doors.
end</lang>
file: door.e <lang eiffel>note description: "A door with an address and an open or closed state." date: "08-JUL-2015" revision: "1.1"
class DOOR
create make_closed, make
feature {NONE} -- initialization
make_closed (a_address: INTEGER) -- Initialize Current {DOOR} at `a_address' and state of `Is_closed'. require positive: a_address >= {APPLICATION}.min_door_count and a_address >= Min_door_count do make (a_address, Is_closed) ensure closed: is_open = Is_closed end
make (a_address: INTEGER; a_status: BOOLEAN) -- Initialize Current {DOOR} with `a_address' and `a_status', denoting position and `is_open' or `Is_closed'. require positive: a_address >= {APPLICATION}.min_door_count and a_address >= Min_door_count do address := a_address is_open := a_status ensure address_set: address = a_address status_set: is_open = a_status end
feature -- access
address: INTEGER -- `address' of Current {DOOR}.
is_open: BOOLEAN assign set_open -- `is_open' (or not) status of Current {DOOR}.
feature -- Setters
set_open (a_status: BOOLEAN) -- Set `status' with `a_status' do is_open := a_status ensure open_updated: is_open = a_status end
feature {APPLICATION} -- Basic Operations
toggle_door -- Toggle Current {DOOR} from `is_open' to not `is_open'. do is_open := not is_open ensure toggled: is_open /= old is_open end
feature {NONE} -- Implementation: Constants
Is_closed: BOOLEAN = False -- State of being not `is_open'.
Min_door_count: INTEGER = 1 -- Minimum door count.
invariant one_or_more: address >= 1 consistency: is_open implies not Is_closed
end</lang>
Ela
Standard Approach
<lang ela>open generic
type Door = Open | Closed
deriving Show
gate [] _ = [] gate (x::xs) (y::ys)
| x == y = Open :: gate xs ys | else = Closed :: gate xs ys
run n = gate [1..n] [& k*k \\ k <- [1..]]</lang>
Alternate Approach <lang ela>open list run n = takeWhile (<n) [& k*k \\ k <- [1..]]</lang>
Elena
ELENA 4.0 : <lang elena>import system'routines; import extensions;
public program() {
var Doors := Array.allocate(100).populate:(n=>false); for(int i := 0, i < 100, i := i + 1) { for(int j := i, j < 100, j := j + i + 1) { Doors[j] := Doors[j].Inverted } }; for(int i := 0, i < 100, i := i + 1) { console.printLine("Door #",i + 1," :",Doors[i].iif("Open","Closed")) }; console.readChar()
}</lang>
Elixir
<lang Elixir>defmodule HundredDoors do
def doors(n \\ 100) do List.duplicate(false, n) end def toggle(doors, n) do List.update_at(doors, n, &(!&1)) end def toggle_every(doors, n) do Enum.reduce( Enum.take_every((n-1)..99, n), doors, fn(n, acc) -> toggle(acc, n) end ) end
end
- unoptimized
final_state = Enum.reduce(1..100, HundredDoors.doors, fn(n, acc) -> HundredDoors.toggle_every(acc, n) end)
open_doors = Enum.with_index(final_state)
|> Enum.filter_map(fn {door,_} -> door end, fn {_,index} -> index+1 end)
IO.puts "All doors are closed except these: #{inspect open_doors}"
- optimized
final_state = Enum.reduce(1..10, HundredDoors.doors, fn(n, acc) -> HundredDoors.toggle(acc, n*n-1) end)
open_doors = Enum.with_index(final_state)
|> Enum.filter_map(fn {door,_} -> door end, fn {_,index} -> index+1 end)
IO.puts "All doors are closed except these: #{inspect open_doors}"</lang>
- Output:
All doors are closed except these: [1, 4, 9, 16, 25, 36, 49, 64, 81, 100]
Elm
<lang Elm>-- Unoptimized import List exposing (indexedMap, foldl, repeat, range) import Html exposing (text) import Debug exposing (toString)
type Door = Open | Closed
toggle d = if d == Open then Closed else Open
toggleEvery : Int -> List Door -> List Door toggleEvery k doors = indexedMap
(\i door -> if modBy k (i+1) == 0 then toggle door else door) doors
n = 100
main =
text (toString (foldl toggleEvery (repeat n Closed) (range 1 n)))
</lang>
Emacs Lisp
Unoptimized
<lang lisp>(defun create-doors ()
"Returns a list of closed doors
Each door only has two status: open or closed. If a door is closed it has the value 0, if it's open it has the value 1."
(let ((return_value '(0)) ;; There is already a door in the return_value, so k starts at 1 ;; otherwise we would need to compare k against 99 and not 100 in ;; the while loop (k 1)) (while (< k 100) (setq return_value (cons 0 return_value)) (setq k (+ 1 k))) return_value))
(defun toggle-single-door (doors)
"Toggle the stat of the door at the `car' position of the DOORS list
DOORS is a list of integers with either the value 0 or 1 and it represents a row of doors.
Returns a list where the `car' of the list has it's value toggled (if open it becomes closed, if closed it becomes open)."
(if (= (car doors) 1) (cons 0 (cdr doors)) (cons 1 (cdr doors))))
(defun toggle-doors (doors step original-step)
"Step through all elements of the doors' list and toggle a door when step is 1
DOORS is a list of integers with either the value 0 or 1 and it represents a row of doors. STEP is the number of doors we still need to transverse before we arrive at a door that has to be toggled. ORIGINAL-STEP is the value of the argument step when this function is called for the first time.
Returns a list of doors"
(cond ((null doors) '()) ((= step 1) (cons (car (toggle-single-door doors)) (toggle-doors (cdr doors) original-step original-step))) (t (cons (car doors) (toggle-doors (cdr doors) (- step 1) original-step)))))
(defun main-program ()
"The main loop for the program" (let ((doors_list (create-doors)) (k 1) ;; We need to define max-specpdl-size and max-specpdl-size to big ;; numbers otherwise the loop reaches the max recursion depth and ;; throws an error. ;; If you want more information about these variables, press Ctrl ;; and h at the same time and then press v and then type the name ;; of the variable that you want to read the documentation. (max-specpdl-size 5000) (max-lisp-eval-depth 2000)) (while (< k 101) (setq doors_list (toggle-doors doors_list k k)) (setq k (+ 1 k))) doors_list))
(defun print-doors (doors)
"This function prints the values of the doors into the current buffer.
DOORS is a list of integers with either the value 0 or 1 and it represents a row of doors. "
;; As in the main-program function, we need to set the variable ;; max-lisp-eval-depth to a big number so it doesn't reach max recursion ;; depth. (let ((max-lisp-eval-depth 5000)) (unless (null doors) (insert (int-to-string (car doors))) (print-doors (cdr doors)))))
- Returns a list with the final solution
(main-program)
- Print the final solution on the buffer
(print-doors (main-program))</lang>
Erlang
non-optimized <lang erlang> -module(hundoors).
-export([go/0]).
toggle(closed) -> open; toggle(open) -> closed.
go() -> go([closed || _ <- lists:seq(1, 100)],[], 1, 1). go([], L, N, _I) when N =:= 101 -> lists:reverse(L); go([], L, N, _I) -> go(lists:reverse(L), [], N + 1, 1); go([H|T], L, N, I) ->
H2 = case I rem N of 0 -> toggle(H); _ -> H end, go(T, [H2|L], N, I + 1).
</lang>
optimized
<lang erlang>doors() ->
F = fun(X) -> Root = math:pow(X,0.5), Root == trunc(Root) end, Out = fun(X, true) -> io:format("Door ~p: open~n",[X]); (X, false)-> io:format("Door ~p: close~n",[X]) end, [Out(X,F(X)) || X <- lists:seq(1,100)].</lang>
ERRE
<lang ERRE> ! "100 Doors" program for ERRE LANGUAGE ! Author: Claudio Larini ! Date: 21-Nov-2014 ! ! PC Unoptimized version translated from a QB version
PROGRAM 100DOORS
!$INTEGER
CONST N=100
DIM DOOR[N]
BEGIN
FOR STRIDE=1 TO N DO
FOR INDEX=STRIDE TO N STEP STRIDE DO DOOR[INDEX]=NOT(DOOR[INDEX]) END FOR
END FOR
PRINT("Open doors:";) FOR INDEX=1 TO N DO
IF DOOR[INDEX] THEN PRINT(INDEX;) END IF
END FOR PRINT
END PROGRAM </lang>
Euler Math Toolbox
<lang Euler Math Toolbox> >function Doors () ... $ doors:=zeros(1,100); $ for i=1 to 100 $ for j=i to 100 step i $ doors[j]=!doors[j]; $ end; $ end; $ return doors $endfunction >nonzeros(Doors())
[ 1 4 9 16 25 36 49 64 81 100 ]
</lang>
Euphoria
unoptimised <lang Euphoria>-- doors.ex include std/console.e sequence doors doors = repeat( 0, 100 ) -- 1 to 100, initialised to false
for pass = 1 to 100 do for door = pass to 100 by pass do --printf( 1, "%d", doors[door] ) --printf( 1, "%d", not doors[door] ) doors[door] = not doors[door] end for end for
sequence oc
for i = 1 to 100 do if doors[i] then oc = "open" else oc = "closed" end if
printf( 1, "door %d is %s\n", { i, oc } )
end for </lang>
Excel
Note: The use of Auto Fill saves a lot of time when entering this code. One can refer to Excel help pages to learn about Auto Fill features.
Create a labelling column (A) and row (1) labelling the number of the door (column A, labelling starts in row 2 with a "1" and continues counting up to "100" in row 101) and the number of the pass (row 1, labelling starts in column B with a "0" and continues counting up to "100" in column CX). Additonally, you can label cell A1 as "Door/Pass" or so.
Closed doors are represented by zeroes ("0"), open doors are represented by ones ("1"). To represent the initial condition fill rows 2 to 101 in column B (pass "0") with zeroes.
Starting in column C, row 2, you enter code as shown in the examples below. The examples show the code to be entered in cells C2, C3, and D2. Continue to write code for the rest of the 4245 data cells, accordingly. Excel Auto Fill feature is best used for this.
Cell C2: <lang Excel> =IF($A2/C$1=INT($A2/C$1),IF(B2=0,1,IF(B2=1,0)),B2) </lang> Cell C3: <lang Excel> =IF($A3/C$1=INT($A3/C$1),IF(B3=0,1,IF(B3=1,0)),B3) </lang> Cell D2: <lang Excel> =IF($A2/D$1=INT($A2/D$1),IF(C2=0,1,IF(C2=1,0)),C2) </lang>
The last column (column CX, labelled "100") shows a "1" for each door (labelled by the rows in column A) that is open after the 100th pass. It shows a "1" for the following doors: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100.
F#
Requires #light in versions of F# prior to 2010 beta. <lang fsharp>let answerDoors =
let ToggleNth n (lst:bool array) = // Toggle every n'th door [(n-1) .. n .. 99] // For each appropriate door |> Seq.iter (fun i -> lst.[i] <- not lst.[i]) // toggle it let doors = Array.create 100 false // Initialize all doors to closed Seq.iter (fun n -> ToggleNth n doors) [1..100] // toggle the appropriate doors for each pass doors // Initialize all doors to closed
</lang> Unoptimized / functional <lang fsharp> let modifier doors skip =
let rec modifierInner doors skip counter = match doors with | [] -> [] //base case: end of hall | first::rest when counter >= skip -> //case: reached door marked for change not first::(modifierInner rest skip 0) // open or close that door | first::rest -> //case: reached door to skip first::(modifierInner rest skip (counter+1)) // skip it modifierInner doors skip 0 //Initial state for walkthrough
let answerDoors doors =
let rec modifyDoors skipRange doors modifier = //fold each door result to the next with List.fold modifier doors skipRange //with an increasing skip modifyDoors [0..99] doors modifier //Initial starting state
let initDoors = Array.create 100 false |> Array.toList //Initialize all doors to closed (false)
answerDoors initDoors |> printfn "%A" //print answer (false is closed door) </lang> Tail-Recursive Optimized/Functional <lang fsharp> let modifier doors skip =
let rec modifier' doors skip counter result = match doors with | [] -> result |> List.rev //base case: end of hall | first::rest when counter >= skip -> //case: reached door marked for change modifier' rest skip 0 ((not first)::result) // open or close that door | first::rest -> //case: reached door to skip modifier' rest skip (counter+1) (first::result) // skip it modifier' doors skip 0 [] //Initial state for walkthrough
</lang> Following is the solution using perfect squares. The coercions in PerfectSquare are, I believe, slightly different in versions prior to 2010 beta and, again, #light is required in those versions. <lang fsharp>open System let answer2 =
let PerfectSquare n = let sqrt = int(Math.Sqrt(float n)) n = sqrt * sqrt [| for i in 1..100 do yield PerfectSquare i |]</lang>
Simple single line solution using nothing but List <lang fsharp> [1..100] |> List.fold (fun doors pass->List.mapi (fun i x->if ((i + 1) % pass)=0 then not x else x) doors) (List.init 100 (fun _->false)) </lang>
Factor
Unoptimized <lang Factor>USING: bit-arrays formatting fry kernel math math.ranges sequences ; IN: rosetta.doors
CONSTANT: number-of-doors 100
- multiples ( n -- range )
0 number-of-doors rot <range> ;
- toggle-multiples ( n doors -- )
[ multiples ] dip '[ _ [ not ] change-nth ] each ;
- toggle-all-multiples ( doors -- )
[ number-of-doors [1,b] ] dip '[ _ toggle-multiples ] each ;
- print-doors ( doors -- )
[ swap "open" "closed" ? "Door %d is %s\n" printf ] each-index ;
- main ( -- )
number-of-doors 1 + <bit-array> [ toggle-all-multiples ] [ print-doors ] bi ;
main</lang>
Optimized <lang Factor> USING:
formatting math math.primes.factors math.ranges sequences ;
IN: rosetta-doors2
- main ( -- )
100 [1,b] [ divisors length odd? ] filter "Open %[%d, %]\n" printf ;
</lang>
Falcon
Unoptimized code <lang falcon>doors = arrayBuffer( 101, false )
for pass in [ 0 : doors.len() ]
for door in [ 0 : doors.len() : pass+1 ] doors[ door ] = not doors[ door ] end
end
for door in [ 1 : doors.len() ] // Show Output
> "Door ", $door, " is: ", ( doors[ door ] ) ? "open" : "closed"
end </lang> Optimized code <lang falcon> for door in [ 1 : 101 ]: > "Door ", $door, " is: ", fract( door ** 0.5 ) ? "closed" : "open"</lang>
FALSE
<lang false>100[$][0 1ø:1-]# {initialize doors} % [s;[$101\>][$$;~\:s;+]#%]d: {function d, switch door state function} 1s:[s;101\>][d;!s;1+s:]# {increment step width from 1 to 100, execute function d each time} 1[$101\>][$$." ";$["open "]?~["closed "]?1+]# {loop through doors, print door number and state}</lang>
Result:
<lang dup>1 open 2 closed 3 closed 4 open 5 closed 6 closed 7 closed 8 closed 9 open 10 closed ... 98 closed 99 closed 100 open</lang>
Compare this solution to the DUP solution of this problem.
Fantom
Unoptimized <lang fantom>
states := (1..100).toList 100.times |i| { states = states.map |state| { state % (i+1) == 0 ? -state : +state } } echo("Open doors are " + states.findAll { it < 0 }.map { -it })
</lang> Optimized <lang fantom>
echo("Open doors are " + (1..100).toList.findAll { it.toFloat.pow(0.5f).toInt.pow(2) == it})
</lang>
FBSL
Unoptimised <lang qbasic>#AppType Console
Dim doors[], n As Integer = 100
For Dim i = 1 To n For Dim j = i To n Step i doors[j] = Not doors[j] Next Next
For i = 1 To n If doors[i] Then Print "Door ", i, " is open" Next
Pause</lang> Optimised (by ML) <lang qbasic>#APPTYPE CONSOLE
DIM i = 0, j = 0, door = 1
WHILE INCR(i) < 101
IF i = door THEN PRINT "Door ", door, " open" INCR(door, INCR((INCR(j) << 1))) END IF
WEND
PAUSE</lang>
Fhidwfe
unoptomized <lang Fhidwfe> doors = malloc$ 100u for uint [0u, sizeof$ doors) with l1 {
put_byte$ + doors l1 as false byte
} function void pass(step:uint) {
location = step while <= location sizeof$ doors { ac = - + doors location 1u put_byte$ ac ~ deref_byte$ ac// true is represented as 255 (0xff) location = + location step }
} for uint (0u, sizeof$ doors] with l2 {//range exclusive of 0, inclusive of 100
pass$ l2
} count = 1u for ubyte as doors listubyte with isopen {// list for-each
if as isopen bool {// cast byte to bool puts$ "door " putui$ count puts$ " is open\n" } ; count = + count 1u
} free$ doors </lang>
Fish
Unoptimized <lang fish>1001-p01. >0101-p02. >101-g001-g+:::aa*)?v101-p03. >02-g?v1}02-p02. >05.
>0}02-p02.
>~~~0101-p001-g:1+001-paa*)?v02.
>07.
>0101-p08. >101-g::02-g?v >1+:101-paa*=?;
>n" "o^</lang>
FOCAL
<lang FOCAL>1.1 F N=1,100;S D(N)=0 1.2 F M=1,100;F N=M,M,100;S D(N)=1-D(N) 1.3 F N=1,100;D 2.0 1.4 Q 2.1 I (D(N)),,2.2;R 2.2 T "OPEN DOOR ",%3.0,N,!</lang>
- Output:
OPEN DOOR = 1 OPEN DOOR = 4 OPEN DOOR = 9 OPEN DOOR = 16 OPEN DOOR = 25 OPEN DOOR = 36 OPEN DOOR = 49 OPEN DOOR = 64 OPEN DOOR = 81 OPEN DOOR = 100
Forth
Unoptimized <lang forth>: toggle ( c-addr -- ) \ toggle the byte at c-addr
dup c@ 1 xor swap c! ;
100 1+ ( 1-based indexing ) constant ndoors create doors ndoors allot
- init ( -- ) doors ndoors erase ; \ close all doors
- pass ( n -- ) \ toggle every nth door
ndoors over do doors i + toggle dup ( n ) +loop drop ;
- run ( -- ) ndoors 1 do i pass loop ;
- display ( -- ) \ display open doors
ndoors 1 do doors i + c@ if i . then loop cr ;
init run display</lang>
Optimized <lang forth>: squared ( n -- n' ) dup * ;
- doors ( n -- )
1 begin 2dup squared >= while dup squared . 1+ repeat 2drop ;
100 doors</lang>
Fortran
unoptimized
<lang fortran>program doors
implicit none integer, allocatable :: door(:) character(6), parameter :: s(0:1) = [character(6) :: "closed", "open"] integer :: i, n print "(A)", "Number of doors?" read *, n allocate (door(n)) door = 1 do i = 1, n door(i:n:i) = 1 - door(i:n:i) print "(A,G0,2A)", "door ", i, " is ", s(door(i)) end do
end program</lang>
optimized
<lang fortran>PROGRAM DOORS
INTEGER, PARAMETER :: n = 100 ! Number of doors INTEGER :: i LOGICAL :: door(n) = .TRUE. ! Initially closed DO i = 1, SQRT(REAL(n)) door(i*i) = .FALSE. END DO DO i = 1, n WRITE(*,"(A,I3,A)", ADVANCE="NO") "Door ", i, " is " IF (door(i)) THEN WRITE(*,"(A)") "closed" ELSE WRITE(*,"(A)") "open" END IF END DO
END PROGRAM DOORS</lang>
Free Pascal
<lang pascal> program OneHundredIsOpen;
const
DoorCount = 100;
var
IsOpen: array[1..DoorCount] of boolean; Door, Jump: integer;
begin
// Close all doors for Door := 1 to DoorCount do IsOpen[Door] := False; // Iterations for Jump := 1 to DoorCount do begin Door := Jump; repeat IsOpen[Door] := not IsOpen[Door]; Door := Door + Jump; until Door > DoorCount; end; // Show final status for Door := 1 to DoorCount do begin Write(Door, ' '); if IsOpen[Door] then WriteLn('open') else WriteLn('closed'); end; // Wait for <enter> Readln;
end. </lang>
FreeBASIC
Toggle
<lang freebasic>' version 27-10-2016 ' compile with: fbc -s console
- Define max_doors 100
Dim As ULong c, n, n1, door(1 To max_doors)
' toggle, at start all doors are closed (0) ' 0 = door closed, 1 = door open For n = 1 To max_doors
For n1 = n To max_doors Step n door(n1) = 1 - door(n1) Next
Next
' count the doors that are open (1) Print "doors that are open nr: "; For n = 1 To max_doors
If door(n) = 1 Then Print n; " "; c = c + 1 End If
Next
Print : Print Print "There are " + Str(c) + " doors open"
' empty keyboard buffer While InKey <> "" : Wend Print : Print "hit any key to end program" Sleep End</lang>
- Output:
doors that are open nr: 1 4 9 16 25 36 49 64 81 100 There are 10 doors open
Count
<lang freebasic>' version 27-10-2016 ' compile with: fbc -s console
- Define max_doors 100
Dim As ULong c, n, n1, door(1 To max_doors)
' at start all doors are closed ' simple add 1 each time we open or close a door ' doors with odd numbers are open ' doors with even numbers are closed For n = 1 To max_doors
For n1 = n To max_doors Step n door(n1) += 1 Next
Next
Print "doors that are open nr: "; For n = 1 To max_doors
If door(n) And 1 Then Print n; " "; c = c + 1 End If
Next
Print : Print Print "There are " + Str(c) + " doors open"
' empty keyboard buffer While InKey <> "" : Wend Print : Print "hit any key to end program" Sleep End</lang> Output is the same as the first version.
Optimized
<lang freebasic>' version 27-10-2016 ' compile with: fbc -s console
- Define max_doors 100
Dim As ULong c, n
Print "doors that are open nr: "; For n = 1 To 10
Print n * n; " "; c = c + 1
Next
Print : Print Print "There are " + Str(c) + " doors open"
' empty keyboard buffer While InKey <> "" : Wend Print : Print "hit any key to end program" Sleep End</lang> Output is the same as the first version.
Ultra optimizado
<lang freebasic>' version 16-06-2021 ' portado desde Julia
For i As Integer = 1 To 10
If (i Mod i^2) < 11 Then Print "La puerta"; i^2; " esta abierta"
Next i Sleep </lang>
friendly interactive shell
Unoptimized <lang fishshell># Set doors to empty list set doors
- Initialize doors arrays
for i in (seq 100)
set doors[$i] 0
end
for i in (seq 100)
set j $i while test $j -le 100 # Logical not on doors set doors[$j] (math !$doors[$j]) set j (math $j + $i) end
end
- Print every door
for i in (seq (count $doors))
echo -n "$i " if test $doors[$i] -eq 0 echo closed else echo open end
end </lang>
Optimized <lang fishshell># Set doors to empty list set doors
for i in (seq 100)
set doors[(math "$i * $i")] 1 echo -n "$i " if test $doors[$i] -eq 1 echo open else echo closed end
end</lang>
Frink
<lang frink> doors = new array[[101], false] for pass=1 to 100
for door=pass to 100 step pass doors@door = ! doors@door
print["Open doors: "] for door=1 to 100
if doors@door print["$door "]
</lang>
FunL
Unoptimized
<lang funl>for i <- 1..100
r = foldl1( \a, b -> a xor b, [(a|i) | a <- 1..100] ) println( i + ' ' + (if r then 'open' else 'closed') )</lang>
Optimized
<lang funl>import math.sqrt
for i <- 1..100
println( i + ' ' + (if sqrt(i) is Integer then 'open' else 'closed') )</lang>
Futhark
<lang Futhark> let main(n: i32): [n]bool =
loop is_open = replicate n false for i < n do let js = map (*i+1) (iota n) let flips = map (\j -> if j < n then unsafe !is_open[j] else true -- Doesn't matter. ) js in scatter is_open js flips
</lang>
FutureBasic
<lang futurebasic> include "NSLog.incl"
NSInteger door, square = 1, increment = 3
for door = 1 to 100
if ( door == square ) NSLog( @"Door %ld is open.", door ) square += increment : increment += 2 else NSLog( @"Door %ld is closed.", door ) end if
next
HandleEvents </lang>
Output:
Door 1 is open. Door 2 is closed. Door 3 is closed. Door 4 is open. Door 5 is closed. Door 6 is closed. Door 7 is closed. Door 8 is closed. Door 9 is open. Door 10 is closed. Door 11 is closed. Door 12 is closed. Door 13 is closed. Door 14 is closed. Door 15 is closed. Door 16 is open. Door 17 is closed. Door 18 is closed. Door 19 is closed. Door 20 is closed. Door 21 is closed. Door 22 is closed. Door 23 is closed. Door 24 is closed. Door 25 is open. Door 26 is closed. Door 27 is closed. Door 28 is closed. Door 29 is closed. Door 30 is closed. Door 31 is closed. Door 32 is closed. Door 33 is closed. Door 34 is closed. Door 35 is closed. Door 36 is open. Door 37 is closed. Door 38 is closed. Door 39 is closed. Door 40 is closed. Door 41 is closed. Door 42 is closed. Door 43 is closed. Door 44 is closed. Door 45 is closed. Door 46 is closed. Door 47 is closed. Door 48 is closed. Door 49 is open. Door 50 is closed. Door 51 is closed. Door 52 is closed. Door 53 is closed. Door 54 is closed. Door 55 is closed. Door 56 is closed. Door 57 is closed. Door 58 is closed. Door 59 is closed. Door 60 is closed. Door 61 is closed. Door 62 is closed. Door 63 is closed. Door 64 is open. Door 65 is closed. Door 66 is closed. Door 67 is closed. Door 68 is closed. Door 69 is closed. Door 70 is closed. Door 71 is closed. Door 72 is closed. Door 73 is closed. Door 74 is closed. Door 75 is closed. Door 76 is closed. Door 77 is closed. Door 78 is closed. Door 79 is closed. Door 80 is closed. Door 81 is open. Door 82 is closed. Door 83 is closed. Door 84 is closed. Door 85 is closed. Door 86 is closed. Door 87 is closed. Door 88 is closed. Door 89 is closed. Door 90 is closed. Door 91 is closed. Door 92 is closed. Door 93 is closed. Door 94 is closed. Door 95 is closed. Door 96 is closed. Door 97 is closed. Door 98 is closed. Door 99 is closed. Door 100 is open.
FUZE BASIC
<lang qbasic>READ x,y,z PRINT "Open doors: ";x;" "; CYCLE
z=x+y PRINT z;" "; x=z y=y+2
REPEAT UNTIL z>=100 DATA 1,3,0 END</lang>
Fōrmulæ
Fōrmulæ programs are not textual, visualization/edition of programs is done showing/manipulating structures but not text. Moreover, there can be multiple visual representations of the same program. Even though it is possible to have textual representation —i.e. XML, JSON— they are intended for storage and transfer purposes more than visualization and edition.
Programs in Fōrmulæ are created/edited online in its website, However they run on execution servers. By default remote servers are used, but they are limited in memory and processing power, since they are intended for demonstration and casual use. A local server can be downloaded and installed, it has no limitations (it runs in your own computer). Because of that, example programs can be fully visualized and edited, but some of them will not run if they require a moderate or heavy computation/memory resources, and no local server is being used.
In this page you can see the program(s) related to this task and their results.
