100 doors
From Rosetta Code
You are encouraged to solve this task according to the task description, using any language you may know.
Problem: You have 100 doors in a row that are all initially closed. You make 100 passes by the doors. The first time through, you visit every door and toggle the door (if the door is closed, you open it; if it is open, you close it). The second time you only visit every 2nd door (door #2, #4, #6, ...). The third time, every 3rd door (door #3, #6, #9, ...), etc, until you only visit the 100th door.
Question: What state are the doors in after the last pass? Which are open, which are closed? [1]
Alternate: As noted in this page's discussion page, the only doors that remain open are whose numbers are perfect squares of integers. Opening only those doors is an optimization that may also be expressed.
[edit] 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
The SET line consists of three functions:
%@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
Here @IF is used to toggle between C and O.
[edit] 6502 Assembly
unoptimized Based on BASIC QB64 unoptimized version
; 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
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
.
;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
22. bytes of code; the specified emulator does not report cycles.
[edit] 68000 Assembly
Some of the macro code is derived from the examples included with EASy68K.
*-----------------------------------------------------------
* 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
[edit] 8086 Assembly
[edit] 8th
\ 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
- Output:
1 4 9 16 25 36 49 64 81 100
[edit] ABAP
unoptimized
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.
optimized
Using 
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.
[edit] ACL2
(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))))
[edit] ActionScript
unoptimized
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);
}
}
}
[edit] Ada
unoptimized
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;
optimized
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;
[edit] 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"))
}
[edit] ALGOL 68
unoptimized
# 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$,i,(the doors[i]|"opened"|"closed")))
OD
);
doors;
optimized
PROC doors optimised = ( INT limit )VOID:
FOR i TO limit DO
REAL num := sqrt(i);
printf(($g" is "gl$,i,(ENTIER num = num |"opened"|"closed") ))
OD
;
doors optimised(limit)
[edit] 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
[edit] APL
unoptimized
out?doors num
? Simulates the 100 doors problem for any number of doors
? Returns a boolean vector with 1 being open
out??num ? num steps
out??¨out ? Count out the spacing for each step
out?1=out ? Make that into a boolean vector
out??¨out ? Flip each vector around
out?(num°?)¨out ? Copy each out to the right size
out??/out ? XOR each vector, toggling each marked door
out??out ? Disclose the results to get a vector
- Output:
10 10?doors 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 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
out?doorsOptimized num;marks
? Returns a boolean vector of the doors that would be left open
marks??num*0.5 ? Take the square root of the size, floored
marks?(?marks)*2 ? Get each door to be opened
out?num?0 ? Make a vector of 0s
out[marks]?1 ? Set the marked doors to 1
- Output:
10 10?doorsOptimized 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 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
Alternate 1-line version 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.
[edit] 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
[edit] 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
[edit] 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]"
[edit] 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]
[edit] AutoHotkey
[edit] Standard Approach
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
[edit] Alternative Approach
Making use of the identity:
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)
[edit] Optimized
While (Door := A_Index ** 2) <= 100
Result .= "Door " Door " is open`n"
MsgBox, %Result%
[edit] 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
[edit] Axiom
Unoptimized:(open,closed,change,open?) := (true,false,not,test);Optimized:
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]
[i for i in 1..100 | perfectSquare? i] -- or
[i^2 for i in 1..sqrt(100)::Integer]
[edit] AWK
unoptimized
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"
}
}
optimized
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"
}
}
[edit] BASIC
unoptimized
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
unoptimized
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
optimized
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
optimized
'lrcvs 04.11.12
CLS
x = 1 : y = 3 : z = 0
PRINT x + " Open"
DO
z = x + y
PRINT z + " Open"
x = z : y = y + 2
UNTIL z >= 100
END
[edit] 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
[edit] Batch File
unoptimized
@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
optimized
@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
)
)
[edit] BBC BASIC
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%
[edit] 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)
}
[edit] Befunge
108p0>:18p;;>:9g!18g9p08g]
*`!0\|+relet|-1`*aap81::+]
;::+1<r]!g9;>$08g1+:08paa[
*`#@_^._aa
[edit] BlitzMax
optimized
Graphics 640,480
i=1
While ((i*i)<=100)
a$=i*i
DrawText a$,10,20*i
Print i*i
i=i+1
Wend
Flip
WaitKey
[edit] Bracmat
Bracmat is not really at home in tasks that involve addressing things by index number. Here are four solutions that each do the task, but none should win a price for cleanliness.
Solution 1. Use an indexable array. Local variables are stored in stacks. Each stack corresponds to one variable name and vice versa. Stacks can also be used as arrays, but because of how local variables are implemented, arrays cannot be declared as local variables.
( 100doors-tbl
= door step
. tbl$(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 }
)
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.
( 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 }
)
)
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.
( 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$!doors
)
Solution 4. Use a list of objects. Each object can be changed without the need to re-create the whole list.
( 100doors-obj
= doors door doorIndex step
. :?doors
& 0:?door
& whl
' ( 1+!door:~>100:?door
& new$(=closed) !doors:?doors
)
& 0:?skip
& whl
' ( !doors:?tododoors
& whl
' ( !tododoors:? [!skip %?door ?tododoors
& ( !(door.):open&closed
| open
)
: ?(door.)
)
& 1+!skip:<100:?skip
)
& out$!doors
)
These four functions are called in the following way:
100doors-tbl$
& 100doors-var$
& 100doors-list$
& 100doors-obj$;
[edit] Burlesque
Version using square numbers:
blsq ) 10ro2?^
{1 4 9 16 25 36 49 64 81 100}
[edit] C
[edit] unoptimized
#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;
}
Using defensive programming, pointers, sentinel values and some other standard programming practices,
#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 #%ld is %s\n", ( doorptr - is_open ) + 1, ( * doorptr ) ? "open" : "closed" ) ;
}
}
[edit] 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 .
#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;
}
The following ultra-short optimized version demonstrates the flexibility of C loops, but isn't really considered good C style:
#include <stdio.h>Or really optimize it -- square of an integer is, well, computable:
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;
}
#include <stdio.h>
int main()
{
int i;
for (i = 1; i * i <= 100; i++)
printf("door %d open\n", i * i);
return 0;
}
[edit] C++
unoptimized
#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;
}
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 
.
