Towers of Hanoi: Difference between revisions
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=={{header|Imp77}}== |
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<syntaxhighlight lang="Imp77"> |
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%begin |
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%routine do hanoi(%integer n, f, t, u) |
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do hanoi(n - 1, f, u, t) %if n >= 2 |
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print string("Move disk from ".itos(f,0)." to ".itos(t,0).to string(nl)) |
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do hanoi(n - 1, u, t, f) %if n >= 2 |
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%end |
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do hanoi(4, 1, 2, 3) |
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print string("Towers of Hanoi puzzle completed!".to string(nl)) |
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%end %of %program |
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</syntaxhighlight> |
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=={{header|Inform 7}}== |
=={{header|Inform 7}}== |
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Revision as of 22:59, 21 May 2024
You are encouraged to solve this task according to the task description, using any language you may know.
- Task
Solve the Towers of Hanoi problem with recursion.
11l
F hanoi(ndisks, startPeg = 1, endPeg = 3) -> Void
I ndisks
hanoi(ndisks - 1, startPeg, 6 - startPeg - endPeg)
print(‘Move disk #. from peg #. to peg #.’.format(ndisks, startPeg, endPeg))
hanoi(ndisks - 1, 6 - startPeg - endPeg, endPeg)
hanoi(ndisks' 3)- Output:
Move disk 1 from peg 1 to peg 3 Move disk 2 from peg 1 to peg 2 Move disk 1 from peg 3 to peg 2 Move disk 3 from peg 1 to peg 3 Move disk 1 from peg 2 to peg 1 Move disk 2 from peg 2 to peg 3 Move disk 1 from peg 1 to peg 3
360 Assembly
* Towers of Hanoi 08/09/2015
HANOITOW CSECT
USING HANOITOW,R12 r12 : base register
LR R12,R15 establish base register
ST R14,SAVE14 save r14
BEGIN LH R2,=H'4' n <===
L R3,=C'123 ' stating position
BAL R14,MOVE r1=move(m,n)
RETURN L R14,SAVE14 restore r14
BR R14 return to caller
SAVE14 DS F static save r14
PG DC CL44'xxxxxxxxxxxx Move disc from pole X to pole Y'
NN DC F'0'
POLEX DS F current poles
POLEN DS F new poles
* .... recursive subroutine move(n, poles) [r2,r3]
MOVE LR R10,R11 save stackptr (r11) in r10 temp
LA R1,STACKLEN amount of storage required
GETMAIN RU,LV=(R1) allocate storage for stack
USING STACKDS,R11 make storage addressable
LR R11,R1 establish stack addressability
ST R14,SAVE14M save previous r14
ST R10,SAVE11M save previous r11
LR R1,R5 restore saved argument r5
BEGINM STM R2,R3,STACK push arguments to stack
ST R3,POLEX
CH R2,=H'1' if n<>1
BNE RECURSE then goto recurse
L R1,NN
LA R1,1(R1) nn=nn+1
ST R1,NN
XDECO R1,PG nn
MVC PG+33(1),POLEX+0 from
MVC PG+43(1),POLEX+1 to
XPRNT PG,44 print "move disk from to"
B RETURNM
RECURSE L R2,N n
BCTR R2,0 n=n-1
MVC POLEN+0(1),POLES+0 from
MVC POLEN+1(1),POLES+2 via
MVC POLEN+2(1),POLES+1 to
L R3,POLEN new poles
BAL R14,MOVE call move(n-1,from,via,to)
LA R2,1 n=1
MVC POLEN,POLES
L R3,POLEN new poles
BAL R14,MOVE call move(1,from,to,via)
L R2,N n
BCTR R2,0 n=n-1
MVC POLEN+0(1),POLES+2 via
MVC POLEN+1(1),POLES+1 to
MVC POLEN+2(1),POLES+0 from
L R3,POLEN new poles
BAL R14,MOVE call move(n-1,via,to,from)
RETURNM LM R2,R3,STACK pull arguments from stack
LR R1,R11 current stack
L R14,SAVE14M restore r14
L R11,SAVE11M restore r11
LA R0,STACKLEN amount of storage to free
FREEMAIN A=(R1),LV=(R0) free allocated storage
BR R14 return to caller
LTORG
DROP R12 base no longer needed
STACKDS DSECT dynamic area
SAVE14M DS F saved r14
SAVE11M DS F saved r11
STACK DS 0F stack
N DS F r2 n
POLES DS F r3 poles
STACKLEN EQU *-STACKDS
YREGS
END HANOITOW- Output:
1 Move disc from pole 1 to pole 3
2 Move disc from pole 1 to pole 2
3 Move disc from pole 3 to pole 2
4 Move disc from pole 1 to pole 3
5 Move disc from pole 2 to pole 1
6 Move disc from pole 2 to pole 3
7 Move disc from pole 1 to pole 3
8 Move disc from pole 1 to pole 2
9 Move disc from pole 3 to pole 2
10 Move disc from pole 3 to pole 1
11 Move disc from pole 2 to pole 1
12 Move disc from pole 3 to pole 2
13 Move disc from pole 1 to pole 3
14 Move disc from pole 1 to pole 2
15 Move disc from pole 3 to pole 2
6502 Assembly
This should work on any Commodore 8-bit computer; just set `temp` to an appropriate zero-page location.
temp = $FB ; this works on a VIC-20 or C-64; adjust for other machines. Need two bytes zero-page space unused by the OS.
; kernal print-char routine
chrout = $FFD2
; Main Towers of Hanoi routine. To call, load the accumulator with the number of disks to move,
; the X register with the source peg (1-3), and the Y register with the target peg.
hanoi: cmp #$00 ; do nothing if the number of disks to move is zero
bne nonzero
rts
nonzero: pha ; save registers on stack
txa
pha
tya
pha
pha ; and make room for the spare peg number
; Parameters are now on the stack at these offsets:
count = $0104
source = $0103
target = $0102
spare = $0101
; compute spare rod number (6 - source - dest)
tsx
lda #6
sec
sbc source, x
sec
sbc target, x
sta spare, x
; prepare for first recursive call
tay ; target is the spare peg
tsx
lda source, x ; source is the same
sta temp ; we're using X to access the stack, so save its value here for now
lda count, x ; move count - 1 disks
sec
sbc #1
ldx temp ; now load X for call
; and recurse
jsr hanoi
; restore X and Y for print call
tsx
ldy target, x
lda source, x
tax
; print instructions to move the last disk
jsr print_move
; prepare for final recursive call
tsx
lda spare, x ; source is now spare
sta temp
lda target, x ; going to the original target
tay
lda count, x ; and again moving count-1 disks
sec
sbc #1
ldx temp
jsr hanoi
; pop our stack frame, restore registers, and return
pla
pla
tay
pla
tax
pla
rts
; constants for printing
prelude: .asciiz "MOVE DISK FROM "
interlude: .asciiz " TO "
postlude: .byte 13,0
; print instructions: move disk from (X) to (Y)
print_move:
pha
txa
pha
tya
pha
; Parameters are now on the stack at these offsets:
from = $0102
to = $0101
lda #<prelude
ldx #>prelude
jsr print_string
tsx
lda from,x
clc
adc #$30
jsr chrout
lda #<interlude
ldx #>interlude
jsr print_string
tsx
lda to,x
clc
adc #$30
jsr chrout
lda #<postlude
ldx #>postlude
jsr print_string
pla
tay
pla
tax
pla
rts
; utility routine: print null-terminated string at address AX
print_string:
sta temp
stx temp+1
ldy #0
loop: lda (temp),y
beq done_print
jsr chrout
iny
bne loop
done_print:
rts- Output:
MOVE DISK FROM 1 TO 2 MOVE DISK FROM 1 TO 3 MOVE DISK FROM 2 TO 3 MOVE DISK FROM 1 TO 2 MOVE DISK FROM 3 TO 1 MOVE DISK FROM 3 TO 2 MOVE DISK FROM 1 TO 2 MOVE DISK FROM 1 TO 3 MOVE DISK FROM 2 TO 3 MOVE DISK FROM 2 TO 1 MOVE DISK FROM 3 TO 1 MOVE DISK FROM 2 TO 3 MOVE DISK FROM 1 TO 2 MOVE DISK FROM 1 TO 3 MOVE DISK FROM 2 TO 3
8080 Assembly
org 100h
lhld 6 ; Top of CP/M usable memory
sphl ; Put the stack there
lxi b,0401h ; Set up first arguments to move()
lxi d,0203h
call move ; move(4, 1, 2, 3)
rst 0 ; quit program
;;; Move B disks from C via D to E.
move: dcr b ; One fewer disk in next iteration
jz mvout ; If this was the last disk, print move and stop
push b ; Otherwise, save registers,
push d
mov a,d ; First recursive call
mov d,e
mov e,a
call move ; move(B-1, C, E, D)
pop d ; Restore registers
pop b
call mvout ; Print current move
mov a,c ; Second recursive call
mov c,d
mov d,a
jmp move ; move(B-1, D, C, E) - tail call optimization
;;; Print move, saving registers.
mvout: push b ; Save registers on stack
push d
mov a,c ; Store 'from' as ASCII digit in 'from' space
adi '0'
sta out1
mov a,e ; Store 'to' as ASCII digit in 'to' space
adi '0'
sta out2
lxi d,outstr
mvi c,9 ; CP/M call to print the string
call 5
pop d ; Restore register contents
pop b
ret
;;; Move output with placeholder for pole numbers
outstr: db 'Move disk from pole '
out1: db '* to pole '
out2: db '*',13,10,'$'- Output:
Move disk from pole 1 to pole 2 Move disk from pole 1 to pole 3 Move disk from pole 2 to pole 3 Move disk from pole 1 to pole 2 Move disk from pole 3 to pole 1 Move disk from pole 3 to pole 2 Move disk from pole 1 to pole 2 Move disk from pole 1 to pole 3 Move disk from pole 2 to pole 3 Move disk from pole 2 to pole 1 Move disk from pole 3 to pole 1 Move disk from pole 2 to pole 3 Move disk from pole 1 to pole 2 Move disk from pole 1 to pole 3 Move disk from pole 2 to pole 3
8086 Assembly
cpu 8086
bits 16
org 100h
section .text
mov bx,0402h ; Set up first arguments to move()
mov cx,0103h ; Registers chosen s.t. CX contains output
;;; Move BH disks from CH via BL to CL
move: dec bh ; One fewer disk in next iteration
jz .out ; If this was last disk, just print move
push bx ; Save the registers for a recursive call
push cx
xchg bl,cl ; Swap the 'to' and 'via' registers
call move ; move(BH, CH, CL, BL)
pop cx ; Restore the registers from the stack
pop bx
call .out ; Print the move
xchg ch,bl ; Swap the 'from' and 'via' registers
jmp move ; move(BH, BL, CH, CL)
;;; Print the move
.out: mov ax,'00' ; Add ASCII 0 to both 'from' and 'to'
add ax,cx ; in one 16-bit operation
mov [out1],ah ; Store 'from' field in output
mov [out2],al ; Store 'to' field in output
mov dx,outstr ; MS-DOS system call to print string
mov ah,9
int 21h
ret
section .data
outstr: db 'Move disk from pole '
out1: db '* to pole '
out2: db '*',13,10,'$'
- Output:
Move disk from pole 1 to pole 2 Move disk from pole 1 to pole 3 Move disk from pole 2 to pole 3 Move disk from pole 1 to pole 2 Move disk from pole 3 to pole 1 Move disk from pole 3 to pole 2 Move disk from pole 1 to pole 2 Move disk from pole 1 to pole 3 Move disk from pole 2 to pole 3 Move disk from pole 2 to pole 1 Move disk from pole 3 to pole 1 Move disk from pole 2 to pole 3 Move disk from pole 1 to pole 2 Move disk from pole 1 to pole 3 Move disk from pole 2 to pole 3
8th
5 var, disks
var sa
var sb
var sc
: save sc ! sb ! sa ! disks ! ;
: get sa @ sb @ sc @ ;
: get2 get swap ;
: hanoi
save disks @ not if ;; then
disks @ get
disks @ n:1- get2 hanoi save
cr
" move a ring from " . sa @ . " to " . sb @ .
disks @ n:1- get2 rot hanoi
;
" Tower of Hanoi, with " . disks @ . " rings: " .
disks @ 1 2 3 hanoi cr bye
ABC
HOW TO MOVE n DISKS FROM src VIA via TO dest:
IF n>0:
MOVE n-1 DISKS FROM src VIA dest TO via
WRITE "Move disk from pole", src, "to pole", dest/
MOVE n-1 DISKS FROM via VIA dest TO src
MOVE 4 DISKS FROM 1 VIA 2 TO 3- Output:
Move disk from pole 1 to pole 2 Move disk from pole 1 to pole 3 Move disk from pole 2 to pole 1 Move disk from pole 1 to pole 2 Move disk from pole 3 to pole 2 Move disk from pole 3 to pole 1 Move disk from pole 2 to pole 3 Move disk from pole 1 to pole 3 Move disk from pole 2 to pole 1 Move disk from pole 2 to pole 3 Move disk from pole 1 to pole 2 Move disk from pole 2 to pole 1 Move disk from pole 3 to pole 1 Move disk from pole 3 to pole 2 Move disk from pole 1 to pole 3
Action!