Gambas
Click this link to run this code <lang gambas>Public Sub Main() Dim bDoor As New Boolean[101] Dim siCount1, siCount2, siStart As Short
For siCount1 = 1 To 100
Inc siStart For siCount2 = siStart To 100 Step siCount1 bDoor[siCount2] = Not bDoor[siCount2] Next
Next
For siCount1 = 1 To 100
If bDoor[siCount1] Then Print siCount1;;
Next
End</lang> Output:
1 4 9 16 25 36 49 64 81 100
GAP
<lang gap>doors := function(n)
local a,j,s; a := [ ]; for j in [1 .. n] do a[j] := 0; od; for s in [1 .. n] do j := s; while j <= n do a[j] := 1 - a[j]; j := j + s; od; od; return Filtered([1 .. n], j -> a[j] = 1);
end;
doors(100);
- [ 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 ]</lang>
GDScript
<lang GDScript>func Doors(door_count:int) -> void :
var doors : Array doors.resize(door_count)
# Note : Initialization is not necessarily mandatory (by default values are false) # Intentionally left here for i in door_count : doors[i] = false
# do visits for i in door_count : for j in range(i,door_count,i+1) : doors[j] = not doors[j] # print results var results : String = "" for i in door_count : results += str(i+1) + " " if doors[i] else "" print("Doors open : %s" % [results] )
- calling the function from the _ready function
func _ready() -> void :
Doors(100)
</lang>
Output:
Doors open : 1 4 9 16 25 36 49 64 81 100
Genie
<lang genie> // 100 doors problem // Author: Sinuhe masan (2019) init
// 100 elements array of boolean type doors:bool[100]
for var i = 1 to 100 doors[i] = false // set all doors closed
for var i = 1 to 100
j:int = i
while j <= 100 do
doors[j] = not doors[j]
j = j + i
print("Doors open: ") for var i = 1 to 100 if doors[i] stdout.printf ("%d ", i)
</lang>
Glee
<lang glee>100` *=0=>d $$ create vector 1..100, create bit pattern d, marking all equal to 0
- for (1..100[.s]){ $$ loop s from 1 to 100
d^(100` %s *=0 )=>d;} $$ d = d xor (bit pattern of vector 1..100 % s)
d $$ output d </lang>
The resulting output is the bit pattern showing the state of the 100 doors:
<lang glee>Result: 10010000 10000001 00000000 10000000 00010000 00000000 10000000 00000001 00000000 00000000 10000000 00000000 0001</lang>
GML
<lang gml>var doors,a,i; //Sets up the array for all of the doors. for (i = 1; i<=100; i += 1)
{ doors[i]=0; }
//This first for loop goes through and passes the interval down to the next for loop. for (i = 1; i <= 100; i += 1;)
{ //This for loop opens or closes the doors and uses the interval(if interval is 2 it only uses every other etc..) for (a = 0; a <= 100; a += i;) { //Opens or closes a door. doors[a] = !doors[a]; } }
open_doors = ;
//This for loop goes through the array and checks for open doors. //If the door is open it adds it to the string then displays the string. for (i = 1; i <= 100; i += 1;)
{ if (doors[i] == 1) { open_doors += "Door Number "+string(i)+" is open#"; } }
show_message(open_doors); game_end();</lang>
Go
unoptimized <lang go>package main
import "fmt"
func main() {
doors := [100]bool{}
// the 100 passes called for in the task description for pass := 1; pass <= 100; pass++ { for door := pass-1; door < 100; door += pass { doors[door] = !doors[door] } }
// one more pass to answer the question for i, v := range doors { if v { fmt.Print("1") } else { fmt.Print("0") }
if i%10 == 9 { fmt.Print("\n") } else { fmt.Print(" ") }
}
}</lang> Output:
1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
optimized <lang go>package main
import "fmt"
func main() {
var door int = 1 var incrementer = 0
for current := 1; current <= 100; current++ { fmt.Printf("Door %d ", current)
if current == door { fmt.Printf("Open\n") incrementer++ door += 2*incrementer + 1 } else { fmt.Printf("Closed\n") } }
}</lang>
optimized 2 <lang go>// 100 (optimized) doors in Go
package main
import (
"fmt" "math"
)
func main() {
for i := 1; i <= 100; i++ { f := math.Sqrt(float64(i)) if math.Mod(f, 1) == 0 { fmt.Print("O") } else { fmt.Print("-") } } fmt.Println()
}</lang> Output:
O--O----O------O--------O----------O------------O--------------O----------------O------------------O
Golfscript
<lang golfscript>100:c;[{0}c*]:d; c,{.c,>\)%{.d<\.d=1^\)d>++:d;}/}/ [c,{)"door "\+" is"+}%d{{"open"}{"closed"}if}%]zip {" "*puts}/</lang>
optimized with sqrt (Original version of GolfScript has no sqrt operator, but it can be added easily; the code was tested using a work-in-progress C interpreter for a language compatible enough with Golfscript) <lang golfscript>100,{)}% {:d.sqrt 2?= {"open"}{"close"}if"door "d+" is "+\+puts}/</lang>
optimized without sqrt <lang golfscript>[{"close"}100*]:d; 10,{)2?(.d<\["open"]\)d>++:d;}/ [100,{)"door "\+" is"+}%d]zip {" "*puts}/</lang>
Gosu
unoptimized <lang scala> uses java.util.Arrays
var doors = new boolean[100] Arrays.fill( doors, false )
for( pass in 1..100 ) {
var counter = pass-1 while( counter < 100 ) { doors[counter] = !doors[counter] counter += pass }
}
for( door in doors index i ) {
print( "door ${i+1} is ${door ? 'open' : 'closed'}" )
}
</lang>
optimized <lang scala> var door = 1 var delta = 0
for( i in 1..100 ) {
if( i == door ) { print( "door ${i} is open" ) delta++ door += 2*delta + 1 } else { print( "door ${i} is closed" ) }
} </lang>
Groovy
unoptimized <lang groovy>doors = [false] * 100 (0..99).each {
it.step(100, it + 1) { doors[it] ^= true }
} (0..99).each {
println("Door #${it + 1} is ${doors[it] ? 'open' : 'closed'}.")
}</lang>
optimized a Using square roots
<lang groovy>(1..100).each {
println("Door #${it} is ${Math.sqrt(it).with{it==(int)it} ? 'open' : 'closed'}.")
}</lang>
optimized b Without using square roots <lang groovy>doors = ['closed'] * 100 (1..10).each { doors[it**2 - 1] = 'open' } (0..99).each {
println("Door #${it + 1} is ${doors[it]}.")
}</lang>
GW-BASIC
<lang qbasic>10 DIM A(100) 20 FOR OFFSET = 1 TO 100 30 FOR I = 0 TO 100 STEP OFFSET 40 A(I) = A(I) + 1 50 NEXT I 60 NEXT OFFSET 70 ' Print "opened" doors 80 FOR I = 1 TO 100 90 IF A(I) MOD 2 = 1 THEN PRINT I 100 NEXT I</lang>
Output:
1 4 9 16 25 36 49 64 81 100
Harbour
Unoptimized code: <lang visualfoxpro>#define ARRAY_ELEMENTS 100 PROCEDURE Main()
LOCAL aDoors := Array( ARRAY_ELEMENTS ) LOCAL i, j
AFill( aDoors, .F. ) FOR i := 1 TO ARRAY_ELEMENTS FOR j := i TO ARRAY_ELEMENTS STEP i aDoors[ j ] = ! aDoors[ j ] NEXT NEXT AEval( aDoors, {|e, n| QQout( Padl(n,3) + " is " + Iif(aDoors[n], "*open*", "closed" ) + "|" ), Iif( n%5 == 0, Qout(), e:=NIL) } ) RETURN</lang>
Optimized code <lang visualfoxpro>#define ARRAY_ELEMENTS 100 PROCEDURE Main()
LOCAL aDoors := Array( ARRAY_ELEMENTS )
AFill( aDoors, .F. ) AEval( aDoors, {|e, n| aDoors[n] := e := Iif( Int(Sqrt(n))==Sqrt(n), .T., .F. ) } ) AEval( aDoors, {|e, n| QQout( Padl(n,3) + " is " + Iif(aDoors[n], "*open*", "closed" ) + "|" ), Iif( n%5 == 0, Qout(), e:=NIL )} ) RETURN</lang>
Output:
1 is *open*| 2 is closed| 3 is closed| 4 is *open*| 5 is closed| 6 is closed| 7 is closed| 8 is closed| 9 is *open*| 10 is closed| 11 is closed| 12 is closed| 13 is closed| 14 is closed| 15 is closed| 16 is *open*| 17 is closed| 18 is closed| 19 is closed| 20 is closed| 21 is closed| 22 is closed| 23 is closed| 24 is closed| 25 is *open*| 26 is closed| 27 is closed| 28 is closed| 29 is closed| 30 is closed| 31 is closed| 32 is closed| 33 is closed| 34 is closed| 35 is closed| 36 is *open*| 37 is closed| 38 is closed| 39 is closed| 40 is closed| 41 is closed| 42 is closed| 43 is closed| 44 is closed| 45 is closed| 46 is closed| 47 is closed| 48 is closed| 49 is *open*| 50 is closed| 51 is closed| 52 is closed| 53 is closed| 54 is closed| 55 is closed| 56 is closed| 57 is closed| 58 is closed| 59 is closed| 60 is closed| 61 is closed| 62 is closed| 63 is closed| 64 is *open*| 65 is closed| 66 is closed| 67 is closed| 68 is closed| 69 is closed| 70 is closed| 71 is closed| 72 is closed| 73 is closed| 74 is closed| 75 is closed| 76 is closed| 77 is closed| 78 is closed| 79 is closed| 80 is closed| 81 is *open*| 82 is closed| 83 is closed| 84 is closed| 85 is closed| 86 is closed| 87 is closed| 88 is closed| 89 is closed| 90 is closed| 91 is closed| 92 is closed| 93 is closed| 94 is closed| 95 is closed| 96 is closed| 97 is closed| 98 is closed| 99 is closed|100 is *open*|
Haskell
unoptimized <lang haskell>data Door
= Open | Closed deriving (Eq, Show)
toggle :: Door -> Door toggle Open = Closed toggle Closed = Open
toggleEvery :: Int -> [Door] -> [Door] toggleEvery k = zipWith toggleK [1 ..]
where toggleK n door | n `mod` k == 0 = toggle door | otherwise = door
run :: Int -> [Door] run n = foldr toggleEvery (replicate n Closed) [1 .. n]
main :: IO () main = print $ filter ((== Open) . snd) $ zip [1 ..] (run 100)</lang>
- Output:
[(1,Open),(4,Open),(9,Open),(16,Open),(25,Open),(36,Open),(49,Open),(64,Open),(81,Open),(100,Open)]
optimized
(without using square roots)
<lang haskell>gate :: Eq a => [a] -> [a] -> [Door]
gate (x:xs) (y:ys) | x == y = Open : gate xs ys
gate (x:xs) ys = Closed : gate xs ys
gate [] _ = []
run n = gate [1..n] [k*k | k <- [1..]]</lang>
alternatively, returning a list of all open gates, it's a one-liner:
<lang haskell>run n = takeWhile (< n) [k*k | k <- [1..]]</lang>
Haxe
<lang haxe>class RosettaDemo {
static public function main() { findOpenLockers(100); }
static function findOpenLockers(n : Int) { var i = 1;
while((i*i) <= n) { Sys.print(i*i + "\n"); i++; } }
}</lang>
HicEst
Unoptimized <lang hicest>REAL :: n=100, open=1, door(n)
door = 1 - open ! = closed DO i = 1, n
DO j = i, n, i door(j) = open - door(j) ENDDO
ENDDO DLG(Text=door, TItle=SUM(door)//" doors open") </lang> Optimized <lang hicest>door = 1 - open ! = closed DO i = 1, n^0.5
door(i*i) = open
ENDDO DLG(Text=door, TItle=SUM(door)//" doors open") </lang>
HolyC
<lang holyc>U8 is_open[100]; U8 pass = 0, door = 0;
/* do the 100 passes */ for (pass = 0; pass < 100; ++pass)
for (door = pass; door < 100; door += pass + 1) is_open[door] = !is_open[door];
/* output the result */ for (door = 0; door < 100; ++door)
if (is_open[door]) Print("Door #%d is open.\n", door + 1); else Print("Door #%d is closed.\n", door + 1);
</lang>
Hoon
<lang hoon>|^ =/ doors=(list ?) (reap 100 %.n) =/ passes=(list (list ?)) (turn (gulf 1 100) pass-n) |- ?~ passes doors $(doors (toggle doors i.passes), passes t.passes) ++ pass-n
|= n=@ud (turn (gulf 1 100) |=(k=@ud =((mod k n) 0)))
++ toggle
|= [a=(list ?) b=(list ?)] =| c=(list ?) |- ?: |(?=(~ a) ?=(~ b)) (flop c) $(a t.a, b t.b, c [=((mix i.a i.b) 1) c])
--</lang>
Huginn
<lang huginn>#! /bin/sh exec huginn --no-argv -E "${0}"
- ! huginn
import Algorithms as algo;
main() {
doorCount = 100; doors = [].resize( doorCount, false );
for ( pass : algo.range( doorCount ) ) { i = 0; step = pass + 1; while ( i < doorCount ) { doors[i] = ! doors[i]; i += step; } }
for ( i : algo.range( doorCount ) ) { if ( doors[i] ) { print( "door {} is open\n".format( i ) ); } } return ( 0 );
}</lang>
Hy
<lang lisp>(setv doors (* [False] 100))
(for [pass (range (len doors))]
(for [i (range pass (len doors) (inc pass))] (assoc doors i (not (get doors i)))))
(for [i (range (len doors))]
(print (.format "Door {} is {}." (inc i) (if (get doors i) "open" "closed"))))</lang>
I
<lang i>software { var doors = len(100)
for pass over [1, 100] var door = pass - 1 loop door < len(doors) { doors[door] = doors[door]/0 door += pass } end
for door,isopen in doors if isopen print("Door ",door+1,": open") end end print("All other doors are closed") }</lang>
Icon and Unicon
Icon and Unicon don't have a boolean type because most often, logic is expressed in terms of success or failure, which affects flow at run time.
Unoptimized solution. <lang icon> procedure main()
door := table(0) # default value of entries is 0 every pass := 1 to 100 do every door[i := pass to 100 by pass] := 1 - door[i]
every write("Door ", i := 1 to 100, " is ", if door[i] = 1 then "open" else "closed")
end </lang>
Optimized solution. <lang icon> procedure main()
every write("Door ", i := 1 to 100, " is ", if integer(sqrt(i)) = sqrt(i) then "open" else "closed")
end </lang>
or
<lang icon>procedure main(args)
dMap := table("closed") every dMap[(1 to sqrt(100))^2] := "open" every write("Door ",i := 1 to 100," is ",dMap[i])
end</lang>
Idris
<lang idris>import Data.Vect
-- Creates list from 0 to n (not including n) upTo : (m : Nat) -> Vect m (Fin m) upTo Z = [] upTo (S n) = 0 :: (map FS (upTo n))
data DoorState = DoorOpen | DoorClosed
toggleDoor : DoorState -> DoorState toggleDoor DoorOpen = DoorClosed toggleDoor DoorClosed = DoorOpen
isOpen : DoorState -> Bool isOpen DoorOpen = True isOpen DoorClosed = False
initialDoors : Vect 100 DoorState initialDoors = fromList $ map (\_ => DoorClosed) [1..100]
iterate : (n : Fin m) -> Vect m DoorState -> Vect m DoorState iterate n doors {m} =
map (\(idx, doorState) => if ((S (finToNat idx)) `mod` (S (finToNat n))) == Z then toggleDoor doorState else doorState) (zip (upTo m) doors)
-- Returns all doors left open at the end solveDoors : List (Fin 100) solveDoors =
findIndices isOpen $ foldl (\doors,val => iterate val doors) initialDoors (upTo 100)
main : IO () main = print $ map (\n => S (finToNat n)) solveDoors</lang>
Inform 7
<lang inform7>Hallway is a room.
A toggle door is a kind of thing. A toggle door can be open or closed. It is usually closed. A toggle door has a number called the door number. Understand the door number property as referring to a toggle door. Rule for printing the name of a toggle door: say "door #[door number]".
There are 100 toggle doors.
When play begins (this is the initialize doors rule): let the next door number be 1; repeat with D running through toggle doors: now the door number of D is the next door number; increment the next door number.
To toggle (D - open toggle door): now D is closed. To toggle (D - closed toggle door): now D is open.
When play begins (this is the solve puzzle rule): let the door list be the list of toggle doors; let the door count be the number of entries in the door list; repeat with iteration running from 1 to 100: let N be the iteration; while N is less than the door count: toggle entry N in the door list; increase N by the iteration; say "Doors left open: [list of open toggle doors]."; end the story.</lang>
Informix 4GL
<lang Informix 4GL> MAIN
DEFINE i, pass SMALLINT, doors ARRAY[100] OF SMALLINT FOR i = 1 TO 100 LET doors[i] = FALSE END FOR FOR pass = 1 TO 100 FOR i = pass TO 100 STEP pass LET doors[i] = NOT doors[i] END FOR END FOR FOR i = 1 TO 100 IF doors[i] THEN DISPLAY i USING "Door <<& is open" ELSE DISPLAY i USING "Door <<& is closed" END IF END FOR
END MAIN </lang>
Io
simple boolean list solution: <lang io>doors := List clone 100 repeat(doors append(false)) for(i,1,100,
for(x,i,100, i, doors atPut(x - 1, doors at(x - 1) not))
) doors foreach(i, x, if(x, "Door #{i + 1} is open" interpolate println))</lang> Optimized solution: <lang io>(Range 1 to(10) asList) foreach(v, "Door #{v ** 2} is open." interpolate println)</lang>
Sample output:
Door 1 is open. Door 4 is open. Door 9 is open. Door 16 is open. Door 25 is open. Door 36 is open. Door 49 is open. Door 64 is open. Door 81 is open. Door 100 is open.
Ioke
Unoptimized Object Oriented solution. <lang ioke>NDoors = Origin mimic
NDoors Toggle = Origin mimic do(
initialize = method(toggled?, @toggled? = toggled?) toggle! = method(@toggled? = !toggled?. self)
)
NDoors Doors = Origin mimic do(
initialize = method(n, @n = n @doors = {} addKeysAndValues(1..n, (1..n) map(_, NDoors Toggle mimic(false))) ) numsToToggle = method(n, for(x <- (1..@n), (x % n) zero?, x)) toggleThese = method(nums, nums each(x, @doors[x] = @doors at(x) toggle)) show = method(@doors filter:dict(value toggled?) keys sort println)
)
- Test code
x = NDoors Doors mimic(100) (1..100) each(n, x toggleThese(x numsToToggle(n))) x show</lang>
Isabelle
<lang Isabelle>theory Scratch
imports Main
begin
section‹100 Doors›
datatype doorstate = Open | Closed fun toggle :: "doorstate ⇒ doorstate" where "toggle Open = Closed" | "toggle Closed = Open" fun walk :: "('a ⇒ 'a) ⇒ nat ⇒ nat ⇒ 'a list ⇒ 'a list" where "walk f _ _ [] = []" | "walk f every 0 (x#xs) = (f x) # walk f every every xs" | "walk f every (Suc n) (x#xs) = x # walk f every n xs" text‹Example: \<^const>‹toggle› every second door. (second = 1, because of 0 indexing)› lemma "walk toggle 1 1 [Open, Open, Open, Open, Open, Open] = [Open, Closed, Open, Closed, Open, Closed]" by code_simp text‹Example: \<^const>‹toggle› every third door.› lemma "walk toggle 2 2 [Open, Open, Open, Open, Open, Open] = [Open, Open, Closed, Open, Open, Closed]" by code_simp text‹Walking each door is essentially the same as the common \<^const>‹map› function.› lemma "walk f 0 0 xs = map f xs" by(induction xs) (simp)+ lemma walk_beginning: "walk f every n xs = (walk f every n (take (Suc n) xs)) @ (walk f every every (drop (Suc n) xs))" by(induction f every n xs rule:walk.induct) (simp)+ text‹A convenience definition to take the off-by-one into account and setting the starting position.› definition visit_every :: "('a ⇒ 'a) ⇒ nat ⇒ 'a list ⇒ 'a list" where "visit_every f every xs ≡ walk f (every - 1) (every - 1) xs" fun iterate :: "nat ⇒ (nat ⇒ 'a ⇒ 'a) ⇒ nat ⇒ 'a ⇒ 'a" where "iterate 0 _ _ a = a" | "iterate (Suc i) f n a = iterate i f (Suc n) (f n a)" text‹The 100 doors problem.› definition "onehundred_doors ≡ iterate 100 (visit_every toggle) 1 (replicate 100 Closed)" lemma "onehundred_doors = [Open, Closed, Closed, Open, Closed, Closed, Closed, Closed, Open, Closed, Closed, Closed, Closed, Closed, Closed, Open, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Open, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Open, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Open, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Open, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Open, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Open]" by code_simp text‹Filtering for the open doors, we get the same result as the Haskell implementation.› lemma "[(i, door) ← enumerate 1 onehundred_doors. door = Open] = [(1,Open),(4,Open),(9,Open),(16,Open),(25,Open),(36,Open),(49,Open),(64,Open),(81,Open),(100,Open)]" by code_simp
section‹Equivalence to Haskell Implementation› text‹ We will now present an alternative implementation, which is similar to the Haskell implementation on 🌐‹https://rosettacode.org/wiki/100_doors#Haskell›. We will prove, that the two behave the same; in general, not just for a fixed set of 100 doors. ›
definition map_every_start :: "('a ⇒ 'a) ⇒ nat ⇒ nat ⇒ 'a list ⇒ 'a list" where "map_every_start f every start xs ≡ map (λ(i, x). if i mod every = 0 then f x else x) (enumerate start xs)"
definition visit_every_alt :: "('a ⇒ 'a) ⇒ nat ⇒ 'a list ⇒ 'a list" where "visit_every_alt f every xs ≡ map_every_start f every 1 xs" text‹Essentially, \<^term>‹start› and \<^term>‹start mod every› behave the same.› lemma map_every_start_cycle: "map_every_start f every (start + k*every) xs = map_every_start f every start xs" proof(induction xs arbitrary: start) case Nil show "map_every_start f every (start + k * every) [] = map_every_start f every start []" by(simp add: map_every_start_def) next case (Cons x xs) from Cons.IH[of "Suc start"] show "map_every_start f every (start + k * every) (x # xs) = map_every_start f every start (x # xs)" by(simp add: map_every_start_def) qed corollary map_every_start_cycle_zero: "map_every_start f every every xs = map_every_start f every 0 xs" using map_every_start_cycle[where k=1 and start=0, simplified] by blast lemma map_every_start_fst_zero: "map_every_start f every 0 (x # xs) = f x # map_every_start f every (Suc 0) xs" by(simp add: map_every_start_def) text‹ The first \<^term>‹n› elements are not processed by \<^term>‹f›, as long as \<^term>‹n› is less than the \<^term>‹every› cycle. › lemma map_every_start_skip_first: "Suc n < every ⟹ map_every_start f every (every - (Suc n)) (x # xs) = x # map_every_start f every (every - n) xs" by(simp add: map_every_start_def Suc_diff_Suc)
lemma map_every_start_append: "map_every_start f n s (ds1 @ ds2) = map_every_start f n s ds1 @ map_every_start f n (s + length ds1) ds2" by(simp add: map_every_start_def enumerate_append_eq)
text‹ The \<^const>‹walk› function and \<^const>‹map_every_start› behave the same, as long as the starting \<^term>‹n› is less than the \<^term>‹every› cycle, because \<^const>‹walk› allows pushing the start arbitrarily far and \<^const>‹map_every_start› only allows deferring the start within the \<^term>‹every› cycle. This generalization is needed to strengthen the induction hypothesis for the proof. › lemma walk_eq_map_every_start: "n ≤ every ⟹ walk f every n xs = map_every_start f (Suc every) (Suc every - n) xs" proof(induction xs arbitrary: n) case Nil show "walk f every n [] = map_every_start f (Suc every) (Suc every - n) []" by(simp add: map_every_start_def) next case (Cons x xs) then show "walk f every n (x # xs) = map_every_start f (Suc every) (Suc every - n) (x # xs)" proof(cases n) case 0 with Cons.IH show ?thesis by(simp add: map_every_start_cycle_zero map_every_start_fst_zero) next case (Suc n2) with Cons.prems map_every_start_skip_first[of n2 "Suc every"] have "map_every_start f (Suc every) (Suc every - Suc n2) (x # xs) = x # map_every_start f (Suc every) (Suc every - n2) xs" by fastforce with Suc Cons show ?thesis by(simp) qed qed corollary walk_eq_visit_every_alt: "walk f every every xs = visit_every_alt f (Suc every) xs" unfolding visit_every_alt_def using walk_eq_map_every_start by fastforce
text‹ Despite their very different implementations, our alternative visit function behaves the same as our original visit function. Text the theorem includes \<^term>‹Suc every› to express that we exclude \<^term>‹every = 0›. › theorem visit_every_eq_visit_every_alt: "visit_every f (Suc every) xs = visit_every_alt f (Suc every) xs" unfolding visit_every_def using walk_eq_visit_every_alt by fastforce
text‹Also, the \<^const>‹iterate› function we implemented above can be implemented by a simple \<^const>‹fold›.› lemma fold_upt_helper: assumes n_geq_1: "Suc 0 ≤ n" shows "fold f [Suc s..<n + s] (f s xs) = fold f [s..<n + s] xs" proof - from n_geq_1 have "[s..<n + s] = s#[Suc s..<n + s]" by (simp add: Suc_le_lessD upt_rec) from this have "fold f [s..<n + s] xs = fold f (s#[Suc s..<n + s]) xs" by simp also have "fold f (s#[Suc s..<n + s]) xs = fold f [Suc s..<n + s] (f s xs)" by(simp) ultimately show ?thesis by simp qed theorem iterate_eq_fold: "iterate n f s xs = fold f [s ..< n+s] xs" proof(induction n arbitrary: s xs) case 0 then show "iterate 0 f s xs = fold f [s..<0 + s] xs" by simp next case (Suc n) from Suc show "iterate (Suc n) f s xs = fold f [s..<Suc n + s] xs" by(simp add: fold_upt_helper not_less_eq_eq) qed
section‹Efficient Implementation› text ‹ As noted on this page, the only doors that remain open are those whose numbers are perfect squares. Yet, rosettacode does not want us to take this shortcut, since we want to compare implementations across programming languages. But we can prove that our code computes the same result as reporting all doors with a perfect square number as open: ›
theorem "[(i, door) ← enumerate 1 onehundred_doors. door = Open] = [(i*i, Open). i ← [1..<11]]" by code_simp
end</lang>
J
unoptimized <lang j> ~:/ (100 $ - {. 1:)"0 >:i.100 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ...
~:/ 0=|/~ >:i.100 NB. alternative
1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ...</lang> optimized <lang j> (e. *:) 1+i.100 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ...
1 (<:*:i.10)} 100$0 NB. alternative
1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ...</lang>
with formatting <lang j> 'these doors are open: ',": I. (i.101) e. *: 1+i.10 these doors are open: 1 4 9 16 25 36 49 64 81 100 </lang>
Janet
<lang janet> (def doors (seq [_ :range [0 100]] false))
(loop [pass :range [0 100]
door :range [pass 100 (inc pass)]] (put doors door (not (doors door))))
(print "open doors: " ;(seq [i :range [0 100] :when (doors i)] (string (inc i) " "))) </lang>
Output:
open doors: 1 4 9 16 25 36 49 64 81 100
Java
With an array of boolean
<lang java>class HundredDoors {
public static void main(String[] args) { boolean[] doors = new boolean[101];
for (int i = 1; i < doors.length; i++) { for (int j = i; j < doors.length; j += i) { doors[j] = !doors[j]; } }
for (int i = 1; i < doors.length; i++) { if (doors[i]) { System.out.printf("Door %d is open.%n", i); } } }
}</lang>
With a BitSet
<lang java>import java.util.BitSet;
public class HundredDoors {
public static void main(String[] args) { final int n = 100; var a = new BitSet(n); for (int i = 1; i <= n; i++) { for (int j = i - 1; j < n; j += i) { a.flip(j); } } a.stream().map(i -> i + 1).forEachOrdered(System.out::println); }
}</lang>
Only print the result
<lang java>class HundredDoors {
public static void main(String[] args) { for (int i = 1; i <= 10; i++) System.out.printf("Door %d is open.%n", i * i); }
}</lang>
Output:
Door 1 is open. Door 4 is open. Door 9 is open. Door 16 is open. Door 25 is open. Door 36 is open. Door 49 is open. Door 64 is open. Door 81 is open. Door 100 is open.