#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;
}
The only calculation that's really needed:
#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;
}
[edit] C#
[edit] Unoptimized with Modulus % Operator
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);
}
}
}
[edit] Optimized for Increments
namespace ConsoleApplication1
{
using System;
class Program
{
static void Main()
{
//The o variable stores the number of the next OPEN door.
int o = 1;
//The n variable is used to help calculate the next value of the o variable.
int n = 0;
//The d variable determines the door to be output next.
for (int d = 1; d <= 100; d++)
{
Console.Write("Door #{0}: ", d);
if (d == o)
{
Console.WriteLine("Open");
n++;
o += 2 * n + 1;
}
else
Console.WriteLine("Closed");
}
Console.ReadKey(true);
}
}
}
[edit] 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.)
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);
}
}
}
[edit] Unoptimized but Concise
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);
}
}
}
[edit] Optimized for brevity
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);
}
}
}
[edit] C1R
100_doors
[edit] 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
[edit] CLIPS
Unoptimized
(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)
)
)
Optimized
(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)
)
[edit] Clojure
Unoptimized / mutable array
(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)))))
Unoptimized / functional
(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)))))
Optimized / functional
(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)))))
[edit] 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
.
[edit] Coco
We use the naive algorithm.
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'
[edit] CoffeeScript
unoptimized:
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
optimized:
isInteger = (i) -> Math.floor(i) == i
console.log door for door in [1..100] when isInteger Math.sqrt door
ultra-optimized:
console.log Math.pow(i,2) for i in [1..10]
[edit] ColdFusion
Basic Solution: Returns List of 100 values: 1=open 0=closed
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;
}
Squares of Integers Solution: Returns List of 100 values: 1=open 0=closed
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;
}
Display only
// Display all doors
<cfloop from="1" to="100" index="x">
Door #x# Open: #YesNoFormat(ListGetAt(doorList,x))#<br />
</cfloop>
// Output only open doors
<cfloop from="1" to="100" index="x">
<cfif ListGetAt(doorList,x) EQ 1>
#x#<br />
</cfif>
</cfloop>
Another Route
<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>
[edit] 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.
(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))))
Unoptimized / imperative This is a version that closely follows the problem description and is still quite short.
(define-modify-macro toggle () not)
(defun 100-doors ()
(let ((doors (make-array 100 :initial-element nil)))
(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)))))
Optimized This is an optimized version of the above, using the perfect square algorithm (Note: This is non-functional as the state of the doors variable gets modified by a function call)
(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)
'_)))
Optimized (2) This version displays a much more functional solution through the use of MAPCAR (note however that this is imperative as it does variable mutation)
(let ((i 0))
(mapcar (lambda (x)
(if (zerop (mod (sqrt (incf i)) 1))
"_" "#"))
(make-list 100)))
[edit] Component Pascal
BlackBox Component Builder
MODULE Doors100;
IMPORT StdLog;
PROCEDURE Do*;
VAR
i,j: INTEGER;
closed: ARRAY 101 OF BOOLEAN;
BEGIN
(* initilization of close 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.
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
[edit] Coq
Basic solution:
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.
Optimized version ((n+1)^2 = n^2 + 2n + 1):
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.
Unit test:
Goal prison 100 = prisoo 100. compute. reflexivity. Qed.
Full proof at github:
Goal forall n, prison n = prisoo n. Abort.
[edit] Crystal
doors = Array.new(100, false)
1.upto(100) do |i|
i.step(by: i, limit: 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
[edit] 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 (int 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;
}
- 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:
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
}
[edit] Dart
unoptimized
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");
}
}
optimized version (including generating squares without multiplication)
main() {
for(int i=1,s=3;i<=100;i+=s,s+=2)
print("door $i is open");
}
[edit] DCL
Adapted from optimized Batch example
$! 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
[edit] Delphi
- See Pascal
[edit] Déjà Vu
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 " " )
- Output:
Open doors: 1 4 9 16 25 36 49 64 81 100
[edit] DWScript
Unoptimized
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];
for i := 1 to 100 do
if doors[i] then
PrintLn('Door '+IntToStr(i)+' is open');
[edit] Dylan
Unoptimized
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
[edit] E
Graphical
This version animates the changes of the doors (as checkboxes).
#!/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)
[edit] ECL
optimized version
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;
unoptimized version - demonstrating LOOP
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);
unoptimized version - using ITERATE This is a bit more efficient than the LOOP version
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')));
[edit] Eero
#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
[edit] 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
[edit] 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.
file: application.e
note
description: "100 Doors problem"
date: "07-AUG-2011"
revision: "1.0"
class
APPLICATION
create
make
feature {NONE} -- Initialization
doors: LINKED_LIST [DOOR]
-- A set of doors
once
create Result.make
end
make
-- Run application.
local
count, i: INTEGER
do
--initialize doors
count := 100
from
i := 1
until
i > count
loop
doors.extend (create {DOOR}.make (i, false))
i := i + 1
end
-- toggle doors
from
i := 1
until
i > count
loop
across
doors as this
loop
if this.item.address \\ i = 0 then
this.item.open := not this.item.open
end
end -- across doors
i := i + 1
end -- for i
-- print results
doors.do_all (agent (door: DOOR)
do
if door.open then
io.put_string ("Door " + door.address.out + " is open.")
elseif not door.open then
io.put_string ("Door " + door.address.out + " is closed.")
end
io.put_new_line
end)
end -- make
end -- APPLICATION
file: door.e
note
description: "A door with an address and an open or closed state."
date: "07-AUG-2011"
revision: "1.0"
class
DOOR
create
make
feature -- initialization
make (addr: INTEGER; status: BOOLEAN)
-- create door with address and status
require
valid_address: addr /= '%U'
valid_status: status /= '%U'
do
address := addr
open := status
ensure
address_set: address = addr
status_set: open = status
end
feature -- access
address: INTEGER
open: BOOLEAN assign set_open
feature -- mutators
set_open (status: BOOLEAN)
require
valid_status: status /= '%U'
do
open := status
ensure
open_updated: open = status
end
end
[edit] Ela
Standard Approach
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..]]
Alternate Approach
open list
run n = takeWhile (<n) [& k*k \\ k <- [1..]]