...via PL/M
;;; Iterative Towers of Hanoi; translated from Tiny BASIC via PL/M
;;;
DEFINE NUMBER_OF_DISCS = "4"
PROC Main()
INT d, n, x
n = 1
FOR d = 1 TO NUMBER_OF_DISCS DO
n = n + n
OD
FOR x = 1 TO n - 1 DO
; as with Algol W, PL/M, Action! has bit and MOD operators
Print( "Move disc on peg " )
Put( '1 + ( ( x AND ( x - 1 ) ) MOD 3 ) )
Print( " to peg " )
Put( '1 + ( ( ( x OR ( x - 1 ) ) + 1 ) MOD 3 ) )
PutE()
OD
RETURN- Output:
Move disc on peg 1 to peg 3 Move disc on peg 1 to peg 2 Move disc on peg 3 to peg 2 Move disc on peg 1 to peg 3 Move disc on peg 2 to peg 1 Move disc on peg 2 to peg 3 Move disc on peg 1 to peg 3 Move disc on peg 1 to peg 2 Move disc on peg 3 to peg 2 Move disc on peg 3 to peg 1 Move disc on peg 2 to peg 1 Move disc on peg 3 to peg 2 Move disc on peg 1 to peg 3 Move disc on peg 1 to peg 2 Move disc on peg 3 to peg 2
ActionScript
public function move(n:int, from:int, to:int, via:int):void
{
if (n > 0)
{
move(n - 1, from, via, to);
trace("Move disk from pole " + from + " to pole " + to);
move(n - 1, via, to, from);
}
}
Ada
with Ada.Text_Io; use Ada.Text_Io;
procedure Towers is
type Pegs is (Left, Center, Right);
procedure Hanoi (Ndisks : Natural; Start_Peg : Pegs := Left; End_Peg : Pegs := Right; Via_Peg : Pegs := Center) is
begin
if Ndisks > 0 then
Hanoi(Ndisks - 1, Start_Peg, Via_Peg, End_Peg);
Put_Line("Move disk" & Natural'Image(Ndisks) & " from " & Pegs'Image(Start_Peg) & " to " & Pegs'Image(End_Peg));
Hanoi(Ndisks - 1, Via_Peg, End_Peg, Start_Peg);
end if;
end Hanoi;
begin
Hanoi(4);
end Towers;
Agena
move := proc(n::number, src::number, dst::number, via::number) is
if n > 0 then
move(n - 1, src, via, dst)
print(src & ' to ' & dst)
move(n - 1, via, dst, src)
fi
end
move(4, 1, 2, 3)ALGOL 60
begin
procedure movedisk(n, f, t);
integer n, f, t;
begin
outstring (1, "Move disk from");
outinteger(1, f);
outstring (1, "to");
outinteger(1, t);
outstring (1, "\n");
end;
procedure dohanoi(n, f, t, u);
integer n, f, t, u;
begin
if n < 2 then
movedisk(1, f, t)
else
begin
dohanoi(n - 1, f, u, t);
movedisk(1, f, t);
dohanoi(n - 1, u, t, f);
end;
end;
dohanoi(4, 1, 2, 3);
outstring(1,"Towers of Hanoi puzzle completed!")
end- Output:
Move disk from 1 to 3 Move disk from 1 to 2 Move disk from 3 to 2 Move disk from 1 to 3 Move disk from 2 to 1 Move disk from 2 to 3 Move disk from 1 to 3 Move disk from 1 to 2 Move disk from 3 to 2 Move disk from 3 to 1 Move disk from 2 to 1 Move disk from 3 to 2 Move disk from 1 to 3 Move disk from 1 to 2 Move disk from 3 to 2 Towers of Hanoi puzzle completed!
ALGOL 68
PROC move = (INT n, from, to, via) VOID:
IF n > 0 THEN
move(n - 1, from, via, to);
printf(($"Move disk from pole "g" to pole "gl$, from, to));
move(n - 1, via, to, from)
FI
;
main: (
move(4, 1,2,3)
)
COMMENT Disk number is also printed in this code (works with a68g): COMMENT
PROC move = (INT n, from, to, via) VOID:
IF n > 0 THEN
move(n - 1, from, via, to);
printf(($"Move disk "g" from pole "g" to pole "gl$, n, from, to));
move(n - 1, via, to, from)
FI ;
main: (
move(4, 1,2,3)
)ALGOL-M
begin
procedure move(n, src, via, dest);
integer n;
string(1) src, via, dest;
begin
if n > 0 then
begin
move(n-1, src, dest, via);
write("Move disk from pole ");
writeon(src);
writeon(" to pole ");
writeon(dest);
move(n-1, via, src, dest);
end;
end;
move(4, "1", "2", "3");
end- Output:
Move disk from pole 1 to pole 2 Move disk from pole 1 to pole 3 Move disk from pole 2 to pole 3 Move disk from pole 1 to pole 2 Move disk from pole 3 to pole 1 Move disk from pole 3 to pole 2 Move disk from pole 1 to pole 2 Move disk from pole 1 to pole 3 Move disk from pole 2 to pole 3 Move disk from pole 2 to pole 1 Move disk from pole 3 to pole 1 Move disk from pole 2 to pole 3 Move disk from pole 1 to pole 2 Move disk from pole 1 to pole 3 Move disk from pole 2 to pole 3
ALGOL W
Recursive
Following Agena, Algol 68, AmigaE...
begin
procedure move ( integer value n, from, to, via ) ;
if n > 0 then begin
move( n - 1, from, via, to );
write( i_w := 1, s_w := 0, "Move disk from peg: ", from, " to peg: ", to );
move( n - 1, via, to, from )
end move ;
move( 4, 1, 2, 3 )
end.
Iterative
begin % iterative towers of hanoi - translated from Tiny Basic %
integer d, n;
while begin writeon( "How many disks? " );
read( d );
d < 1 or d > 10
end
do begin end;
n := 1;
while d not = 0 do begin
d := d - 1;
n := 2 * n
end;
for x := 1 until n - 1 do begin
integer s, t;
% Algol W has the necessary bit and modulo operators so these are used here %
% instead of implementing them via subroutines %
s := number( bitstring( x ) and bitstring( x - 1 ) ) rem 3;
t := ( number( bitstring( x ) or bitstring( x - 1 ) ) + 1 ) rem 3;
write( i_w := 1, s_w := 0, "Move disc on peg ", s + 1, " to peg ", t + 1 )
end
end.
AmigaE
PROC move(n, from, to, via)
IF n > 0
move(n-1, from, via, to)
WriteF('Move disk from pole \d to pole \d\n', from, to)
move(n-1, via, to, from)
ENDIF
ENDPROC
PROC main()
move(4, 1,2,3)
ENDPROCAmazing Hopper
#include <hopper.h>
#proto hanoi(_X_,_Y_,_Z_,_W_)
main:
get arg number (2,discos)
{discos}!neg? do{fail=0,mov(fail),{"I need a positive (or zero) number here, not: ",fail}println,exit(0)}
pos? do{
_hanoi( discos, "A", "B", "C" )
}
exit(0)
.locals
hanoi(discos,inicio,aux,fin)
iif( {discos}eqto(1), {inicio, "->", fin, "\n"};print, _hanoi({discos}minus(1), inicio,fin,aux);\
{inicio, "->", fin, "\n"};print;\
_hanoi({discos}minus(1), aux, inicio, fin))
back- Output:
For 4 discs: A->B A->C B->C A->B C->A C->B A->B A->C B->C B->A C->A B->C A->B A->C B->C
APL
hanoi←{
move←{
n from to via←⍵
n≤0:⍬
l←∇(n-1) from via to
r←∇(n-1) via to from
l,(⊂from to),r
}
'⊂Move disk from pole ⊃,I1,⊂ to pole ⊃,I1'⎕FMT↑move ⍵
}
- Output:
hanoi 4 1 2 3 Move disk from pole 1 to pole 3 Move disk from pole 1 to pole 2 Move disk from pole 3 to pole 2 Move disk from pole 1 to pole 3 Move disk from pole 2 to pole 1 Move disk from pole 2 to pole 3 Move disk from pole 1 to pole 3 Move disk from pole 1 to pole 2 Move disk from pole 3 to pole 2 Move disk from pole 3 to pole 1 Move disk from pole 2 to pole 1 Move disk from pole 3 to pole 2 Move disk from pole 1 to pole 3 Move disk from pole 1 to pole 2 Move disk from pole 3 to pole 2
AppleScript
--------------------- TOWERS OF HANOI --------------------
-- hanoi :: Int -> (String, String, String) -> [(String, String)]
on hanoi(n, abc)
script go
on |λ|(n, {x, y, z})
if n > 0 then
set m to n - 1
|λ|(m, {x, z, y}) & ¬
{{x, y}} & |λ|(m, {z, y, x})
else
{}
end if
end |λ|
end script
go's |λ|(n, abc)
end hanoi
--------------------------- TEST -------------------------
on run
unlines(map(intercalate(" -> "), ¬
hanoi(3, {"left", "right", "mid"})))
end run
-------------------- GENERIC FUNCTIONS -------------------
-- intercalate :: String -> [String] -> String
on intercalate(delim)
script
on |λ|(xs)
set {dlm, my text item delimiters} to ¬
{my text item delimiters, delim}
set s to xs as text
set my text item delimiters to dlm
s
end |λ|
end script
end intercalate
-- Lift 2nd class handler function into 1st class script wrapper
-- mReturn :: First-class m => (a -> b) -> m (a -> b)
on mReturn(f)
if class of f is script then
f
else
script
property |λ| : f
end script
end if
end mReturn
-- map :: (a -> b) -> [a] -> [b]
on map(f, xs)
tell mReturn(f)
set lng to length of xs
set lst to {}
repeat with i from 1 to lng
set end of lst to |λ|(item i of xs, i, xs)
end repeat
return lst
end tell
end map
-- unlines :: [String] -> String
on unlines(xs)
set {dlm, my text item delimiters} to ¬
{my text item delimiters, linefeed}
set str to xs as text
set my text item delimiters to dlm
str
end unlines
- Output:
left -> right left -> mid right -> mid left -> right mid -> left mid -> right left -> right
More illustratively:
(I've now eliminated the recursive |move|() handler's tail calls. So it's now only called 2 ^ (n - 1) times as opposed to 2 ^ (n + 1) - 1 with full recursion. The maximum call depth of n is only reached once, whereas with full recursion, the maximum depth was n + 1 and this was reached 2 ^ n times.)
on hanoi(n, source, target)
set t1 to tab & "tower 1: " & tab
set t2 to tab & "tower 2: " & tab
set t3 to tab & "tower 3: " & tab
script o
property m : 0
property tower1 : {}
property tower2 : {}
property tower3 : {}
property towerRefs : {a reference to tower1, a reference to tower2, a reference to tower3}
property process : missing value
on |move|(n, source, target)
set aux to 6 - source - target
repeat with n from n to 2 by -1 -- Tail call elimination repeat.