If only printing the result is required, using streams. <lang java>import java.util.stream.Collectors; import java.util.stream.IntStream;
class HundredDoors {
public static void main(String args[]) { String openDoors = IntStream.rangeClosed(1, 100) .filter(i -> Math.pow((int) Math.sqrt(i), 2) == i) .mapToObj(Integer::toString) .collect(Collectors.joining(", ")); System.out.printf("Open doors: %s%n", openDoors); }
} </lang>
Output:
Open doors: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100
JavaScript
ES5
Iterative
<lang javascript>var doors=[]; for (var i=0;i<100;i++)
doors[i]=false;
for (var i=1;i<=100;i++)
for (var i2=i-1,g;i2<100;i2+=i) doors[i2]=!doors[i2];
for (var i=1;i<=100;i++)
console.log("Door %d is %s",i,doors[i-1]?"open":"closed")</lang>
Functional Composition
Naive search <lang JavaScript>(function (n) {
"use strict"; function finalDoors(n) { var lstRange = range(1, n); return lstRange .reduce(function (a, _, k) { var m = k + 1; return a.map(function (x, i) { var j = i + 1; return [j, j % m ? x[1] : !x[1]]; }); }, zip( lstRange, replicate(n, false) )); }; function zip(xs, ys) { return xs.length === ys.length ? ( xs.map(function (x, i) { return [x, ys[i]]; }) ) : undefined; } function replicate(n, a) { var v = [a], o = []; if (n < 1) return o; while (n > 1) { if (n & 1) o = o.concat(v); n >>= 1; v = v.concat(v); } return o.concat(v); } function range(m, n, delta) { var d = delta || 1, blnUp = n > m, lng = Math.floor((blnUp ? n - m : m - n) / d) + 1, a = Array(lng), i = lng; if (blnUp) while (i--) a[i] = (d * i) + m; else while (i--) a[i] = m - (d * i); return a; } return finalDoors(n) .filter(function (tuple) { return tuple[1]; }) .map(function (tuple) { return { door: tuple[0], open: tuple[1] }; });
})(100);</lang>
Optimized (iterative)
<lang javascript>for (var door = 1; door <= 100; door++) {
var sqrt = Math.sqrt(door); if (sqrt === (sqrt | 0)) { console.log("Door %d is open", door); }
}</lang> Simple for loop. Optimizing the optimized? <lang javascript>for(var door=1;i<10/*Math.sqrt(100)*/;i++){
console.log("Door %d is open",i*i);
}</lang>
Optimized (functional)
The question of which doors are flipped an odd number of times reduces to the question of which numbers have an odd number of integer factors. We can simply search for these: <lang JavaScript>(function (n) {
"use strict"; return range(1, 100) .filter(function (x) { return integerFactors(x) .length % 2; }); function integerFactors(n) { var rRoot = Math.sqrt(n), intRoot = Math.floor(rRoot), lows = range(1, intRoot) .filter(function (x) { return (n % x) === 0; }); return lows.concat(lows.map(function (x) { return n / x; }) .reverse() .slice((rRoot === intRoot) | 0)); } function range(m, n, delta) { var d = delta || 1, blnUp = n > m, lng = Math.floor((blnUp ? n - m : m - n) / d) + 1, a = Array(lng), i = lng; if (blnUp) while (i--) a[i] = (d * i) + m; else while (i--) a[i] = m - (d * i); return a; }
})(100);</lang> Or we can note, on inspection and further reflection, that only perfect squares have odd numbers of integer factors - all other numbers have only matched pairs of factors - low factors below the non-integer square root, and the corresponding quotients above the square root. In the case of perfect squares, the additional integer square root (not paired with any other factor than itself) makes the total number of distinct factors odd. <lang JavaScript>(function (n) {
"use strict"; return perfectSquaresUpTo(100); function perfectSquaresUpTo(n) { return range(1, Math.floor(Math.sqrt(n))) .map(function (x) { return x * x; }); } function range(m, n, delta) { var d = delta || 1, blnUp = n > m, lng = Math.floor((blnUp ? n - m : m - n) / d) + 1, a = Array(lng), i = lng; if (blnUp) while (i--) a[i] = (d * i) + m; else while (i--) a[i] = m - (d * i); return a; }
})(100);</lang>
ES6
<lang javascript> Array.apply(null, { length: 100 })
.map((v, i) => i + 1) .forEach(door => { var sqrt = Math.sqrt(door);
if (sqrt === (sqrt | 0)) { console.log("Door %d is open", door); } });</lang>
<lang javascript>// Array comprehension style
[ for (i of Array.apply(null, { length: 100 })) i ].forEach((_, i) => {
var door = i + 1 var sqrt = Math.sqrt(door);
if (sqrt === (sqrt | 0)) { console.log("Door %d is open", door); }
});</lang>
The result is always:
Door 1 is open Door 4 is open Door 9 is open Door 16 is open Door 25 is open Door 36 is open Door 49 is open Door 64 is open Door 81 is open Door 100 is open
Or using a more general function for listing perfect squares:
<lang JavaScript>(function (n) {
// ONLY PERFECT SQUARES HAVE AN ODD NUMBER OF INTEGER FACTORS // (Leaving the door open at the end of the process) return perfectSquaresUpTo(n); // perfectSquaresUpTo :: Int -> [Int] function perfectSquaresUpTo(n) { return range(1, Math.floor(Math.sqrt(n))) .map(x => x * x); } // GENERIC // range(intFrom, intTo, optional intStep) // Int -> Int -> Maybe Int -> [Int] function range(m, n, step) { let d = (step || 1) * (n >= m ? 1 : -1); return Array.from({ length: Math.floor((n - m) / d) + 1 }, (_, i) => m + (i * d)); }
})(100);</lang>
- Output:
<lang JavaScript>[1, 4, 9, 16, 25, 36, 49, 64, 81, 100]</lang>
School example
<lang JavaScript>"use strict";
// Doors can be open or closed. const open = "O"; const closed = "C";
// There are 100 doors in a row that are all initially closed. const doorsCount = 100; const doors = []; for (let i = 0; i < doorsCount; doors[i] = closed, i++);
// You make 100 passes by the doors, visiting every door and toggle the door (if // the door is closed, open it; if it is open, close it), according to the rules // of the task. for (let pass = 1; pass <= doorsCount; pass++)
for (let i = pass - 1; i < doorsCount; i += pass) doors[i] = doors[i] == open ? closed : open;
// Answer the question: what state are the doors in after the last pass? doors.forEach((v, i) =>
console.log(`Doors ${i + 1} are ${v == open ? 'opened' : 'closed'}.`));
// Which are open, which are closed? let openKeyList = []; let closedKeyList = []; for (let door of doors.entries())
if (door[1] == open) openKeyList.push(door[0] + 1); else closedKeyList.push(door[0] + 1);
console.log("These are open doors: " + openKeyList.join(", ") + "."); console.log("These are closed doors: " + closedKeyList.join(", ") + ".");
// Assert: const expected = []; for (let i = 1; i * i <= doorsCount; expected.push(i * i), i++); if (openKeyList.every((v, i) => v === expected[i]))
console.log("The task is solved.")
else
throw "These aren't the doors you're looking for.";</lang>
jq
jq arrays have 0 as their index origin, but in the following, the 100 doors are numbered from 1 to 100.
Solution by simulation<lang jq># Solution for n doors:
def doors(n):
def print: . as $doors | range(1; length+1) | if $doors[.] then "Door \(.) is open" else empty end;
[range(n+1)|null] as $doors | reduce range(1; n+1) as $run ( $doors; reduce range($run; n+1; $run ) as $door ( .; .[$door] = (.[$door] | not) ) ) | print ;
</lang> Analytical solution<lang jq># Solution for 100 doors: def solution:
range(1;11) | "Door \(. * .) is open";
</lang>
Julia
Simple:
- falses(100) creates a 100-element Bool array filled with false values,
- 'b in a:a:100' translates to 'start:step:end',
- string concatenation by '*'.
<lang julia>doors = falses(100)
for a in 1:100, b in a:a:100
doors[b] = !doors[b]
end for a = 1:100
println("Door $a is " * (doors[a] ? "open." : "closed."))
end</lang>
Gimmicky-optimized: <lang julia>for i in 1:10 println("Door $(i^2) is open.") end</lang>
K
unoptimized / converted from Q . <lang k> `closed `open ![ ; 2 ] @ #:' 1 _ = ,/ &:' 0 = t !\:/: t : ! 101</lang>
optimized / 1 origin indices <lang k> ( 1 + ! 10 ) ^ 2</lang>
/ As parameterized function : <lang k> { ( 1 + ! _ x ^ % 2 ) ^ 2 } 100 </lang>
Klingphix
<lang Klingphix>include ..\Utilitys.tlhy
%n 100 !n 0 $n repeat
$n [dup sqrt int dup * over == ( [1 swap set] [drop] ) if] for
$n [ ( "The door " over " is " ) lprint get ( ["OPEN"] ["closed"] ) if print nl] for
( "Time elapsed: " msec " seconds" ) lprint nl
pstack " " input</lang>
Klong
unoptimized
<lang K> flip::{,/{(1-*x),1_x}'x:#y} i::0;(100{i::i+1;flip(i;x)}:*100:^0)?1 </lang>
optimized
<lang K> (1+!9)^2 </lang>
Kotlin
<lang scala>fun oneHundredDoors(): List<Int> {
val doors = BooleanArray(100, { false }) for (i in 0..99) { for (j in i..99 step (i + 1)) { doors[j] = !doors[j] } } return doors .mapIndexed { i, b -> i to b } .filter { it.second } .map { it.first + 1 }
}</lang>
KQL
<lang KQL>range InitialDoor from 1 to 100 step 1 | extend DoorsVisited=range(InitialDoor, 100, InitialDoor) | mvexpand DoorVisited=DoorsVisited to typeof(int) | summarize VisitCount=count() by DoorVisited | project Door=DoorVisited, IsOpen=(VisitCount % 2) == 1</lang>
LabVIEW
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- Optimized
This image is a VI Snippet, an executable image of LabVIEW code. The LabVIEW version is shown on the top-right hand corner. You can download it, then drag-and-drop it onto the LabVIEW block diagram from a file browser, and it will appear as runnable, editable code.
langur
not optimized
<lang langur>var .doors = arr 100, false
for .i of .doors {
for .j = .i; .j <= len(.doors); .j += .i { .doors[.j] = not .doors[.j] }
}
writeln wherekeys .doors</lang>
We could also use a for loop value to produce the output (instead of the wherekeys function), as in the following example.
<lang langur>writeln for[=[]] .i of .doors { if(.doors[.i]: _for ~= [.i]) }</lang>
Or, we could use the foldfrom() function to produce the output. <lang langur>writeln foldfrom(f if(.b: .a~[.c]; .a), [], .doors, series 1..len .doors)</lang>
optimized
<lang langur>writeln map(f .x ^ 2, series 1..10)</lang>
<lang langur>writeln map f{^2}, 1..10</lang>
- Output:
[1, 4, 9, 16, 25, 36, 49, 64, 81, 100]
lambdatalk
Translation from Python
<lang Scheme> 1) unoptimized version
{def doors
{A.new {S.map {lambda {} false} {S.serie 1 100}}}}
-> doors
{def toggle
{lambda {:i :a} {let { {_ {A.set! :i {not {A.get :i :a}} :a} }}}}}
-> toggle
{S.map {lambda {:b}
{S.map {lambda {:i} {toggle :i {doors}}} {S.serie :b 99 {+ :b 1}}}} {S.serie 0 99}}
->
{S.replace \s by space in
{S.map {lambda {:i} {if {A.get :i {doors}} then {+ :i 1} else}} {S.serie 0 99}}}
-> 1 4 9 16 25 36 49 64 81 100
2.2) optimized version
{S.replace \s by space in
{S.map {lambda {:i} {let { {:root {sqrt :i}} } {if {= :root {round :root}} then {* :root :root} else}}} {S.serie 1 100}}}
-> 1 4 9 16 25 36 49 64 81 100 </lang>
Lasso
Loop
<lang Lasso>loop(100) => {^
local(root = math_sqrt(loop_count))
local(state = (#root == math_ceil(#root) ? 'open' | 'closed'))
#state != 'closed' ? 'Door ' + loop_count + ': ' + #state + '
'
^}</lang>
- Output:
Door 1: open Door 4: open Door 9: open Door 16: open Door 25: open Door 36: open Door 49: open Door 64: open Door 81: open Door 100: open
Latitude
<lang latitude>use 'format importAllSigils.
doors := Object clone. doors missing := { False. }. doors check := {
self slot ($1 ordinal).
}. doors toggle := {
self slot ($1 ordinal) = self slot ($1 ordinal) not.
}. 1 upto 101 do {
takes '[i]. local 'j = i. while { j <= 100. } do { doors toggle (j). j = j + i. }.
}. $stdout printf: ~fmt "The open doors are: ~A", 1 upto 101 filter { doors check. } to (Array).</lang>
Lhogho
This implementation defines 100 variables, named "1 through "100, rather than using a list. Thanks to Pavel Boytchev, the author of Lhogho, for help with the code.
<lang Logo>to doors ;Problem 100 Doors ;Lhogho
for "p [1 100] [ make :p "false ]
for "a [1 100 1] [ for "b [:a 100 :a] [ if :b < 101 [ make :b not thing :b ] ] ]
for "c [1 100] [ if thing :c [ (print "door :c "is "open) ] ] end
doors</lang>
Liberty BASIC
<lang lb>dim doors(100) for pass = 1 to 100
for door = pass to 100 step pass doors(door) = not(doors(door)) next door
next pass print "open doors "; for door = 1 to 100
if doors(door) then print door;" ";
next door</lang>
Lily
<lang Lily>var doors = List.fill(100, false)
for i in 0...99:
for j in i...99 by i + 1: doors[j] = !doors[j]
- The type must be specified since the list starts off empty.
var open_doors: List[Integer] = []
doors.each_index{|i|
if doors[i]: open_doors.push(i + 1)
}
print($"Open doors: ^(open_doors)")</lang>
- Output:
Open doors: [1, 4, 9, 16, 25, 36, 49, 64, 81, 100]
xTalk
<lang lb> on mouseUp
repeat with tStep = 1 to 100 repeat with tDoor = tStep to 100 step tStep put not tDoors[tDoor] into tDoors[tDoor] end repeat if tDoors[tStep] then put "Door " & tStep & " is open" & cr after tList end repeat set the text of field "Doors" to tList
end mouseUp </lang>
Logo
<lang Logo>to doors
- Problem 100 Doors
- FMSLogo
- lrcvs 2010
make "door (vector 100 1) for [p 1 100][setitem :p :door 0]
for [a 1 100 1][for [b :a 100 :a][make "x item :b :door ifelse :x = 0 [setitem :b :door 1][setitem :b :door 0] ] ]
for [c 1 100][make "y item :c :door ifelse :y = 0 [pr (list :c "Close)] [pr (list :c "Open)] ] end</lang>
LOLCODE
<lang LOLCODE>HAI 1.3
I HAS A doors ITZ A BUKKIT IM IN YR hallway UPPIN YR door TIL BOTH SAEM door AN 100
doors HAS A SRS door ITZ FAIL BTW, INISHULIZE ALL TEH DOORZ AS CLOZD
IM OUTTA YR hallway
IM IN YR hallway UPPIN YR pass TIL BOTH SAEM pass AN 100
I HAS A door ITZ pass IM IN YR passer doors'Z SRS door R NOT doors'Z SRS door door R SUM OF door AN SUM OF pass AN 1 DIFFRINT door AN SMALLR OF door AN 99, O RLY? YA RLY, GTFO OIC IM OUTTA YR passer
IM OUTTA YR hallway
IM IN YR printer UPPIN YR door TIL BOTH SAEM door AN 100
VISIBLE "Door #" SUM OF door AN 1 " is "! doors'Z SRS door, O RLY? YA RLY, VISIBLE "open." NO WAI, VISIBLE "closed." OIC
IM OUTTA YR printer
KTHXBYE</lang>
Lua
<lang lua>local is_open = {}
for pass = 1,100 do
for door = pass,100,pass do is_open[door] = not is_open[door] end
end
for i,v in next,is_open do
print ('Door '..i..':',v and 'open' or 'close')
end</lang>
M2000 Interpreter
Second dim preserve values except explicit assign a value for each item using = or a different value using << and a lambda function as generator.
Here we use =false to make all items false (which is a double value of 0).
M2000 use True and False as -1 and 0 (type of double), but from comparisons return Boolean True and False, which used as -1 and 0 also. Using =1=1 we get Boolean True and =1=0 we get Boolean False. We can check type from a variable using Type$(), so x=1=1 : Print Type$(x)="Boolean". We can chack type of an expression using a function: Def ExpressionType$(x)=Type$(x)
<lang M2000 Interpreter> Module Doors100 {
Dim Doors(1 to 100) For i=1 to 100 For j=i to 100 step i Doors(j)~ Next j Next i DispAll() ' optimization Dim Doors(1 to 100)=False For i=1 to 10 Doors(i**2)=True Next i Print DispAll() Sub DispAll() Local i For i=1 to 100 if Doors(i) then print i, Next i Print End Sub
} Doors100 </lang>
M4
<lang m4>define(`_set', `define(`$1[$2]', `$3')')dnl define(`_get', `defn(`$1[$2]')')dnl define(`for',`ifelse($#,0,``$0,`ifelse(eval($2<=$3),1, `pushdef(`$1',$2)$5`'popdef(`$1')$0(`$1',eval($2+$4),$3,$4,`$5')')')')dnl define(`opposite',`_set(`door',$1,ifelse(_get(`door',$1),`closed',`open',`closed'))')dnl define(`upper',`100')dnl for(`x',`1',upper,`1',`_set(`door',x,`closed')')dnl for(`x',`1',upper,`1',`for(`y',x,upper,x,`opposite(y)')')dnl for(`x',`1',upper,`1',`door x is _get(`door',x) ')dnl</lang>
MAD
<lang MAD> NORMAL MODE IS INTEGER
DIMENSION OPEN(100) PRINT COMMENT $ $ R MAKE SURE ALL DOORS ARE CLOSED AT BEGINNING THROUGH CLOSE, FOR DOOR=1, 1, DOOR.G.100
CLOSE OPEN(DOOR) = 0
R MAKE 100 PASSES THROUGH TOGGLE, FOR PASS=1, 1, PASS.G.100 THROUGH TOGGLE, FOR DOOR=PASS, PASS, DOOR.G.100
TOGGLE OPEN(DOOR) = 1 - OPEN(DOOR)
R PRINT THE DOORS THAT ARE OPEN THROUGH SHOW, FOR DOOR=1, 1, DOOR.G.100
SHOW WHENEVER OPEN(DOOR).E.1, PRINT FORMAT ISOPEN, DOOR
VECTOR VALUES ISOPEN = $5HDOOR ,I3,S1,8HIS OPEN.*$ END OF PROGRAM</lang>
- Output:
DOOR 1 IS OPEN. DOOR 4 IS OPEN. DOOR 9 IS OPEN. DOOR 16 IS OPEN. DOOR 25 IS OPEN. DOOR 36 IS OPEN. DOOR 49 IS OPEN. DOOR 64 IS OPEN. DOOR 81 IS OPEN. DOOR 100 IS OPEN.
Maple
<lang Maple> NDoors := proc( N :: posint )
# Initialise, using 0 to represent "closed" local pass, door, doors := Array( 1 .. N, 'datatype' = 'integer'[ 1 ] ); # Now do N passes for pass from 1 to N do for door from pass by pass while door <= N do doors[ door ] := 1 - doors[ door ] end do end do; # Output for door from 1 to N do printf( "Door %d is %s.\n", door, `if`( doors[ door ] = 0, "closed", "open" ) ) end do; # Since this is a printing routine, return nothing. NULL
end proc: </lang> To solve the problem, call it with 100 as argument (output not shown here). <lang Maple> > NDoors( 100 ); </lang> Here is the optimised version, which outputs only the open doors. <lang Maple> > seq( i^2, i = 1 .. isqrt( 100 ) );
1, 4, 9, 16, 25, 36, 49, 64, 81, 100
</lang> Alternatively, <lang Maple> > [seq]( 1 .. 10 )^~2;
[1, 4, 9, 16, 25, 36, 49, 64, 81, 100]
</lang>
Mathematica/Wolfram Language
unoptimized 1 <lang mathematica>n=100; tmp=ConstantArray[-1,n]; Do[tmpi;;;;i*=-1;,{i,n}]; Do[Print["door ",i," is ",If[tmpi==-1,"closed","open"]],{i,1,Length[tmp]}]</lang>
unoptimized 2 <lang mathematica>f[n_] = "Closed"; Do[Do[If[f[n] == "Closed", f[n] = "Open", f[n] = "Closed"], {n, k, 100, k}], {k, 1, 100}]; Table[f[n], {n, 1, 100}]</lang>
unoptimized 3
Mathematica also supports immutable data paradigms, like so: <lang Mathematica> Fold[
ReplacePart[#1, (i_ /; Mod[i, #2] == 0) :> (-#1i)] &, ConstantArray[-1, {100}], Range[100]
] /. {1 -> "Open", -1 -> "Closed"} </lang>
optimized 1
<lang mathematica>Do[Print["door ",i," is ",If[IntegerQ[Sqrt[i]],"open","closed"]],{i,100}]</lang>
optimized 2 <lang mathematica>n=100; a=Range[1,Sqrt[n]]^2 Do[Print["door ",i," is ",If[MemberQ[a,i],"open","closed"]],{i,100}]</lang>
optimized 3 <lang mathematica>n=100 nn=1 a=0 For[i=1,i<=n,i++,
If[i==nn, Print["door ",i," is open"]; a++; nn+=2a+1; , Print["door ",i," is closed"]; ];
]</lang>
These will only give the indices for the open doors: unoptimized 2 <lang mathematica>Pick[Range[100], Xor@@@Array[Divisible[#1,#2]&, {100,100}]]</lang>
optimized 4 <lang mathematica>Range[Sqrt[100]]^2</lang>
MATLAB / Octave
Iterative Method
Unoptimized <lang MATLAB>a = false(1,100); for b=1:100
for i = b:b:100 a(i) = ~a(i); end
end a </lang> Optimized <lang MATLAB> for x=1:100;
if sqrt(x) == floor(sqrt(x)) a(i)=1; end
end a </lang> More Optimized <lang MATLAB> a = zeros(100,1); for counter = 1:sqrt(100);
a(counter^2) = 1;
end a </lang>
Vectorized Method
<lang MATLAB>function [doors,opened,closed] = hundredDoors()
%Initialize the doors, make them booleans for easy vectorization doors = logical( (1:1:100) ); %Go through the flipping process, ignore the 1 case because the doors %array is already initialized to all open for initialPosition = (2:100) doors(initialPosition:initialPosition:100) = not( doors(initialPosition:initialPosition:100) ); end opened = find(doors); %Stores the numbers of the open doors closed = find( not(doors) ); %Stores the numbers of the closed doors
end</lang>
Known-Result Method
<lang MATLAB> doors((1:10).^2) = 1;
doors </lang>
Maxima
<lang maxima>doors(n) := block([v], local(v),
v: makelist(true, n), for i: 2 thru n do for j: i step i thru n do v[j]: not v[j], sublist_indices(v, 'identity));</lang>
Usage: <lang maxima>doors(100); /* [1, 4, 9, 16, 25, 36, 49, 64, 81, 100] */</lang>
MAXScript
unoptimized <lang maxscript>doorsOpen = for i in 1 to 100 collect false
for pass in 1 to 100 do (
for door in pass to 100 by pass do ( doorsOpen[door] = not doorsOpen[door] )
)
for i in 1 to doorsOpen.count do (
format ("Door % is open?: %\n") i doorsOpen[i]
)</lang> optimized <lang maxscript>for i in 1 to 100 do (
root = pow i 0.5 format ("Door % is open?: %\n") i (root == (root as integer))
)</lang>
Mercury
<lang Mercury>:- module doors.
- - interface.
- - import_module io.
- - pred main(io::di, io::uo) is det.
- - implementation.
- - import_module bitmap, bool, list, string, int.
- - func doors = bitmap.
doors = bitmap.init(100, no).
- - pred walk(int, bitmap, bitmap).
- - mode walk(in, bitmap_di, bitmap_uo) is det.
walk(Pass, !Doors) :-
walk(Pass, Pass, !Doors).
- - pred walk(int, int, bitmap, bitmap).
- - mode walk(in, in, bitmap_di, bitmap_uo) is det.
walk(At, By, !Doors) :-
( if bitmap.in_range(!.Doors, At - 1) then bitmap.unsafe_flip(At - 1, !Doors), walk(At + By, By, !Doors) else true ).
- - pred report(bitmap, int, io, io).
- - mode report(bitmap_di, in, di, uo) is det.
report(Doors, N, !IO) :-
( if is_set(Doors, N - 1) then State = "open" else State = "closed" ), io.format("door #%d is %s\n", [i(N), s(State)], !IO).
main(!IO) :-
list.foldl(walk, 1 .. 100, doors, Doors), list.foldl(report(Doors), 1 .. 100, !IO).</lang>
Metafont
<lang metafont>boolean doors[]; for i = 1 upto 100: doors[i] := false; endfor for i = 1 upto 100:
for j = 1 step i until 100: doors[j] := not doors[j]; endfor
endfor for i = 1 upto 100:
message decimal(i) & " " & if doors[i]: "open" else: "close" fi;
endfor end</lang>
Microsoft Small Basic
<lang microsoftsmallbasic> For offset = 1 To 100
For i = 0 To 100 Step offset a[i] = a[i] + 1 EndFor
EndFor ' Print "opened" doors For i = 1 To 100
If math.Remainder(a[i], 2) = 1 Then TextWindow.WriteLine(i) EndIf
EndFor </lang>
Output:
1 4 9 16 25 36 49 64 81 100
MiniScript
Using a map to hold the set of open doors: <lang MiniScript>d = {} for p in range(1, 100)
for t in range(p, 100, p) if d.hasIndex(t) then d.remove t else d.push t end for
end for
print d.indexes.sort</lang>
- Output:
[1, 4, 9, 16, 25, 36, 49, 64, 81, 100]
Using an array of boolean values to keep track of door state, and a separate list of indexes of the open doors: <lang MiniScript>d = [false] * 101 open = [] for p in range(1, 100)
for t in range(p, 100, p) d[t] = not d[t] end for if d[p] then open.push p
end for
print open</lang>
(Output same as above.)