[edit] Elixir
defmodule HundredDoors do
def doors() do
Enum.to_list(Stream.take(Stream.cycle([false]), 100))
end
def toggle(doors, n) do
Enum.take(doors, n) ++ [not Enum.at(doors,n)] ++ Enum.drop(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)
# optimized
final_state = Enum.reduce(1..10, HundredDoors.doors, fn(n, acc) -> HundredDoors.toggle(acc, n*n-1) end)
open_doors = Enum.map(Enum.filter( Enum.with_index(final_state), fn({door,_}) -> door end ),
fn({_,index}) -> index+1 end)
IO.puts "All doors are closed except these: #{inspect open_doors}"
- Output:
All doors are closed except these: [1, 4, 9, 16, 25, 36, 49, 64, 81, 100]
[edit] Emacs Lisp
Unoptimized
(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))
[edit] Erlang
non-optimized
-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).
optimized
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)].
[edit] 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
END PROGRAM
[edit] 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 ]
[edit] Euphoria
unoptimised
-- 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
[edit] F#
Requires #light in versions of F# prior to 2010 beta.
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
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.
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 |]
[edit] Factor
Unoptimized
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 ;
Optimized
USING:
formatting
math math.primes.factors math.ranges
sequences ;
IN: rosetta-doors2
: main ( -- )
100 [1,b] [ divisors length odd? ] filter "Open %[%d, %]\n" printf ;
[edit] Falcon
Unoptimized code
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
Optimized code
for door in [ 1 : 101 ]: > "Door ", $door, " is: ", fract( door ** 0.5 ) ? "closed" : "open"
[edit] Fantom
Unoptimized
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 })
Optimized
echo("Open doors are " + (1..100).toList.findAll { it.toFloat.pow(0.5f).toInt.pow(2) == it})
[edit] FBSL
Unoptimised
#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
Optimised (by ML)
#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
[edit] friendly interactive shell
Unoptimized
# 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
Optimized
# 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
[edit] Forth
Unoptimized
: 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
Optimized
: squared ( n -- n' ) dup * ;
: doors ( n -- )
1 begin 2dup squared >= while
dup squared .
1+ repeat 2drop ;
100 doors
[edit] Fortran
unoptimized
PROGRAM DOORS
INTEGER, PARAMETER :: n = 100 ! Number of doors
INTEGER :: i, j
LOGICAL :: door(n) = .TRUE. ! Initially closed
DO i = 1, n
DO j = i, n, i
door(j) = .NOT. door(j)
END DO
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
optimized
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
[edit] 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 "]
[edit] FunL
[edit] Unoptimized
for i <- 1..100
r = foldl1( \a, b -> a xor b, [(a|i) | a <- 1..100] )
println( i + ' ' + (if r then 'open' else 'closed') )
[edit] Optimized
import math.sqrt
for i <- 1..100
println( i + ' ' + (if sqrt(i) is Integer then 'open' else 'closed') )
[edit] 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 ]
[edit] 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();
[edit] Go
unoptimized
package main
import "fmt"
func main() {
doors := make([]bool, 100)
// 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(" ")
}
}
}
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
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")
}
}
}
[edit] Golfscript
100:c;[{0}c*]:d;
c,{.c,>\)%{.d<\.d=1^\)d>++:d;}/}/
[c,{)"door "\+" is"+}%d{{"open"}{"closed"}if}%]zip
{" "*puts}/
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)
100,{)}%
{:d.sqrt 2?=
{"open"}{"close"}if"door "d+" is "+\+puts}/
optimized without sqrt
[{"close"}100*]:d;
10,{)2?(.d<\["open"]\)d>++:d;}/
[100,{)"door "\+" is"+}%d]zip
{" "*puts}/
[edit] Gosu
unoptimized
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'}" )
}
optimized
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 ${i} is closed" )
}
}
[edit] Groovy
unoptimized
doors = [false] * 100
(0..99).each {
it.step(100, it + 1) {
doors[it] ^= true
}
}
(0..99).each {
println("Door #${it + 1} is ${doors[it] ? 'open' : 'closed'}.")
}
optimized a Using square roots
(1..100).each {
println("Door #${it} is ${Math.sqrt(it).with{it==(int)it} ? 'open' : 'closed'}.")
}
optimized b Without using square roots
doors = ['closed'] * 100
(1..10).each { doors[it**2 - 1] = 'open' }
(0..99).each {
println("Door #${it + 1} is ${doors[it]}.")
}
[edit] Harbour
Unoptimized code:
#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
Optimized code
#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
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*|
[edit] Haskell
unoptimized
data Door = Open | Closed deriving Show
toggle Open = Closed
toggle Closed = Open
toggleEvery :: [Door] -> Int -> [Door]
toggleEvery xs k = zipWith ($) fs xs
where fs = cycle $ (replicate (k-1) id) ++ [toggle]
run n = foldl toggleEvery (replicate n Closed) [1..n]
Variation.
data Door = Open | Closed deriving Show
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 n = foldr toggleEvery (replicate n Closed) [1..n]
optimized (without using square roots)
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..]]
alternatively, returning a list of all open gates, it's a one-liner:
run n = takeWhile (< n) [k*k | k <- [1..]]
[edit] 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++;
}
}
}
[edit] HicEst
Unoptimized
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")
Optimized
door = 1 - open ! = closed
DO i = 1, n^0.5
door(i*i) = open
ENDDO
DLG(Text=door, TItle=SUM(door)//" doors open")
[edit] Hy
(def 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"))))
[edit] 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.
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
Optimized solution.
procedure main()
every write("Door ", i := 1 to 100, " is ", if integer(sqrt(i)) = sqrt(i) then "open" else "closed")
end
or
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
[edit] Inform 7
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.
[edit] 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
[edit] Io
simple boolean list solution:
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))
Optimized solution:
(Range 1 to(10) asList) foreach(v, "Door #{v ** 2} is open." interpolate println)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.
[edit] Ioke
Unoptimized Object Oriented solution.