|move|(n - 1, source, aux)
set end of item target of my towerRefs to n
tell item source of my towerRefs to set its contents to reverse of rest of its reverse
set m to m + 1
set end of my process to ¬
{(m as text) & ". move disc " & n & (" from tower " & source) & (" to tower " & target & ":"), ¬
t1 & tower1, ¬
t2 & tower2, ¬
t3 & tower3}
tell source
set source to aux
set aux to it
end tell
end repeat
-- Specific code for n = 1:
set end of item target of my towerRefs to 1
tell item source of my towerRefs to set its contents to reverse of rest of its reverse
set m to m + 1
set end of my process to ¬
{(m as text) & ". move disc 1 from tower " & source & (" to tower " & target & ":"), ¬
t1 & tower1, ¬
t2 & tower2, ¬
t3 & tower3}
end |move|
end script
repeat with i from n to 1 by -1
set end of item source of o's towerRefs to i
end repeat
set astid to AppleScript's text item delimiters
set AppleScript's text item delimiters to ", "
set o's process to {"Starting with " & n & (" discs on tower " & (source & ":")), ¬
t1 & o's tower1, t2 & o's tower2, t3 & o's tower3}
if (n > 0) then tell o to |move|(n, source, target)
set end of o's process to "That's it!"
set AppleScript's text item delimiters to linefeed
set process to o's process as text
set AppleScript's text item delimiters to astid
return process
end hanoi
-- Test:
set numberOfDiscs to 3
set sourceTower to 1
set destinationTower to 2
hanoi(numberOfDiscs, sourceTower, destinationTower)
- Output:
"Starting with 3 discs on tower 1:
tower 1: 3, 2, 1
tower 2:
tower 3:
1. move disc 1 from tower 1 to tower 2:
tower 1: 3, 2
tower 2: 1
tower 3:
2. move disc 2 from tower 1 to tower 3:
tower 1: 3
tower 2: 1
tower 3: 2
3. move disc 1 from tower 2 to tower 3:
tower 1: 3
tower 2:
tower 3: 2, 1
4. move disc 3 from tower 1 to tower 2:
tower 1:
tower 2: 3
tower 3: 2, 1
5. move disc 1 from tower 3 to tower 1:
tower 1: 1
tower 2: 3
tower 3: 2
6. move disc 2 from tower 3 to tower 2:
tower 1: 1
tower 2: 3, 2
tower 3:
7. move disc 1 from tower 1 to tower 2:
tower 1:
tower 2: 3, 2, 1
tower 3:
That's it!"
ARM Assembly
.text
.global _start
_start: mov r0,#4 @ 4 disks,
mov r1,#1 @ from pole 1,
mov r2,#2 @ via pole 2,
mov r3,#3 @ to pole 3.
bl move
mov r0,#0 @ Exit to Linux afterwards
mov r7,#1
swi #0
@@@ Move r0 disks from r1 via r2 to r3
move: subs r0,r0,#1 @ One fewer disk in next iteration
beq show @ If last disk, just print move
push {r0-r3,lr} @ Save all the registers incl. link register
eor r2,r2,r3 @ Swap the 'to' and 'via' registers
eor r3,r2,r3
eor r2,r2,r3
bl move @ Recursive call
pop {r0-r3} @ Restore all the registers except LR
bl show @ Show current move
eor r1,r1,r3 @ Swap the 'to' and 'via' registers
eor r3,r1,r3
eor r1,r1,r3
pop {lr} @ Restore link register
b move @ Tail call
@@@ Show move
show: push {r0-r3,lr} @ Save all the registers
add r1,r1,#'0 @ Write the source pole
ldr lr,=spole
strb r1,[lr]
add r3,r3,#'0 @ Write the destination pole
ldr lr,=dpole
strb r3,[lr]
mov r0,#1 @ 1 = stdout
ldr r1,=moves @ Pointer to string
ldr r2,=mlen @ Length of string
mov r7,#4 @ 4 = Linux write syscall
swi #0 @ Print the move
pop {r0-r3,pc} @ Restore all the registers and return
.data
moves: .ascii "Move disk from pole "
spole: .ascii "* to pole "
dpole: .ascii "*\n"
mlen = . - moves
- Output:
Move disk from pole 1 to pole 2 Move disk from pole 1 to pole 3 Move disk from pole 3 to pole 1 Move disk from pole 1 to pole 2 Move disk from pole 2 to pole 3 Move disk from pole 2 to pole 1 Move disk from pole 1 to pole 2 Move disk from pole 1 to pole 3 Move disk from pole 3 to pole 1 Move disk from pole 3 to pole 2 Move disk from pole 2 to pole 3 Move disk from pole 3 to pole 1 Move disk from pole 1 to pole 2 Move disk from pole 1 to pole 3 Move disk from pole 3 to pole 1
Arturo
hanoi: function [n f dir via][
if n>0 [
hanoi n-1 f via dir
print ["Move disk" n "from" f "to" dir]
hanoi n-1 via dir f
]
]
hanoi 3 'L 'M 'R
- Output:
Move disk 1 from L to M Move disk 2 from L to R Move disk 1 from M to R Move disk 3 from L to M Move disk 1 from R to L Move disk 2 from R to M Move disk 1 from L to M
AutoHotkey
move(n, from, to, via) ;n = # of disks, from = start pole, to = end pole, via = remaining pole
{
if (n = 1)
{
msgbox , Move disk from pole %from% to pole %to%
}
else
{
move(n-1, from, via, to)
move(1, from, to, via)
move(n-1, via, to, from)
}
}
move(64, 1, 3, 2)
AutoIt
Func move($n, $from, $to, $via)
If ($n = 1) Then
ConsoleWrite(StringFormat("Move disk from pole "&$from&" To pole "&$to&"\n"))
Else
move($n - 1, $from, $via, $to)
move(1, $from, $to, $via)
move($n - 1, $via, $to, $from)
EndIf
EndFunc
move(4, 1,2,3)
AWK
$ awk 'func hanoi(n,f,t,v){if(n>0){hanoi(n-1,f,v,t);print(f,"->",t);hanoi(n-1,v,t,f)}}
BEGIN{hanoi(4,"left","middle","right")}'
- Output:
left -> right left -> middle right -> middle left -> right middle -> left middle -> right left -> right left -> middle right -> middle right -> left middle -> left right -> middle left -> right left -> middle right -> middle
BASIC
Using a Subroutine
SUB move (n AS Integer, fromPeg AS Integer, toPeg AS Integer, viaPeg AS Integer)
IF n>0 THEN
move n-1, fromPeg, viaPeg, toPeg
PRINT "Move disk from "; fromPeg; " to "; toPeg
move n-1, viaPeg, toPeg, fromPeg
END IF
END SUB
move 4,1,2,3Using GOSUBs
Here's an example of implementing recursion in an old BASIC that only has global variables:
10 DEPTH=4: REM SHOULD EQUAL NUMBER OF DISKS
20 DIM N(DEPTH), F(DEPTH), T(DEPTH), V(DEPTH): REM STACK PER PARAMETER
30 SP = 0: REM STACK POINTER
40 N(SP) = 4: REM START WITH 4 DISCS
50 F(SP) = 1: REM ON PEG 1
60 T(SP) = 2: REM MOVE TO PEG 2
70 V(SP) = 3: REM VIA PEG 3
80 GOSUB 100
90 END
99 REM MOVE SUBROUTINE
100 IF N(SP) = 0 THEN RETURN
110 OS = SP: REM STORE STACK POINTER
120 SP = SP + 1: REM INCREMENT STACK POINTER
130 N(SP) = N(OS) - 1: REM MOVE N-1 DISCS
140 F(SP) = F(OS) : REM FROM START PEG
150 T(SP) = V(OS) : REM TO VIA PEG
160 V(SP) = T(OS) : REM VIA TO PEG
170 GOSUB 100
180 OS = SP - 1: REM OS WILL HAVE CHANGED
190 PRINT "MOVE DISC FROM"; F(OS); "TO"; T(OS)
200 N(SP) = N(OS) - 1: REM MOVE N-1 DISCS
210 F(SP) = V(OS) : REM FROM VIA PEG
220 T(SP) = T(OS) : REM TO DEST PEG
230 V(SP) = F(OS) : REM VIA FROM PEG
240 GOSUB 100
250 SP = SP - 1 : REM RESTORE STACK POINTER FOR CALLER
260 RETURNUsing binary method
Very fast version in BASIC V2 on Commodore C-64
10 DEF FNM3(X)=X-INT(X/3)*3:REM MODULO 3
20 N=4:GOSUB 100
30 END
99 REM HANOI
100 :FOR M=1 TO 2^N-1
110 ::PRINT MID$(STR$(M),2);":",FNM3(M AND M-1)+1;"TO";FNM3((M OR M-1)+1)+1
130 :NEXT M
140 RETURN- Output:
1: 1 TO 3 2: 1 TO 2 3: 3 TO 2 4: 1 TO 3 5: 2 TO 1 6: 2 TO 3 7: 1 TO 3 8: 1 TO 2 9: 3 TO 2 10: 3 TO 1 11: 2 TO 1 12: 3 TO 2 13: 1 TO 3 14: 1 TO 2 15: 3 TO 2
BASIC256
call move(4,1,2,3)
print "Towers of Hanoi puzzle completed!"
end
subroutine move (n, fromPeg, toPeg, viaPeg)
if n>0 then
call move(n-1, fromPeg, viaPeg, toPeg)
print "Move disk from "+fromPeg+" to "+toPeg
call move(n-1, viaPeg, toPeg, fromPeg)
end if
end subroutine- Output:
Move disk from 1 to 3 Move disk from 1 to 2 Move disk from 3 to 2 Move disk from 1 to 3 Move disk from 2 to 1 Move disk from 2 to 3 Move disk from 1 to 3 Move disk from 1 to 2 Move disk from 3 to 2 Move disk from 3 to 1 Move disk from 2 to 1 Move disk from 3 to 2 Move disk from 1 to 3 Move disk from 1 to 2 Move disk from 3 to 2 Towers of Hanoi puzzle completed!
IS-BASIC
100 PROGRAM "Hanoi.bas"
110 CALL HANOI(4,1,3,2)
120 DEF HANOI(DISK,FRO,TO,WITH)
130 IF DISK>0 THEN
140 CALL HANOI(DISK-1,FRO,WITH,TO)
150 PRINT "Move disk";DISK;"from";FRO;"to";TO
160 CALL HANOI(DISK-1,WITH,TO,FRO)
170 END IF
180 END DEFBatch File
@echo off
setlocal enabledelayedexpansion
%==The main thing==%
%==First param - Number of disks==%
%==Second param - Start pole==%
%==Third param - End pole==%
%==Fourth param - Helper pole==%
call :move 4 START END HELPER
echo.
pause
exit /b 0
%==The "function"==%
:move
setlocal
set n=%1
set from=%2
set to=%3
set via=%4
if %n% gtr 0 (
set /a x=!n!-1
call :move !x! %from% %via% %to%
echo Move top disk from pole %from% to pole %to%.
call :move !x! %via% %to% %from%
)
exit /b 0- Output:
Move top disk from pole START to pole HELPER. Move top disk from pole START to pole END. Move top disk from pole HELPER to pole END. Move top disk from pole START to pole HELPER. Move top disk from pole END to pole START. Move top disk from pole END to pole HELPER. Move top disk from pole START to pole HELPER. Move top disk from pole START to pole END. Move top disk from pole HELPER to pole END. Move top disk from pole HELPER to pole START. Move top disk from pole END to pole START. Move top disk from pole HELPER to pole END. Move top disk from pole START to pole HELPER. Move top disk from pole START to pole END. Move top disk from pole HELPER to pole END. Press any key to continue . . .