MIPS Assembly
<lang mips>.data
doors: .space 100 num_str: .asciiz "Number " comma_gap: .asciiz " is " newline: .asciiz "\n"
.text main:
- Clear all the cells to zero
li $t1, 100 la $t2, doors
clear_loop:
sb $0, ($t2) add $t2, $t2, 1 sub $t1, $t1, 1 bnez $t1, clear_loop
- Now start the loops
li $t0, 1 # This will the the step size li $t4, 1 # just an arbitrary 1
loop1:
move $t1, $t0 # Counter la $t2, doors # Current pointer add $t2, $t2, $t0 addi $t2, $t2, -1
loop2:
lb $t3, ($t2) sub $t3, $t4, $t3 sb $t3, ($t2) add $t1, $t1, $t0 add $t2, $t2, $t0 ble $t1, 100, loop2
addi $t0, $t0, 1 ble $t0, 100, loop1
# Now display everything la $t0, doors li $t1, 1
loop3:
li $v0, 4 la $a0, num_str syscall li $v0, 1 move $a0, $t1 syscall
li $v0, 4 la $a0, comma_gap syscall
li $v0, 1 lb $a0, ($t0) syscall
li $v0, 4, la $a0, newline syscall
addi $t0, $t0, 1 addi $t1, $t1, 1 bne $t1, 101 loop3
</lang>
Mirah
<lang Mirah>import java.util.ArrayList
class Door :state
def initialize @state=false end
def closed?; !@state; end def open?; @state; end
def close; @state=false; end def open; @state=true; end
def toggle if closed? open else close end end
def toString; Boolean.toString(@state); end end
doors=ArrayList.new 1.upto(100) do
doors.add(Door.new)
end
1.upto(100) do |multiplier|
index = 0 doors.each do |door| Door(door).toggle if (index+1)%multiplier == 0 index += 1 end
end
i = 0 doors.each do |door|
puts "Door #{i+1} is #{door}." i+=1
end </lang>
mIRC Scripting Language
<lang mirc>var %d = $str(0 $+ $chr(32),100), %m = 1 while (%m <= 100) {
var %n = 1 while ($calc(%n * %m) <= 100) { var %d = $puttok(%d,$iif($gettok(%d,$calc(%n * %m),32),0,1),$calc(%n * %m),32) inc %n } inc %m
} echo -ag All Doors (Boolean): %d var %n = 1 while (%n <= $findtok(%d,1,0,32)) {
var %t = %t $findtok(%d,1,%n,32) inc %n
} echo -ag Open Door Numbers: %t</lang>
ML/I
<lang ML/I>MCSKIP "WITH" NL "" 100 doors MCINS %. MCSKIP MT,<> "" Doors represented by P1-P100, 0 is closed MCPVAR 100 "" Set P variables to 0 MCDEF ZEROPS WITHS NL AS <MCSET T1=1 %L1.MCSET PT1=0 MCSET T1=T1+1 MCGO L1 UNLESS T1 EN 101 > ZEROPS "" Generate door state MCDEF STATE WITHS () AS <MCSET T1=%A1. MCGO L1 UNLESS T1 EN 0 closed<>MCGO L0 %L1.open> "" Main macro - no arguments "" T1 is pass number "" T2 is door number MCDEF DOORS WITHS NL AS <MCSET T1=1 "" pass loop %L1.MCGO L4 IF T1 GR 100 "" door loop MCSET T2=T1 %L2.MCGO L3 IF T2 GR 100 MCSET PT2=1-PT2 MCSET T2=T2+T1 MCGO L2 %L3.MCSET T1=T1+1 MCGO L1 %L4."" now output the result MCSET T1=1 %L5.door %T1. is STATE(%PT1.) MCSET T1=T1+1 MCGO L5 UNLESS T1 GR 100 > "" Do it DOORS</lang>
MMIX
See 100 doors/MMIX
Modula-2
unoptimized <lang modula2>MODULE Doors; IMPORT InOut;
TYPE State = (Closed, Open); TYPE List = ARRAY [1 .. 100] OF State;
VAR
Doors: List; I, J: CARDINAL;
BEGIN
FOR I := 1 TO 100 DO FOR J := 1 TO 100 DO IF J MOD I = 0 THEN IF Doors[J] = Closed THEN Doors[J] := Open ELSE Doors[J] := Closed END END END END;
FOR I := 1 TO 100 DO InOut.WriteCard(I, 3); InOut.WriteString(' is ');
IF Doors[I] = Closed THEN InOut.WriteString('Closed.') ELSE InOut.WriteString('Open.') END;
InOut.WriteLn END
END Doors.</lang>
optimized <lang modula2>MODULE DoorsOpt; IMPORT InOut;
TYPE State = (Closed, Open); TYPE List = ARRAY [1 .. 100] OF State;
VAR
Doors: List; I: CARDINAL;
BEGIN
FOR I := 1 TO 10 DO Doors[I*I] := Open END;
FOR I := 1 TO 100 DO InOut.WriteCard(I, 3); InOut.WriteString(' is '); IF Doors[I] = Closed THEN InOut.WriteString('Closed.') ELSE InOut.WriteString('Open.') END; InOut.WriteLn END
END DoorsOpt.</lang>
Modula-3
unoptimized <lang modula3>MODULE Doors EXPORTS Main;
IMPORT IO, Fmt;
TYPE State = {Closed, Open}; TYPE List = ARRAY [1..100] OF State;
VAR doors := List{State.Closed, ..};
BEGIN
FOR i := 1 TO 100 DO FOR j := FIRST(doors) TO LAST(doors) DO IF j MOD i = 0 THEN IF doors[j] = State.Closed THEN doors[j] := State.Open; ELSE doors[j] := State.Closed; END; END; END; END;
FOR i := FIRST(doors) TO LAST(doors) DO IO.Put(Fmt.Int(i) & " is "); IF doors[i] = State.Closed THEN IO.Put("Closed.\n"); ELSE IO.Put("Open.\n"); END; END;
END Doors.</lang>
optimized
<lang modula3>MODULE DoorsOpt EXPORTS Main;
IMPORT IO, Fmt;
TYPE State = {Closed, Open}; TYPE List = ARRAY [1..100] OF State;
VAR doors := List{State.Closed, ..};
BEGIN
FOR i := 1 TO 10 DO doors[i * i] := State.Open; END;
FOR i := FIRST(doors) TO LAST(doors) DO IO.Put(Fmt.Int(i) & " is "); IF doors[i] = State.Closed THEN IO.Put("Closed.\n"); ELSE IO.Put("Open.\n"); END; END;
END DoorsOpt.</lang>
MontiLang
<lang MontiLang>101 var l .
for l 0 endfor arr
0 var i . for l
i 1 + var i var j . j l < var pass . while pass get j not insert j . j i + var j l < var pass . endwhile
endfor print /# show all doors #/
/# show only open doors #/ || print . 0 var i . for l
get i if : i out | | out . . endif . i 1 + var i .
endfor
input . /# pause until ENTER key pressed #/</lang>
MOO
<lang moo>is_open = make(100); for pass in [1..100]
for door in [pass..100] if (door % pass) continue; endif is_open[door] = !is_open[door]; endfor
endfor
"output the result"; for door in [1..100]
player:tell("door #", door, " is ", (is_open[door] ? "open" : "closed"), ".");
endfor</lang>
MoonScript
<lang MoonScript>is_open = [false for door = 1,100]
for pass = 1,100
for door = pass,100,pass is_open[door] = not is_open[door]
for i,v in ipairs is_open
print "Door #{i}: " .. if v then 'open' else 'closed'</lang>
MUMPS
<lang MUMPS>doors new door,pass For door=1:1:100 Set door(door)=0 For pass=1:1:100 For door=pass:pass:100 Set door(door)='door(door) For door=1:1:100 If door(door) Write !,"Door",$j(door,4)," is open" Write !,"All other doors are closed." Quit Do doors Door 1 is open Door 4 is open Door 9 is open Door 16 is open Door 25 is open Door 36 is open Door 49 is open Door 64 is open Door 81 is open Door 100 is open All other doors are closed.</lang>
Myrddin
<lang myrddin> use std
const main = { var isopen : bool[100]
std.slfill(isopen[:], false) for var i = 0; i < isopen.len; i++ for var j = i; j < isopen.len; j += i + 1 isopen[j] = !isopen[j] ;; ;;
for var i = 0; i < isopen.len; i++ if isopen[i] std.put("door {} is open\n", i + 1) ;; ;; } </lang>
- Output:
door 1 is open door 4 is open door 9 is open door 16 is open door 25 is open door 36 is open door 49 is open door 64 is open door 81 is open door 100 is open
MySQL
<lang mysql> DROP PROCEDURE IF EXISTS one_hundred_doors;
DELIMITER |
CREATE PROCEDURE one_hundred_doors (n INT) BEGIN
DROP TEMPORARY TABLE IF EXISTS doors; CREATE TEMPORARY TABLE doors ( id INTEGER NOT NULL, open BOOLEAN DEFAULT FALSE, PRIMARY KEY (id) );
SET @i = 1; create_doors: LOOP INSERT INTO doors (id, open) values (@i, FALSE); SET @i = @i + 1; IF @i > n THEN LEAVE create_doors; END IF; END LOOP create_doors;
SET @i = 1; toggle_doors: LOOP UPDATE doors SET open = NOT open WHERE MOD(id, @i) = 0; SET @i = @i + 1; IF @i > n THEN LEAVE toggle_doors; END IF; END LOOP toggle_doors;
SELECT id FROM doors WHERE open;
END|
DELIMITER ;
CALL one_hundred_doors(100); </lang>
- Output:
+-----+ | id | +-----+ | 1 | | 4 | | 9 | | 16 | | 25 | | 36 | | 49 | | 64 | | 81 | | 100 | +-----+ 10 rows in set (0.02 sec)
Nanoquery
<lang Nanoquery>// allocate a boolean array with all closed doors (false) // we need 101 since there will technically be a door 0 doors = {false} * 101
// loop through all the step lengths (1-100) for step in range(1, 100) // loop through all the doors, stepping by step for door in range(0, len(doors) - 1, step) // change the state of the current door doors[door] = !doors[door] end for end for
// loop through and print the doors that are open, skipping door 0 for i in range(1, len(doors) - 1) // if the door is open, display it if doors[i] println "Door " + i + " is open." end if end for</lang>
NetRexx
unoptimized <lang netrexx>/* NetRexx */ options replace format comments java crossref symbols binary
True = Rexx(1 == 1) False = Rexx(\True)
doors = False
loop i_ = 1 to 100
loop j_ = 1 to 100 if 0 = (j_ // i_) then doors[j_] = \doors[j_] end j_ end i_
loop d_ = 1 to 100
if doors[d_] then state = 'open' else state = 'closed'
say 'Door Nr.' Rexx(d_).right(4) 'is' state end d_</lang>
optimized (Based on the Java 'optimized' version)
<lang netrexx>/* NetRexx */ options replace format comments java crossref symbols binary
True = (1 == 1) False = \True
doors = boolean[100]
loop i_ = 0 to 9
doors[(i_ + 1) * (i_ + 1) - 1] = True; end i_
loop i_ = 0 to 99
if doors[i_] then state = 'open' else state = 'closed'
say 'Door Nr.' Rexx(i_ + 1).right(4) 'is' state end i_</lang>
optimized 2 (Based on the Java 'optimized 2' version)
<lang netrexx>/* NetRexx */ options replace format comments java crossref savelog symbols binary
resultstring =
loop i_ = 1 to 10
resultstring = resultstring || 'Door Nr.' Rexx(i_ * i_).right(4) 'is open\n' end i_
say resultstring</lang>
optimized 3 <lang netrexx>/* NetRexx */
loop i = 1 to 10
say 'Door Nr.' i * i 'is open.' end i</lang>
newLISP
<lang newLisp>(define (status door-num)
(let ((x (int (sqrt door-num)))) (if (= (* x x) door-num) (string "Door " door-num " Open") (string "Door " door-num " Closed"))))
(dolist (n (map status (sequence 1 100)))
(println n))
</lang>
Not optimized: <lang newLISP> (set 'Doors (array 100)) ;; Default value: nil (Closed)
(for (x 0 99)
(for (y x 99 (+ 1 x)) (setf (Doors y) (not (Doors y)))))
(for (x 0 99) ;; Display open doors
(if (Doors x) (println (+ x 1) " : Open")))
</lang> Output:
1 : Open 4 : Open 9 : Open 16 : Open 25 : Open 36 : Open 49 : Open 64 : Open 81 : Open 100 : Open
Nial
unoptimized solution (works with Q'Nial7):
Output of the boolean array showing the status of the doors. Truth values in Nial arrays are shown as l
(true) and o
(false):
<lang nial> n:=100;reduce xor (count n eachright mod count n eachall<1) looloooolooooooloooooooolooooooooooloooooooooooolooooooooooooooloooooooooooooooo
looooooooooooooooool</lang>
Indices of the open doors:
<lang nial> true findall (n:=100;reduce xor (count n eachright mod count n eachall<1))+1 1 4 9 16 25 36 49 64 81 100</lang>
optimized solution:
<lang nial> count 10 power 2 1 4 9 16 25 36 49 64 81 100</lang>
Nim
unoptimized: <lang Nim>from strutils import `%`
const numDoors = 100 var doors: array[1..numDoors, bool]
for pass in 1..numDoors:
for door in countup(pass, numDoors, pass): doors[door] = not doors[door]
for door in 1..numDoors:
echo "Door $1 is $2." % [$door, if doors[door]: "open" else: "closed"]</lang>
Challenging C++'s compile time computation: https://rosettacode.org/wiki/100_doors#C.2B.2B
outputString is evaluated at compile time. Check the resulting binary in case of doubt.
<lang Nim>from strutils import `%`
const numDoors = 100 var doors {.compileTime.}: array[1..numDoors, bool]
proc calcDoors(): string =
for pass in 1..numDoors: for door in countup(pass, numDoors, pass): doors[door] = not doors[door] for door in 1..numDoors: result.add("Door $1 is $2.\n" % [$door, if doors[door]: "open" else: "closed"])
const outputString: string = calcDoors()
echo outputString</lang>
Oberon
Oberon-07, by Niklaus Wirth. <lang oberon>MODULE Doors;
IMPORT Out; PROCEDURE Do*; (* In Oberon an asterisk after an identifier is an export mark *) CONST N = 100; len = N + 1; VAR i, j: INTEGER; closed: ARRAY len OF BOOLEAN; (* Arrays in Oberon always start with index 0; closed[0] is not used *) BEGIN FOR i := 1 TO N DO closed[i] := TRUE END; FOR i := 1 TO N DO j := 1; WHILE j < len DO IF j MOD i = 0 THEN closed[j] := ~closed[j] END; INC(j) (* ~ = NOT *) END END; (* Print a state diagram of all doors *) FOR i := 1 TO N DO IF (i - 1) MOD 10 = 0 THEN Out.Ln END; IF closed[i] THEN Out.String("- ") ELSE Out.String("+ ") END END; Out.Ln; (* Print the numbers of the open doors *) FOR i := 1 TO N DO IF ~closed[i] THEN Out.Int(i, 0); Out.Char(" ") END END; Out.Ln END Do;
END Doors. </lang>
Execute: Doors.Do
- Output:
+ – – + – – – – + – – – – – – + – – – – – – – – + – – – – – – – – – – + – – – – – – – – – – – – + – – – – – – – – – – – – – – + – – – – – – – – – – – – – – – – + – – – – – – – – – – – – – – – – – – + 1 4 9 16 25 36 49 64 81 100
Objeck
optimized <lang objeck> bundle Default {
class Doors { function : Main(args : String[]) ~ Nil { doors := Bool->New[100]; for(pass := 0; pass < 10; pass += 1;) { doors[(pass + 1) * (pass + 1) - 1] := true; }; for(i := 0; i < 100; i += 1;) { IO.Console->GetInstance()->Print("Door #")->Print(i + 1)->Print(" is "); if(doors[i]) { "open."->PrintLine(); } else { "closed."->PrintLine(); }; }; } }
} </lang>
Objective-C
A basic implementation in Objective-C:
This is a very basic Objective-C sample that shows the usage of standard types and classes such as NSInteger and NSMutableArray.
It uses modern Objective-C syntax such as literals, blocks, and a compiler module import statement. <lang Objective-C> @import Foundation;
int main(int argc, const char * argv[]) {
@autoreleasepool { // Create a mutable array NSMutableArray *doorArray = [@[] mutableCopy]; // Fill the doorArray with 100 closed doors for (NSInteger i = 0; i < 100; ++i) { doorArray[i] = @NO; } // Do the 100 passes for (NSInteger pass = 0; pass < 100; ++pass) { for (NSInteger door = pass; door < 100; door += pass+1) { doorArray[door] = [doorArray[door] isEqual: @YES] ? @NO : @YES; } } // Print the results [doorArray enumerateObjectsUsingBlock:^(id obj, NSUInteger idx, BOOL *stop) { if ([obj isEqual: @YES]) { NSLog(@"Door number %lu is open", idx + 1); } }]; }
} </lang> A more typical implementation in Objective-C:
This example is more along the lines of what typical Objective-C program would look like.
Language features used include:
- MVC design pattern with separate classes for the data model, user interface, and controller (Here, main steps in to represent the controller class.)
- Class category to extend the standard NSMutableArray class to add doors without a subclass
- Class inheritance in the DoorViewClass when subclassing NSObject
- Pragma mark statements for IDE navigation in Xcode
In a real world program classes are normally separated into different files.
<lang Objective-C> @import Foundation;
- pragma mark - Classes
//////////////////////////////////////////////////// // Model class header - A we are using a category to add a method to MSMutableArray @interface NSMutableArray (DoorModelExtension)
- (void)setNumberOfDoors:(NSUInteger)doors;
@end
// Model class implementation @implementation NSMutableArray (DoorModelExtension)
- (void)setNumberOfDoors:(NSUInteger)doors {
// Fill the doorArray with 100 closed doors for (NSInteger i = 0; i < doors; ++i) { self[i] = @NO; }
} @end ////////////////////////////////////////////////////
// View class header - A simple class to handle printing our values @interface DoorViewClass : NSObject
- (void)printResultsOfDoorTask:(NSMutableArray *)doors;
@end
// View class implementation @implementation DoorViewClass
- (void)printResultsOfDoorTask:(NSMutableArray *)doors {
// Print the results, using an enumeration block for easy index tracking [doors enumerateObjectsUsingBlock:^(id obj, NSUInteger idx, BOOL *stop) { if ([obj isEqual: @YES]) { NSLog(@"Door number %lu is open", idx + 1); } }];
}
@end ////////////////////////////////////////////////////
- pragma mark - main
// With our classes set we can use them from our controller, in this case main int main(int argc, const char * argv[]) {
// Init our classes NSMutableArray *doorArray = [NSMutableArray array]; DoorViewClass *doorView = [DoorViewClass new]; // Use our class category to add the doors [doorArray setNumberOfDoors:100]; // Do the 100 passes for (NSUInteger pass = 0; pass < 100; ++pass) { for (NSUInteger door = pass; door < 100; door += pass+1) { doorArray[door] = [doorArray[door] isEqual: @YES] ? @NO : @YES; } } // Print the results [doorView printResultsOfDoorTask:doorArray];
} </lang>
OCaml
unoptimized <lang ocaml>let max_doors = 100
let show_doors =
Array.iteri (fun i x -> Printf.printf "Door %d is %s\n" (i+1) (if x then "open" else "closed"))
let flip_doors doors =
for i = 1 to max_doors do let rec flip idx = if idx < max_doors then begin doors.(idx) <- not doors.(idx); flip (idx + i) end in flip (i - 1) done; doors
let () =
show_doors (flip_doors (Array.make max_doors false))</lang>
optimized <lang ocaml>let optimised_flip_doors doors =
for i = 1 to int_of_float (sqrt (float_of_int max_doors)) do doors.(i*i - 1) <- true done; doors
let () =
show_doors (optimised_flip_doors (Array.make max_doors false))</lang>
This variant is more functional style (loops are recursions), unoptimized, and we do rather 100 passes on first element, then 100 * second, to avoid mutable data structures and many intermediate lists. <lang ocaml>type door = Open | Closed (* human readable code *)
let flipdoor = function Open -> Closed | Closed -> Open
let string_of_door =
function Open -> "is open." | Closed -> "is closed."
let printdoors ls =
let f i d = Printf.printf "Door %i %s\n" (i + 1) (string_of_door d) in List.iteri f ls
let outerlim = 100 let innerlim = 100
let rec outer cnt accu =
let rec inner i door = match i > innerlim with (* define inner loop *) | true -> door | false -> inner (i + 1) (if (cnt mod i) = 0 then flipdoor door else door) in (* define and do outer loop *) match cnt > outerlim with | true -> List.rev accu | false -> outer (cnt + 1) (inner 1 Closed :: accu) (* generate new entries with inner *)
let () = printdoors (outer 1 [])</lang>
Octave
<lang octave>doors = false(100,1); for i = 1:100
for j = i:i:100 doors(j) = !doors(j); endfor
endfor for i = 1:100
if ( doors(i) ) s = "open"; else s = "closed"; endif printf("%d %s\n", i, s);
endfor</lang>
See also the solutions in Matlab. They will work in Octave, too.
Oforth
<lang Oforth>: doors | i j l |
100 false Array newWith dup ->l 100 loop: i [ i 100 i step: j [ l put ( j , j l at not ) ] ]
</lang>
Ol
<lang scheme> (define (flip doors every)
(map (lambda (door num) (mod (+ door (if (eq? (mod num every) 0) 1 0)) 2)) doors (iota (length doors) 1)))
(define doors
(let loop ((doors (repeat 0 100)) (n 1)) (if (eq? n 100) doors (loop (flip doors n) (+ n 1)))))
(print "100th doors: " doors) </lang>
Output:
100th doors: (1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0)
Onyx
<lang Onyx>$Door dict def 1 1 100 {Door exch false put} for $Toggle {dup Door exch get not Door up put} def $EveryNthDoor {dup 100 {Toggle} for} def $Run {1 1 100 {EveryNthDoor} for} def $ShowDoor {dup `Door no. ' exch cvs cat ` is ' cat
exch Door exch get {`open.\n'}{`shut.\n'} ifelse cat print flush} def
Run 1 1 100 {ShowDoor} for</lang>
- Output:
Door no. 1 is open. Door no. 2 is shut. Door no. 3 is shut. Door no. 4 is open. Door no. 5 is shut. Door no. 6 is shut. Door no. 7 is shut. Door no. 8 is shut. Door no. 9 is open. Door no. 10 is shut. Door no. 11 is shut. Door no. 12 is shut. Door no. 13 is shut. Door no. 14 is shut. Door no. 15 is shut. Door no. 16 is open. Door no. 17 is shut. Door no. 18 is shut. Door no. 19 is shut. Door no. 20 is shut. Door no. 21 is shut. Door no. 22 is shut. Door no. 23 is shut. Door no. 24 is shut. Door no. 25 is open. Door no. 26 is shut. Door no. 27 is shut. Door no. 28 is shut. Door no. 29 is shut. Door no. 30 is shut. Door no. 31 is shut. Door no. 32 is shut. Door no. 33 is shut. Door no. 34 is shut. Door no. 35 is shut. Door no. 36 is open. Door no. 37 is shut. Door no. 38 is shut. Door no. 39 is shut. Door no. 40 is shut. Door no. 41 is shut. Door no. 42 is shut. Door no. 43 is shut. Door no. 44 is shut. Door no. 45 is shut. Door no. 46 is shut. Door no. 47 is shut. Door no. 48 is shut. Door no. 49 is open. Door no. 50 is shut. Door no. 51 is shut. Door no. 52 is shut. Door no. 53 is shut. Door no. 54 is shut. Door no. 55 is shut. Door no. 56 is shut. Door no. 57 is shut. Door no. 58 is shut. Door no. 59 is shut. Door no. 60 is shut. Door no. 61 is shut. Door no. 62 is shut. Door no. 63 is shut. Door no. 64 is open. Door no. 65 is shut. Door no. 66 is shut. Door no. 67 is shut. Door no. 68 is shut. Door no. 69 is shut. Door no. 70 is shut. Door no. 71 is shut. Door no. 72 is shut. Door no. 73 is shut. Door no. 74 is shut. Door no. 75 is shut. Door no. 76 is shut. Door no. 77 is shut. Door no. 78 is shut. Door no. 79 is shut. Door no. 80 is shut. Door no. 81 is open. Door no. 82 is shut. Door no. 83 is shut. Door no. 84 is shut. Door no. 85 is shut. Door no. 86 is shut. Door no. 87 is shut. Door no. 88 is shut. Door no. 89 is shut. Door no. 90 is shut. Door no. 91 is shut. Door no. 92 is shut. Door no. 93 is shut. Door no. 94 is shut. Door no. 95 is shut. Door no. 96 is shut. Door no. 97 is shut. Door no. 98 is shut. Door no. 99 is shut. Door no. 100 is open.
ooRexx
<lang ooRexx>doors = .array~new(100) -- array containing all of the doors do i = 1 to doors~size -- initialize with a collection of closed doors
doors[i] = .door~new(i)
end
do inc = 1 to doors~size
do d = inc to doors~size by inc doors[d]~toggle end
end say "The open doors after 100 passes:" do door over doors
if door~isopen then say door
end
- class door -- simple class to represent a door
- method init -- initialize an instance of a door
expose id state -- instance variables of a door use strict arg id -- set the id state = .false -- initial state is closed
- method toggle -- toggle the state of the door
expose state state = \state
- method isopen -- test if the door is open
expose state return state
- method string -- return a string value for a door
expose state id if state then return "Door" id "is open" else return "Door" id "is closed"
- method state -- return door state as a descriptive string
expose state if state then return "open" else return "closed"</lang>
The two programs in the Rexx section run under ooRexx when '#' is replaced by, e.g., 'dd'.
'#' is not supported by ooRexx as part of or as a symbol.
Neither are @ and $.
OpenEdge/Progress
<lang OpenEdge/Progress>DEFINE VARIABLE lopen AS LOGICAL NO-UNDO EXTENT 100. DEFINE VARIABLE idoor AS INTEGER NO-UNDO. DEFINE VARIABLE ipass AS INTEGER NO-UNDO. DEFINE VARIABLE cresult AS CHARACTER NO-UNDO.
DO ipass = 1 TO 100:
idoor = 0. DO WHILE idoor <= 100: idoor = idoor + ipass. IF idoor <= 100 THEN lopen[ idoor ] = NOT lopen[ idoor ]. END.
END.
DO idoor = 1 TO 100:
cresult = cresult + STRING( lopen[ idoor ], "1 /0 " ). IF idoor MODULO 10 = 0 THEN cresult = cresult + "~r":U.
END.
MESSAGE cresult VIEW-AS ALERT-BOX. </lang>
OxygenBasic
def doors 100 int door[doors],i ,j, c string cr,tab,pr ' for i=1 to doors for j=i to doors step i door[j]=1-door[j] if door[j] then c++ else c-- next next ' cr=chr(13) chr(10) pr="Doors Open: " c cr cr ' for i=1 to doors if door[i] then pr+=i cr next print pr
Oz
<lang oz>declare
NumDoors = 100 NumPasses = 100
fun {NewDoor} closed end
fun {Toggle Door} case Door of closed then open [] open then closed end end
fun {Pass Doors I} {List.mapInd Doors fun {$ Index Door} if Index mod I == 0 then {Toggle Door} else Door end end} end Doors0 = {MakeList NumDoors} {ForAll Doors0 NewDoor}
DoorsN = {FoldL {List.number 1 NumPasses 1} Pass Doors0}
in
%% print open doors {List.forAllInd DoorsN proc {$ Index Door} if Door == open then
{System.showInfo "Door "#Index#" is open."}
end end }</lang>
Output:
Door 1 is open. Door 4 is open. Door 9 is open. Door 16 is open. Door 25 is open. Door 36 is open. Door 49 is open. Door 64 is open. Door 81 is open. Door 100 is open.
PARI/GP
Unoptimized version. <lang parigp> v=vector(d=100);/*set 100 closed doors*/ for(i=1,d,forstep(j=i,d,i,v[j]=1-v[j])); for(i=1,d,if(v[i],print("Door ",i," is open."))) </lang> Optimized version. <lang parigp>for(n=1,sqrt(100),print("Door ",n^2," is open."))</lang>
Unoptimized version. <lang pari/gp> doors =vector(100); print("open doors are : "); for(i=1,100,for(j=i,100,doors[j]=!doors[j];j +=i-1)) for(k=1,100,if(doors[k]==1,print1(" ",k))) </lang> Output:
Open doors are: 1 4 9 16 25 36 49 64 81 100
Pascal
<lang pascal>Program OneHundredDoors;
var
doors : Array[1..100] of Boolean; i, j : Integer;
begin
for i := 1 to 100 do doors[i] := False; for i := 1 to 100 do begin j := i; while j <= 100 do begin
doors[j] := not doors[j]; j := j + i
end end; for i := 1 to 100 do begin Write(i, ' '); if doors[i] then
WriteLn('open')
else
WriteLn('closed');
end
end.</lang>
Optimized version.
<lang pascal>program OneHundredDoors;
{$APPTYPE CONSOLE}
uses
math, sysutils;
var
AOpendoors : String; ACloseDoors : String; i : Integer;
begin
for i := 1 to 100 do begin if (sqrt(i) = floor(sqrt(i))) then AOpenDoors := AOpenDoors + IntToStr(i) + ';' else ACloseDoors := ACloseDoors + IntToStr(i) +';'; end;
WriteLn('Open doors: ' + AOpenDoors); WriteLn('Close doors: ' + ACloseDoors);
end. </lang>
Perl
unoptimized
<lang perl>my @doors; for my $pass (1 .. 100) {
for (1 .. 100) { if (0 == $_ % $pass) { $doors[$_] = not $doors[$_]; }; };
};
print "Door $_ is ", $doors[$_] ? "open" : "closed", "\n" for 1 .. 100;</lang>
semi-optimized
This version flips doors, but doesn't visit (iterate over) doors that aren't toggled. Note: I represent open doors as 0 and closed as 1 just for preference. (When I print it as a bit vector, 0 looks more like an open door to me.) <lang perl>
- !/usr/bin/perl
use strict; use warnings;
my @doors = (1) x 100; for my $N (1 .. 100) {
$doors[$_]=1-$doors[$_] for map { $_*$N - 1 } 1 .. int(100/$N);
} print join("\n", map { "Door $_ is Open" } grep { ! $doors[$_-1] } 1 .. 100), "\n"; print "The rest are closed\n"; </lang>
optimized
<lang perl>print "Door $_ is open\n" for map $_**2, 1 .. 10;</lang> <lang perl>print "Door $_ is ", qw"closed open"[int sqrt == sqrt], "\n" for 1..100;</lang> <lang perl>while( ++$i <= 100 ) {
$root = sqrt($i); if ( int( $root ) == $root ) { print "Door $i is open\n"; } else { print "Door $i is closed\n"; }
}</lang>
Perl5i
<lang Perl5i> use perl5i::2;
package doors {
use perl5i::2; use Const::Fast;
const my $OPEN => 1; const my $CLOSED => 0;
# ---------------------------------------- # Constructor: door->new( @args ); # input: N - how many doors? # returns: door object # method new($class: @args ) { my $self = bless {}, $class; $self->_init( @args ); return $self; }
# ---------------------------------------- # class initializer. # input: how many doors? # sets N, creates N+1 doors ( door zero is not used ). # method _init( $N ) { $self->{N} = $N; $self->{doors} = [ ($CLOSED) x ($N+1) ]; }
# ---------------------------------------- # $self->toggle( $door_number ); # input: number of door to toggle. # OPEN a CLOSED door; CLOSE an OPEN door. # method toggle( $which ) { $self->{doors}[$which] = ( $self->{doors}[$which] == $OPEN ? $CLOSED : $OPEN ); }
# ---------------------------------------- # $self->toggle_n( $cycle ); # input: number. # Toggle doors 0, $cycle, 2 * $cycle, 3 * $cycle, .. $self->{N} # method toggle_n( $n ) { $self->toggle($_) for map { $n * $_ } ( 1 .. int( $self->{N} / $n) );
}
# ---------------------------------------- # $self->toggle_all(); # Toggle every door, then every other door, every third door, ... # method toggle_all() { $self->toggle_n( $_ ) for ( 1 .. $self->{N} ); }
# ---------------------------------------- # $self->print_open(); # Print list of which doors are open. # method print_open() { say join ', ', grep { $self->{doors}[$_] == $OPEN } ( 1 ... $self->{N} ); }
}
- ----------------------------------------------------------------------
- Main Thread
my $doors = doors->new(100); $doors->toggle_all(); $doors->print_open(); </lang>
Phix
unoptimised
sequence doors = repeat(false,100) for i=1 to 100 do for j=i to 100 by i do doors[j] = not doors[j] end for end for for i=1 to 100 do if doors[i] == true then printf(1,"Door #%d is open.\n", i) end if end for
- Output:
Door #1 is open. Door #4 is open. Door #9 is open. Door #16 is open. Door #25 is open. Door #36 is open. Door #49 is open. Door #64 is open. Door #81 is open. Door #100 is open.
optimised
function doors(integer n) -- returns the perfect squares<=n integer door = 1, step = 1 sequence res = {} while door<=n do res &= door step += 2 door += step end while return res end function ?doors(100)
- Output:
{1,4,9,16,25,36,49,64,81,100}
Phixmonti
<lang Phixmonti>101 var l 0 l repeat
l for
var s s l s 3 tolist for var i i get not i set endfor
endfor
l for
var i i get if i print " " print endif
endfor</lang> Another way <lang Phixmonti>100 var n /# Number of doors #/ 0 n repeat /# Make the doors #/
n for
dup sqrt int dup * over == if 1 swap set else drop endif
endfor
n for
"The door " print dup print " is " print get if "OPEN." else "closed." endif print nl
endfor</lang> Optimized <lang Phixmonti>100 sqrt for dup * print " " print endfor</lang>
PHL
unoptimized
<lang phl>module doors;
extern printf;
@Integer main [ @Array<@Boolean> doors = new @Array<@Boolean>.init(100); var i = 1; while (i <= 100) { var j = i-1; while (j < 100) { doors.set(j, doors.get(j)::not); j = j + i; } i = i::inc; } i = 0; while (i < 100) { printf("%i %s\n", i+1, iif(doors.get(i), "open", "closed")); i = i::inc; } return 0; ]</lang>
optimized
<lang phl>module var;
extern printf;
@Integer main [ var door = 1; var incrementer = 0; var current = 1;
while (current <= 100) {
printf("Door %i ", current); if (current == door) { printf("open\n"); incrementer = incrementer::inc; door = door + 2 * incrementer + 1; } else printf("closed\n");
current = current + 1;
}
return 0; ]</lang>
PHP
See: Demo optimized <lang php><?php for ($i = 1; $i <= 100; $i++) { $root = sqrt($i); $state = ($root == ceil($root)) ? 'open' : 'closed'; echo "Door {$i}: {$state}\n"; } ?></lang>
unoptimized <lang php><?php $doors = array_fill(1, 100, false); for ($pass = 1; $pass <= 100; ++$pass) { for ($nr = 1; $nr <= 100; ++$nr) { if ($nr % $pass == 0) { $doors[$nr] = !$doors[$nr]; } } } for ($nr = 1; $nr <= 100; ++$nr) printf("Door %d: %s\n", $nr, ($doors[$nr])?'open':'closed'); ?></lang>
Picat
Non-optimized: <lang Picat>doors(N) =>
Doors = new_array(N), foreach(I in 1..N) Doors[I] := 0 end, foreach(I in 1..N) foreach(J in I..I..N) Doors[J] := 1^Doors[J] end, if N <= 10 then print_open(Doors) end end, println(Doors), print_open(Doors), nl.
print_open(Doors) => println([I : I in 1..Doors.length, Doors[I] == 1]). </lang>
optimized version 1: <lang Picat>doors_opt(N) =>
foreach(I in 1..N) Root = sqrt(I), println([I, cond(Root == 1.0*round(Root), open, closed)]) end, nl.