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
[edit] J
unoptimized
~:/ (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 ...
optimized
(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 ...
with formatting
'these doors are open' ; >: I. (>:i.100) e. *: i.11
+------------------------------------------------+
¦these doors are open¦1 4 9 16 25 36 49 64 81 100¦
+------------------------------------------------+
[edit] Java
unoptimized
public class HundredDoors {
public static void main(String[] args) {
boolean[] doors = new boolean[101];
for (int i = 1; i <= 100; i++) {
for (int j = i; j <= 100; j++) {
if(j % i == 0) doors[j] = !doors[j];
}
}
for (int i = 1; i <= 100; i++) {
System.out.printf("Door %d: %s%n", i, doors[i] ? "open" : "closed");
}
}
}
If a boolean array is required.
public class Doors
{
public static void main(String[] args)
{
boolean[] doors=new boolean[100];
for(int i=0;i<10;i++)
doors[i*(i+2)]=true;
for(int i=0;i<100;i++)
System.out.println("Door #"+(i+1)+" is"+(doors[i]?"open.":" closed."));
}
}
If only printing the result is required.
public class Doors
{
public static void main(String[] args)
{
for(int i=0;i<10;i++)
System.out.println("Door #"+(i*(i+2)+1)+" is open.");
}
}
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.
optimized
public class Doors
{
public static void main(final String[] args)
{
boolean[] doors = new boolean[100];
for (int pass = 0; pass < 10; pass++)
doors[(pass + 1) * (pass + 1) - 1] = true;
for(int i = 0; i < 100; i++)
System.out.println("Door #" + (i + 1) + " is " + (doors[i] ? "open." : "closed."));
}
}
optimized 2
public class Doors
{
public static void main(final String[] args)
{
StringBuilder sb = new StringBuilder();
for (int i = 1; i <= 10; i++)
sb.append("Door #").append(i*i).append(" is open\n");
System.out.println(sb.toString());
}
}
optimized 3
public class Doors{
public static void main(String[] args){
int i;
for(i = 1; i < 101; i++){
double sqrt = Math.sqrt(i);
if(sqrt != (int)sqrt){
System.out.println("Door " + i + " is closed");
}else{
System.out.println("Door " + i + " is open");
}
}
}
}
[edit] JavaScript
[edit] ES5
[edit] unoptimized
var doors=[];
for(var i=0;i<100;i++)
doors[i]=false; //create doors
for(var i=1;i<=100;i++)
for(var i2=i-1,g;i2<100;i2+=i)
doors[i2]=!doors[i2]; //toggle doors
for(var i=1;i<=100;i++) //read doors
console.log("Door %d is %s",i,doors[i-1]?"open":"closed")
[edit] optimized
for (var door = 1; door <= 100; door++) {
var sqrt = Math.sqrt(door);
if (sqrt === (sqrt | 0)) {
console.log("Door %d is open", door);
}
}
Array.apply(null, { length: 100 })
.map(function(v, i) { return i + 1; })
.forEach(function(door) {
var sqrt = Math.sqrt(door);
if (sqrt === (sqrt | 0)) {
console.log("Door %d is open", door);
}
});
Simple for loop. Optimizing the optimized?
for(var door=1;i<10/*Math.sqrt(100)*/;i++){
console.log("Door %d is open",i*i);
}
[edit] ES6
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);
}
});
// 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);
}
});
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
[edit] 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
# Solution for n doors:Analytical solution
def doors(n):
def print:
. as $doors
| range(1; length+1)
| if $doors[.] then "Door \(.) is open" else empty end;
([][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 ;
# Solution for 100 doors:
def solution:
range(1;11) | "Door \(. * .) is open";
[edit] Julia
unoptimized:
-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 '*'
doors = falses(100)
for a = 1:100, b in a:a:100
doors[b] = !doors[b]
end
for a = 1:100
println("Door $a is " * (doors[a] ? "open" : "close"))
end
ultra-optimized:
for i = 1:10 println("Door $(i^2) is open") end
[edit] K
unoptimized / converted from Q .
`closed `open ![ ; 2 ] @ #:' 1 _ = ,/ &:' 0 = t !\:/: t : ! 101
optimized / 1 origin indices
( 1 + ! 10 ) ^ 2
/ As parameterized function :
{ ( 1 + ! _ x ^ % 2 ) ^ 2 } 100
[edit] Kotlin
fun oneHundredDoors(): List<Int> {
val doors = Array<Boolean>(100, { false })
for (i in 0..99)
for (j in i..99 step (i + 1))
doors[j] = !doors[j]
return IndexIterator(doors.iterator()).filter { it.second }
.map { it.first + 1 }
.toList()
}
[edit] LabVIEW
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.
- 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.
[edit] Lasso
[edit] Loop
loop(100) => {^
local(root = math_sqrt(loop_count))
local(state = (#root == math_ceil(#root) ? '<strong>open</strong>' | 'closed'))
#state != 'closed' ? 'Door ' + loop_count + ': ' + #state + '<br>'
^}
- 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
[edit] 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.
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
[edit] Liberty BASIC
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
[edit] 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
[edit] 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
[edit] Lua
is_open = {}
for door = 1,100 do is_open[door] = false end
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
if v then
print ('Door '..i..':','open')
else
print ('Door '..i..':', 'close')
end
end
[edit] 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
[edit] 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:
To solve the problem, call it with 100 as argument (output not shown here).
> NDoors( 100 );
Here is the optimised version, which outputs only the open doors.
> seq( i^2, i = 1 .. isqrt( 100 ) );
1, 4, 9, 16, 25, 36, 49, 64, 81, 100
Alternatively,
> [seq]( 1 .. 10 )^~2;
[1, 4, 9, 16, 25, 36, 49, 64, 81, 100]
[edit] Mathematica
unoptimized 1
n=100;
tmp=ConstantArray[-1,n];
Do[tmp[[i;;;;i]]*=-1;,{i,n}];
Do[Print["door ",i," is ",If[tmp[[i]]==-1,"closed","open"]],{i,1,Length[tmp]}]
unoptimized 2
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}]
unoptimized 3
Mathematica also supports immutable data paradigms, like so:
Fold[
ReplacePart[#1, (i_ /; Mod[i, #2] == 0) :> (-#1[[i]])] &,
ConstantArray[-1, {100}],
Range[100]
] /. {1 -> "Open", -1 -> "Closed"}
optimized 1
Do[Print["door ",i," is ",If[IntegerQ[Sqrt[i]],"open","closed"]],{i,100}]
optimized 2
n=100;
a=Range[1,Sqrt[n]]^2
Do[Print["door ",i," is ",If[MemberQ[a,i],"open","closed"]],{i,100}]
optimized 3
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"];
];
]
These will only give the indices for the open doors: unoptimized 2
Pick[Range[100], Xor@@@Array[Divisible[#1,#2]&, {100,100}]]
optimized 4
Range[Sqrt[100]]^2
[edit] MATLAB / Octave
[edit] Iterative Method
Unoptimized
a=zeros(1,100);
for b=1:100;
for i=b:b:100;
if a(i)==1
a(i)=0;
else
a(i)=1;
end
end
end
a
Optimized
for x=1:100;
if sqrt(x) == floor(sqrt(x))
a(i)=1;
end
end
a
More Optimized
a = zeros(100,1);
for counter = 1:sqrt(100);
a(counter^2) = 1;
end
a
[edit] Vectorized Method
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
[edit] Known-Result Method
doors((1:10).^2) = 1;
doors
[edit] 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));
Usage:
doors(100);
/* [1, 4, 9, 16, 25, 36, 49, 64, 81, 100] */
[edit] MAXScript
unoptimized
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]
)
optimized
for i in 1 to 100 do
(
root = pow i 0.5
format ("Door % is open?: %\n") i (root == (root as integer))
)
[edit] Mercury
:- module doors.