BBC BASIC
DIM Disc$(13),Size%(3)
FOR disc% = 1 TO 13
Disc$(disc%) = STRING$(disc%," ")+STR$disc%+STRING$(disc%," ")
IF disc%>=10 Disc$(disc%) = MID$(Disc$(disc%),2)
Disc$(disc%) = CHR$17+CHR$(128+disc%-(disc%>7))+Disc$(disc%)+CHR$17+CHR$128
NEXT disc%
MODE 3
OFF
ndiscs% = 13
FOR n% = ndiscs% TO 1 STEP -1
PROCput(n%,1)
NEXT
INPUT TAB(0,0) "Press Enter to start" dummy$
PRINT TAB(0,0) SPC(20);
PROChanoi(ndiscs%,1,2,3)
VDU 30
END
DEF PROChanoi(a%,b%,c%,d%)
IF a%=0 ENDPROC
PROChanoi(a%-1,b%,d%,c%)
PROCtake(a%,b%)
PROCput(a%,c%)
PROChanoi(a%-1,d%,c%,b%)
ENDPROC
DEF PROCput(disc%,peg%)
PRINTTAB(13+26*(peg%-1)-disc%,20-Size%(peg%))Disc$(disc%);
Size%(peg%) = Size%(peg%)+1
ENDPROC
DEF PROCtake(disc%,peg%)
Size%(peg%) = Size%(peg%)-1
PRINTTAB(13+26*(peg%-1)-disc%,20-Size%(peg%))STRING$(2*disc%+1," ");
ENDPROC
BCPL
get "libhdr"
let start() be move(4, 1, 2, 3)
and move(n, src, via, dest) be if n > 0 do
$( move(n-1, src, dest, via)
writef("Move disk from pole %N to pole %N*N", src, dest);
move(n-1, via, src, dest)
$)- Output:
Move disk from pole 1 to pole 2 Move disk from pole 1 to pole 3 Move disk from pole 2 to pole 3 Move disk from pole 1 to pole 2 Move disk from pole 3 to pole 1 Move disk from pole 3 to pole 2 Move disk from pole 1 to pole 2 Move disk from pole 1 to pole 3 Move disk from pole 2 to pole 3 Move disk from pole 2 to pole 1 Move disk from pole 3 to pole 1 Move disk from pole 2 to pole 3 Move disk from pole 1 to pole 2 Move disk from pole 1 to pole 3 Move disk from pole 2 to pole 3
Befunge
This is loosely based on the Python sample. The number of disks is specified by the first integer on the stack (the initial character 4 in the example below). If you want the program to prompt the user for that value, you can replace the 4 with a & (the read integer command).
48*2+1>#v_:!#@_0" ksid evoM">:#,_$:8/:.v
>8v8:<$#<+9-+*2%3\*3/3:,+55.+1%3:$_,#!>#:<
: >/!#^_:0\:8/1-8vv,_$8%:3/1+.>0" gep ot"^
^++3-%3\*2/3:%8\*<>:^:"from peg "0\*8-1<
- Output:
Move disk 1 from peg 1 to peg 2 Move disk 2 from peg 1 to peg 3 Move disk 1 from peg 2 to peg 3 Move disk 3 from peg 1 to peg 2 Move disk 1 from peg 3 to peg 1 Move disk 2 from peg 3 to peg 2 Move disk 1 from peg 1 to peg 2 Move disk 4 from peg 1 to peg 3 Move disk 1 from peg 2 to peg 3 Move disk 2 from peg 2 to peg 1 Move disk 1 from peg 3 to peg 1 Move disk 3 from peg 2 to peg 3 Move disk 1 from peg 1 to peg 2 Move disk 2 from peg 1 to peg 3 Move disk 1 from peg 2 to peg 3
BQN
Based on: APL
Move ← {
𝕩⊑⊸≤0 ? ⟨⟩;
𝕊 n‿from‿to‿via:
l ← 𝕊 ⟨n-1, from, via, to⟩
r ← 𝕊 ⟨n-1, via, to, from⟩
l∾(<from‿to)∾r
}
{"Move disk from pole "∾(•Fmt 𝕨)∾" to pole "∾•Fmt 𝕩}´˘>Move 4‿1‿2‿3
┌─
╵"Move disk from pole 1 to pole 3
Move disk from pole 1 to pole 2
Move disk from pole 3 to pole 2
Move disk from pole 1 to pole 3
Move disk from pole 2 to pole 1
Move disk from pole 2 to pole 3
Move disk from pole 1 to pole 3
Move disk from pole 1 to pole 2
Move disk from pole 3 to pole 2
Move disk from pole 3 to pole 1
Move disk from pole 2 to pole 1
Move disk from pole 3 to pole 2
Move disk from pole 1 to pole 3
Move disk from pole 1 to pole 2
Move disk from pole 3 to pole 2"
┘
Bracmat
( ( move
= n from to via
. !arg:(?n,?from,?to,?via)
& ( !n:>0
& move$(!n+-1,!from,!via,!to)
& out$("Move disk from pole " !from " to pole " !to)
& move$(!n+-1,!via,!to,!from)
|
)
)
& move$(4,1,2,3)
);- Output:
Move disk from pole 1 to pole 3 Move disk from pole 1 to pole 2 Move disk from pole 3 to pole 2 Move disk from pole 1 to pole 3 Move disk from pole 2 to pole 1 Move disk from pole 2 to pole 3 Move disk from pole 1 to pole 3 Move disk from pole 1 to pole 2 Move disk from pole 3 to pole 2 Move disk from pole 3 to pole 1 Move disk from pole 2 to pole 1 Move disk from pole 3 to pole 2 Move disk from pole 1 to pole 3 Move disk from pole 1 to pole 2 Move disk from pole 3 to pole 2
Brainf***
[
This implementation is recursive and uses
a stack, consisting of frames that are 8
bytes long. The layout is as follows:
Byte Description
0 recursion flag
(the program stops if the flag is
zero)
1 the step which is currently
executed
4 means a call to
move(a, c, b, n - 1)
3 means a call to
move(a, b, c, 1)
2 means a call to
move(b, a, c, n - 1)
1 prints the source and dest pile
2 flag to check whether the current
step has already been done or if
it still must be executed
3 the step which will be executed
in the next loop
4 the source pile
5 the helper pile
6 the destination pile
7 the number of disks to move
The first stack frame (0 0 0 0 0 0 0 0)
is used to abort the recursion.
]
>>>>>>>>
These are the parameters for the program
(1 4 1 0 'a 'b 'c 5)
+>++++>+>>
>>>>++++++++[<++++++++++++>-]<
[<<<+>+>+>-]<<<+>++>+++>+++++>
<<<<<<<<
[> while (recurse)
[- if (step gt 0)
>[-]+< todo = 1
[- if (step gt 1)
[- if (step gt 2)
[- if (step gt 3)
>>+++<< next = 3
>-< todo = 0
>>>>>>[>+>+<<-]>[<+>-]> n dup
-
[[-] if (sub(n 1) gt 0)
<+>>>++++> push (1 0 0 4)
copy and push a
<<<<<<<<[>>>>>>>>+>+
<<<<<<<<<-]>>>>>>>>
>[<<<<<<<<<+>>>>>>>>>-]< >
copy and push c
<<<<<<<[>>>>>>>+>+
<<<<<<<<-]>>>>>>>
>[<<<<<<<<+>>>>>>>>-]< >
copy and push b
<<<<<<<<<[>>>>>>>>>+>+
<<<<<<<<<<-]>>>>>>>>>
>[<<<<<<<<<<+>>>>>>>>>>-]< >
copy n and push sub(n 1)
<<<<<<<<[>>>>>>>>+>+
<<<<<<<<<-]>>>>>>>>
>[<<<<<<<<<+>>>>>>>>>-]< -
>>
]
<<<<<<<<
]
>[-< if ((step gt 2) and todo)
>>++<< next = 2
>>>>>>>
+>>>+> push 1 0 0 1 a b c 1
<<<<<<<<[>>>>>>>>+>+
<<<<<<<<<-]>>>>>>>>
>[<<<<<<<<<+>>>>>>>>>-]< > a
<<<<<<<<[>>>>>>>>+>+
<<<<<<<<<-]>>>>>>>>
>[<<<<<<<<<+>>>>>>>>>-]< > b
<<<<<<<<[>>>>>>>>+>+
<<<<<<<<<-]>>>>>>>>
>[<<<<<<<<<+>>>>>>>>>-]< > c
+ >>
>]<
]
>[-< if ((step gt 1) and todo)
>>>>>>[>+>+<<-]>[<+>-]> n dup
-
[[-] if (n sub 1 gt 0)
<+>>>++++> push (1 0 0 4)
copy and push b
<<<<<<<[>>>>>>>+
<<<<<<<-]>>>>>>>
>[<<<<<<<<+>>>>>>>>-]< >
copy and push a
<<<<<<<<<[>>>>>>>>>+
<<<<<<<<<-]>>>>>>>>>
>[<<<<<<<<<<+>>>>>>>>>>-]< >
copy and push c
<<<<<<<<[>>>>>>>>+
<<<<<<<<-]>>>>>>>>
>[<<<<<<<<<+>>>>>>>>>-]< >
copy n and push sub(n 1)
<<<<<<<<[>>>>>>>>+>+
<<<<<<<<<-]>>>>>>>>
>[<<<<<<<<<+>>>>>>>>>-]< -
>>
]
<<<<<<<<
>]<
]
>[-< if ((step gt 0) and todo)
>>>>>>>
>++++[<++++++++>-]<
>>++++++++[<+++++++++>-]<++++
>>++++++++[<++++++++++++>-]<+++++
>>+++++++++[<++++++++++++>-]<+++
<<<
>.+++++++>.++.--.<<.
>>-.+++++.----.<<.
>>>.<---.+++.>+++.+.+.<.<<.
>.>--.+++++.---.++++.
-------.+++.<<.
>>>++.-------.-.<<<.
>+.>>+++++++.---.-----.<<<.
<<<<.>>>>.
>>----.>++++++++.<+++++.<<.
>.>>.---.-----.<<<.
<<.>>++++++++++++++.
>>>[-]<[-]<[-]<[-]
+++++++++++++.---.[-]
<<<<<<<
>]<
>>[<<+>>-]<< step = next
]
return with clear stack frame
<[-]>[-]>[-]>[-]>[-]>[-]>[-]>[-]<<<<<<
<<<<<<<<
>>[<<+>>-]<< step = next
<
]
Bruijn
:import std/Combinator .
:import std/Number .
:import std/String .
hanoi y [[[[=?2 empty go]]]]
go [(4 --3 2 0) ++ str ++ (4 --3 0 1)] ((+6) - 1 - 0)
str "Move " ++ disk ++ " from " ++ source ++ " to " ++ destination ++ "\n"
disk number→string 3
source number→string 2
destination number→string 1C
#include <stdio.h>
void move(int n, int from, int via, int to)
{
if (n > 1) {
move(n - 1, from, to, via);
printf("Move disk from pole %d to pole %d\n", from, to);
move(n - 1, via, from, to);
} else {
printf("Move disk from pole %d to pole %d\n", from, to);
}
}
int main()
{
move(4, 1,2,3);
return 0;
}
Animate it for fun:
#include <stdio.h>
#include <stdlib.h>
#include <unistd.h>
typedef struct { int *x, n; } tower;
tower *new_tower(int cap)
{
tower *t = calloc(1, sizeof(tower) + sizeof(int) * cap);
t->x = (int*)(t + 1);
return t;
}
tower *t[3];
int height;
void text(int y, int i, int d, const char *s)
{
printf("\033[%d;%dH", height - y + 1, (height + 1) * (2 * i + 1) - d);
while (d--) printf("%s", s);
}
void add_disk(int i, int d)
{
t[i]->x[t[i]->n++] = d;
text(t[i]->n, i, d, "==");
usleep(100000);
fflush(stdout);
}
int remove_disk(int i)
{
int d = t[i]->x[--t[i]->n];
text(t[i]->n + 1, i, d, " ");
return d;
}
void move(int n, int from, int to, int via)
{
if (!n) return;
move(n - 1, from, via, to);
add_disk(to, remove_disk(from));
move(n - 1, via, to, from);
}
int main(int c, char *v[])
{
puts("\033[H\033[J");
if (c <= 1 || (height = atoi(v[1])) <= 0)
height = 8;
for (c = 0; c < 3; c++) t[c] = new_tower(height);
for (c = height; c; c--) add_disk(0, c);
move(height, 0, 2, 1);
text(1, 0, 1, "\n");
return 0;
}
C#
public void move(int n, int from, int to, int via) {
if (n == 1) {
System.Console.WriteLine("Move disk from pole " + from + " to pole " + to);
} else {
move(n - 1, from, via, to);
move(1, from, to, via);
move(n - 1, via, to, from);
}
}
C++
void move(int n, int from, int to, int via) {
if (n == 1) {
std::cout << "Move disk from pole " << from << " to pole " << to << std::endl;
} else {
move(n - 1, from, via, to);
move(1, from, to, via);
move(n - 1, via, to, from);
}
}
Chipmunk Basic
100 cls
110 print "Three disks" : print
120 hanoi(3,1,2,3)
130 print chr$(10)"Four disks" chr$(10)
140 hanoi(4,1,2,3)
150 print : print "Towers of Hanoi puzzle completed!"