</lang>
optimized version 2: <lang Picat>doors_opt2(N) =>
println([I**2 : I in 1..N, I**2 <= N]).
</lang>
PicoLisp
unoptimized <lang PicoLisp>(let Doors (need 100)
(for I 100 (for (D (nth Doors I) D (cdr (nth D I))) (set D (not (car D))) ) ) (println Doors) )</lang>
optimized <lang PicoLisp>(let Doors (need 100)
(for I (sqrt 100) (set (nth Doors (* I I)) T) ) (println Doors) )</lang>
Output in both cases:
(T NIL NIL T NIL NIL NIL NIL T NIL NIL NIL NIL NIL NIL T NIL NIL NIL NIL NIL NIL NIL NIL T NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL T NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL T NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL T NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL T NIL NIL NIL N IL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL T)
With formatting: <lang PicoLisp>(let Doors (need 100)
(for I (sqrt 100) (set (nth Doors (* I I)) T) ) (make (for (N . D) Doors (when D (link N)) ) ) )</lang>
Output:
(1 4 9 16 25 36 49 64 81 100)
Piet
Pike
<lang pike>array onehundreddoors() {
array doors = allocate(100); foreach(doors; int i;) for(int j=i; j<100; j+=i+1) doors[j] = !doors[j]; return doors;
}</lang> optimized version: <lang pike>array doors = map(enumerate(100,1,1), lambda(int x)
{ return sqrt((float)x)%1 == 0.0; });</lang>
<lang pike>write("%{%d %d %d %d %d %d %d %d %d %d\n%}\n", doors/10)</lang> output:
1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
PL/I
<lang pli> declare door(100) bit (1) aligned; declare closed bit (1) static initial ('0'b),
open bit (1) static initial ('1'b);
declare (i, inc) fixed binary;
door = closed; inc = 1; do until (inc >= 100);
do i = inc to 100 by inc; door(i) = ^door(i); /* close door if open; open it if closed. */ end; inc = inc+1;
end;
do i = 1 to 100;
put skip edit ('Door ', trim(i), ' is ') (a); if door(i) then put edit (' open.') (a); else put edit (' closed.') (a);
end; </lang>
See also #Polyglot:PL/I and PL/M
PL/I-80
<lang pli> /* Solution to the 100 doors problem in PLI-80 */
hundred_doors:
procedure options (main);
%replace open_door by '1'b, closed_door by '0'b, numdoors by 100;
dcl doors(1:numdoors) bit(1), (i, j) fixed bin(15);
/* all doors are initially closed */ do i = 1 to numdoors; doors(i) = closed_door; end;
/* cycle through at increasing intervals and flip doors */ do i = 1 to numdoors; j = i; do while (j <= numdoors); doors(j) = ^doors(j); j = j + i; end; end;
/* show results - open doors should all be perfect squares */ put skip list ('The open doors are:'); do i = 1 to numdoors; if doors(i) = open_door then put edit (i) (F(4)); end;
end hundred_doors; </lang>
- Output:
The open doors are: 1 4 9 16 25 36 49 64 81 100
See also #Polyglot:PL/I and PL/M
PL/M
<lang pli>100H: /* FIND THE FIRST FEW SQUARES VIA THE UNOPTIMISED DOOR FLIPPING METHOD */
/* BDOS SYSTEM CALL */ BDOS: PROCEDURE( FN, ARG ); DECLARE FN BYTE, ARG ADDRESS; GO TO 5; END BDOS;
/* PRINTS A BYTE AS A CHARACTER */ PRINT$CHAR: PROCEDURE( CH ); DECLARE CH BYTE; CALL BDOS( 2, CH ); END PRINT$CHAR;
/* PRINTS A BYTE AS A NUMBER */ PRINT$BYTE: PROCEDURE( N ); DECLARE N BYTE; DECLARE ( V, D3, D2 ) BYTE; V = N; D3 = V MOD 10; IF ( V := V / 10 ) <> 0 THEN DO; D2 = V MOD 10; IF ( V := V / 10 ) <> 0 THEN CALL PRINT$CHAR( '0' + V ); CALL PRINT$CHAR( '0' + D2 ); END; CALL PRINT$CHAR( '0' + D3 ); END PRINT$BYTE;
DECLARE DOOR$DCL LITERALLY '101'; DECLARE FALSE LITERALLY '0'; DECLARE CR LITERALLY '0DH'; DECLARE LF LITERALLY '0AH';
/* ARRAY OF DOORS - DOOR( I ) IS TRUE IF OPEN, FALSE IF CLOSED */ DECLARE DOOR( DOOR$DCL ) BYTE; DECLARE ( I, J ) BYTE;
/* SET ALL DOORS TO CLOSED */ DO I = 0 TO LAST( DOOR ); DOOR( I ) = FALSE; END; /* REPEATEDLY FLIP THE DOORS */ DO I = 1 TO LAST( DOOR ); DO J = I TO LAST( DOOR ) BY I; DOOR( J ) = NOT DOOR( J ); END; END; /* DISPLAY THE RESULTS */ DO I = 1 TO LAST( DOOR ); IF DOOR( I ) THEN DO; CALL PRINT$CHAR( ' ' ); CALL PRINT$BYTE( I ); END; END; CALL PRINT$CHAR( CR ); CALL PRINT$CHAR( LF );
EOF </lang>
- Output:
1 4 9 16 25 36 49 64 81 100
See Also #Polyglot:PL/I and PL/M
PL/SQL
Unoptimized
<lang plsql> DECLARE
TYPE doorsarray IS VARRAY(100) OF BOOLEAN; doors doorsarray := doorsarray();
BEGIN
doors.EXTEND(100); --ACCOMMODATE 100 DOORS
FOR i IN 1 .. doors.COUNT --MAKE ALL 100 DOORS FALSE TO INITIALISE
LOOP doors(i) := FALSE; END LOOP;
FOR j IN 1 .. 100 --ITERATE THRU USING MOD LOGIC AND FLIP THE DOOR RIGHT OPEN OR CLOSE
LOOP FOR k IN 1 .. 100 LOOP IF MOD(k,j)=0 THEN doors(k) := NOT doors(k); END IF; END LOOP; END LOOP;
FOR l IN 1 .. doors.COUNT --PRINT THE STATUS IF ALL 100 DOORS AFTER ALL ITERATION
LOOP DBMS_OUTPUT.PUT_LINE('DOOR '||l||' IS -->> '||CASE WHEN SYS.DBMS_SQLTCB_INTERNAL.I_CONVERT_FROM_BOOLEAN(doors(l)) = 'TRUE' THEN 'OPEN' ELSE 'CLOSED' END); END LOOP;
END; </lang>
Pointless
<lang pointless>output =
range(1, 100) |> map(visit(100)) |> println
toggle(state) =
if state == Closed then Open else Closed
-- Door state on iteration i is recursively -- defined in terms of previous door state
visit(i, index) = cond {
case (i == 0) Closed case (index % i == 0) toggle(lastState) else lastState
} where lastState = visit(i - 1, index)</lang>
- Output:
[Open, Closed, Closed, Open, Closed, Closed, Closed, Closed, Open, Closed, Closed, Closed, Closed, Closed, Closed, Open, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Open, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Open, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Open, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Open, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Open, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Closed, Open]
Polyglot:PL/I and PL/M
... under CP/M (or an emulator)
Should work with many PL/I implementations.
The PL/I include file "pg.inc" can be found on the Polyglot:PL/I and PL/M page.
Note the use of text in column 81 onwards to hide the PL/I specifics from the PL/M compiler.
<lang pli>/* FIND THE FIRST FEW SQUARES VIA THE UNOPTIMISED DOOR FLIPPING METHOD */
doors_100H: procedure options (main);
/* PROGRAM-SPECIFIC %REPLACE STATEMENTS MUST APPEAR BEFORE THE %INCLUDE AS */ /* E.G. THE CP/M PL/I COMPILER DOESN'T LIKE THEM TO FOLLOW PROCEDURES */
/* PL/I */ %replace dcldoors by 100; /* PL/M */ /* DECLARE DCLDOORS LITERALLY '101'; /* */
/* PL/I DEFINITIONS */ %include 'pg.inc'; /* PL/M DEFINITIONS: CP/M BDOS SYSTEM CALL AND CONSOLE I/O ROUTINES, ETC. */ /*
DECLARE BINARY LITERALLY 'ADDRESS', CHARACTER LITERALLY 'BYTE'; DECLARE FIXED LITERALLY ' ', BIT LITERALLY 'BYTE'; DECLARE STATIC LITERALLY ' ', RETURNS LITERALLY ' '; DECLARE FALSE LITERALLY '0', TRUE LITERALLY '1'; DECLARE HBOUND LITERALLY 'LAST', SADDR LITERALLY '.'; BDOSF: PROCEDURE( FN, ARG )BYTE; DECLARE FN BYTE, ARG ADDRESS; GOTO 5; END; BDOS: PROCEDURE( FN, ARG ); DECLARE FN BYTE, ARG ADDRESS; GOTO 5; END; PRCHAR: PROCEDURE( C ); DECLARE C BYTE; CALL BDOS( 2, C ); END; PRSTRING: PROCEDURE( S ); DECLARE S ADDRESS; CALL BDOS( 9, S ); END; PRNL: PROCEDURE; CALL PRCHAR( 0DH ); CALL PRCHAR( 0AH ); END; PRNUMBER: PROCEDURE( N ); DECLARE N ADDRESS; DECLARE V ADDRESS, N$STR( 6 ) BYTE, W BYTE; N$STR( W := LAST( N$STR ) ) = '$'; N$STR( W := W - 1 ) = '0' + ( ( V := N ) MOD 10 ); DO WHILE( ( V := V / 10 ) > 0 ); N$STR( W := W - 1 ) = '0' + ( V MOD 10 ); END; CALL BDOS( 9, .N$STR( W ) ); END PRNUMBER; MODF: PROCEDURE( A, B )ADDRESS; DECLARE ( A, B ) ADDRESS; RETURN A MOD B; END MODF;
/* END LANGUAGE DEFINITIONS */
/* TASK */
/* ARRAY OF DOORS - DOOR( I ) IS TRUE IF OPEN, FALSE IF CLOSED */ DECLARE DOOR( DCLDOORS ) BIT; DECLARE ( I, J, MAXDOOR ) FIXED BINARY;
MAXDOOR = HBOUND( DOOR ,1 );
/* SET ALL DOORS TO CLOSED */ DO I = 0 TO MAXDOOR; DOOR( I ) = FALSE; END; /* REPEATEDLY FLIP THE DOORS */ DO I = 1 TO MAXDOOR; DO J = I TO MAXDOOR BY I; DOOR( J ) = NOT( DOOR( J ) ); END; END; /* DISPLAY THE RESULTS */ DO I = 1 TO MAXDOOR; IF DOOR( I ) THEN DO; CALL PRCHAR( ' ' ); CALL PRNUMBER( I ); END; END; CALL PRNL;
EOF: end doors_100H;</lang>
- Output:
1 4 9 16 25 36 49 64 81 100
Pony
Combined Optimized and Unoptimized
Probably also rather pointless in its use of actors, but, after all, they're cheap. <lang pony> actor Toggler
let doors:Array[Bool] let env: Env new create(count:USize,_env:Env) => var i:USize=0 doors=Array[Bool](count) env=_env while doors.size() < count do doors.push(false) end be togglin(interval : USize)=> var i:USize=0 try while i < doors.size() do doors.update(i,not doors(i)?)? i=i+interval end else env.out.print("Errored while togglin'!") end be printn(onlyOpen:Bool)=> try for i in doors.keys() do if onlyOpen and not doors(i)? then continue end env.out.print("Door " + i.string() + " is " + if doors(i)? then "Open" else "closed" end) end else env.out.print("Error!") end true
actor OptimizedToggler
let doors:Array[Bool] let env:Env new create(count:USize,_env:Env)=> env=_env doors=Array[Bool](count) while doors.size()<count do doors.push(false) end be togglin()=> var i:USize=0 if alreadydone then return end try doors.update(0,true)? doors.update(1,true)? while i < doors.size() do i=i+1 let z=i*i let x=z*z if z > doors.size() then break else doors.update(z,true)? end if x < doors.size() then doors.update(x,true)? end end end be printn(onlyOpen:Bool)=> try for i in doors.keys() do if onlyOpen and not doors(i)? then continue end env.out.print("Door " + i.string() + " is " + if doors(i)? then "Open" else "closed" end) end else env.out.print("Error!") end true
actor Main
new create(env:Env)=> var count: USize =100 try let index=env.args.find("-n",0,0,{(l,r)=>l==r})? try match env.args(index+1)?.read_int[USize]()? | (let x:USize, _)=>count=x end else env.out.print("You either neglected to provide an argument after -n or that argument was not an integer greater than zero.") return end end if env.args.contains("optimized",{(l,r)=>r==l}) then let toggler=OptimizedToggler(count,env) var i:USize = 1 toggler.togglin() toggler.printn(env.args.contains("onlyopen", {(l,r)=>l==r})) else let toggler=Toggler(count,env) var i:USize = 1 while i < count do toggler.togglin(i) i=i+1 end toggler.printn(env.args.contains("onlyopen", {(l,r)=>l==r})) end
</lang>
Pop11
unoptimized <lang pop11>lvars i; lvars doors = {% for i from 1 to 100 do false endfor %}; for i from 1 to 100 do
for j from i by i to 100 do not(doors(j)) -> doors(j); endfor;
endfor;
- Print state
for i from 1 to 100 do
printf('Door ' >< i >< ' is ' >< if doors(i) then 'open' else 'closed' endif, '%s\n');
endfor;</lang>
optimized <lang pop11>for i to 100 do
lvars root = sqrt(i); i; if root = round(root) then ' open' ><; else ' closed' ><; endif; =>
endfor;</lang>
PostScript
Bruteforce:<lang PostScript>/doors [ 100 { false } repeat ] def
1 1 100 { dup 1 sub exch 99 {
dup doors exch get not doors 3 1 roll put
} for } for doors pstack</lang>Shows: <lang>[true false false true false false false false true false ...<90 doors later>... true]</lang>
Potion
<lang Potion>square=1, i=3 1 to 100(door):
if (door == square): ("door", door, "is open") say square += i i += 2.
.</lang>
PowerShell
unoptimized
<lang powershell>$doors = @(0..99) for($i=0; $i -lt 100; $i++) {
$doors[$i] = 0 # start with all doors closed
} for($i=0; $i -lt 100; $i++) {
$step = $i + 1 for($j=$i; $j -lt 100; $j = $j + $step) { $doors[$j] = $doors[$j] -bxor 1 }
} foreach($doornum in 1..100) {
if($doors[($doornum-1)] -eq $true) {"$doornum open"} else {"$doornum closed"}
}</lang>
Alternative Method
<lang powershell>function Get-DoorState($NumberOfDoors) {
begin { $Doors = @() $Multiple = 1 }
process { for ($i = 1; $i -le $NumberOfDoors; $i++) { $Door = [pscustomobject]@{ Name = $i Open = $false }
$Doors += $Door }
While ($Multiple -le $NumberOfDoors) {
Foreach ($Door in $Doors) { if ($Door.name % $Multiple -eq 0)
{
If ($Door.open -eq $False){$Door.open = $True} Else {$Door.open = $False} } }
$Multiple++ } }
end {$Doors}
}</lang>
unoptimized Pipeline
<lang powershell>$doors = 1..100 | ForEach-Object {0} 1..100 | ForEach-Object { $a=$_;1..100 | Where-Object { -not ( $_ % $a ) } | ForEach-Object { $doors[$_-1] = $doors[$_-1] -bxor 1 }; if ( $doors[$a-1] ) { "door opened" } else { "door closed" } } </lang>
unoptimized Pipeline 2
<lang powershell>$doors = 1..100 | ForEach-Object {0} $visited = 1..100 1..100 | ForEach-Object { $a=$_;$visited[0..([math]::floor(100/$a)-1)] | Where-Object { -not ( $_ % $a ) } | ForEach-Object { $doors[$_-1] = $doors[$_-1] -bxor 1;$visited[$_/$a-1]+=($_/$a) }; if ( $doors[$a-1] ) { "door opened" } else { "door closed" } } </lang>
unoptimized Pipeline 3 (dynamically build pipeline)
<lang powershell>1..100|foreach-object {$pipe += "toggle $_ |"} -begin {$pipe=""} filter toggle($pass) {$_.door = $_.door -xor !($_.index % $pass);$_} invoke-expression "1..100| foreach-object {@{index=`$_;door=`$false}} | $pipe out-host" </lang>
Using Powershell Workflow for Parallelism
<lang powershell>
Workflow Calc-Doors {
Foreach –parallel ($number in 1..100) { "Door " + $number.ToString("0000") + ": " + @{$true="Closed";$false="Open"}[([Math]::pow($number, 0.5)%1) -ne 0] }
} Calc-Doors | sort
</lang>
optimized
<lang powershell> 1..10|%{"Door "+ $_*$_ + " is open"} </lang>
Processing
Unoptimized: <lang processing>boolean[] doors = new boolean[100];
void setup() {
for (int i = 0; i < 100; i++) { doors[i] = false; } for (int i = 1; i < 100; i++) { for (int j = 0; j < 100; j += i) { doors[j] = !doors[j]; } } println("Open:"); for (int i = 1; i < 100; i++) { if (doors[i]) { println(i); } } exit();
}</lang>
- Output:
Open: 1 4 9 16 25 36 49 64 81
Processing.R
Unoptimized: <lang r>setup <- function() {
for(door in doors(100, 100)) { stdout$print(paste(door, "")) }
}
doors <- function(ndoors=100,passes=100) {
doors <- rep(FALSE,ndoors) for (ii in seq(1,passes)) { mask <- seq(0,ndoors,ii) doors[mask] <- !doors[mask] } return (which(doors == TRUE))
}</lang>
- Output:
1 4 9 16 25 36 49 64 81 100
ProDOS
Uses math module. <lang ProDOS>enableextensions enabledelayedexpansion editvar /newvar /value=0 /title=closed editvar /newvar /value=1 /title=open editvar /newvar /range=1-100 /increment=1 /from=2 editvar /newvar /value=2 /title=next
- doors
for /alloccurrences (!next!-!102!) do editvar /modify /value=-open- editvar /modify /value=-next-=+1 if -next- /hasvalue=100 goto :cont else goto :doors
- cont
printline !1!-!102! stoptask</lang>
Prolog
unoptimized
Declarative:
<lang Prolog>main :-
forall(between(1,100,Door), ignore(display(Door))).
% show output if door is open after the 100th pass display(Door) :-
status(Door, 100, open), format("Door ~d is open~n", [Door]).
% true if Door has Status after Pass is done status(Door, Pass, Status) :-
Pass > 0, Remainder is Door mod Pass, toggle(Remainder, OldStatus, Status), OldPass is Pass - 1, status(Door, OldPass, OldStatus).
status(_Door, 0, closed).
toggle(Remainder, Status, Status) :-
Remainder > 0.
toggle(0, open, closed). toggle(0, closed, open). </lang>
Doors as a list:
<lang Prolog>doors_unoptimized(N) :- length(L, N), maplist(init, L), doors(N, N, L, L1), affiche(N, L1).
init(close).
doors(Max, 1, L, L1) :- !,
inverse(1, 1, Max, L, L1).
doors(Max, N, L, L1) :- N1 is N - 1, doors(Max, N1, L, L2), inverse(N, 1, Max, L2, L1).
inverse(N, Max, Max, [V], [V1]) :-
!,
0 =:= Max mod N -> inverse(V, V1); V1 = V.
inverse(N, M, Max, [V|T], [V1|T1]) :- M1 is M+1, inverse(N, M1, Max, T, T1), ( 0 =:= M mod N -> inverse(V, V1); V1 = V).
inverse(open, close).
inverse(close, open).
affiche(N, L) :- forall(between(1, N, I), ( nth1(I, L, open) -> format('Door ~w is open.~n', [I]); true)). </lang>
Using dynamic-rules. Tried to be ISO:
<lang prolog>doors(Num, Passes) :-
forall(( everyNth(1,Passes,1,Pass) , forall((everyNth(Pass,Num,Pass,Door), toggle(Door))) )) , show(Num) .
toggle(Door) :-
Opened = opened(Door) , ( clause(Opened,_) -> retract(Opened) ; asserta(Opened) ).
show(Num) :-
forall(( between(1,Num,Door) , (opened(Door) -> State = opened ; State = closed) , write(Door), write(' '), write(State), nl )).
% utils
forall(X) :- findall(_, X, _).
everyNth(From,To,Step,X) :-
From =< To , ( X = From ; From1 is From + Step, everyNth(From1,To,Step,X) ) .
main :- doors(100,100), halt.</lang>
optimized
<lang Prolog>doors_optimized(N) :- Max is floor(sqrt(N)), forall(between(1, Max, I), ( J is I*I,format('Door ~w is open.~n',[J]))).
</lang>
Pure
<lang Pure>using system;
// initialize doors as pairs: number, status where 0 means open let doors = zip (1..100) (repeat 1);
toogle (x,y) = x,~y;
toogleEvery n d = map (tooglep n) d with
tooglep n d@((x,_)) = toogle d if ~(x mod n); = d otherwise; end;
// show description of given doors status (n,x) = (str n) + (case x of
1 = " close"; 0 = " open"; end);
let result = foldl (\a n -> toogleEvery n a) doors (1..100);
// pretty print the result (only open doors) showResult = do (puts.status) final when
final = filter open result with open (_,x) = ~x; end; end;
</lang>
- Output:
> showResult; 1 open 4 open 9 open 16 open 25 open ...
Pure Data
<lang Pure Data>100Doors.pd
- N canvas 241 375 414 447 10;
- X obj 63 256 expr doors[$f1] = doors[$f1] ^ 1;
- X msg 83 118 \; doors const 0;
- X msg 44 66 bang;
- X obj 44 92 t b b b;
- X obj 43 28 table doors 101;
- X obj 44 360 sel 0;
- X obj 44 336 expr if (doors[$f1] == 1 \, $f1 \, 0);
- X obj 63 204 t b f f;
- X text 81 66 run;
- X obj 71 384 print -n;
- X text 132 310 print results (open doors);
- X obj 63 179 loop 1 100 1;
- X obj 63 231 loop 1 100 1;
- X obj 44 310 loop 1 100 1;
- X text 148 28 create array;
- X text 151 180 100 passes;
- X text 179 123 set values to 0;
- X connect 2 0 3 0;
- X connect 3 0 13 0;
- X connect 3 1 11 0;
- X connect 3 2 1 0;
- X connect 5 1 9 0;
- X connect 6 0 5 0;
- X connect 7 0 12 0;
- X connect 7 1 12 1;
- X connect 7 2 12 3;
- X connect 11 0 7 0;
- X connect 12 0 0 0;
- X connect 13 0 6 0;
loop.pd
- N canvas 656 375 427 447 10;
- X obj 62 179 until;
- X obj 102 200 f;
- X obj 62 89 inlet;
- X obj 303 158 f \$3;
- X obj 270 339 outlet;
- X obj 223 89 inlet;
- X obj 138 89 inlet;
- X obj 324 89 inlet;
- X obj 117 158 f \$1;
- X text 323 68 step;
- X obj 202 158 f \$2;
- X obj 62 118 t b b b b;
- X obj 270 315 spigot;
- X obj 89 314 sel 0;
- X obj 137 206 +;
- X obj 102 237 expr $f1 \; if ($f3 > 0 \, if ($f1 > $f2 \, 0 \, 1)
\, if ($f3 < 0 \, if ($f1 < $f2 \, 0 \, 1) \, 0)), f 34;
- X text 63 68 run;
- X text 136 68 start;
- X text 227 68 end;
- X text 58 31 loop (abstraction);
- X connect 0 0 1 0;
- X connect 1 0 14 0;
- X connect 1 0 15 0;
- X connect 2 0 11 0;
- X connect 3 0 14 1;
- X connect 3 0 15 2;
- X connect 5 0 10 1;
- X connect 6 0 8 1;
- X connect 7 0 3 1;
- X connect 8 0 1 1;
- X connect 10 0 15 1;
- X connect 11 0 0 0;
- X connect 11 1 8 0;
- X connect 11 2 10 0;
- X connect 11 3 3 0;
- X connect 12 0 4 0;
- X connect 13 0 0 1;
- X connect 14 0 1 1;
- X connect 15 0 12 0;
- X connect 15 1 12 1;
- X connect 15 1 13 0;
</lang>
PureBasic
unoptimized <lang purebasic>Dim doors.i(100)
For x = 1 To 100
y = x While y <= 100 doors(y) = 1 - doors(y) y + x Wend
Next
OpenConsole() PrintN("Following Doors are open:") For x = 1 To 100
If doors(x) Print(Str(x) + ", ") EndIf
Next Input()</lang>
optimized <lang PureBasic>OpenConsole() PrintN("Following Doors are open:") For i = 1 To 100
root.f = Sqr(i) If root = Int(root) Print (Str(i) + ", ") EndIf
Next Input()</lang>
Output:
Following Doors are open: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100,
Pyret
<lang pyret> data Door:
| open | closed
end
fun flip-door(d :: Door) -> Door:
cases(Door) d: | open => closed | closed => open end
end
fun flip-doors(doors :: List<Door>) -> List<Door>:
doc:```Given a list of door positions, repeatedly switch the positions of every nth door for every nth pass, and return the final list of door positions``` for fold(flipped-doors from doors, n from range(1, doors.length() + 1)): for map_n(m from 1, d from flipped-doors): if num-modulo(m, n) == 0: flip-door(d) else: d end end end
where:
flip-doors([list: closed, closed, closed]) is [list: open, closed, closed]
flip-doors([list: closed, closed, closed, closed]) is [list: open, closed, closed, open]
flip-doors([list: closed, closed, closed, closed, closed, closed]) is [list: open, closed, closed, open, closed, closed]
closed-100 = for map(_ from range(1, 101)): closed end answer-100 = for map(n from range(1, 101)): if num-is-integer(num-sqrt(n)): open else: closed end end
flip-doors(closed-100) is answer-100
end
fun find-indices<A>(pred :: (A -> Boolean), xs :: List<A>) -> List<Number>:
doc:```Given a list and a predicate function, produce a list of index positions where there's a match on the predicate``` ps = map_n(lam(n,e): if pred(e): n else: -1 end end, 1, xs) ps.filter(lam(x): x >= 0 end)
where:
find-indices((lam(i): i == true end), [list: true,false,true]) is [list:1,3]
end
fun run(n):
doc:```Given a list of doors that are closed, make repeated passes over the list, switching the positions of every nth door for each nth pass. Return a list of positions in the list where the door is Open.``` doors = repeat(n, closed) ys = flip-doors(doors) find-indices((lam(y): y == open end), ys)
where:
run(4) is [list: 1,4]
end
run(100)
</lang>
Python
unoptimized <lang python> doors = [False] * 100 for i in range(100):
for j in range(i, 100, i+1): doors[j] = not doors[j] print("Door %d:" % (i+1), 'open' if doors[i] else 'close')
</lang>
optimized
A version that only visits each door once:
<lang python>for i in xrange(1, 101):
root = i ** 0.5 print "Door %d:" % i, 'open' if root == int(root) else 'close'</lang>
One liner using a list comprehension, item lookup, and is_integer
<lang python>print '\n'.join(['Door %s is %s' % (i, ('closed', 'open')[(i**0.5).is_integer()]) for i in xrange(1, 101)])</lang>
One liner using a generator expression, ternary operator, and modulo
<lang python>print '\n'.join('Door %s is %s' % (i, 'closed' if i**0.5 % 1 else 'open') for i in range(1, 101))</lang>
<lang python> for i in range(1, 101):
if i**0.5 % 1: state='closed' else: state='open' print("Door {}:{}".format(i, state))
</lang>
ultra-optimized: ported from Julia version
<lang python>for i in range(1,101): print("Door %s is open" % i**2)</lang>
Q
unoptimized <lang q>`closed`open(100#0b){@[x;where y;not]}/100#'(til[100]#'0b),'1b</lang>
Binary function {@[x;where y;not]}
is applied using Over. The initial state is 100#0b
and the right argument is a list of 100 boolean masks. The boolean vector result is used to index the pair of states.