:- interface.
:- import_module array, io, int.
:- type door ---> open ; closed.
:- type doors == array(door).
:- func toggle(door) = door.
:- pred walk(int::in, doors::in, doors::out) is semidet.
:- pred walks(int::in, int::in, doors::in, doors::out) is det.
:- pred main(io::di, io::uo) is det.
:- implementation.
toggle(open) = closed.
toggle(closed) = open.
walk(N, !D) :- walk(N, N, !D).
:- pred walk(int::in, int::in, doors::in, doors::out) is semidet.
walk(At, By, !D) :-
semidet_lookup(!.D, At - 1, Door),
slow_set(At - 1, toggle(Door), !D),
( walk(At + By, By, !D) -> true ; true ).
walks(N, End, !D) :-
( N =< End, walk(N, !D) -> walks(N + 1, End, !D) ; true ).
main(!IO) :-
io.write(Doors1, !IO), io.nl(!IO),
array.init(100, closed, Doors0),
walks(1, 100, Doors0, Doors1).
[edit] 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
[edit] MIPS Assembly
.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
[edit] 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
[edit] mIRC Scripting Language
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
[edit] 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
[edit] MMIX
See 100 doors/MMIX
[edit] Modula-2
unoptimized
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.
optimized
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.
[edit] Modula-3
unoptimized
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.
optimized
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.
[edit] 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
[edit] 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'
[edit] 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.
[edit] NetRexx
unoptimized
/* NetRexx */
options replace format comments java crossref savelog 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_
optimized (Based on the Java 'optimized' version)
/* NetRexx */
options replace format comments java crossref savelog 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_
optimized 2 (Based on the Java 'optimized 2' version)
/* 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
optimized 3
/* NetRexx */
loop i = 1 to 10
say 'Door Nr.' i * i 'is open.'
end i
[edit] 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))
[edit] Nim
unoptimized:
from strutils import format
proc check_doors() =
const n = 100
var is_open : array[1..n, bool] # auto-initialized to false
# pass over the doors n times
for pass in 1..n:
var i = pass
while i <= n:
is_open[i] = not is_open[i]
i += pass
# print the result
for door in 1..n:
echo format("door $1 is $2.", door, (if is_open[door]: "open" else: "closed"))
check_doors()
another:
var isOpen: array[1..100, bool]
for pass in countup(1, 100):
for door in countup(pass,100,pass):
isOpen[door] = not isOpen[door]
for i in countup(1, 100):
if isOpen[i]:
echo("Door ",i," is open.")
[edit] Objeck
optimized
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();
};
};
}
}
}
[edit] 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.
@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);
}
}];
}
}
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.
@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];
}
[edit] OCaml
unoptimized
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))
optimized
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))
[edit] 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
see also the solutions in Matab. They will work in Octave, too.
[edit] Oforth
func: doors
{
| i j l |
ListBuffer new #[ dup add(false) ] times(100) ->l
100 loop: i [
i 100 i step: j [ l put(j, l at(j) not) ]
]
l println
}
[edit] 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"
The four examples in the Rexx section also run unchanged under ooRexx
[edit] 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.
[edit] 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
[edit] 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
}
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.
[edit] PARI/GP
Unoptimized version.
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.")))
Optimized version.
for(n=1,sqrt(100),print("Door ",n^2," is open."))
[edit] 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.
Optimized version.
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.
[edit] Perl
unoptimized
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;
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.)
#!/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";
optimized
print "Door $_ is open\n" for map $_**2, 1 .. 10;
print "Door $_ is ", qw"closed open"[int sqrt == sqrt], "\n" for 1..100;
while( ++$i <= 100 )
{
$root = sqrt($i);
if ( int( $root ) == $root )
{
print "Door $i is open\n";
}
else
{
print "Door $i is closed\n";
}
}
[edit] 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();
$doors->print_open();
[edit] Perl 6
unoptimizedmy @doors = False xx 101;
($_ = !$_ for @doors[0, * + $_ ...^ * > 100]) for 1..100;
say "Door $_ is ", <closed open>[ @doors[$_] ] for 1..100;
optimized
say "Door $_ is open" for map {$^n ** 2}, 1..10;
Here's a version using the cross meta-operator instead of a map:
say "Door $_ is open" for 1..10 X** 2;
This one prints both opened and closed doors:
say "Door $_ is ", <closed open>[.sqrt == .sqrt.floor] for 1..100;
[edit] PHL
[edit] unoptimized
module doors;
extern printf;
@Integer main [
@Array<@Boolean> doors = new @Array<@Boolean>.init(100);
var i = 1;
while (i <= 100) {
var j = i-1;
while (j < 100) {
doors.set(j, doors.get(j)::not);
j = j + i;
}
i = i::inc;
}
i = 0;
while (i < 100) {
printf("%i %s\n", i+1, iif(doors.get(i), "open", "closed"));
i = i::inc;
}
return 0;
]
[edit] optimized
module var;
extern printf;
@Integer main [
var door = 1;
var incrementer = 0;
var current = 1;
while (current <= 100)
{
printf("Door %i ", current);
if (current == door)
{
printf("open\n");
incrementer = incrementer::inc;
door = door + 2 * incrementer + 1;
}
else
printf("closed\n");
current = current + 1;
}
return 0;
]
[edit] PHP
See: Demo optimized
<?php
for ($i = 1; $i <= 100; $i++) {
$root = sqrt($i);
$state = ($root == ceil($root)) ? 'open' : 'closed';
echo "Door {$i}: {$state}\n";
}
?>
unoptimized
<?php
$toggleState = array('open' => 'closed', 'closed' => 'open');
$doors = array_fill(1, 100, 'closed');
for ($pass = 1; $pass <= 100; ++$pass) {
for ($nr = 1; $nr <= 100; ++$nr) {