160 end
170 sub hanoi(n,desde,hasta,via)
180 if n > 0 then
190 hanoi(n-1,desde,via,hasta)
200 print "Move disk " n "from pole " desde "to pole " hasta
210 hanoi(n-1,via,hasta,desde)
220 endif
230 end sub
Clojure
Side-Effecting Solution
(defn towers-of-hanoi [n from to via]
(when (pos? n)
(towers-of-hanoi (dec n) from via to)
(printf "Move from %s to %s\n" from to)
(recur (dec n) via to from)))
Lazy Solution
(defn towers-of-hanoi [n from to via]
(when (pos? n)
(lazy-cat (towers-of-hanoi (dec n) from via to)
(cons [from '-> to]
(towers-of-hanoi (dec n) via to from)))))
CLU
move = proc (n, from, via, to: int)
po: stream := stream$primary_output()
if n > 0 then
move(n-1, from, to, via)
stream$putl(po, "Move disk from pole "
|| int$unparse(from)
|| " to pole "
|| int$unparse(to))
move(n-1, via, from, to)
end
end move
start_up = proc ()
move(4, 1, 2, 3)
end start_up- Output:
Move disk from pole 1 to pole 2 Move disk from pole 1 to pole 3 Move disk from pole 2 to pole 3 Move disk from pole 1 to pole 2 Move disk from pole 3 to pole 1 Move disk from pole 3 to pole 2 Move disk from pole 1 to pole 2 Move disk from pole 1 to pole 3 Move disk from pole 2 to pole 3 Move disk from pole 2 to pole 1 Move disk from pole 3 to pole 1 Move disk from pole 2 to pole 3 Move disk from pole 1 to pole 2 Move disk from pole 1 to pole 3 Move disk from pole 2 to pole 3
COBOL
>>SOURCE FREE
IDENTIFICATION DIVISION.
PROGRAM-ID. towers-of-hanoi.
PROCEDURE DIVISION.
CALL "move-disk" USING 4, 1, 2, 3
.
END PROGRAM towers-of-hanoi.
IDENTIFICATION DIVISION.
PROGRAM-ID. move-disk RECURSIVE.
DATA DIVISION.
LINKAGE SECTION.
01 n PIC 9 USAGE COMP.
01 from-pole PIC 9 USAGE COMP.
01 to-pole PIC 9 USAGE COMP.
01 via-pole PIC 9 USAGE COMP.
PROCEDURE DIVISION USING n, from-pole, to-pole, via-pole.
IF n > 0
SUBTRACT 1 FROM n
CALL "move-disk" USING CONTENT n, from-pole, via-pole, to-pole
DISPLAY "Move disk from pole " from-pole " to pole " to-pole
CALL "move-disk" USING CONTENT n, via-pole, to-pole, from-pole
END-IF
.
END PROGRAM move-disk.
IDENTIFICATION DIVISION.
PROGRAM-ID. towers-of-hanoi.
PROCEDURE DIVISION.
CALL "move-disk" USING 4, 1, 2, 3
.
END PROGRAM towers-of-hanoi.
IDENTIFICATION DIVISION.
PROGRAM-ID. move-disk RECURSIVE.
DATA DIVISION.
LINKAGE SECTION.
01 n PIC 9 USAGE COMP.
01 from-pole PIC 9 USAGE COMP.
01 to-pole PIC 9 USAGE COMP.
01 via-pole PIC 9 USAGE COMP.
PROCEDURE DIVISION USING n, from-pole, to-pole, via-pole.
IF n > 0
SUBTRACT 1 FROM n
CALL "move-disk" USING CONTENT n, from-pole, via-pole, to-pole
ADD 1 TO n
DISPLAY "Move disk number "n " from pole " from-pole " to pole " to-pole
SUBTRACT 1 FROM n
CALL "move-disk" USING CONTENT n, via-pole, to-pole, from-pole
END-IF
.
END PROGRAM move-disk.
ANSI-74 solution
Early versions of COBOL did not have recursion. There are no locally-scoped variables and the call of a procedure does not have to use a stack to save return state. Recursion would cause undefined results. It is therefore necessary to use an iterative algorithm. This solution is an adaptation of Kolar's Hanoi Tower algorithm no. 1.
IDENTIFICATION DIVISION.
PROGRAM-ID. ITERATIVE-TOWERS-OF-HANOI.
AUTHOR. SOREN ROUG.
DATE-WRITTEN. 2019-06-28.
ENVIRONMENT DIVISION.
CONFIGURATION SECTION.
SOURCE-COMPUTER. LINUX.
OBJECT-COMPUTER. KAYPRO4.
INPUT-OUTPUT SECTION.
FILE-CONTROL.
DATA DIVISION.
WORKING-STORAGE SECTION.
77 NUM-DISKS PIC 9 VALUE 4.
77 N1 PIC 9 COMP.
77 N2 PIC 9 COMP.
77 FROM-POLE PIC 9 COMP.
77 TO-POLE PIC 9 COMP.
77 VIA-POLE PIC 9 COMP.
77 FP-TMP PIC 9 COMP.
77 TO-TMP PIC 9 COMP.
77 P-TMP PIC 9 COMP.
77 TMP-P PIC 9 COMP.
77 I PIC 9 COMP.
77 DIV PIC 9 COMP.
01 STACKNUMS.
05 NUMSET OCCURS 3 TIMES.
10 DNUM PIC 9 COMP.
01 GAMESET.
05 POLES OCCURS 3 TIMES.
10 STACK OCCURS 10 TIMES.
15 POLE PIC 9 USAGE COMP.
PROCEDURE DIVISION.
HANOI.
DISPLAY "TOWERS OF HANOI PUZZLE WITH ", NUM-DISKS, " DISKS.".
ADD NUM-DISKS, 1 GIVING N1.
ADD NUM-DISKS, 2 GIVING N2.
MOVE 1 TO DNUM (1).
MOVE N1 TO DNUM (2), DNUM (3).
MOVE N1 TO POLE (1, N1), POLE (2, N1), POLE (3, N1).
MOVE 1 TO POLE (1, N2).
MOVE 2 TO POLE (2, N2).
MOVE 3 TO POLE (3, N2).
MOVE 1 TO I.
PERFORM INIT-PUZZLE UNTIL I = N1.
MOVE 1 TO FROM-POLE.
DIVIDE 2 INTO NUM-DISKS GIVING DIV.
MULTIPLY 2 BY DIV.
IF DIV NOT = NUM-DISKS PERFORM INITODD ELSE PERFORM INITEVEN.
PERFORM MOVE-DISK UNTIL DNUM (3) NOT > 1.
DISPLAY "TOWERS OF HANOI PUZZLE COMPLETED!".
STOP RUN.
INIT-PUZZLE.
MOVE I TO POLE (1, I).
MOVE 0 TO POLE (2, I), POLE (3, I).
ADD 1 TO I.
INITEVEN.
MOVE 2 TO TO-POLE.
MOVE 3 TO VIA-POLE.
INITODD.
MOVE 3 TO TO-POLE.
MOVE 2 TO VIA-POLE.
MOVE-DISK.
MOVE DNUM (FROM-POLE) TO FP-TMP.
MOVE POLE (FROM-POLE, FP-TMP) TO I.
DISPLAY "MOVE DISK FROM ", POLE (FROM-POLE, N2),
" TO ", POLE (TO-POLE, N2).
ADD 1 TO DNUM (FROM-POLE).
MOVE VIA-POLE TO TMP-P.
SUBTRACT 1 FROM DNUM (TO-POLE).
MOVE DNUM (TO-POLE) TO TO-TMP.
MOVE I TO POLE (TO-POLE, TO-TMP).
DIVIDE 2 INTO I GIVING DIV.
MULTIPLY 2 BY DIV.
IF I NOT = DIV PERFORM MOVE-TO-VIA ELSE
PERFORM MOVE-FROM-VIA.
MOVE-TO-VIA.
MOVE TO-POLE TO VIA-POLE.
MOVE DNUM (FROM-POLE) TO FP-TMP.
MOVE DNUM (TMP-P) TO P-TMP.
IF POLE (FROM-POLE, FP-TMP) > POLE (TMP-P, P-TMP)
PERFORM MOVE-FROM-TO
ELSE MOVE TMP-P TO TO-POLE.
MOVE-FROM-TO.
MOVE FROM-POLE TO TO-POLE.
MOVE TMP-P TO FROM-POLE.
MOVE DNUM (FROM-POLE) TO FP-TMP.
MOVE DNUM (TMP-P) TO P-TMP.
MOVE-FROM-VIA.
MOVE FROM-POLE TO VIA-POLE.
MOVE TMP-P TO FROM-POLE.
CoffeeScript
hanoi = (ndisks, start_peg=1, end_peg=3) ->
if ndisks
staging_peg = 1 + 2 + 3 - start_peg - end_peg
hanoi(ndisks-1, start_peg, staging_peg)
console.log "Move disk #{ndisks} from peg #{start_peg} to #{end_peg}"
hanoi(ndisks-1, staging_peg, end_peg)
hanoi(4)
Common Lisp
(defun move (n from to via)
(cond ((= n 1)
(format t "Move from ~A to ~A.~%" from to))
(t
(move (- n 1) from via to)
(format t "Move from ~A to ~A.~%" from to)
(move (- n 1) via to from))))
D
Recursive Version
import std.stdio;
void hanoi(in int n, in char from, in char to, in char via) {
if (n > 0) {
hanoi(n - 1, from, via, to);
writefln("Move disk %d from %s to %s", n, from, to);
hanoi(n - 1, via, to, from);
}
}
void main() {
hanoi(3, 'L', 'M', 'R');
}
- Output:
Move disk 1 from L to M Move disk 2 from L to R Move disk 1 from M to R Move disk 3 from L to M Move disk 1 from R to L Move disk 2 from R to M Move disk 1 from L to M
Fast Iterative Version
See: The shortest and "mysterious" TH algorithm
// Code found and then improved by Glenn C. Rhoads,
// then some more by M. Kolar (2000).
void main(in string[] args) {
import core.stdc.stdio, std.conv, std.typetuple;
immutable size_t n = (args.length > 1) ? args[1].to!size_t : 3;
size_t[3] p = [(1 << n) - 1, 0, 0];
// Show the start configuration of the pegs.