Following expressions simply flag perfect squares.
optimized <lang q>`closed`open (1+til 100) in {x*x} 1+til 10</lang>
alternative <lang q>@[100#`closed; -1+{x*x}1+til 10; :; `open]</lang>
QB64
<lang QB64 > Const Opened = -1, Closed = 0 Dim Doors(1 To 100) As Integer, Passes As Integer, Index As Integer Rem Normal implementation Print "100doors Normal method" For Passes = 1 To 100 Step 1
Doors(Passes) = Closed
Next Passes For Passes = 1 To 100 Step 1
For Index = 0 To 100 Step Passes If Index > 100 Then Exit For If Index > 0 Then If Doors(Index) = Opened Then Doors(Index) = Closed Else Doors(Index) = Opened Next Index
Next Passes Print "OPEN DOORS after 100th passes" For Passes = 1 To 100 Step 1
If Doors(Passes) = Opened Then Print Passes; " ";
Next
Rem Alternative solution of perfect squares
Print "Alternative method" Passes = 0 For Passes = 1 To 100 Step 1
Doors(Passes) = Closed
Next Passes For Passes = 1 To 100 Step 1
If Sqr(Passes) = Int(Sqr(Passes)) Then Doors(Passes) = Opened
Next Print "Opened doors found by SQR method" For Passes = 1 To 100 Step 1
If Doors(Passes) = Opened Then Print Passes; " ";
Next Passes End </lang>
Quackery
unoptimized <lang Quackery>/O> [ bit ^ ] is toggle ( f n --> f ) ... ... [ 0 ... 100 times ... [ i^ 1+ swap ... 101 times ... [ i^ toggle over step ] ... nip ] ] is toggledoors ( --> f ) ... ... [ 100 times ... [ 1 >> dup 1 & ... if [ i^ 1+ echo sp ] ] ... drop ] is echodoors ( f --> ) ... ... toggledoors ... say " These doors are open: " echodoors cr ... say " The rest are closed." cr ...
These doors are open: 1 4 9 16 25 36 49 64 81 100 The rest are closed.
Stack empty. </lang>
R
Using a loop <lang r>doors_puzzle <- function(ndoors=100,passes=100) {
doors <- rep(FALSE,ndoors) for (ii in seq(1,passes)) { mask <- seq(0,ndoors,ii) doors[mask] <- !doors[mask] } return (which(doors == TRUE))
}
doors_puzzle()</lang>
optimized
<lang r>x <- rep(1, 100)
for (i in 1:100-1) {
x <- xor(x, rep(c(rep(0,i),1), length.out=100))
} which(!x)</lang>
Using a **ply function <lang r>doors_puzzle <- function(ndoors=100,passes=100) { names(which(table(unlist(sapply(1:passes, function(X) seq(0, ndoors, by=X)))) %% 2 == 1)) }
doors_puzzle()</lang>
Using Reduce
<lang R>H=100 f=rep(F,H) which(Reduce(function(d,n) xor(replace(f,seq(n,H,n),T),d), 1:H, f))</lang>
- Output:
1 4 9 16 25 36 49 64 81 100
Racket
<lang racket>
- lang racket
- Applies fun to every step-th element of seq, leaving the others unchanged.
(define (map-step fun step seq)
(for/list ([elt seq] [i (in-naturals)]) ((if (zero? (modulo i step)) fun values) elt)))
(define (toggle-nth n seq)
(map-step not n seq))
(define (solve seq)
(for/fold ([result seq]) ([_ seq] [pass (in-naturals 1)]) (toggle-nth pass result)))
(for ([door (solve (make-vector 101 #f))] [index (in-naturals)]
#:when (and door (> index 0))) (printf "~a is open~%" index))
</lang>
Optimized: <lang racket>
- lang racket
(for ([x (in-range 1 101)] #:when (exact-integer? (sqrt x)))
(printf "~a is open\n" x))
</lang>
Unoptimized imperative, with graphic rendering: <lang racket>
- lang slideshow
(define-syntax-rule (vector-neg! vec pos)
(vector-set! vec pos (not (vector-ref vec pos))))
(define (make-doors)
(define doors (make-vector 100 #f)) (for* ([i 100] [j (in-range i 100 (add1 i))]) (vector-neg! doors j)) doors)
(displayln (list->string (for/list ([d (make-doors)]) (if d #\o #\-))))
(define closed-door (inset (filled-rectangle 4 20) 2)) (define open-door (inset (rectangle 4 20) 2))
(for/fold ([doors (rectangle 0 0)]) ([open? (make-doors)])
(hc-append doors (if open? open-door closed-door)))
</lang>
Output:
Raku
(formerly Perl 6)
unoptimized
<lang perl6>my @doors = False xx 101;
(.=not for @doors[0, $_ ... 100]) for 1..100;
say "Door $_ is ", <closed open>[ @doors[$_] ] for 1..100;</lang>
optimized
<lang perl6>say "Door $_ is open" for map {$^n ** 2}, 1..10;</lang>
probably the most compact idiom
<lang perl6>say 'Door $_ is open' for (1..10)»²;</lang>
Here's a version using the cross meta-operator instead of a map:
<lang perl6> say "Door $_ is open" for 1..10 X** 2;</lang>
This one prints both opened and closed doors:
<lang perl6>say "Door $_ is ", <closed open>[.sqrt == .sqrt.floor] for 1..100;</lang>
verbose version, but uses ordinary components
<lang perl6> sub output( @arr, $max ) {
my $output = 1; for 1..^$max -> $index {
if @arr[$index] { printf "%4d", $index; say if $output++ %% 10; }
} say ;
}
sub MAIN ( Int :$doors = 100 ) {
my $doorcount = $doors + 1; my @door[$doorcount] = 0 xx ($doorcount); INDEX: for 1...^$doorcount -> $index { # flip door $index & its multiples, up to last door. #
for ($index, * + $index ... *)[^$doors] -> $multiple { next INDEX if $multiple > $doors; @door[$multiple] = @door[$multiple] ?? 0 !! 1; }
} output @door, $doors+1;
} </lang>
- Output:
$ ./100_doors.pl6 -doors=100 1 4 9 16 25 36 49 64 81
RapidQ
<lang vb> dim x as integer, y as integer dim door(1 to 100) as byte
'initialize array for x = 1 to 100 : door(x) = 0 : next
'set door values for y = 1 to 100
for x = y to 100 step y door(x) = not door(x) next x
next y
'print result for x = 1 to 100
if door(x) then print "Door " + str$(x) + " = open"
next
while inkey$="":wend end </lang> Output
Door 1 = open Door 4 = open Door 9 = open Door 16 = open Door 25 = open Door 36 = open Door 49 = open Door 64 = open Door 81 = open Door 100 = open
REBOL
Unoptimized
<lang rebol>doors: array/initial 100 'closed repeat i 100 [
door: at doors i forskip door i [change door either 'open = first door ['closed] ['open]]
]</lang>
Optimized
<lang rebol>doors: array/initial 100 'closed repeat i 10 [doors/(i * i): 'open] </lang>
Red
Unoptimized
<lang Red>Red [
Purpose: "100 Doors Problem (Perfect Squares)" Author: "Barry Arthur" Date: "07-Oct-2016"
] doors: make vector! [char! 8 100] repeat i 100 [change at doors i #"."]
repeat i 100 [
j: i while [j <= 100] [ door: at doors j change door either #"O" = first door [#"."] [#"O"] j: j + i ]
]
repeat i 10 [
print copy/part at doors (i - 1 * 10 + 1) 10
] </lang>
Using bitset! type
<lang Red>Red ["Doors"]
doors: make bitset! len: 100 repeat step len [ repeat n to-integer len / step [ m: step * n doors/:m: not doors/:m ] ] repeat n len [if doors/:n [print n]] </lang>
Relation
<lang Relation> relation door, state set i = 1 while i <= 100 insert i, 1 set i = i+1 end while set i = 2 while i <= 100 update state = 1-state where not (door mod i) set i = i+1 end while update state = "open" where state update state = "closed" where state !== "open" print </lang>
door | state |
---|---|
1 | open |
2 | closed |
3 | closed |
4 | open |
5 | closed |
6 | closed |
7 | closed |
8 | closed |
9 | open... |
Retro
<lang Retro>:doors (n-) [ #1 repeat dup-pair n:square gt? 0; drop dup n:square n:put sp n:inc again ] do drop-pair ;
- 100 doors</lang>
REXX
the idiomatic way
<lang rexx>/*REXX pgm solves the 100 doors puzzle, doing it the hard way by opening/closing doors.*/ parse arg doors . /*obtain the optional argument from CL.*/ if doors== | doors=="," then doors=100 /*not specified? Then assume 100 doors*/
/* 0 = the door is closed. */ /* 1 = " " " open. */
door.=0 /*assume all doors are closed at start.*/
do #=1 for doors /*process a pass─through for all doors.*/ do j=# by # to doors /* ··· every Jth door from this point.*/ door.j= \door.j /*toggle the "openness" of the door. */ end /*j*/ end /*#*/
say 'After ' doors " passes, the following doors are open:" say
do k=1 for doors if door.k then say right(k, 20) /*add some indentation for the output. */ end /*k*/ /*stick a fork in it, we're all done. */</lang>
- output when using the default input:
After 100 passes, the following doors are open: 1 4 9 16 25 36 49 64 81 100
the shortcut way
<lang rexx>/*REXX pgm solves the 100 doors puzzle, doing it the easy way by calculating squares.*/ parse arg doors . /*obtain the optional argument from CL.*/ if doors== | doors=="," then doors=100 /*not specified? Then assume 100 doors*/ say 'After ' doors " passes, the following doors are open:" say
do #=1 while #**2 <= doors /*process easy pass─through (squares).*/ say right(#**2, 20) /*add some indentation for the output. */ end /*#*/ /*stick a fork in it, we're all done. */</lang>
- output is identical to the 1st REXX version.
Ring
Unoptimized <lang ring>doors = list(100) for i = 1 to 100 doors[i] = false next
For pass = 1 To 100
For door = pass To 100 if doors[door] doors[door] = false else doors[door] = true ok door += pass-1 Next
Next
For door = 1 To 100
see "Door (" + door + ") is " If doors[door] see "Open" else see "Closed" ok see nl
Next</lang>
Optimized <lang ring>doors = list(100) for i = 1 to 100 doors[i] = false next
For p = 1 To 10
doors[pow(p,2)] = True
Next
For door = 1 To 100
see "Door (" + door + ") is " If doors[door] see "Open" else see "Closed" ok see nl
Next</lang>
Ruby
<lang ruby>doors = Array.new(101,0) print "Open doors " (1..100).step(){ |i| (i..100).step(i) { |d|
doors[d] = doors[d]^= 1 if i == d and doors[d] == 1 then print "#{i} " end }
}</lang>Output:
Open doors 1 4 9 16 25 36 49 64 81 100
unoptimized; Ruby-way
<lang ruby>class Door
attr_reader :state
def initialize @state = :closed end def close @state = :closed end
def open @state = :open end def closed? @state == :closed end def open? @state == :open end def toggle if closed? then open else close end end def to_s @state.to_s end
end
doors = Array.new(100) { Door.new } 1.upto(100) do |multiplier|
doors.each_with_index do |door, i| door.toggle if (i + 1) % multiplier == 0 end
end
doors.each_with_index { |door, i| puts "Door #{i+1} is #{door}." }</lang>
unoptimized
<lang ruby>n = 100 Open = "open" Closed = "closed" def Open.toggle
Closed
end def Closed.toggle
Open
end doors = [Closed] * (n + 1) for mul in 1..n
for x in (mul..n).step(mul) doors[x] = doors[x].toggle end
end doors.each_with_index do |b, i|
puts "Door #{i} is #{b}" if i > 0
end</lang>
optimized
<lang ruby>n = 100 (1..n).each do |i|
puts "Door #{i} is #{i**0.5 == (i**0.5).round ? "open" : "closed"}"
end</lang>
generic true/false, with another way of handling the inner loop demonstrating Range#step
<lang ruby>doors = [false] * 100 100.times do |i|
(i ... doors.length).step(i + 1) do |j| doors[j] = !doors[j] end
end puts doors.map.with_index(1){|d,i| "Door #{i} is #{d ? 'open' : 'closed'}."}</lang>
- Output:
Door 1 is open Door 2 is closed Door 3 is closed Door 4 is open Door 5 is closed Door 6 is closed Door 7 is closed Door 8 is closed Door 9 is open Door 10 is closed Door 11 is closed Door 12 is closed Door 13 is closed Door 14 is closed Door 15 is closed Door 16 is open Door 17 is closed Door 18 is closed Door 19 is closed Door 20 is closed Door 21 is closed Door 22 is closed Door 23 is closed Door 24 is closed Door 25 is open Door 26 is closed Door 27 is closed Door 28 is closed Door 29 is closed Door 30 is closed Door 31 is closed Door 32 is closed Door 33 is closed Door 34 is closed Door 35 is closed Door 36 is open Door 37 is closed Door 38 is closed Door 39 is closed Door 40 is closed Door 41 is closed Door 42 is closed Door 43 is closed Door 44 is closed Door 45 is closed Door 46 is closed Door 47 is closed Door 48 is closed Door 49 is open Door 50 is closed Door 51 is closed Door 52 is closed Door 53 is closed Door 54 is closed Door 55 is closed Door 56 is closed Door 57 is closed Door 58 is closed Door 59 is closed Door 60 is closed Door 61 is closed Door 62 is closed Door 63 is closed Door 64 is open Door 65 is closed Door 66 is closed Door 67 is closed Door 68 is closed Door 69 is closed Door 70 is closed Door 71 is closed Door 72 is closed Door 73 is closed Door 74 is closed Door 75 is closed Door 76 is closed Door 77 is closed Door 78 is closed Door 79 is closed Door 80 is closed Door 81 is open Door 82 is closed Door 83 is closed Door 84 is closed Door 85 is closed Door 86 is closed Door 87 is closed Door 88 is closed Door 89 is closed Door 90 is closed Door 91 is closed Door 92 is closed Door 93 is closed Door 94 is closed Door 95 is closed Door 96 is closed Door 97 is closed Door 98 is closed Door 99 is closed Door 100 is open
Run BASIC
<lang Runbasic>dim doors(100) print "Open doors "; for i = 1 to 100
for door = i to 100 step i doors(door) = (doors(door) <> 1) if i = door and doors(door) = 1 then print i;" "; next door
next i</lang>Output:
Open doors 1 4 9 16 25 36 49 64 81 100
Rust
<lang rust>fn main() {
let mut door_open = [false; 100]; for pass in 1..101 { let mut door = pass; while door <= 100 { door_open[door - 1] = !door_open[door - 1]; door += pass; } } for (i, &is_open) in door_open.iter().enumerate() { println!("Door {} is {}.", i + 1, if is_open {"open"} else {"closed"}); }
}</lang>
Declarative version of above:
<lang rust>fn main() {
let doors = vec![false; 100].iter_mut().enumerate() .map(|(door, door_state)| (1..100).into_iter() .filter(|pass| (door + 1) % pass == 0) .map(|_| { *door_state = !*door_state; *door_state }) .last().unwrap()).collect::<Vec<_>>();
println!("{:?}", doors);
} </lang>
Optimized version:
(In this case the printing is the bottleneck so this version is not faster than the above one.)
<lang rust>fn main() {
let squares: Vec<_> = (1..11).map(|n| n*n).collect(); let is_square = |num| squares.binary_search(&num).is_ok();
for i in 1..101 { let state = if is_square(i) {"open"} else {"closed"}; println!("Door {} is {}", i, state); }
}</lang>
ultra-optimized: ported from Julia version <lang rust>fn main() {
for i in 1u32..11u32{ println!("Door {} is open", i.pow(2)); }
}</lang>
S-BASIC
<lang Basic> $constant DOOR_OPEN = 1 $constant DOOR_CLOSED = 0 $constant MAX_DOORS = 100
var i, j = integer dim integer doors(MAX_DOORS)
rem - all doors are initially closed for i = 1 to MAX_DOORS
doors(i) = DOOR_CLOSED
next i
rem - cycle through at increasing intervals and flip doors for i = 1 to MAX_DOORS
for j = i to MAX_DOORS step i doors(j) = 1 - doors(j) next j
next i
rem - report results print "The open doors are:" for i = 1 to MAX_DOORS
if doors(i) = DOOR_OPEN then print i;
next i
end </lang>
- Output:
The open doors are: 1 4 9 16 25 36 49 64 81 100
S-lang
<lang s-lang>variable door,
isOpen = Char_Type [101], pass;
for (door = 1; door <= 100; door++) {
isOpen[door] = 0;
}
for (pass = 1; pass <= 100; pass++) {
for (door = pass; door <= 100; door += pass) { isOpen[door] = not isOpen[door]; }
}
for (door = 1; door <= 100; door++) {
if (isOpen[door]) { print("Door " + string(door) + ":open"); } else { print("Door " + string(door) + ":close"); }
}</lang>
Salmon
Here's an unoptimized version: <lang Salmon>variable open := <<(* --> false)>>; for (pass; 1; pass <= 100)
for (door_num; pass; door_num <= 100; pass) open[door_num] := !(open[door_num]);;;
iterate (door_num; [1...100])
print("Door ", door_num, " is ", (open[door_num] ? "open.\n" : "closed.\n"));;</lang>
And here's an optimized one-line version:
<lang Salmon>iterate (x; [1...10]) { iterate (y; [(x-1)*(x-1)+1...x*x-1]) { print("Door ", y, " is closed.\n"); }; print("Door ", x*x, " is open.\n"); };</lang>
And a shorter optimized one-line version:
<lang Salmon>variable y:=1;for(x;1;x<101)"Door "~sprint(x)~" is "~(x==y*y?{++y;return"open";}:"closed")!;</lang>
SAS
<lang sas>data _null_;
open=1; close=0; array Door{100}; do Pass = 1 to 100; do Current = Pass to 100 by Pass; if Door{Current} ne open then Door{Current} = open; else Door{Current} = close; end; end; NumberOfOpenDoors = sum(of Door{*}); put "Number of Open Doors: " NumberOfOpenDoors;
run;</lang>
Sather
<lang sather>class MAIN is
main is doors :ARRAY{BOOL} := #(100); loop pass::= doors.ind!; loop i::= pass.stepto!(doors.size - 1, pass + 1); doors[i] := ~doors[i]; end; end; loop #OUT + (doors.ind! + 1) + " " + doors.elt! + "\n"; end; end;
end;</lang>
Scala
<lang scala>for { i <- 1 to 100
r = 1 to 100 map (i % _ == 0) reduceLeft (_^_) } println (i +" "+ (if (r) "open" else "closed"))</lang>
The map operation maps each door (i) to a boolean sequence of toggles, one for each pass: true toggles, false leaves the same.
The reduceLeft method combines all the toggles sequentially, using the XOR operator.
And then we just need to output the result.
I made a version that optional accepts an argument for the number of doors. It is also a little more a ‘classical’ solution: <lang scala> def openDoors(length : Int = 100) = {
var isDoorOpen = new Array[Boolean](length)
for (i <- 0 until length) { for (j <- i until length by i + 1) { isDoorOpen(j) ^= true } } isDoorOpen
}
val doorState = scala.collection.immutable.Map(false -> "closed", true -> "open") val isDoorOpen = openDoors()
for (doorNo <- 0 until isDoorOpen.length) {
println("Door %d is %s".format(doorNo + 1, doorState(isDoorOpen(doorNo))))
} </lang>
I created the function openDoors which gives back an array signifying if a door is open and optional accepts an argument for the number of doors. (I like to make things general.) I call the function and use the result to display the status of the doors.
"Optimized" version: <lang scala>val o = 1 to 10 map (i => i * i) println("open: " + o) println("closed: " + (1 to 100 filterNot o.contains))</lang>
Scheme
unoptimized <lang scheme>(define *max-doors* 100)
(define (show-doors doors)
(let door ((i 0) (l (vector-length doors))) (cond ((= i l) (newline)) (else (printf "~nDoor ~a is ~a" (+ i 1) (if (vector-ref doors i) "open" "closed")) (door (+ i 1) l)))))
(define (flip-doors doors)
(define (flip-all i) (cond ((> i *max-doors*) doors) (else (let flip ((idx (- i 1))) (cond ((>= idx *max-doors*) (flip-all (+ i 1))) (else (vector-set! doors idx (not (vector-ref doors idx))) (flip (+ idx i)))))))) (flip-all 1))
(show-doors (flip-doors (make-vector *max-doors* #f)))</lang>
optimized <lang scheme>(define (optimised-flip-doors doors)
(define (flip-all i) (cond ((> i (floor (sqrt *max-doors*))) doors) (else (vector-set! doors (- (* i i) 1) #t) (flip-all (+ i 1))))) (flip-all 1))
(show-doors (optimised-flip-doors (make-vector *max-doors* #f)))</lang>
the 3rd version <lang scheme>(define (N_doors N)
(define (init) (define (str n) (if (> n N) '() (cons 0 (str (+ 1 n))))) (str 1)) (define (toggle x str) (define (s n lis) (define (revert x) (if (eq? x 0) 1 0)) (cond ((null? lis) '()) ((zero? (remainder n x)) (cons (revert (car lis)) (s (+ n 1) (cdr lis)))) (else (cons (car lis) (s (+ n 1) (cdr lis)))))) (s 1 str)) (define (iterate x lis) (if (> x N) lis (iterate (+ x 1) (toggle x lis)))) (iterate 1 (init)))
(N_doors 100)</lang>
Output of the 3rd version: 1 represents open, 0 represents closed.
(1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1)
Scilab
<lang>doors=zeros(1,100); for i = 1:100
for j = i:i:100 doors(j) = ~doors(j); end
end for i = 1:100
if ( doors(i) ) s = "open"; else s = "closed"; end printf("%d %s\n", i, s);
end</lang>
- Output:
1 open 2 closed 3 closed 4 open 5 closed 6 closed 7 closed 8 closed 9 open 10 closed 11 closed 12 closed 13 closed 14 closed 15 closed 16 open 17 closed 18 closed 19 closed 20 closed 21 closed 22 closed 23 closed 24 closed 25 open 26 closed 27 closed 28 closed 29 closed 30 closed 31 closed 32 closed 33 closed 34 closed 35 closed 36 open 37 closed 38 closed 39 closed 40 closed 41 closed 42 closed 43 closed 44 closed 45 closed 46 closed 47 closed 48 closed 49 open 50 closed 51 closed 52 closed 53 closed 54 closed 55 closed 56 closed 57 closed 58 closed 59 closed 60 closed 61 closed 62 closed 63 closed 64 open 65 closed 66 closed 67 closed 68 closed 69 closed 70 closed 71 closed 72 closed 73 closed 74 closed 75 closed 76 closed 77 closed 78 closed 79 closed 80 closed 81 open 82 closed 83 closed 84 closed 85 closed 86 closed 87 closed 88 closed 89 closed 90 closed 91 closed 92 closed 93 closed 94 closed 95 closed 96 closed 97 closed 98 closed 99 closed 100 open
Scratch
Scratch is a visual programming language. Click the link, then "see inside" to see the code.
https://scratch.mit.edu/projects/168687954/
Output: 100 indications that "Door ___ is _____," where doors with perfect square indices are open and the rest are closed.
Seed7
unoptimized <lang seed7>$ include "seed7_05.s7i";
const proc: main is func
local var array boolean: doorOpen is 100 times FALSE; var integer: pass is 0; var integer: index is 0; var array[boolean] string: closedOrOpen is [boolean] ("closed", "open"); begin for pass range 1 to 100 do for key index range doorOpen do if index rem pass = 0 then doorOpen[index] := not doorOpen[index]; end if; end for; end for; for key index range doorOpen do write(index lpad 3 <& " is " <& closedOrOpen[doorOpen[index]] rpad 7); if index rem 5 = 0 then writeln; end if; end for; end func;</lang>
optimized <lang seed7>$ include "seed7_05.s7i";
const proc: main is func
local var integer: index is 0; var integer: number is 0; var array[boolean] string: closedOrOpen is [boolean] ("closed", "open"); begin for index range 1 to 100 do number := sqrt(index); write(index lpad 3 <& " is " <& closedOrOpen[number**2 = index] rpad 7); if index rem 5 = 0 then writeln; end if; end for; end func;</lang>
Output of both programs:
1 is open 2 is closed 3 is closed 4 is open 5 is closed 6 is closed 7 is closed 8 is closed 9 is open 10 is closed 11 is closed 12 is closed 13 is closed 14 is closed 15 is closed 16 is open 17 is closed 18 is closed 19 is closed 20 is closed 21 is closed 22 is closed 23 is closed 24 is closed 25 is open 26 is closed 27 is closed 28 is closed 29 is closed 30 is closed 31 is closed 32 is closed 33 is closed 34 is closed 35 is closed 36 is open 37 is closed 38 is closed 39 is closed 40 is closed 41 is closed 42 is closed 43 is closed 44 is closed 45 is closed 46 is closed 47 is closed 48 is closed 49 is open 50 is closed 51 is closed 52 is closed 53 is closed 54 is closed 55 is closed 56 is closed 57 is closed 58 is closed 59 is closed 60 is closed 61 is closed 62 is closed 63 is closed 64 is open 65 is closed 66 is closed 67 is closed 68 is closed 69 is closed 70 is closed 71 is closed 72 is closed 73 is closed 74 is closed 75 is closed 76 is closed 77 is closed 78 is closed 79 is closed 80 is closed 81 is open 82 is closed 83 is closed 84 is closed 85 is closed 86 is closed 87 is closed 88 is closed 89 is closed 90 is closed 91 is closed 92 is closed 93 is closed 94 is closed 95 is closed 96 is closed 97 is closed 98 is closed 99 is closed 100 is open
SenseTalk
<lang sensetalk> put false repeated 100 times as a list into Doors100
repeat 1 to 100 set step to it repeat step to 100 by step set newValue to not item it of Doors100 set item it of Doors100 to newValue end repeat end repeat
put the counter for each item of Doors100 which is true </lang> Output:
(1,4,9,16,25,36,49,64,81,100)
SequenceL
Unoptimized <lang sequencel> import <Utilities/Sequence.sl>;
main:= let doors := flipDoors(duplicate(false, 100), 1); open[i] := i when doors[i]; in open;
flipDoors(doors(1), count) := let newDoors[i] := not doors[i] when i mod count = 0 else doors[i]; in doors when count >= 100 else flipDoors(newDoors, count + 1); </lang>
Optimized <lang sequencel> main := flipDoors([1], 2);
flipDoors(openDoors(1), i) := openDoors when i * i >= 100 else flipDoors(openDoors ++ [i * i], i + 1); </lang>
SETL
Unoptimized <lang setl>program hundred_doors;
const toggle := {['open', 'closed'], ['closed', 'open']};
doorStates := ['closed'] * 100;
(for interval in [1..100])
doorStates := [if i mod interval = 0 then toggle(prevState) else prevState end: prevState = doorStates(i)];
end;
(for finalState = doorStates(i))
print('door', i, 'is', finalState);
end;
end program;</lang> If 'open' weren't a reserved word, we could omit the single quotes around it.