if ($nr % $pass == 0) {
$doors[$nr] = $toggleState[$doors[$nr]];
}
}
}
for ($nr = 1; $nr <= 100; ++$nr)
printf("Door %d is %s\n", $nr, $doors[$nr]);
?>
[edit] PicoLisp
unoptimized
(let Doors (need 100)
(for I 100
(for (D (nth Doors I) D (cdr (nth D I)))
(set D (not (car D))) ) )
(println Doors) )
optimized
(let Doors (need 100)
(for I (sqrt 100)
(set (nth Doors (* I I)) T) )
(println Doors) )
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:
(let Doors (need 100)
(for I (sqrt 100)
(set (nth Doors (* I I)) T) )
(make
(for (N . D) Doors
(when D (link N)) ) ) )
Output:
(1 4 9 16 25 36 49 64 81 100)
[edit] Piet
[edit] 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;
}
optimized version:
array doors = map(enumerate(100,1,1), lambda(int x)
{
return sqrt((float)x)%1 == 0.0;
});
write("%{%d %d %d %d %d %d %d %d %d %d\n%}\n", doors/10)
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
[edit] PL/I
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;
[edit] PL/SQL
Unoptimized
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;
[edit] Pop11
unoptimized
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;
optimized
for i to 100 do
lvars root = sqrt(i);
i; if root = round(root) then ' open' ><; else ' closed' ><; endif; =>
endfor;
[edit] PostScript
Bruteforce:/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 pstackShows: [true false false true false false false false true false ...<90 doors later>... true]
[edit] Potion
square=1, i=3
1 to 100(door):
if (door == square):
("door", door, "is open") say
square += i
i += 2.
.
[edit] PowerShell
[edit] unoptimized
$doors = @(0..99)
for($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 {"$doornum closed"}
}
[edit] Alternative Method
function Get-DoorState($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}
}
[edit] unoptimized Pipeline
$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" } }
[edit] unoptimized Pipeline 2
$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" } }
[edit] unoptimized Pipeline 3 (dynamically build pipeline)
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}} | $pipe out-host"
[edit] Using Powershell Workflow for Parallelism
Workflow Calc-Doors {
Foreach –parallel ($number in 1..100) {
"Door " + $number.ToString("0000") + ": " + @{$true="Closed";$false="Open"}[([Math]::pow($number, 0.5)%1) -ne 0]
}
}
Calc-Doors | sort
[edit] optimized
1..10|%{"Door "+ $_*$_ + " is open"}
[edit] ProDOS
Uses math module.
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
[edit] Prolog
[edit] unoptimized
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)).
Using dynamic-rules. Tried to be ISO.
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.
[edit] optimized
doors_optimized(N) :-
Max is floor(sqrt(N)),
forall(between(1, Max, I),
( J is I*I,format('Door ~w is open.~n',[J]))).
[edit] PureBasic
unoptimized
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()
optimized
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()
Output:
Following Doors are open: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100,
[edit] Python
unoptimized
doors = [False] * 100
for i in xrange(100):
for j in xrange(i, 100, i+1):
doors[j] = not doors[j]
print "Door %d:" % (i+1), 'open' if doors[i] else 'close'
optimized
A version that only visits each door once:
for i in xrange(1, 101):
root = i ** 0.5
print "Door %d:" % i, 'open' if root == int(root) else 'close'
One liner using a list comprehension, item lookup, and is_integer
print '\n'.join(['Door %s is %s' % (i, ('closed', 'open')[(i**0.5).is_integer()]) for i in xrange(1, 101)])
One liner using a generator expression, ternary operator, and modulo
print '\n'.join('Door %s is %s' % (i, 'closed' if i**0.5 % 1 else 'open') for i in range(1, 101))
for i in range(1, 101):
if i**0.5 % 1:
state='open'
else:
state='close'
print("Door {}:{}".format(i, state))
ultra-optimized: ported from Julia version
for i in range(1,11): print("Door %s is open" % i**2)
[edit] Q
unoptimized
`closed`open mod[;2]count each 1 _ group raze where each 0=t mod\:/:t:til 101
optimized
`closed`open (1+til 100) in `int$xexp[;2] 1+til 10
[edit] R
Using a loop
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()
optimized
x <- rep(1, 100)
for (i in 1:100-1) {
x <- xor(x, rep(c(rep(0,i),1), length.out=100))
}
which(!x)
Using a **ply function
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()
[edit] 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))
Optimized:
#lang racket
(for ([x (in-range 1 101)] #:when (exact-integer? (sqrt x)))
(printf "~a is open\n" x))
Unoptimized imperative, with graphic rendering:
#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)))
Output:
[edit] RapidQ
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
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
[edit] REALbasic
'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
[edit] REBOL
[edit] Unoptimized
doors: array/initial 100 'closed
repeat i 100 [
door: at doors i
forskip door i [change door either 'open = first door ['closed] ['open]]
]
[edit] Optimized
doors: array/initial 100 'closed
repeat i 10 [doors/(i * i): 'open]
[edit] Retro
: squared ( n-n ) dup * ;
: doors ( n- ) [ 1 repeat 2over squared > 0; drop dup squared putn space 1+ again ] do 2drop ;
100 doors
[edit] REXX
[edit] version 1
/*rexx*/
door. = 0
do inc = 1 to 100
do d = inc to 100 by inc
door.d = \door.d
end
end
say "The open doors after 100 passes:"
do i = 1 to 100
if door.i = 1 then say i
end
[edit] version 2, the hard way
Here is another version, solving it the hard way.
/*REXX program to solve the 100 door puzzle, the hard-way version. */
parse arg doors . /*get the first argument (# of doors.) */
if doors=='' then doors=100 /*not specified? Then assume 100 doors*/
/* 0 = closed. */
/* 1 = open. */
door.=0 /*assume all that all doors are closed.*/
do j=1 for doors /*process a pass-through for all doors.*/
do k=j by j to doors /* ... every Jth door from this point. */
door.k=\door.k /*toggle the "openness" of the door. */
end /*k*/
end /*j*/
say
say 'After' doors "passes, the following doors are open:"
say
do n=1 for doors
if door.n then say right(n,20)
end /*n*/
output using the default input
After 100 passes, the following doors are open:
1
4
9
16
25
36
49
64
81
100
[edit] version 3, the easy way
Here is another version, solving it the easy way.