'|'.putchar;
foreach_reverse (immutable i; 1 .. n + 1)
printf(" %d", i);
"\n|\n|".puts;
foreach (immutable size_t x; 1 .. (1 << n)) {
{
immutable size_t i1 = x & (x - 1);
immutable size_t fr = (i1 + i1 / 3) & 3;
immutable size_t i2 = (x | (x - 1)) + 1;
immutable size_t to = (i2 + i2 / 3) & 3;
size_t j = 1;
for (size_t w = x; !(w & 1); w >>= 1, j <<= 1) {}
// Now j is not the number of the disk to move,
// it contains the single bit to be moved:
p[fr] &= ~j;
p[to] |= j;
}
// Show the current configuration of pegs.
foreach (immutable size_t k; TypeTuple!(0, 1, 2)) {
"\n|".printf;
size_t j = 1 << n;
foreach_reverse (immutable size_t w; 1 .. n + 1) {
j >>= 1;
if (j & p[k])
printf(" %zd", w);
}
}
'\n'.putchar;
}
}
- Output:
| 3 2 1 | | | 3 2 | | 1 | 3 | 2 | 1 | 3 | 2 1 | | | 2 1 | 3 | 1 | 2 | 3 | 1 | | 3 2 | | | 3 2 1
Dart
main() {
moveit(from,to) {
print("move ${from} ---> ${to}");
}
hanoi(height,toPole,fromPole,usePole) {
if (height>0) {
hanoi(height-1,usePole,fromPole,toPole);
moveit(fromPole,toPole);
hanoi(height-1,toPole,usePole,fromPole);
}
}
hanoi(3,3,1,2);
}
The same as above, with optional static type annotations and styled according to http://www.dartlang.org/articles/style-guide/
main() {
String say(String from, String to) => "$from ---> $to";
hanoi(int height, int toPole, int fromPole, int usePole) {
if (height > 0) {
hanoi(height - 1, usePole, fromPole, toPole);
print(say(fromPole.toString(), toPole.toString()));
hanoi(height - 1, toPole, usePole, fromPole);
}
}
hanoi(3, 3, 1, 2);
}
- Output:
move 1 ---> 3 move 1 ---> 2 move 3 ---> 2 move 1 ---> 3 move 2 ---> 1 move 2 ---> 3 move 1 ---> 3
Dc
From Here
[ # move(from, to)
n # print from
[ --> ]n # print " --> "
p # print to\n
sw # p doesn't pop, so get rid of the value
]sm
[ # init(n)
sw # tuck n away temporarily
9 # sentinel as bottom of stack
lw # bring n back
1 # "from" tower's label
3 # "to" tower's label
0 # processed marker
]si
[ # Move()
lt # push to
lf # push from
lmx # call move(from, to)
]sM
[ # code block <d>
ln # push n
lf # push from
lt # push to
1 # push processed marker 1
ln # push n
1 # push 1
- # n - 1
lf # push from
ll # push left
0 # push processed marker 0
]sd
[ # code block <e>
ln # push n
1 # push 1
- # n - 1
ll # push left
lt # push to
0 # push processed marker 0
]se
[ # code block <x>
ln 1 =M
ln 1 !=d
]sx
[ # code block <y>
lMx
lex
]sy
[ # quit()
q # exit the program
]sq
[ # run()
d 9 =q # if stack empty, quit()
sp # processed
st # to
sf # from
sn # n
6 #
lf #
- #
lt #
- # 6 - from - to
sl #
lp 0 =x #
lp 0 !=y #
lrx # loop
]sr
5lix # init(n)
lrx # run()
Delphi
See Pascal.
Draco
proc move(byte n, src, via, dest) void:
if n>0 then
move(n-1, src, dest, via);
writeln("Move disk from pole ",src," to pole ",dest);
move(n-1, via, src, dest)
fi
corp
proc nonrec main() void:
move(4, 1, 2, 3)
corp- Output:
Move disk from pole 1 to pole 2 Move disk from pole 1 to pole 3 Move disk from pole 2 to pole 3 Move disk from pole 1 to pole 2 Move disk from pole 3 to pole 1 Move disk from pole 3 to pole 2 Move disk from pole 1 to pole 2 Move disk from pole 1 to pole 3 Move disk from pole 2 to pole 3 Move disk from pole 2 to pole 1 Move disk from pole 3 to pole 1 Move disk from pole 2 to pole 3 Move disk from pole 1 to pole 2 Move disk from pole 1 to pole 3 Move disk from pole 2 to pole 3
Dyalect
func hanoi(n, a, b, c) {
if n > 0 {
hanoi(n - 1, a, c, b)
print("Move disk from \(a) to \(c)")
hanoi(n - 1, b, a, c)
}
}
hanoi(4, "A", "B", "C")- Output:
Move disk from A to B Move disk from A to C Move disk from B to C Move disk from A to B Move disk from C to A Move disk from C to B Move disk from A to B Move disk from A to C Move disk from B to C Move disk from B to A Move disk from C to A Move disk from B to C Move disk from A to B Move disk from A to C Move disk from B to C
E
def move(out, n, fromPeg, toPeg, viaPeg) {
if (n.aboveZero()) {
move(out, n.previous(), fromPeg, viaPeg, toPeg)
out.println(`Move disk $n from $fromPeg to $toPeg.`)
move(out, n.previous(), viaPeg, toPeg, fromPeg)
}
}
move(stdout, 4, def left {}, def right {}, def middle {})EasyLang
proc hanoi n src dst aux . .
if n >= 1
hanoi n - 1 src aux dst
print "Move " & src & " to " & dst
hanoi n - 1 aux dst src
.
.
hanoi 5 1 2 3
EDSAC order code
The Wikipedia article on EDSAC says "recursive calls were forbidden", and this is true if the standard "Wheeler jump" is used. In the Wheeler jump, the caller (in effect) passes the return address to the subroutine, which uses that address to manufacture a "link order", i.e. a jump back to the caller. This link order is normally stored at a fixed location in the subroutine, so if the subroutine were to call itself then the original link order would be overwritten and lost. However, it is easy enough to make a subroutine save its link orders in a stack, so that it can be called recursively, as the Rosetta Code task requires.
The program has a maximum of 9 discs, so as to simplify the printout of the disc numbers. Discs are numbered 1, 2, 3, ... in increasing order of size. The program could be speeded up by shortening the messages, which at present take up most of the runtime.
[Towers of Hanoi task for Rosetta Code.]
[EDSAC program, Initial Orders 2.]
T100K [load program at location 100 (arbitrary)]
GK
[Number of discs, in the address field]
[0] P3F [<--- edit here, value 1..9]
[Letters to represent the rods]
[1] LF [left]
[2] CF [centre]
[3] RF [right]
[Main routine. Enter with acc = 0]
[4] T1F [1F := 0]
[5] A5@ [initialize recursive subroutine]
G104@
A@ [number of discs]
T1F [pass to subroutines]
A1@ [source rod]
T4F [pass to subroutines]
A3@ [target rod]
T5F [pass to subroutines]
[13] A13@ [call subroutine to write header ]
G18@
[15] A15@ [call recursive subroutine to write moves ]
G104@
ZF [stop]
[Subroutine to write a header]
[Input: 1F = number of discs (in the address field)]
[4F = letter for starting rod]
[5F = letter for ending rod]
[Output: None. 1F, 4F, 5F must be preserved.]
[18] A3F [plant return link as usual]
T35@
A1F [number of discs]
L512F [shift 11 left to make output char]
T39@ [plant in message]
A4F [starting rod]
T53@ [plant in message]
A5F [ending rod]
T58@ [plant in message]
A36@ [O order for first char of message]
E30@ [skip next order (code for 'O' is positive)]
[29] A37@ [restore acc after test below]
[30] U31@ [plant order to write next character]
[31] OF [(planted) write next character]
A2F [inc address in previous order]
S37@ [finished yet?]
G29@ [if not, loop back]
[35] ZF [(planted) exit with acc = 0]
[36] O38@ [O order for start of message]
[37] O61@ [O order for exclusive end of message]
[38] #F
[39] PFK2048F!FDFIFSFCFSF!FFFRFOFMF!F
[53] PF!FTFOF!F
[58] PF@F&F
[61]
[Subroutine to write a move of one disc.]
[Input: 1F = disc number 1..9 (in the address field)]
[4F = letter for source rod]
[5F = letter for target rod]
[Output: None. 1F, 4F, 5F must be preserved.]
[Condensed to save space; very similar to previous subroutine.]
[61] A3FT78@A1FL512FT88@ A4FT96@A5FT101@A79@E73@
[72] A80@
[73] U74@
[74] OFA2FS80@G72@
[78] ZF [(planted) exit with acc = 0]
[79] O81@
[80] O104@
[81] K2048FMFOFVFEF!F#F
[88] PFK2048F!FFFRFOFMF!F
[96] PF!FTFOF!F
[101] PF@F&F
[104]
[Recursive subroutine to move discs 1..n, where 1 <= n <= 9.]
[Call with n = 0 to initialize.]
[Input: 1F = n (in the address field)]
[4F = letter for source rod]
[5F = letter for target rod]
[Output: None. 1F, 4F, 5F must be preserved.]
[104] A3F [plant link as usual ]
T167@
[The link will be saved in a stack if recursive calls are required.]
S1F [load -n]
G115@ [jump if n > 0]
[Here if n = 0. Initialize; no recursive calls.]
A169@ [initialize push order to start of stack]
T122@
A1@ [find total of the codes for the rod letters]
A2@
A3@
T168@ [store for future use]
E167@ [jump to link]
[Here with acc = -n in address field]
[115] A2F [add 1]
G120@ [jump if n > 1]
[Here if n = 1. Just write the move; no recursive calls.]
[117] A117@ [call write subroutine]
G61@
E167@ [jump to link]
[Here if n > 1. Recursive calls are required.]
[120] TF [clear acc]
A167@ [load link order]
[122] TF [(planted) push link order onto stack]
A122@ [inc address in previous order]
A2F
T122@
[First recursive call. Modify parameters 1F and 5F; 4F stays the same]
A1F [load n]
S2F [make n - 1]
T1F [pass as parameter]
A168@ [get 3rd rod, neither source nor target]
S4F
S5F
T5F
[133] A133@ [recursive call]
G104@
[Returned, restore parameters]
A1F
A2F
T1F
A168@
S4F
S5F
T5F
[Write move of largest disc]
[142] A142@
G61@
[Second recursive call. Modify parameters 1F and 4F; 5F stays the same]
[Condensed to save space; very similar to first recursice call.]
A1FS2FT1FA168@S4FS5FT4F
[151] A151@G104@A1FA2FT1FA168@S4FS5FT4F
[Pop return link off stack]
A122@ [dec address in push order]
S2F
U122@
A170@ [make A order with same address]
T165@ [plant in code]
[165] AF [(planted) pop return link from stack]
T167@ [plant in code]
[167] ZF [(planted) return to caller]
[Constants]
[168] PF [(planted) sum of letters for rods]
[169] T171@ [T order for start of stack]
[170] MF [add to T order to make A order, same address]
[Stack: placed at end of program, grows into free space.]
[171]
E4Z [define entry point]
PF [acc = 0 on entry]
[end]- Output:
3 DISCS FROM L TO R MOVE 1 FROM L TO R MOVE 2 FROM L TO C MOVE 1 FROM R TO C MOVE 3 FROM L TO R MOVE 1 FROM C TO L MOVE 2 FROM C TO R MOVE 1 FROM L TO R
Eiffel
class
APPLICATION
create
make
feature {NONE} -- Initialization
make
do
move (4, "A", "B", "C")
end
feature -- Towers of Hanoi
move (n: INTEGER; frm, to, via: STRING)
require
n > 0
do
if n = 1 then
print ("Move disk from pole " + frm + " to pole " + to + "%N")
else
move (n - 1, frm, via, to)
move (1, frm, to, via)
move (n - 1, via, to, frm)
end
end
end
Ela
open monad io
:::IO
//Functional approach
hanoi 0 _ _ _ = []
hanoi n a b c = hanoi (n - 1) a c b ++ [(a,b)] ++ hanoi (n - 1) c b a
hanoiIO n = mapM_ f $ hanoi n 1 2 3 where
f (x,y) = putStrLn $ "Move " ++ show x ++ " to " ++ show y
//Imperative approach using IO monad
hanoiM n = hanoiM' n 1 2 3 where
hanoiM' 0 _ _ _ = return ()
hanoiM' n a b c = do
hanoiM' (n - 1) a c b
putStrLn $ "Move " ++ show a ++ " to " ++ show b
hanoiM' (n - 1) c b aElena
ELENA 4.x :
move = (n,from,to,via)
{
if (n == 1)
{
console.printLine("Move disk from pole ",from," to pole ",to)
}
else
{
move(n-1,from,via,to);
move(1,from,to,via);
move(n-1,via,to,from)
}
};Elixir
defmodule RC do
def hanoi(n) when 0<n and n<10, do: hanoi(n, 1, 2, 3)
defp hanoi(1, f, _, t), do: move(f, t)
defp hanoi(n, f, u, t) do
hanoi(n-1, f, t, u)
move(f, t)
hanoi(n-1, u, f, t)
end
defp move(f, t), do: IO.puts "Move disk from #{f} to #{t}"
end
RC.hanoi(3)
- Output:
Move disk from 1 to 3 Move disk from 1 to 2 Move disk from 3 to 2 Move disk from 1 to 3 Move disk from 2 to 1 Move disk from 2 to 3 Move disk from 1 to 3
Emacs Lisp
(defun move (n from to via)
(if (= n 1)
(message "Move from %S to %S" from to)
(move (- n 1) from via to)
(message "Move from %S to %S" from to)
(move (- n 1) via to from)))
EMal
fun move = void by int n, int from, int to, int via
if n == 1
writeLine("Move disk from pole " + from + " to pole " + to)
return
end
move(n - 1, from, via, to)
move(1, from, to, via)
move(n - 1, via, to, from)
end
move(3, 1, 2, 3)- Output:
Move disk from pole 1 to pole 2 Move disk from pole 1 to pole 3 Move disk from pole 2 to pole 3 Move disk from pole 1 to pole 2 Move disk from pole 3 to pole 1 Move disk from pole 3 to pole 2 Move disk from pole 1 to pole 2
Erlang
move(1, F, T, _V) ->
io:format("Move from ~p to ~p~n", [F, T]);
move(N, F, T, V) ->
move(N-1, F, V, T),
move(1 , F, T, V),
move(N-1, V, T, F).