Optimized Exploits the fact that squares are separated by successive odd numbers. Use array replication to insert the correct number of closed doors in between the open ones. <lang setl>program hundred_doors;
doorStates := (+/ [['closed'] * oddNum with 'open': oddNum in [1,3..17]]);
(for finalState = doorStates(i))
print('door', i, 'is', finalState);
end;
end program;</lang>
SheerPower 4GL
<lang sp4gl> !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% ! I n i t i a l i z a t i o n !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% doors% = 100
dim doorArray?(doors%)
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% ! M a i n L o g i c A r e a !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
// Initialize Array for index% = 1 to doors%
doorArray?(index%) = false
next index%
// Execute routine toggle_doors
// Print results for index% = 1 to doors%
if doorArray?(index%) = true then print index%, ' is open'
next index%
stop
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
! R o u t i n e s
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
routine toggle_doors
for index_outer% = 1 to doors% for index_inner% = 1 to doors% if mod(index_inner%, index_outer%) = 0 then doorArray?(index_inner%) = not doorArray?(index_inner%) end if next index_inner% next index_outer%
end routine
end
</lang>
Sidef
Unoptimized <lang ruby>var doors = []
{ |pass|
{ |i| if (pass `divides` i) { doors[i] := false -> not! } } << 1..100
} << 1..100
{ |i|
say ("Door %3d is %s" % (i, doors[i] ? 'open' : 'closed'))
} << 1..100</lang>
Optimized <lang ruby>{ |i|
"Door %3d is %s\n".printf(i, <closed open>[i.is_sqr])
} << 1..100</lang>
Simula
<lang simula>BEGIN
INTEGER LIMIT = 100, door, stride; BOOLEAN ARRAY DOORS(1:LIMIT); TEXT intro;
FOR stride := 1 STEP 1 UNTIL LIMIT DO FOR door := stride STEP stride UNTIL LIMIT DO DOORS(door) := NOT DOORS(door);
intro :- "All doors closed but "; FOR door := 1 STEP 1 UNTIL LIMIT DO IF DOORS(door) THEN BEGIN OUTTEXT(intro); OUTINT(door, 0); intro :- ", " END; OUTIMAGE
END.</lang>
- Output:
All doors closed but 1, 4, 9, 16, 25, 36, 49, 64, 81, 100
Slate
Unoptimized <lang slate>define: #a -> (Array newSize: 100). a infect: [| :_ | False].
a keysDo: [| :pass |
pass to: a indexLast by: pass do: [| :door | a at: door infect: #not `er]].
a keysAndValuesDo: [| :door :isOpen |
inform: 'door #' ; door ; ' is ' ; (isOpen ifTrue: ['open'] ifFalse: ['closed'])].</lang>
Optimized <lang slate>define: #a -> (Array newSize: 100). a infect: [| :_ | False].
0 below: 10 do: [| :door | a at: door squared put: True]. a keysAndValuesDo: [| :door :isOpen |
inform: 'door #' ; door ; ' is ' ; (isOpen ifTrue: ['open'] ifFalse: ['closed'])].</lang>
Smalltalk
Unoptimized <lang smalltalk>|a| a := Array new: 100 . 1 to: 100 do: [ :i | a at: i put: false ].
1 to: 100 do: [ :pass |
pass to: 100 by: pass do: [ :door | a at: door put: (a at: door) not . ]
].
"output" 1 to: 100 do: [ :door |
( 'door #%1 is %2' % { door . (a at: door) ifTrue: [ 'open' ] ifFalse: [ 'closed' ] } ) displayNl
]</lang> Optimized
<lang smalltalk>|a| a := (1 to: 100) collect: [ :x | false ]. 1 to: 10 do: [ :i | a at: (i squared) put: true ]. 1 to: 100 do: [ :i |
( 'door #%1 is %2' % { i . (a at: i) ifTrue: [ 'open' ] ifFalse: [ 'closed' ] } ) displayNl
]</lang>
Unoptimized, using Morphs <lang smalltalk> | m w h smh smw delay closedDoor border subMorphList |
closedDoor := Color black. border := Color veryLightGray. delay := Delay forMilliseconds: 50. w := World bounds corner x. h := (World bounds corner y) / 2. smw := w/100. smh := h/2.
m := BorderedMorph new position: 0@h. m height: smh; width: w; borderColor: border. m color: Color veryLightGray.
1 to: 100 do: [ :pos || sm | sm := BorderedMorph new height: smh ; width: smw ; borderColor: border; color: closedDoor; position: (smw*pos)@h. m addMorph: sm asElementNumber: pos].
m openInWorld. delay wait. subMorphList := m submorphs. "display every step" [1 to: 100 do: [ :step | step to: 100 by: step do: [ :pos | | subMorph | subMorph := subMorphList at: pos. subMorph color: subMorph color negated. delay wait]]] fork. </lang>
smart BASIC
<lang qbasic>x=1!y=3!z=0 PRINT "Open doors: ";x;" "; DO
z=x+y PRINT z;" "; x=z y=y+2
UNTIL z>=100 END</lang>
SNOBOL4
unoptimized <lang snobol4> DEFINE('PASS(A,I),O') :(PASS.END) PASS O = 0 PASS.LOOP O = O + I EQ(A<O>,1) :S(PASS.1)F(PASS.0) PASS.0 A<O> = 1 :S(PASS.LOOP)F(RETURN) PASS.1 A<O> = 0 :S(PASS.LOOP)F(RETURN) PASS.END
MAIN D = ARRAY(100,0) I = 0
MAIN.LOOP I = LE(I,100) I + 1 :F(OUTPUT) PASS(D,I) :(MAIN.LOOP)
OUTPUT I = 1 ; OPEN = 'Opened doors are: ' OUTPUT.LOOP OPEN = OPEN EQ(D,1) " " I I = LE(I,100) I + 1 :S(OUTPUT.LOOP)F(OUTPUT.WRITE) OUTPUT.WRITE OUTPUT = OPEN
END </lang>
A run of this using CSNOBOL4 looks like this:
$ snobol4 100doors.sno
The Macro Implementation of SNOBOL4 in C (CSNOBOL4) Version 1.3+
by Philip L. Budne, January 23, 2011
SNOBOL4 (Version 3.11, May 19, 1975)
Bell Telephone Laboratories, Incorporated
No errors detected in source program
Opened doors are: 1 4 9 16 25 36 49 64 81 100
Normal termination at level 0
100doors.sno:18: Last statement executed was 19
(There are command flags to remove the header and the summary, but these have been left in to keep the original SNOBOL4 experience intact.)
optimized <lang snobol4> MAIN D = ARRAY(100,0) I = 1
MAIN.LOOP LE(I, 10) :F(OUTPUT) D = 1 I = I + 1 :(MAIN.LOOP)
OUTPUT I = 1 ; O = 'Opened doors are: ' OUTPUT.LOOP O = O EQ(D,1) " " I I = LE(I,100) I + 1 :S(OUTPUT.LOOP)F(OUTPUT.WRITE) OUTPUT.WRITE OUTPUT = O END </lang>
The output of this version is almost identical to the above.
Sparkling
unoptimized
<lang Sparkling>/* declare the variables */ var isOpen = {}; var pass, door;
/* initialize the doors */ for door = 0; door < 100; door++ { isOpen[door] = true; }
/* do the 99 remaining passes */ for pass = 1; pass < 100; ++pass { for door = pass; door < 100; door += pass+1 {
isOpen[door] = !isOpen[door];
} }
/* print the results */ var states = { true: "open", false: "closed" }; for door = 0; door < 100; door++ { printf("Door #%d is %s.\n", door+1, states[isOpen[door]]); }</lang>
optimized
<lang Sparkling>/* declare the variables */ var door_sqrt = 1; var door;
/* print the perfect square doors as open */ for door = 0; door < 100; door++ { if (door_sqrt*door_sqrt == door+1) { printf("Door #%d is open.\n", door+1); door_sqrt ++; } else { printf("Door #%d is closed.\n", door+1); } }</lang>
Spin
<lang Spin>con
_clkmode = xtal1+pll16x _clkfreq = 80_000_000
obj
ser : "FullDuplexSerial.spin"
pub init
ser.start(31, 30, 0, 115200)
doors
waitcnt(_clkfreq + cnt) ser.stop cogstop(0)
var
byte door[101] ' waste one byte by using only door[1..100]
pri doors | i,j
repeat i from 1 to 100 repeat j from i to 100 step i not door[j]
ser.str(string("Open doors: "))
repeat i from 1 to 100 if door[i] ser.dec(i) ser.tx(32)
ser.str(string(13,10))</lang>
- Output:
Open doors: 1 4 9 16 25 36 49 64 81 100
SQL
optimized <lang SQL> DECLARE @sqr int, @i int, @door int;
SELECT @sqr =1, @i = 3, @door = 1;
WHILE(@door <=100) BEGIN IF(@door = @sqr) BEGIN PRINT 'Door ' + RTRIM(CAST(@door as char)) + ' is open.'; SET @sqr= @sqr+@i; SET @i=@i+2; END ELSE BEGIN PRINT 'Door ' + RTRIM(CONVERT(char,@door)) + ' is closed.'; END SET @door = @door + 1 END
</lang>
SQL PL
With SQL only: <lang sql pl> --#SET TERMINATOR @
SET SERVEROUTPUT ON @
BEGIN
DECLARE TYPE DOORS_ARRAY AS BOOLEAN ARRAY [100]; DECLARE DOORS DOORS_ARRAY; DECLARE I SMALLINT; DECLARE J SMALLINT; DECLARE STATUS CHAR(10); DECLARE SIZE SMALLINT DEFAULT 100;
-- Initializes the array, with all spaces (doors) as false (closed). SET I = 1; WHILE (I <= SIZE) DO SET DOORS[I] = FALSE; SET I = I + 1; END WHILE;
-- Processes the doors. SET I = 1; WHILE (I <= SIZE) DO SET J = 1; WHILE (J <= SIZE) DO IF (MOD(J, I) = 0) THEN IF (DOORS[J] = TRUE) THEN SET DOORS[J] = FALSE; ELSE SET DOORS[J] = TRUE; END IF; END IF; SET J = J + 1; END WHILE; SET I = I + 1; END WHILE;
-- Prints the final status o the doors. SET I = 1; WHILE (I <= SIZE) DO SET STATUS = (CASE WHEN (DOORS[I] = TRUE) THEN 'OPEN' ELSE 'CLOSED' END); CALL DBMS_OUTPUT.PUT_LINE('Door ' || I || ' is '|| STATUS); SET I = I + 1; END WHILE;
END @ </lang> Output:
db2 -td@ db2 => BEGIN ... db2 (cont.) => END @ DB20000I The SQL command completed successfully. Door 1 is OPEN Door 2 is CLOSED Door 3 is CLOSED Door 4 is OPEN Door 5 is CLOSED Door 6 is CLOSED Door 7 is CLOSED Door 8 is CLOSED Door 9 is OPEN Door 10 is CLOSED Door 11 is CLOSED Door 12 is CLOSED Door 13 is CLOSED Door 14 is CLOSED Door 15 is CLOSED Door 16 is OPEN Door 17 is CLOSED Door 18 is CLOSED Door 19 is CLOSED Door 20 is CLOSED Door 21 is CLOSED Door 22 is CLOSED Door 23 is CLOSED Door 24 is CLOSED Door 25 is OPEN Door 26 is CLOSED Door 27 is CLOSED Door 28 is CLOSED Door 29 is CLOSED Door 30 is CLOSED Door 31 is CLOSED Door 32 is CLOSED Door 33 is CLOSED Door 34 is CLOSED Door 35 is CLOSED Door 36 is OPEN Door 37 is CLOSED Door 38 is CLOSED Door 39 is CLOSED Door 40 is CLOSED Door 41 is CLOSED Door 42 is CLOSED Door 43 is CLOSED Door 44 is CLOSED Door 45 is CLOSED Door 46 is CLOSED Door 47 is CLOSED Door 48 is CLOSED Door 49 is OPEN Door 50 is CLOSED Door 51 is CLOSED Door 52 is CLOSED Door 53 is CLOSED Door 54 is CLOSED Door 55 is CLOSED Door 56 is CLOSED Door 57 is CLOSED Door 58 is CLOSED Door 59 is CLOSED Door 60 is CLOSED Door 61 is CLOSED Door 62 is CLOSED Door 63 is CLOSED Door 64 is OPEN Door 65 is CLOSED Door 66 is CLOSED Door 67 is CLOSED Door 68 is CLOSED Door 69 is CLOSED Door 70 is CLOSED Door 71 is CLOSED Door 72 is CLOSED Door 73 is CLOSED Door 74 is CLOSED Door 75 is CLOSED Door 76 is CLOSED Door 77 is CLOSED Door 78 is CLOSED Door 79 is CLOSED Door 80 is CLOSED Door 81 is OPEN Door 82 is CLOSED Door 83 is CLOSED Door 84 is CLOSED Door 85 is CLOSED Door 86 is CLOSED Door 87 is CLOSED Door 88 is CLOSED Door 89 is CLOSED Door 90 is CLOSED Door 91 is CLOSED Door 92 is CLOSED Door 93 is CLOSED Door 94 is CLOSED Door 95 is CLOSED Door 96 is CLOSED Door 97 is CLOSED Door 98 is CLOSED Door 99 is CLOSED Door 100 is OPEN
Standard ML
<lang SML> datatype Door = Closed | Opened
fun toggle Closed = Opened
| toggle Opened = Closed
fun pass (step, doors) = List.map (fn (index, door) => if (index mod step) = 0 then (index, toggle door) else (index, door)) doors
(* [1..n] *) fun runs n = List.tabulate (n, fn k => k+1)
fun run n =
let
val initialdoors = List.tabulate (n, fn i => (i+1, Closed)) val counter = runs n
in
foldl pass initialdoors counter
end
fun opened_doors n = List.mapPartial (fn (index, Closed) => NONE | (index, Opened) => SOME (index)) (run n) </lang>
- Output:
- opened_doors 100; val it = [1,4,9,16,25,36,49,64,81,100] : int list
Stata
<lang stata>clear set obs 100 gen doors=0 gen index=_n forvalues i=1/100 { quietly replace doors=!doors if mod(_n,`i')==0 } list index if doors, noobs noheader
+-------+ | 1 | | 4 | | 9 | | 16 | | 25 | |-------| | 36 | | 49 | | 64 | | 81 | | 100 | +-------+</lang>
SuperCollider
<lang SuperCollider>( var n = 100, doors = false ! n; var pass = { |j| (0, j .. n-1).do { |i| doors[i] = doors[i].not } }; (1..n-1).do(pass); doors.selectIndices { |open| open }; // all are closed except [ 0, 1, 4, 9, 16, 25, 36, 49, 64, 81 ] )</lang>
Swift
unoptimized
<lang Swift>/* declare enum to identify the state of a door */ enum DoorState : String {
case Opened = "Opened" case Closed = "Closed"
}
/* declare list of doors state and initialize them */ var doorsStateList = [DoorState](count: 100, repeatedValue: DoorState.Closed)
/* do the 100 passes */ for i in 1...100 {
/* map on a strideTo instance to only visit the needed doors on each iteration */ map(stride(from: i - 1, to: 100, by: i)) { doorsStateList[$0] = doorsStateList[$0] == .Opened ? .Closed : .Opened }
}
/* print the results */ for (index, item) in enumerate(doorsStateList) {
println("Door \(index+1) is \(item.rawValue)")
}</lang>
optimized
<lang Swift>/* declare enum to identify the state of a door */ enum DoorState : String {
case Opened = "Opened" case Closed = "Closed"
}
/* declare list of doors state and initialize them */ var doorsStateList = [DoorState](count: 100, repeatedValue: DoorState.Closed)
/* set i^2 doors to opened */ var i = 1 do {
doorsStateList[(i*i)-1] = DoorState.Opened ++i
} while (i*i) <= doorsStateList.count
/* print the results */ for (index, item) in enumerate(doorsStateList) {
println("Door \(index+1) is \(item.rawValue)")
}</lang>
Tailspin
<lang tailspin> source hundredDoors
@: [ 1..100 -> 0 ]; templates toggle def jump: $; $jump..100:$jump -> \(when <?($@hundredDoors($) <=0>)> do @hundredDoors($): 1; otherwise @hundredDoors($): 0;\) -> !VOID end toggle 1..100 -> toggle -> !VOID $@ -> \[i](<=1> ' $i;' !\) !
end hundredDoors
$hundredDoors -> 'Open doors:$...;' -> !OUT::write </lang>
- Output:
Open doors: 1 4 9 16 25 36 49 64 81 100
Tcl
unoptimized
<lang tcl>package require Tcl 8.5 set n 100 set doors [concat - [lrepeat $n 0]] for {set step 1} {$step <= $n} {incr step} {
for {set i $step} {$i <= $n} {incr i $step} { lset doors $i [expr { ! [lindex $doors $i]}] }
} for {set i 1} {$i <= $n} {incr i} {
puts [format "door %d is %s" $i [expr {[lindex $doors $i] ? "open" : "closed"}]]
}</lang>
optimized
<lang tcl>package require Tcl 8.5 set doors [lrepeat [expr {$n + 1}] closed] for {set i 1} {$i <= sqrt($n)} {incr i} {
lset doors [expr {$i ** 2}] open
} for {set i 1} {$i <= $n} {incr i} {
puts [format "door %d is %s" $i [lindex $doors $i]]
}</lang>
graphical
Inspired by the E solution, here's a visual representation <lang tcl>package require Tcl 8.5 package require Tk
array set door_status {}
- create the gui
set doors [list x] for {set i 0} {$i < 10} {incr i} {
for {set j 0} {$j < 10} {incr j} { set k [expr {1 + $j + 10*$i}] lappend doors [radiobutton .d_$k -text $k -variable door_status($k) \ -indicatoron no -offrelief flat -width 3 -value open] grid [lindex $doors $k] -column $j -row $i }
}
- create the controls
button .start -command go -text Start label .i_label -text " door:" entry .i -textvariable i -width 4 label .step_label -text " step:" entry .step -textvariable step -width 4 grid .start - .i_label - .i - .step_label - .step - -row $i grid configure .start -sticky ew grid configure .i_label .step_label -sticky e grid configure .i .step -sticky w
proc go {} {
global doors door_status i step
# initialize the door_status (all closed) for {set d 1} {$d <= 100} {incr d} { set door_status($d) closed } # now, begin opening and closing for {set step 1} {$step <= 100} {incr step} { for {set i 1} {$i <= 100} {incr i} { if {$i % $step == 0} { [lindex $doors $i] [expr {$door_status($i) eq "open" ? "deselect" : "select"}] update after 50 } } }
}</lang>
TI-83 BASIC
Naive
seq(0,X,1,100 For(X,1,100 0 or Ans-not(fPart(cumSum(1 or Ans)/A End Pause Ans
A-1cumsum(1 or Ans should be able to replace cumsum(1 or Ans)/A (saving a byte because of the unnecessary closing parenthesis) but it falls victim to a rounding error that causes X^(-1)*X to be stored as 0.99999999999999... (although it's still displayed as the original X). When the fPart( [fractional part] command evaluates this, it returns .999999999, which not( turns to 0 (meaning a closed door). Regular division, as shown, isn't prone to this.
Optimized
Pause not(fPart(√(seq(X,X,1,100
TI-89 BASIC
<lang ti89b>Define doors(fast) = Func
Local doors,i,j seq(false,x,1,100) ? doors If fast Then For i,1,10,1 true ? doors[i^2] EndFor Else For i,1,100,1 For j,i,100,i not doors[j] ? doors[j] EndFor EndFor EndIf Return doors
EndFunc</lang>
TorqueScript
<lang Torque>for(%steps = 1; %a <= 100; %a++) for(%current = %steps; %current <= 100; %current += %steps) %door[%current] = !%door[%current]; for(%a = 1; %a <= 100; %a++) echo("Door #" @ %a @ " is" SPC %door[%current] ? "Open" : "Closed" @ ".");</lang>
Transact-SQL
<lang sql> WITH OneToTen (N) AS ( SELECT N
FROM ( VALUES (0), (1), (2), (3), (4), (5), (6), (7), (8), (9) ) V(N) ) , InitDoors (Num, IsOpen)
AS ( SELECT 1
+ 1 * Units.N + 10 * Tens.N As Num , Convert(Bit, 0) As IsOpen FROM OneToTen As Units CROSS JOIN OneToTen As Tens ) -- This part could be easier with a tally table or equivalent table-valued function , States (NbStep, Num, IsOpen)
AS ( SELECT 0 As NbStep
, Num , IsOpen FROM InitDoors As InitState UNION ALL SELECT 1 + NbStep , Num , CASE Num % (1 + NbStep) WHEN 0 THEN ~IsOpen ELSE IsOpen END FROM States WHERE NbStep < 100 )
SELECT Num As DoorNumber
, Concat( 'Door number ', Num, ' is ' , CASE IsOpen WHEN 1 THEN ' open' ELSE ' closed' END ) As Result -- Concat needs SQL Server 2012
FROM States WHERE NbStep = 100 ORDER By Num
- -- Fortunately, maximum recursion is 100 in SQL Server.
-- For more doors, the MAXRECURSION hint should be used. -- More doors would also need an InitDoors with more rows. </lang>
School example
<lang Transact-SQL>SET NOCOUNT ON;
-- Doors can be open or closed. DECLARE @open CHAR(1) = 'O'; DECLARE @closed CHAR(1) = 'C';
-- There are 100 doors in a row that are all initially closed. DECLARE @doorsCount INT = 100; DECLARE @doors TABLE (doorKey INT PRIMARY KEY, doorState CHAR(1)); WITH sample100 AS (
SELECT TOP(100) object_id FROM sys.objects
) INSERT @doors
SELECT ROW_NUMBER() OVER (ORDER BY A.object_id) AS doorKey, @closed AS doorState FROM sample100 AS A CROSS JOIN sample100 AS B CROSS JOIN sample100 AS C CROSS JOIN sample100 AS D ORDER BY 1 OFFSET 0 ROWS FETCH NEXT @doorsCount ROWS ONLY;
-- You make 100 passes by the doors, visiting every door and toggle the door (if -- the door is closed, open it; if it is open, close it), according to the rules -- of the task. DECLARE @pass INT = 1; WHILE @pass <= @doorsCount BEGIN
UPDATE @doors SET doorState = CASE doorState WHEN @open THEN @closed ELSE @open END WHERE doorKey >= @pass AND doorKey % @pass = 0;
SET @pass = @pass + 1;
END;
-- Answer the question: what state are the doors in after the last pass? -- The answer as the query result is: SELECT doorKey, doorState FROM @doors; -- The answer as the console output is: DECLARE @log VARCHAR(max); DECLARE @doorKey INT = (SELECT MIN(doorKey) FROM @doors); WHILE @doorKey <= @doorsCount BEGIN
SET @log = ( SELECT TOP(1) CONCAT('Doors ', doorKey, ' are ', CASE doorState WHEN @open THEN ' open' ELSE 'closed' END, '.') FROM @doors WHERE doorKey = @doorKey ); RAISERROR (@log, 0, 1) WITH NOWAIT;
SET @doorKey = (SELECT MIN(doorKey) FROM @doors WHERE doorKey > @doorKey);
END;
-- Which are open, which are closed? -- The answer as the query result is: SELECT doorKey, doorState FROM @doors WHERE doorState = @open; SELECT doorKey, doorState FROM @doors WHERE doorState = @closed; -- The answer as the console output is: SET @log = (
SELECT CONCAT('These are open doors: ', STRING_AGG(CAST(doorKey AS VARCHAR(max)), ', '), '.') FROM @doors WHERE doorState = @open
); RAISERROR (@log, 0, 1) WITH NOWAIT; SET @log = (
SELECT CONCAT('These are closed doors: ', STRING_AGG(CAST(doorKey AS VARCHAR(max)), ', '), '.') FROM @doors WHERE doorState = @closed
); RAISERROR (@log, 0, 1) WITH NOWAIT;
-- Assert: DECLARE @expected TABLE (doorKey INT PRIMARY KEY); SET @doorKey = 1; WHILE @doorKey * @doorKey <= @doorsCount BEGIN
INSERT @expected VALUES (@doorKey * @doorKey); SET @doorKey = @doorKey + 1;
END; IF NOT EXISTS (
SELECT doorKey FROM @doors WHERE doorState = @open EXCEPT SELECT doorKey FROM @expected ) AND NOT EXISTS ( SELECT doorKey FROM @expected EXCEPT SELECT doorKey FROM @doors WHERE doorState = @open ) PRINT 'The task is solved.';
ELSE
THROW 50000, 'These arent the doors youre looking for.', 1;</lang>
Transd
<lang scheme>#lang transd
MainModule: {
doors: Vector<Bool>(100), _start: (λ (for i in Seq(100) do (for k in Seq(i 100 (+ i 1)) do (set-el doors k (not (get doors k))) ))
(for i in Seq(100) do (if (get doors i) (textout (+ i 1) " ")) ))
}
</lang>
- Output:
1 4 9 16 25 36 49 64 81 100
True BASIC
<lang basic> ! Optimized solution with True BASIC
OPTION NOLET x = 1 y = 3 z = 0 PRINT STR$(x) & " Open" DO UNTIL z >= 100 z = x + y PRINT STR$(z) & " Open" x = z y = y + 2 LOOP
END </lang>
TSE SAL
<lang TSE SAL>
// library: math: get: task: door: open: close100 <description></description> <version control></version control> <version>1.0.0.0.11</version> <version control></version control> (filenamemacro=getmaocl.s) [<Program>] [<Research>] [kn, ri, mo, 31-12-2012 22:03:16] PROC PROCMathGetTaskDoorOpenClose( INTEGER doorMaxI, INTEGER passMaxI )
// e.g. PROC Main() // e.g. PROCMathGetTaskDoorOpenClose( 100, 100 ) // e.g. END // e.g. // e.g. <F12> Main() // // === // // The output will be: // // door 1 is open // door 4 is open // door 9 is open // door 16 is open // door 25 is open // door 36 is open // door 49 is open // door 64 is open // door 81 is open // door 100 is open // all other doors are closed // // === // INTEGER passMinI = 1 INTEGER passI = 0 // INTEGER doorminI = 1 INTEGER doorI = 0 // STRING s[255] = "" // INTEGER bufferI = 0 // PushPosition() bufferI = CreateTempBuffer() PopPosition() // FOR doorI = doorMinI TO doorMaxI // SetGlobalInt( Format( "doorsI", doorI ), 0 ) // ENDFOR // FOR passI = passMinI TO passMaxI // doorI = passI - passI // REPEAT // doorI = doorI + passI // SetGlobalInt( Format( "doorsI", doorI ), NOT( GetGlobalInt( Format( "doorsI", doorI ) ) ) ) // UNTIL ( doorI >= doorMaxI ) // ENDFOR // FOR doorI = doorMinI TO doorMaxI // IF ( GetGlobalInt( Format( "doorsI", doorI ) ) > 0 ) // s = "open" // AddLine( Format( "door", " ", doorI, " ", "is", " ", s ), bufferI ) // ELSE // s = "closed" // ENDIF // ENDFOR // AddLine( "all other doors are closed", bufferI ) // GotoBufferId( bufferI ) //
END
PROC Main()
PROCMathGetTaskDoorOpenClose( 100, 100 )
END
</lang>
TUSCRIPT
<lang tuscript> $$ MODE TUSCRIPT DICT doors create COMPILE LOOP door=1,100
LOOP pass=1,100 SET go=MOD (door,pass) DICT doors lookup door,num,cnt,status IF (num==0) THEN SET status="open" DICT doors add door,num,cnt,status ELSE IF (go==0) THEN IF (status=="closed") THEN SET status="open" ELSE SET status="closed" ENDIF DICT doors update door,num,cnt,status ENDIF ENDIF ENDLOOP
ENDLOOP ENDCOMPILE DICT doors unload door,num,cnt,status </lang> Output (variable status):
status = * 1 = open 2 = closed 3 = closed 4 = open 5 = closed 6 = closed 7 = closed 8 = closed 9 = open 10 = closed 11 = closed 12 = closed 13 = closed 14 = closed 15 = closed 16 = open 17 = closed 18 = closed 19 = closed 20 = closed 21 = closed 22 = closed 23 = closed 24 = closed 25 = open 26 = closed 27 = closed 28 = closed 29 = closed 30 = closed 31 = closed 32 = closed 33 = closed 34 = closed 35 = closed 36 = open 37 = closed 38 = closed 39 = closed 40 = closed 41 = closed 42 = closed 43 = closed 44 = closed 45 = closed 46 = closed 47 = closed 48 = closed 49 = open 50 = closed 51 = closed 52 = closed 53 = closed 54 = closed 55 = closed 56 = closed 57 = closed 58 = closed 59 = closed 60 = closed 61 = closed 62 = closed 63 = closed 64 = open 65 = closed 66 = closed 67 = closed 68 = closed 69 = closed 70 = closed 71 = closed 72 = closed 73 = closed 74 = closed 75 = closed 76 = closed 77 = closed 78 = closed 79 = closed 80 = closed 81 = open 82 = closed 83 = closed 84 = closed 85 = closed 86 = closed 87 = closed 88 = closed 89 = closed 90 = closed 91 = closed 92 = closed 93 = closed 94 = closed 95 = closed 96 = closed 97 = closed 98 = closed 99 = closed 100 = open
TypeScript
<lang typescript> interface Door {
id: number; open: boolean;
}
function doors(): Door[] {
var Doors: Door[] = [];
for (let i = 1; i <= 100; i++) { Doors.push({id: i, open: false}); }
for (let secuence of Doors) { for (let door of Doors) { if (door.id % secuence.id == 0) { door.open = !door.open; } } }
return Doors.filter(a => a.open);
} </lang>
TXR
<lang txrlisp>(defun hyaku-mai-tobira ()
(let ((doors (vector 100))) (each ((i (range 0 99))) (each ((j (range i 99 (+ i 1)))) (flip [doors j]))) doors))
(each ((counter (range 1))
(door (hyaku-mai-tobira))) (put-line `door @counter is @(if door "open" "closed")`))</lang>
uBasic/4tH
Deliberately unoptimized. <lang>FOR p = 1 TO 100
FOR d = p TO 100 STEP p @(d) = @(d) = 0 NEXT d
NEXT p
FOR d= 1 TO 100
IF @(d) PRINT "Door ";d;" is open"
NEXT d</lang>
Uniface
unoptimized
<lang Uniface> entry LP_DO_IT
variables string V_DOORS boolean V_DOOR_STATE string V_DOOR_STATE_S numeric V_IDX numeric V_TOTAL_DOORS string V_DOOR_STATE_LIST numeric V_LOOP_COUNT endvariables
V_TOTAL_DOORS = 100 putitem V_DOORS, V_TOTAL_DOORS, 0
V_DOORS = $replace (V_DOORS, 1, "·;", "·;0", -1)
putitem/id V_DOOR_STATE_LIST, "1", "Open" putitem/id V_DOOR_STATE_LIST, "0", "Close"
V_LOOP_COUNT = 1 while (V_LOOP_COUNT <= V_TOTAL_DOORS) V_IDX = 0 V_IDX = V_IDX + V_LOOP_COUNT
getitem V_DOOR_STATE, V_DOORS, V_IDX while (V_IDX <= V_TOTAL_DOORS)
V_DOOR_STATE = !V_DOOR_STATE getitem/id V_DOOR_STATE_S, V_DOOR_STATE_LIST, $number(V_DOOR_STATE) putitem V_DOORS, V_IDX, V_DOOR_STATE
V_IDX = V_IDX + V_LOOP_COUNT getitem V_DOOR_STATE, V_DOORS, V_IDX endwhile
V_LOOP_COUNT = V_LOOP_COUNT + 1
endwhile
V_IDX = 1 getitem V_DOOR_STATE, V_DOORS, V_IDX while (V_IDX <= V_TOTAL_DOORS) getitem/id V_DOOR_STATE_S, V_DOOR_STATE_LIST, $number(V_DOOR_STATE) if (V_DOOR_STATE) putmess "Door %%V_IDX%%% is finally %%V_DOOR_STATE_S%%%" endif
V_IDX = V_IDX + 1 getitem V_DOOR_STATE, V_DOORS, V_IDX endwhile
end ; LP_DO_IT
</lang>
- Output:
Door 1 is finally Open Door 4 is finally Open Door 9 is finally Open Door 16 is finally Open Door 25 is finally Open Door 36 is finally Open Door 49 is finally Open Door 64 is finally Open Door 81 is finally Open Door 100 is finally Open
Unison
<lang Unison>hundredDoors : [Boolean] hundredDoors =
toggleEachNth : Nat -> [Boolean] -> [Boolean] toggleEachNth n doors = go counter = cases [] -> [] (d +: ds) -> if counter == n then (not d) +: go 1 ds else d +: go (counter+1) ds
go 1 doors
foldr toggleEachNth (replicate 100 'false) (range 1 101)
results = filterMap (cases (open, ix) -> if open then Some (ix+1) else None)
(indexed hundredDoors)</lang>
UNIX Shell
<lang bash>#! /bin/bash
declare -a doors for((i=1; i <= 100; i++)); do
doors[$i]=0
done
for((i=1; i <= 100; i++)); do
for((j=i; j <= 100; j += i)); do
echo $i $j doors[$j]=$(( doors[j] ^ 1 ))
done
done
for((i=1; i <= 100; i++)); do
if [[ ${doors[$i]} -eq 0 ]]; then
op="closed"
else
op="open"
fi echo $i $op
done</lang>
Optimised version <lang bash>#!/bin/bash
for i in {1..100}; do
door[$i*$i]=1 [ -z ${door[$i]} ] && echo "$i closed" || echo "$i open"
done</lang>
Ursa
<lang>
- 100 doors
decl int i j decl boolean<> doors
- append 101 boolean values to doors stream
for (set i 0) (or (< i 100) (= i 100)) (inc i)
append false doors
end for
- loop through, opening and closing doors
for (set i 1) (or (< i 100) (= i 100)) (inc i)
for (set j i) (or (< j 100) (= j 100)) (inc j) if (= (mod j i) 0) set doors<j> (not doors<j>) end if end for
end for
- loop through and output which doors are open
for (set i 1) (or (< i 100) (= i 100)) (inc i)
out "Door " i ": " console if doors out "open" endl console else out "closed" endl console end if
end if </lang>
Ursala
The doors are represented as a list of 100 booleans initialized to false. The pass function takes a number and a door list to a door list with doors toggled at indices that are multiples of the number. The main program folds the pass function (to the right) over the list of pass numbers from 100 down to 1, numbers the result, and filters out the numbers of the open doors. <lang Ursala>#import std
- import nat
doors = 0!* iota 100
pass("n","d") = remainder\"n"?l(~&r,not ~&r)* num "d"
- cast %nL
main = ~&rFlS num pass=>doors nrange(100,1)</lang> optimized version: <lang Ursala>#import nat
- cast %nL
main = product*tiiXS iota10</lang> output:
<1,4,9,16,25,36,49,64,81>
UTFool
<lang UTFool> ··· http://rosettacode.org/wiki/100_doors ··· ■ HundredDoors
§ static ▶ main • args⦂ String[] open⦂ boolean: true closed⦂ boolean: false doors⦂ boolean[1+100] · all initially closed 🔁 pass from 1 to 100 ∀ visited ∈ pass‥100 by pass · toggle the visited doors if the doors[visited] are closed let the doors[visited] be open else let the doors[visited] be closed for each door #n in doors⦂ boolean if the door is open System.out.println "Door #⸨n⸩ is open."