/*REXX program to solve the 100 door puzzle, the easy-way version. */
parse arg doors . /*get the first argument (# of doors.) */
if doors=='' then doors=100 /*not specified? Then assume 100 doors*/
/* 0 = closed. */
/* 1 = open. */
door.=0 /*assume all that all doors are closed.*/
say
say 'For the' doors "doors problem, the following doors are open:"
say
do j=1 for doors /*process an easy pass-through. */
p=j**2 /*square the door number. */
if p>doors then leave /*if too large, we're done. */
say right(p,20)
end /*j*/
output
For the 100 doors problem, the following doors are open:
1
4
9
16
25
36
49
64
81
100
[edit] version 4, easy way, 1,000 doors
Here's another easy-way solution (version 2), but for 1,000 doors.
/*REXX program to solve the 100 door puzzle, the easy-way version 2.*/
parse arg doors . /*get the first argument (# of doors.) */
if doors=='' then doors=1000 /*not specified? Then assume 1000 doors*/
/* 0 = closed. */
/* 1 = open. */
door.=0 /*assume all that all doors are closed.*/
say
say 'For the' doors "doors problem, the open doors are:"
say
do j=1 for doors while j**2<=doors /*limit pass-throughs.*/
say right(j**2,20)
end /*j*/
output
For the 1000 doors problem, the open doors are:
1
4
9
16
25
36
49
64
81
100
121
144
169
196
225
256
289
324
361
400
441
484
529
576
625
676
729
784
841
900
961
[edit] Ruby
unoptimized; Ruby-way
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}." }
unoptimized
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
optimized
n = 100
(1..n).each do |i|
puts "Door #{i} is #{i**0.5 == (i**0.5).round ? "open" : "closed"}"
end
generic true/false, with another way of handling the inner loop demonstrating Range#step
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'}."}
- 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
[edit] Run BASIC
dim doors(100)Output:
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
Open doors 1 4 9 16 25 36 49 64 81 100
[edit] Rust
// rust 1.0.0-alpha
#![feature(core)]
use std::iter::{range_step_inclusive};
fn main() {
let mut door_open = [false; 100];
for pass in (1us..101) {
for door in range_step_inclusive(pass, 100, pass) {
door_open[door - 1] = !door_open[door - 1];
}
}
for (i, state) in door_open.iter().enumerate() {
println!("Door {} is {}.", i + 1, if *state {"open"} else {"closed"});
}
}
Port of the Ruby optimized version:
// rust 0.8
fn main() {
for i in std::iter::range_inclusive(1,100) {
let x = (i as f64).pow(&0.5);
let state = if x == x.round() {"open"} else {"closed"};
println!("Door {} is {}", i, state);
}
}
[edit] 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");
}
}
[edit] Salmon
Here's an unoptimized version:
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"));;
And here's an optimized one-line version:
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"); };
And a shorter optimized one-line version:
variable y:=1;for(x;1;x<101)"Door "~sprint(x)~" is "~(x==y*y?{++y;return"open";}:"closed")!;
[edit] 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;
[edit] Scala
for { i <- 1 to 100
r = 1 to 100 map (i % _ == 0) reduceLeft (_^_)
} println (i +" "+ (if (r) "open" else "closed"))
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:
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))))
}
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:
val o = 1 to 10 map (i => i * i)
println("open: " + o)
println("closed: " + (1 to 100 filterNot o.contains))
[edit] Sather
class MAIN is
main is
pass, door :INT;
doors :ARRAY{BOOL} := #(100);
loop
doors[0.upto!(99)] := false;
end;
pass := 0;
loop while!(pass < 100);
door := pass;
loop while! (door < 100);
doors[door] := ~doors[door];
door := door + pass + 1
end;
pass := pass + 1;
end;
loop
door := 0.upto!(99);
#OUT + (door+1) + " " + doors[door] + "\n";
end;
end;
end;
[edit] Scheme
unoptimized
(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)))
optimized
(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)))
the 3rd version
(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)
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)
[edit] Seed7
unoptimized
$ 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;
optimized
$ 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;
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
[edit] SETL
Unoptimized
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;
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.
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;
[edit] Sidef
Unoptimized
var doors = [];
{ |pass|
{ |i|
i %% pass && (
doors[i] := false -> not!
);
} * 100;
} * 100;
{ |i|
"Door %3d is %s\n".printf(i, doors[i] ? 'open' : 'closed');
} * 100;
Optimized
{ |i|
"Door %3d is %s\n".printf(i, ["closed", "open"][i**0.5->isInt]);
} * 100;
[edit] Slate
Unoptimized
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'])].
Optimized
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'])].
[edit] Smalltalk
Unoptimized
|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
]
Optimized
|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
]
Unoptimized, using Morphs
| 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.
[edit] SNOBOL4
unoptimized
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<I>,1) " " I
I = LE(I,100) I + 1 :S(OUTPUT.LOOP)F(OUTPUT.WRITE)
OUTPUT.WRITE OUTPUT = OPEN
END
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
MAIN D = ARRAY(100,0)
I = 1
MAIN.LOOP LE(I, 10) :F(OUTPUT)
D<I ** 2> = 1
I = I + 1 :(MAIN.LOOP)
OUTPUT I = 1 ; O = 'Opened doors are: '
OUTPUT.LOOP O = O EQ(D<I>,1) " " I
I = LE(I,100) I + 1 :S(OUTPUT.LOOP)F(OUTPUT.WRITE)
OUTPUT.WRITE OUTPUT = O
END
The output of this version is almost identical to the above.
[edit] Sparkling
unoptimized
/* 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]]);
}
optimized
/* 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);
}
}
[edit] SQL
optimized
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
[edit] Swift
unoptimized
/* 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)")
}
optimized
/* 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)")
}
[edit] Tcl
unoptimized
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 $i] ? "open" : "closed"}]]
}
optimized
package require Tcl 8.5
set doors [lrepeat [expr {$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 $i]]
}
graphical
Inspired by the E solution, here's a visual representation
package require Tcl 8.5
package require Tk
array set door_status {}
# create the gui
set doors [list x]
for {set i 0} {$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
}
}
}
}
[edit] TI-83 BASIC
[edit] Unoptimized
PROGRAM:DOORS100
:ClrHome
:Disp "SETTING UP LIST"
:Disp "PLEASE WAIT..."