ERRE
!-----------------------------------------------------------
! HANOI.R : solve tower of Hanoi puzzle using a recursive
! modified algorithm.
!-----------------------------------------------------------
PROGRAM HANOI
!$INTEGER
!VAR I,J,MOSSE,NUMBER
PROCEDURE PRINTMOVE
LOCAL SOURCE$,DEST$
MOSSE=MOSSE+1
CASE I OF
1-> SOURCE$="Left" END ->
2-> SOURCE$="Center" END ->
3-> SOURCE$="Right" END ->
END CASE
CASE J OF
1-> DEST$="Left" END ->
2-> DEST$="Center" END ->
3-> DEST$="Right" END ->
END CASE
PRINT("I move a disk from ";SOURCE$;" to ";DEST$)
END PROCEDURE
PROCEDURE MOVE
IF NUMBER<>0 THEN
NUMBER=NUMBER-1
J=6-I-J
MOVE
J=6-I-J
PRINTMOVE
I=6-I-J
MOVE
I=6-I-J
NUMBER=NUMBER+1
END IF
END PROCEDURE
BEGIN
MAXNUM=12
MOSSE=0
PRINT(CHR$(12);TAB(25);"--- TOWERS OF HANOI ---")
REPEAT
PRINT("Number of disks ";)
INPUT(NUMBER)
UNTIL NUMBER>1 AND NUMBER<=MAXNUM
PRINT
PRINT("For ";NUMBER;"disks the total number of moves is";2^NUMBER-1)
I=1 ! number of source pole
J=3 ! number of destination pole
MOVE
END PROGRAM- Output:
--- TOWER OF HANOI --- Number of disks ? 3 For 3 disks the total number of moves is 7 I move a disk from Left to Right I move a disk from Left to Center I move a disk from Right to Center I move a disk from Left to Right I move a disk from Center to Left I move a disk from Center to Right I move a disk from Left to Right
Excel
LAMBDA
With the names HANOI and SHOWHANOI bound to the following lambdas in the Excel worksheet Name Manager:
(See LAMBDA: The ultimate Excel worksheet function)
SHOWHANOI
=LAMBDA(n,
FILTERP(
LAMBDA(x, "" <> x)
)(
HANOI(n)("left")("right")("mid")
)
)
HANOI
=LAMBDA(n,
LAMBDA(l,
LAMBDA(r,
LAMBDA(m,
IF(0 = n,
"",
LET(
next, n - 1,
APPEND(
APPEND(
HANOI(next)(l)(m)(r)
)(
CONCAT(l, " -> ", r)
)
)(
HANOI(next)(m)(r)(l)
)
)
)
)
)
)
)
And assuming that these generic lambdas are also bound to the following names in Name Manager:
APPEND
=LAMBDA(xs,
LAMBDA(ys,
LET(
nx, ROWS(xs),
rowIndexes, SEQUENCE(nx + ROWS(ys)),
colIndexes, SEQUENCE(
1,
MAX(COLUMNS(xs), COLUMNS(ys))
),
IF(
rowIndexes <= nx,
INDEX(xs, rowIndexes, colIndexes),
INDEX(ys, rowIndexes - nx, colIndexes)
)
)
)
)
FILTERP
=LAMBDA(p,
LAMBDA(xs,
FILTER(xs, p(xs))
)
)
In the output below, the expression in B2 defines an array of strings which additionally populate the following cells.
- Output:
| fx | =SHOWHANOI(A2) | ||
|---|---|---|---|
| A | B | ||
| 1 | Disks | Steps | |
| 2 | 3 | left -> right | |
| 3 | left -> mid | ||
| 4 | right -> mid | ||
| 5 | left -> right | ||
| 6 | mid -> left | ||
| 7 | mid -> right | ||
| 8 | left -> right | ||
Ezhil
# (C) 2013 Ezhil Language Project
# Tower of Hanoi – recursive solution
நிரல்பாகம் ஹோனாய்(வட்டுகள், முதல்அச்சு, இறுதிஅச்சு,வட்டு)
@(வட்டுகள் == 1 ) ஆனால்
பதிப்பி “வட்டு ” + str(வட்டு) + “ஐ \t (” + str(முதல்அச்சு) + “ —> ” + str(இறுதிஅச்சு)+ “) அச்சிற்கு நகர்த்துக.”
இல்லை
@( ["இ", "அ", "ஆ"] இல் அச்சு ) ஒவ்வொன்றாக
@( (முதல்அச்சு != அச்சு) && (இறுதிஅச்சு != அச்சு) ) ஆனால்
நடு = அச்சு
முடி
முடி
# solve problem for n-1 again between src and temp pegs
ஹோனாய்(வட்டுகள்-1, முதல்அச்சு,நடு,வட்டுகள்-1)
# move largest disk from src to destination
ஹோனாய்(1, முதல்அச்சு, இறுதிஅச்சு,வட்டுகள்)
# solve problem for n-1 again between different pegs
ஹோனாய்(வட்டுகள்-1, நடு, இறுதிஅச்சு,வட்டுகள்-1)
முடி
முடி
ஹோனாய்(4,”அ”,”ஆ”,0)
F#
#light
let rec hanoi num start finish =
match num with
| 0 -> [ ]
| _ -> let temp = (6 - start - finish)
(hanoi (num-1) start temp) @ [ start, finish ] @ (hanoi (num-1) temp finish)
[<EntryPoint>]
let main args =
(hanoi 4 1 2) |> List.iter (fun pair -> match pair with
| a, b -> printf "Move disc from %A to %A\n" a b)
0
Factor
USING: formatting kernel locals math ;
IN: rosettacode.hanoi
: move ( from to -- )
"%d->%d\n" printf ;
:: hanoi ( n from to other -- )
n 0 > [
n 1 - from other to hanoi
from to move
n 1 - other to from hanoi
] when ;
In the REPL:
( scratchpad ) 3 1 3 2 hanoi 1->3 1->2 3->2 1->3 2->1 2->3 1->3
FALSE
["Move disk from "$!\" to "$!\"
"]p: { to from }
[n;0>[n;1-n: @\ h;! @\ p;! \@ h;! \@ n;1+n:]?]h: { via to from }
4n:["right"]["middle"]["left"]h;!%%%Fermat
Func Hanoi( n, f, t, v ) =
if n = 0 then
!'';
else
Hanoi(n - 1, f, v, t);
!f;!' -> ';!t;!', ';
Hanoi(n - 1, v, t, f)
fi.- Output:
1 -> 3, 1 -> 2, 3 -> 2, 1 -> 3, 2 -> 1, 2 -> 3, 1 -> 3, 1 -> 2, 3 -> 2, 3 -> 1, 2 -> 1, 3 -> 2, 1 -> 3, 1 -> 2, 3 -> 2,
FOCAL
01.10 S N=4;S S=1;S V=2;S T=3
01.20 D 2
01.30 Q
02.02 S N(D)=N(D)-1;I (N(D)),2.2,2.04
02.04 S D=D+1
02.06 S N(D)=N(D-1);S S(D)=S(D-1)
02.08 S T(D)=V(D-1);S V(D)=T(D-1)
02.10 D 2
02.12 S D=D-1
02.14 D 3
02.16 S A=S(D);S S(D)=V(D);S V(D)=A
02.18 G 2.02
02.20 D 3
03.10 T %1,"MOVE DISK FROM POLE",S(D)
03.20 T " TO POLE",T(D),!- Output:
MOVE DISK FROM POLE= 1 TO POLE= 2 MOVE DISK FROM POLE= 1 TO POLE= 3 MOVE DISK FROM POLE= 2 TO POLE= 3 MOVE DISK FROM POLE= 1 TO POLE= 2 MOVE DISK FROM POLE= 3 TO POLE= 1 MOVE DISK FROM POLE= 3 TO POLE= 2 MOVE DISK FROM POLE= 1 TO POLE= 2 MOVE DISK FROM POLE= 1 TO POLE= 3 MOVE DISK FROM POLE= 2 TO POLE= 3 MOVE DISK FROM POLE= 2 TO POLE= 1 MOVE DISK FROM POLE= 3 TO POLE= 1 MOVE DISK FROM POLE= 2 TO POLE= 3 MOVE DISK FROM POLE= 1 TO POLE= 2 MOVE DISK FROM POLE= 1 TO POLE= 3 MOVE DISK FROM POLE= 2 TO POLE= 3
Forth
With locals:
CREATE peg1 ," left "
CREATE peg2 ," middle "
CREATE peg3 ," right "
: .$ COUNT TYPE ;
: MOVE-DISK
LOCALS| via to from n |
n 1 =
IF CR ." Move disk from " from .$ ." to " to .$
ELSE n 1- from via to RECURSE
1 from to via RECURSE
n 1- via to from RECURSE
THEN ;
Without locals, executable pegs:
: left ." left" ;
: right ." right" ;
: middle ." middle" ;
: move-disk ( v t f n -- v t f )
dup 0= if drop exit then
1- >R
rot swap R@ ( t v f n-1 ) recurse
rot swap
2dup cr ." Move disk from " execute ." to " execute
swap rot R> ( f t v n-1 ) recurse
swap rot ;
: hanoi ( n -- )
1 max >R ['] right ['] middle ['] left R> move-disk drop drop drop ;
Fortran
PROGRAM TOWER
CALL Move(4, 1, 2, 3)
CONTAINS
RECURSIVE SUBROUTINE Move(ndisks, from, to, via)
INTEGER, INTENT (IN) :: ndisks, from, to, via
IF (ndisks == 1) THEN
WRITE(*, "(A,I1,A,I1)") "Move disk from pole ", from, " to pole ", to
ELSE
CALL Move(ndisks-1, from, via, to)
CALL Move(1, from, to, via)
CALL Move(ndisks-1, via, to, from)
END IF
END SUBROUTINE Move
END PROGRAM TOWER
Template:More informative version
PROGRAM TOWER2
CALL Move(4, 1, 2, 3)
CONTAINS
RECURSIVE SUBROUTINE Move(ndisks, from, via, to)
INTEGER, INTENT (IN) :: ndisks, from, via, to
IF (ndisks > 1) THEN
CALL Move(ndisks-1, from, to, via)
WRITE(*, "(A,I1,A,I1,A,I1)") "Move disk ", ndisks, " from pole ", from, " to pole ", to
Call Move(ndisks-1,via,from,to)
ELSE
WRITE(*, "(A,I1,A,I1,A,I1)") "Move disk ", ndisks, " from pole ", from, " to pole ", to
END IF
END SUBROUTINE Move
END PROGRAM TOWER2
FreeBASIC
' FB 1.05.0 Win64
Sub move(n As Integer, from As Integer, to_ As Integer, via As Integer)
If n > 0 Then
move(n - 1, from, via, to_)
Print "Move disk"; n; " from pole"; from; " to pole"; to_
move(n - 1, via, to_, from)
End If
End Sub
Print "Three disks" : Print
move 3, 1, 2, 3
Print
Print "Four disks" : Print
move 4, 1, 2, 3
Print "Press any key to quit"
Sleep- Output:
Three disks Move disk 1 from pole 1 to pole 2 Move disk 2 from pole 1 to pole 3 Move disk 1 from pole 2 to pole 3 Move disk 3 from pole 1 to pole 2 Move disk 1 from pole 3 to pole 1 Move disk 2 from pole 3 to pole 2 Move disk 1 from pole 1 to pole 2 Four disks Move disk 1 from pole 1 to pole 3 Move disk 2 from pole 1 to pole 2 Move disk 1 from pole 3 to pole 2 Move disk 3 from pole 1 to pole 3 Move disk 1 from pole 2 to pole 1 Move disk 2 from pole 2 to pole 3 Move disk 1 from pole 1 to pole 3 Move disk 4 from pole 1 to pole 2 Move disk 1 from pole 3 to pole 2 Move disk 2 from pole 3 to pole 1 Move disk 1 from pole 2 to pole 1 Move disk 3 from pole 3 to pole 2 Move disk 1 from pole 1 to pole 3 Move disk 2 from pole 1 to pole 2 Move disk 1 from pole 3 to pole 2
Frink
/** Set up the recursive call for n disks */
hanoi[n] := hanoi[n, 1, 3, 2]
/** The recursive call. */
hanoi[n, source, target, aux] :=
{
if n > 0
{
hanoi[n-1, source, aux, target]
println["Move from $source to $target"]
hanoi[n-1, aux, target, source]
}
}
hanoi[7]FutureBasic
window 1, @"Towers of Hanoi", ( 0, 0, 300, 300 )
void local fn Move( n as long, fromPeg as long, toPeg as long, viaPeg as long )
if n > 0
fn Move( n-1, fromPeg, viaPeg, toPeg )
print "Move disk from "; fromPeg; " to "; toPeg
fn Move( n-1, viaPeg, toPeg, fromPeg )
end if
end fn
fn Move( 4, 1, 2, 3 )
print
print "Towers of Hanoi puzzle solved."