</lang>
Vala
Unoptimized <lang vala>int main() { bool doors_open[101]; for(int i = 1; i < doors_open.length; i++) { for(int j = 1; i*j < doors_open.length; j++) { doors_open[i*j] = !doors_open[i*j]; } stdout.printf("%d: %s\n", i, (doors_open[i] ? "open" : "closed")); } return 0; }</lang> Output:
1: open 2: closed 3: closed 4: open 5: closed 6: closed 7: closed 8: closed 9: open 10: closed 11: closed ...
Optimized <lang vala>int main() { int i = 1; while(i*i <= 100) { stdout.printf("${i*i} open\n"); i++; } return 0; }</lang> Output:
1 open 4 open 9 open 16 open 25 open 36 open 49 open 64 open 81 open 100 open
VAX Assembly
<lang VAX Assembly>
00000064 0000 1 n = 100 0000 0000 2 .entry doors, ^m<> 26'AF 9F 0002 3 pushab b^arr ; offset signed byte 50 64 8F 9A 0005 4 movzbl #n, r0 50 DD 0009 5 pushl r0 ; (sp) -> .ascid arr 000B 6 10$: 51 50 D0 000B 7 movl r0, r1 ; step = start index 000E 8 20$: 25'AF41 01 8C 000E 9 xorb2 #^a"0" \^a"1", b^arr-1[r1] ; \ xor toggle "1"<->"0" FFF5 51 50 6E F1 0013 10 acbl (sp), r0, r1, 20$ ; limit, step, index EF 50 F5 0019 11 sobgtr r0, 10$ ; n..1 001C 12 5E DD 001C 13 pushl sp ; descriptor by reference 00000000'GF 01 FB 001E 14 calls #1, g^lib$put_output ; show result 04 0025 15 ret 0026 16
30'30'30'30'30'30'30'30'30'30'30'30' 0026 17 arr: .byte ^a"0"[n] 30'30'30'30'30'30'30'30'30'30'30'30' 0032 30'30'30'30'30'30'30'30'30'30'30'30' 003E 30'30'30'30'30'30'30'30'30'30'30'30' 004A 30'30'30'30'30'30'30'30'30'30'30'30' 0056 30'30'30'30'30'30'30'30'30'30'30'30' 0062 30'30'30'30'30'30'30'30'30'30'30'30' 006E 30'30'30'30'30'30'30'30'30'30'30'30' 007A
30'30'30'30' 0086 008A 18 .end doors
$ run doors 1001000010000001000000001000000000010000000000001000000000000001000000000000000010000000000000000001 </lang>
VBA
<lang vb> Sub Rosetta_100Doors() Dim Door(100) As Boolean, i As Integer, j As Integer For i = 1 To 100 Step 1
For j = i To 100 Step i Door(j) = Not Door(j) Next j If Door(i) = True Then Debug.Print "Door " & i & " is Open" Else Debug.Print "Door " & i & " is Closed" End If
Next i End Sub
- USE THIS ONE, SEE COMMENTED LINES, DONT KNOW WHY EVERYBODY FOLLOWED OTHERS ANSWERS AND CODED THE PROBLEM DIFFERENTLY ***
- ALWAYS USE AND TEST A READABLE, EASY TO COMPREHEND CODING BEFORE 'OPTIMIZING' YOUR CODE AND TEST THE 'OPTIMIZED' CODE AGAINST THE 'READABLE' ONE.
Panikkos Savvides.
Sub Rosetta_100Doors2()
Dim Door(100) As Boolean, i As Integer, j As Integer
Dim strAns As String
' There are 100 doors in a row that are all initially closed.
' You make 100 passes by the doors.
For j = 1 To 100
' The first time through, visit every door and toggle the door ' (if the door is closed, open it; if it is open, close it). For i = 1 To 100 Step 1 Door(i) = Not Door(i) Next i ' The second time, only visit every 2nd door (door #2, #4, #6, ...), and toggle it. For i = 2 To 100 Step 2 Door(i) = Not Door(i) Next i ' The third time, visit every 3rd door (door #3, #6, #9, ...), etc, until you only visit the 100th door. For i = 3 To 100 Step 3 Door(i) = Not Door(i) Next i
Next j
For j = 1 To 100
If Door(j) = True Then strAns = j & strAns & ", " End If
Next j
If Right(strAns, 2) = ", " Then strAns = Left(strAns, Len(strAns) - 2) If Len(strAns) = 0 Then strAns = "0" Debug.Print "Doors [" & strAns & "] are open, the rest are closed." ' Doors [0] are open, the rest are closed., AKA ZERO DOORS OPEN End Sub </lang>
VBScript
Unoptimized <lang VBScript>Dim doorIsOpen(100), pass, currentDoor, text
For currentDoor = 0 To 99 doorIsOpen(currentDoor) = False Next
For pass = 0 To 99 For currentDoor = pass To 99 Step pass + 1 doorIsOpen(currentDoor) = Not doorIsOpen(currentDoor) Next Next
For currentDoor = 0 To 99 text = "Door #" & currentDoor + 1 & " is " If doorIsOpen(currentDoor) Then text = text & "open." Else text = text & "closed." End If WScript.Echo(text) Next</lang>
Vedit macro language
Unoptimized
This implementation uses a free edit buffer as data array and for displaying the results.
A closed door is represented by a character '-' and an open door by character 'O'.
<lang vedit>Buf_Switch(Buf_Free)
Ins_Char('-', COUNT, 100) // All doors closed
for (#1 = 1; #1 <= 100; #1++) {
for (#2 = #1; #2 <= 100; #2 += #1) { Goto_Col(#2) Ins_Char((Cur_Char^0x62), OVERWRITE) // Toggle between '-' and 'O' }
}</lang>
Optimized <lang vedit>Buf_Switch(Buf_Free) Ins_Char('-', COUNT, 100) for (#1=1; #1 <= 10; #1++) {
Goto_Col(#1*#1) Ins_Char('O', OVERWRITE)
}</lang>
Output:
O--O----O------O--------O----------O------------O--------------O----------------O------------------O
Verilog
<lang Verilog> module main;
integer i; initial begin $display("Las siguientes puertas están abiertas:"); for (i=1; i<=10; i=i+1) if (i%i*i<11) $display(i*i); $finish ; end
endmodule </lang>
VHDL
unoptimized <lang vhdl>library IEEE; use IEEE.STD_LOGIC_1164.ALL;
entity DOORS is port (CLK: in std_logic; OUTPUT: out std_logic_vector(1 to 100)); end DOORS;
architecture Behavioral of DOORS is begin process (CLK) variable TEMP: std_logic_vector(1 to 100); begin --setup closed doors TEMP := (others => '0');
--looping through for i in 1 to TEMP'length loop for j in i to TEMP'length loop if (j mod i) = 0 then TEMP(j) := not TEMP(j); end if; end loop; end loop;
--assign output OUTPUT <= TEMP; end process; end Behavioral; </lang>
unoptimized and synthesizable <lang VHDL>LIBRARY ieee; USE ieee.std_logic_1164.all;
entity doors is
port ( clk : in std_logic; reset : in std_logic; door : buffer std_logic_vector(1 to 100) );
end entity doors;
architecture rtl of doors is
signal step : integer range 1 to 101; signal addr : integer range 1 to 201;
begin
proc_step: process(clk, reset) begin if reset = '1' then step <= 1; addr <= 1; door <= (others => '0'); elsif rising_edge(clk) then if addr <= 100 then door(addr) <= not door(addr); addr <= addr + step; elsif step <= 100 then addr <= step + 1; step <= step + 1; end if; end if; end process;
end;</lang>The synthesis requires 116 FFs plus combinatorial logic. The result is stable after 581 clock cycles.
Visual Basic
<lang vb> Public Sub Doors100()
' the state of a door is represented by the data type boolean (false = door closed, true = door opened) Dim doorstate(1 To 100) As Boolean ' the doorstate()-array is initialized by VB with value 'false' Dim i As Long, j As Long For i = 1 To 100 For j = i To 100 Step i doorstate(j) = Not doorstate(j) Next j Next i Debug.Print "The following doors are open:" For i = 1 To 100 ' print number if door is openend If doorstate(i) Then Debug.Print CStr(i) Next i
End Sub </lang> Output:
The following doors are open: 1 4 9 16 25 36 49 64 81 100
Visual Basic .NET
unoptimized <lang vbnet>Module Module1
Sub Main() Dim doors(100) As Boolean 'Door 1 is at index 0
For pass = 1 To 100 For door = pass - 1 To 99 Step pass doors(door) = Not doors(door) Next Next
For door = 0 To 99 Console.WriteLine("Door # " & (door + 1) & " is " & If(doors(door), "Open", "Closed")) Next
Console.ReadLine() End Sub
End Module</lang> optimized <lang vbnet>Module Module1
Sub Main() Dim doors(100) As Boolean 'Door 1 is at index 0
For i = 1 To 10 doors(i ^ 2 - 1) = True Next
For door = 0 To 99 Console.WriteLine("Door # " & (door + 1) & " is " & If(doors(door), "Open", "Closed")) Next
Console.ReadLine() End Sub
End Module</lang>
Vlang
Unoptimized
<lang go>const number_doors = 101
fn main() {
mut closed_doors := []bool{len: number_doors, init: true} for pass in 0..number_doors { for door := 0; door < number_doors; door += pass + 1 { closed_doors[door] = !closed_doors[door] } } for pass in 1..number_doors { if !closed_doors[pass] { println('Door #$pass Open') } }
}</lang> Output:
Door #1 Open Door #4 Open Door #9 Open Door #16 Open Door #25 Open Door #36 Open Door #49 Open Door #64 Open Door #81 Open Door #100 Open
Optimised GO Inspired
<lang go>const door_number = 100
fn main(){
mut doors := []bool{ len: door_number, init: false } //true open false closed
mut door_nbr := 1 mut increment := 0
for current in 1..( door_number + 1) { if current == door_nbr { doors[current - 1] = true increment++ door_nbr += 2 * increment + 1 } } doors.map( fn( it bool) bool { // graphically represent opened doors print( if it {( 'O')} else {('=')} ) return it }) println()
} </lang>
Output:
O==O====O======O========O==========O============O==============O================O==================O
VTL-2
<lang VTL2>10 D=1 20 :D)=0 30 D=D+1 40 #=100>D*20 50 P=1 60 D=P 70 :D)=:D)=0 80 D=D+P 90 #=100>D*70 100 P=P+1 110 #=100>P*60 120 D=1 130 #=:D)*170 140 D=D+1 150 #=100>D*130 160 #=999 170 ?="DOOR "; 180 ?=D 190 ?=" IS OPEN" 200 #=!</lang>
- Output:
DOOR 1 IS OPEN DOOR 4 IS OPEN DOOR 9 IS OPEN DOOR 16 IS OPEN DOOR 25 IS OPEN DOOR 36 IS OPEN DOOR 49 IS OPEN DOOR 64 IS OPEN DOOR 81 IS OPEN DOOR 100 IS OPEN
Wart
<lang python>def (doors n)
let door (table) for step 1 (step <= n) ++step for j 0 (j < n) (j <- j+step) zap! not door.j
for j 0 (j < n) ++j when door.j pr j pr " "</lang>
WDTE
<lang WDTE>let a => import 'arrays'; let s => import 'stream'; let io => import 'io';
let toggle doors m => a.stream doors -> s.enumerate -> s.map (@ s n => [+ (a.at n 0) 1; a.at n 1]) -> s.map (@ s n => switch n { (@ s n => == (% (a.at n 0) m) 0) => ! (a.at n 1); true => a.at n 1; }) -> s.collect ;
s.range 100 -> s.map false -> s.collect : doors -> s.range 1 100 -> s.reduce doors toggle -> a.stream -> s.map (@ s n => switch 0 { n => 'Open'; true => 'Closed'; } -- io.writeln io.stdout) -> s.drain
- </lang>
Not the most efficient code, to say the least. This has a few more allocations than should sanely be used for a problem like this.
Wortel
<lang wortel>; unoptimized +^[
@var doors [] @for i rangei [1 100] @for j rangei [i 100 i] :!@not `j doors @for i rangei [1 100] @if `i doors !console.log "door {i} is open"
]
- optimized, map square over 1 to 10
!*^@sq @to 10</lang>
Wrapl
Unoptimized <lang wrapl>MOD Doors;
IMP Agg.Table; IMP Std.String; IMP IO.Terminal USE Out;
VAR door <- {}; EVERY door[1:to(100), "closed"];
DEF toggle(num) door[num] <- door[num] = "open" => "closed" // "open";
EVERY WITH pass <- 1:to(100), num <- pass:to(100, pass) DO toggle(num);
Out:write('Doors {door @ String.T}.');
END Doors.</lang> Optimized <lang wrapl>MOD Doors;
IMP IO.Terminal USE Out;
DEF open <- ALL 1:to(100) ^ 2 \ $ <= 100; DEF closed <- ALL 1:to(100) \ NOT $ IN open;
Out:write('Doors {open} are open.\n'); Out:write('Doors {closed} are closed.\n');
END Doors.</lang>
Wren
Unoptimized <lang ecmascript>var doors = [true] * 100 for (i in 1..100) {
var j = i while (j < 100) { doors[j] = !doors[j] j = j + i + 1 }
}
for (i in 0...100) {
if (doors[i]) System.write("%(i + 1) ")
} System.print()</lang>
Optimized <lang ecmascript>var door = 1 var increment = 3 while (door <= 100) {
System.write("%(door) ") door = door + increment increment = increment + 2
} System.print()</lang>
- Output:
For both versions:
1 4 9 16 25 36 49 64 81 100
X86 Assembly
<lang X86 Assembly>
.NOLIST
- The task can be completed in 48 and "half" steps
- On the first pass ALL doors are opened.
- On the second pass every EVEN door is closed.
- So, instead of all closed, the doors can initially be
- Every odd door open, every even door closed and start at pass 3.
- On 51st and all the next passes, only one door is visited per pass
- On 51st pass door 51, on 52nd pass door 52 etc.
- So, after pass 50, we can make "half a pass" starting with door 51
- and toggling every door up to and including 100.
- The code uses only volatile registers, so, no string (STOS etc) instructions.
TITLE 100 Doors PAGE , 132 .686 .MODEL FLAT OPTION CASEMAP:NONE
.SFCOND .LIST
- =============================================================================
.DATA?
Doors BYTE 100 DUP ( ? )
- =============================================================================
.CODE
Pass_Doors PROC
MOV EDX, OFFSET Doors ; Initialize all doors. MOV ECX, SIZEOF Doors / SIZEOF DWORD MOV EAX, 01010101h ; This does first and second pass.
Close_Doors: MOV [ EDX ], EAX ADD EDX, SIZEOF DWORD LOOP Close_Doors
MOV ECX, 2 ; Pass and step.
Pass_Loop: MOV EDX, OFFSET Doors
ASSUME EDX:PTR BYTE
Doors_Loop: XOR [ EDX ], 1 ; Toggle this door. ADD EDX, ECX ; Advance. CMP EDX, OFFSET Doors[ SIZEOF Doors ]
JB Doors_Loop
INC ECX CMP ECX, SIZEOF Doors
JB Pass_Loop
XOR Doors[ SIZEOF Doors -1 ], 1 ; This is pass 100. RET
Pass_Doors ENDP
- =============================================================================
END
</lang>
Xojo
<lang vb> // True=Open; False=Closed Dim doors(100) As Boolean // Booleans default to false For j As Integer = 1 To 100
For i As Integer = 1 to 100 If i Mod j = 0 Then doors(i) = Not doors(i) Next
Next </lang>
XPL0
<lang XPL0>include c:\cxpl\codes; \intrinsic 'code' declarations int Door(100); \You have 100 doors in a row define Open, Closed; int D, Pass, Step;
[for D:= 0 to 100-1 do \that are all initially closed
Door(D):= Closed;
Step:= 1; \The first time through, you visit every door for Pass:= 1 to 100 do \You make 100 passes by the doors
[D:= Step-1; repeat \if the door is closed, you open it; if it is open, you close it if Door(D)=Closed then Door(D):= Open else Door(D):= Closed; D:= D+Step; until D>=100; Step:= Step+1; \The second time you only visit every 2nd door ]; \The third time, every 3rd door \until you only visit the 100th door
\What state are the doors in after the last pass? Text(0, "Open: "); \Which are open? for D:= 0 to 100-1 do
if Door(D)=Open then [IntOut(0, D+1); ChOut(0,^ )];
CrLf(0);
Text(0, "Closed: "); \Which are closed? for D:= 0 to 100-1 do
if Door(D)=Closed then [IntOut(0, D+1); ChOut(0,^ )];
CrLf(0);
\Optimized: The only doors that remain open are those that are perfect squares Text(0, "Open: "); D:= 1; repeat IntOut(0, D*D); ChOut(0,^ );
D:= D+1;
until D*D>100; CrLf(0); ]</lang>
XSLT 1.0
With input document ...
<lang xml><hallway>
<door number="1">closed</door> <door number="2">closed</door> <door number="3">closed</door> <door number="4">closed</door> ... etc ... <door number="100">closed</door>
<hallway></lang>
... visually representing the initial state of the hallway, apply the following XSLT 1.0 style-sheet...
<lang xml><xsl:stylesheet version="1.0"
xmlns:xsl="http://www.w3.org/1999/XSL/Transform" xmlns:exsl="http://exslt.org/common" exclude-result-prefixes="xsl exsl">
<xsl:output method="xml" indent="yes" omit-xml-declaration="yes"/>
<xsl:template match="/*">
<xsl:copy> <xsl:apply-templates select="door" /> </xsl:copy>
</xsl:template>
<xsl:template match="door">
<xsl:variable name="door-num" select="@number" /> <xsl:variable name="knocks"> <xsl:for-each select="/*/door"> <xsl:if test="$door-num mod position() = 0"> <xsl:text>!</xsl:text> </xsl:if> </xsl:for-each> </xsl:variable> <door number="{$door-num}"> <xsl:choose> <xsl:when test="string-length($knocks) mod 2 = 1"> <xsl:text>open</xsl:text> </xsl:when> <xsl:otherwise> <xsl:text>closed</xsl:text> </xsl:otherwise> </xsl:choose> </door>
</xsl:template>
</xsl:stylesheet></lang>
Also see: 100 doors/XSLT
XSLT 2.0
This XSLT 2.0 style-sheet does not use the input document.
<lang xml><xsl:stylesheet version="2.0"
xmlns:xsl="http://www.w3.org/1999/XSL/Transform">
<xsl:output method="xml" indent="yes" omit-xml-declaration="yes"/>
<xsl:template match="/">
<hallway> <xsl:for-each select="1 to 100"> <xsl:variable name="door-num" select="position()" /> <door number="{$door-num}"> <xsl:value-of select="('closed','open')[
number( sum( for $pass in 1 to 100 return number(($door-num mod $pass) = 0)) mod 2 = 1) + 1]" />
</door> </xsl:for-each> </hallway>
</xsl:template>
</xsl:stylesheet></lang>
Yabasic
<lang Yabasic>n = 100 // doors ppa = 1 // next open door p2 = 1
for i = 1 to n print "Door ", i, " is "; if i < p2 then print "closed." else ppa = ppa + 1 p2 = ppa^2 print "OPEN." end if next</lang>
Yorick
Unoptimized, iterative <lang yorick>doors = array(0, 100); for(i = 1; i <= 100; i++)
for(j = i; j <= 100; j += i) doors(j) ~= 1;
print, where(doors);</lang>
Unoptimized, vectorized <lang yorick>doors = array(0, 100); for(i = 1; i <= 100; i++)
doors(i::i) ~= 1;
print, where(doors);</lang>
Optimized <lang yorick>print, indgen(1:long(sqrt(100)))^2</lang>
All of the above output:
[1,4,9,16,25,36,49,64,81,100]
Zig
<lang Zig>pub fn main() !void {
const stdout = @import("std").io.getStdOut().writer(); var doors = [_]bool{false} ** 101; var pass: u8 = 1; var door: u8 = undefined; while (pass <= 100) : (pass += 1) { door = pass; while (door <= 100) : (door += pass) doors[door] = !doors[door]; } for (doors) |open, num| if (open) try stdout.print("Door {d} is open.\n", .{num});
}</lang>
- Output:
Door 1 is open. Door 4 is open. Door 9 is open. Door 16 is open. Door 25 is open. Door 36 is open. Door 49 is open. Door 64 is open. Door 81 is open. Door 100 is open.
zkl
Pure brute force. <lang zkl>doors:=List.createLong(100,False); // list of 100 Falses foreach n,m in (100,[n..99,n+1]){ doors[m]=(not doors[m]); } //foreach{ foreach{} } doors.filterNs().apply('+(1)).println();</lang> The filterNs method returns the index of each item that passes the filter.
- Output:
L(1,4,9,16,25,36,49,64,81,100)
ZX Spectrum Basic
simple calculation
10 REM 100 doors open/closed? 20 DIM d(100) 25 LET o=0 30 FOR a=1 TO 100 40 FOR b=a TO 100 STEP a 50 LET d(b)=NOT d(b) 55 LET o=o+(d(b)=1)-(d(b)=0) 60 NEXT b 70 NEXT a 80 PRINT o;" open doors"
changing viewable grid
10 REM 100 doors open/closed? 20 DIM d(100) 25 GO SUB 170 30 FOR a=1 TO 100 35 PRINT AT 0,0;"step ";a 40 FOR b=a TO 100 STEP a 45 PRINT AT 0,10;"door:";b;" " 50 LET d(b)=NOT d(b) 55 GO SUB 150 60 NEXT b 70 NEXT a 80 GO SUB 170 90 STOP 150 REM print door status 151 LET p=(b-1)/10 152 LET q=1+10*(p-INT p) 153 LET p=INT p 154 LET op=op+(d(b)=1)-(d(b)=0) 156 PRINT AT 2*p+2,2*q;d(b);AT 0,27;op;" " 160 RETURN 165 REM print step status 170 LET op=0 175 FOR p=0 TO 9 180 FOR q=1 TO 10 185 PRINT AT 2*p+2,2*q;d(p*10+q) 188 LET op=op+d(p*10+q) 190 NEXT q 200 NEXT p 205 PRINT AT 0,22;"open:";op;" " 210 RETURN
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