:For(I,1,100,1)
:0?L1(I)
:End
:ClrHome
:Disp "Pass"
:For(I,1,100,1)
:For(J,I,100,I)
:Output(2,1,I)
:not(L1(J))?L1(J)
:End
:End
:ClrHome
[edit] Optimized
PROGRAM:DOORSOPT
:For(I,1,100,1)
:not(fPart(v(I)))?L1(I)
:End
[edit] TI-89 BASIC
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
[edit] TorqueScript
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" @ ".");
[edit] 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
[edit] 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
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
[edit] TXR
@(do (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")`)))
[edit] Uniface
unoptimized
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, $number(V_DOOR_STATE)
if (V_DOOR_STATE)
putmess "Door %%V_IDX%%% is finally %%V_DOOR_STATE_S%%%"
endif
V_IDX = V_IDX + 1
getitem V_DOOR_STATE, V_DOORS, V_IDX
endwhile
end ; LP_DO_IT
- Output:
Door 1 is finally Open Door 4 is finally Open Door 9 is finally Open Door 16 is finally Open Door 25 is finally Open Door 36 is finally Open Door 49 is finally Open Door 64 is finally Open Door 81 is finally Open Door 100 is finally Open
[edit] UNIX Shell
#! /bin/bash
declare -a doors
for((i=1; i <= 100; i++)); do
doors[$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 $op
done
Optimised version
#!/bin/bash
for i in {1..100}; do
door[$i*$i]=1
[ -z ${door[$i]} ] && echo "$i closed" || echo "$i open"
done
[edit] 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.
#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)
optimized version:
#import nat
#cast %nL
main = product*tiiXS iota10
output:
<1,4,9,16,25,36,49,64,81>
[edit] Vala
Unoptimized
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;
}
Output:
1: open 2: closed 3: closed 4: open 5: closed 6: closed 7: closed 8: closed 9: open 10: closed 11: closed ...
Optimized
int main() {
int i = 1;
while(i*i <= 100) {
stdout.printf("${i*i} open\n");
i++;
}
return 0;
}
Output:
1 open 4 open 9 open 16 open 25 open 36 open 49 open 64 open 81 open 100 open
[edit] VBA
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
[edit] VBScript
Unoptimized
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
[edit] 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'.
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'
}
}
Optimized
Buf_Switch(Buf_Free)
Ins_Char('-', COUNT, 100)
for (#1=1; #1 <= 10; #1++) {
Goto_Col(#1*#1)
Ins_Char('O', OVERWRITE)
}
Output:
O--O----O------O--------O----------O------------O--------------O----------------O------------------O
[edit] VHDL
unoptimized
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;
unoptimized and synthesizable
LIBRARY ieee;The synthesis requires 116 FFs plus combinatorial logic.
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;
The result is stable after 581 clock cycles.
[edit] Visual Basic .NET
unoptimized
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
optimized
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
[edit] Wart
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 " "
[edit] 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
[edit] Wrapl
Unoptimized
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.
Optimized
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.
[edit] 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);
]
[edit] XSLT 1.0
With input document ...
<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>
... visually representing the initial state of the hallway, apply the following XSLT 1.0 style-sheet...
<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($knocks) mod 2 = 1">
<xsl:text>open</xsl:text>
</xsl:when>
<xsl:otherwise>
<xsl:text>closed</xsl:text>
</xsl:otherwise>
</xsl:choose>
</door>
</xsl:template>
</xsl:stylesheet>
Also see: 100 doors/XSLT
[edit] XSLT 2.0
This XSLT 2.0 style-sheet does not use the input document.
<xsl:stylesheet version="2.0"
xmlns:xsl="http://www.w3.org/1999/XSL/Transform">
<xsl:output method="xml" indent="yes" omit-xml-declaration="yes"/>
<xsl:template match="/">
<hallway>
<xsl:for-each select="1 to 100">
<xsl:variable name="door-num" select="position()" />
<door number="{$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>
[edit] Yorick
Unoptimized, iterative
doors = array(0, 100);
for(i = 1; i <= 100; i++)
for(j = i; j <= 100; j += i)
doors(j) ~= 1;
print, where(doors);
Unoptimized, vectorized
doors = array(0, 100);
for(i = 1; i <= 100; i++)
doors(i::i) ~= 1;
print, where(doors);
Optimized
print, indgen(1:long(sqrt(100)))^2
All of the above output:
[1,4,9,16,25,36,49,64,81,100]
[edit] zkl
Brute force:
fcn flipDoors{
const N=100;
reg doors=(0).pump(N,List,False).copy(); //-->L(False, ...), mutable
n:=1; while(n<=N)
{ [n-1..N-1,n].apply('wrap(n){ doors[n]=(not doors[n]) }); n+=1; }
doors;
}
Brute force using list comprehension (the guard does two things: side effects and suppresses list generation):
fcn flipDoors{
const N=100;
reg doors=(0).pump(N,List,False).copy();
[[(n,m); [1..N]; {[n-1..N-1,n]},'wrap(n,m){ doors[m]=(not doors[m]); False }; _]];
doors;
}
Just plugging in squares:
fcn flipDoors{
const N=100;
reg doors=(0).pump(N,List,False).copy();
foreach n in ([1..N.toFloat().sqrt()]){ doors[n*n-1]=True }
doors;
}
Output, probably more interesting:
doors:=flipDoors();
println("Open doors: ",
doors.enumerate().filter(fcn([(n,d)]){d}).apply(fcn([(n,d)]){n+1}) );
println("All doors:\n",
doors.pump(String,T(T,Void.Read,9), // read 10 doors
fcn(bs){ vm.arglist.pump(String,fcn(b){b and "O" or "C" }) },
'+("\n") ) // seperate every 10 doors with a newline
);
- Output:
Open doors: L(1,4,9,16,25,36,49,64,81,100) All doors: OCCOCCCCOC CCCCCOCCCC CCCCOCCCCC CCCCCOCCCC CCCCCCCCOC CCCCCCCCCC CCCOCCCCCC CCCCCCCCCC OCCCCCCCCC CCCCCCCCCO
[edit] 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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