HandleEventsOutput:
Move disk from 1 to 3 Move disk from 1 to 2 Move disk from 3 to 2 Move disk from 1 to 3 Move disk from 2 to 1 Move disk from 2 to 3 Move disk from 1 to 3 Move disk from 1 to 2 Move disk from 3 to 2 Move disk from 3 to 1 Move disk from 2 to 1 Move disk from 3 to 2 Move disk from 1 to 3 Move disk from 1 to 2 Move disk from 3 to 2 Towers of Hanoi puzzle solved.
Fōrmulæ
Fōrmulæ programs are not textual, visualization/edition of programs is done showing/manipulating structures but not text. Moreover, there can be multiple visual representations of the same program. Even though it is possible to have textual representation —i.e. XML, JSON— they are intended for storage and transfer purposes more than visualization and edition.
Programs in Fōrmulæ are created/edited online in its website.
In this page you can see and run the program(s) related to this task and their results. You can also change either the programs or the parameters they are called with, for experimentation, but remember that these programs were created with the main purpose of showing a clear solution of the task, and they generally lack any kind of validation.
Solution
Test case
Gambas
Public Sub Main()
Print "Three disks\n"
move_(3, 1, 2, 3)
Print
Print "Four disks\n"
move_(4, 1, 2, 3)
End
Public Sub move_(n As Integer, from As Integer, to As Integer, via As Integer)
If n > 0 Then
move_(n - 1, from, via, to)
Print "Move disk "; n; " from pole "; from; " to pole "; to
move_(n - 1, via, to, from)
End If
End Sub
- Output:
Same as FreeBASIC entry.
GAP
Hanoi := function(n)
local move;
move := function(n, a, b, c) # from, through, to
if n = 1 then
Print(a, " -> ", c, "\n");
else
move(n - 1, a, c, b);
move(1, a, b, c);
move(n - 1, b, a, c);
fi;
end;
move(n, "A", "B", "C");
end;
Hanoi(1);
# A -> C
Hanoi(2);
# A -> B
# A -> C
# B -> C
Hanoi(3);
# A -> C
# A -> B
# C -> B
# A -> C
# B -> A
# B -> C
# A -> C
Go
package main
import "fmt"
// a towers of hanoi solver just has one method, play
type solver interface {
play(int)
}
func main() {
var t solver // declare variable of solver type
t = new(towers) // type towers must satisfy solver interface
t.play(4)
}
// towers is example of type satisfying solver interface
type towers struct {
// an empty struct. some other solver might fill this with some
// data representation, maybe for algorithm validation, or maybe for
// visualization.
}
// play is sole method required to implement solver type
func (t *towers) play(n int) {
// drive recursive solution, per task description
t.moveN(n, 1, 2, 3)
}
// recursive algorithm
func (t *towers) moveN(n, from, to, via int) {
if n > 0 {
t.moveN(n-1, from, via, to)
t.move1(from, to)
t.moveN(n-1, via, to, from)
}
}
// example function prints actions to screen.
// enhance with validation or visualization as needed.
func (t *towers) move1(from, to int) {
fmt.Println("move disk from rod", from, "to rod", to)
}
In other words:
package main
import "fmt"
func main() {
move(3, "A", "B", "C")
}
func move(n uint64, a, b, c string) {
if n > 0 {
move(n-1, a, c, b)
fmt.Println("Move disk from " + a + " to " + c)
move(n-1, b, a, c)
}
}
Groovy
Unlike most solutions here this solution manipulates more-or-less actual stacks of more-or-less actual rings.
def tail = { list, n -> def m = list.size(); list.subList([m - n, 0].max(),m) }
final STACK = [A:[],B:[],C:[]].asImmutable()
def report = { it -> }
def check = { it -> }
def moveRing = { from, to -> to << from.pop(); report(); check(to) }
def moveStack
moveStack = { from, to, using = STACK.values().find { !(it.is(from) || it.is(to)) } ->
if (!from) return
def n = from.size()
moveStack(tail(from, n-1), using, to)
moveRing(from, to)
moveStack(tail(using, n-1), to, from)
}
Test program:
enum Ring {
S('°'), M('o'), L('O'), XL('( )');
private sym
private Ring(sym) { this.sym=sym }
String toString() { sym }
}
report = { STACK.each { k, v -> println "${k}: ${v}" }; println() }
check = { to -> assert to == ([] + to).sort().reverse() }
Ring.values().reverseEach { STACK.A << it }
report()
check(STACK.A)
moveStack(STACK.A, STACK.C)
- Output:
A: [( ), O, o, °] B: [] C: [] A: [( ), O, o] B: [°] C: [] A: [( ), O] B: [°] C: [o] A: [( ), O] B: [] C: [o, °] A: [( )] B: [O] C: [o, °] A: [( ), °] B: [O] C: [o] A: [( ), °] B: [O, o] C: [] A: [( )] B: [O, o, °] C: [] A: [] B: [O, o, °] C: [( )] A: [] B: [O, o] C: [( ), °] A: [o] B: [O] C: [( ), °] A: [o, °] B: [O] C: [( )] A: [o, °] B: [] C: [( ), O] A: [o] B: [°] C: [( ), O] A: [] B: [°] C: [( ), O, o] A: [] B: [] C: [( ), O, o, °]
Haskell
Most of the programs on this page use an imperative approach (i.e., print out movements as side effects during program execution). Haskell favors a purely functional approach, where you would for example return a (lazy) list of movements from a to b via c:
hanoi :: Integer -> a -> a -> a -> [(a, a)]
hanoi 0 _ _ _ = []
hanoi n a b c = hanoi (n-1) a c b ++ [(a,b)] ++ hanoi (n-1) c b a
You can also do the above with one tail-recursion call:
hanoi :: Integer -> a -> a -> a -> [(a, a)]
hanoi n a b c = hanoiToList n a b c []
where
hanoiToList 0 _ _ _ l = l
hanoiToList n a b c l = hanoiToList (n-1) a c b ((a, b) : hanoiToList (n-1) c b a l)
One can use this function to produce output, just like the other programs:
hanoiIO n = mapM_ f $ hanoi n 1 2 3 where
f (x,y) = putStrLn $ "Move " ++ show x ++ " to " ++ show y
or, instead, one can of course also program imperatively, using the IO monad directly:
hanoiM :: Integer -> IO ()
hanoiM n = hanoiM' n 1 2 3 where
hanoiM' 0 _ _ _ = return ()
hanoiM' n a b c = do
hanoiM' (n-1) a c b
putStrLn $ "Move " ++ show a ++ " to " ++ show b
hanoiM' (n-1) c b a
or, defining it as a monoid, and adding some output:
-------------------------- HANOI -------------------------
hanoi ::
Int ->
String ->
String ->
String ->
[(String, String)]
hanoi 0 _ _ _ = mempty
hanoi n l r m =
hanoi (n - 1) l m r
<> [(l, r)]
<> hanoi (n - 1) m r l
--------------------------- TEST -------------------------
main :: IO ()
main = putStrLn $ showHanoi 5
------------------------- DISPLAY ------------------------
showHanoi :: Int -> String
showHanoi n =
unlines $
fmap
( \(from, to) ->
concat [justifyRight 5 ' ' from, " -> ", to]
)
(hanoi n "left" "right" "mid")
justifyRight :: Int -> Char -> String -> String
justifyRight n c = (drop . length) <*> (replicate n c <>)
- Output:
left -> right left -> mid right -> mid left -> right mid -> left mid -> right left -> right left -> mid right -> mid right -> left mid -> left right -> mid left -> right left -> mid right -> mid left -> right mid -> left mid -> right left -> right mid -> left right -> mid right -> left mid -> left mid -> right left -> right left -> mid right -> mid left -> right mid -> left mid -> right left -> right
HolyC
U0 Move(U8 n, U8 from, U8 to, U8 via) {
if (n > 0) {
Move(n - 1, from, via, to);
Print("Move disk from pole %d to pole %d\n", from, to);
Move(n - 1, via, to, from);
}
}
Move(4, 1, 2, 3);Icon and Unicon
The following is based on a solution in the Unicon book.
Imp77
%begin
%routine do hanoi(%integer n, f, t, u)
do hanoi(n - 1, f, u, t) %if n >= 2
print string("Move disk from ".itos(f,0)." to ".itos(t,0).to string(nl))
do hanoi(n - 1, u, t, f) %if n >= 2
%end
do hanoi(4, 1, 2, 3)
print string("Towers of Hanoi puzzle completed!".to string(nl))
%end %of %programInform 7
Hanoi is a room.
A post is a kind of supporter. A post is always fixed in place.
The left post, the middle post, and the right post are posts in Hanoi.
A disk is a kind of supporter.
The red disk is a disk on the left post.
The orange disk is a disk on the red disk.
The yellow disk is a disk on the orange disk.
The green disk is a disk on the yellow disk.
Definition: a disk is topmost if nothing is on it.
When play begins:
move 4 disks from the left post to the right post via the middle post.
To move (N - number) disk/disks from (FP - post) to (TP - post) via (VP - post):
if N > 0:
move N - 1 disks from FP to VP via TP;
say "Moving a disk from [FP] to [TP]...";
let D be a random topmost disk enclosed by FP;
if a topmost disk (called TD) is enclosed by TP, now D is on TD;
otherwise now D is on TP;
move N - 1 disks from VP to TP via FP.
Io
hanoi := method(n, from, to, via,
if (n == 1) then (
writeln("Move from ", from, " to ", to)
) else (
hanoi(n - 1, from, via, to )
hanoi(1 , from, to , via )
hanoi(n - 1, via , to , from)
)
)
Ioke
= method(n, f, u, t,
if(n < 2,
"#{f} --> #{t}" println,
H(n - 1, f, t, u)
"#{f} --> #{t}" println
H(n - 1, u, f, t)
)
)
hanoi = method(n,
H(n, 1, 2, 3)
)
J
Solutions
H =: i.@,&2 ` (({&0 2 1,0 2,{&1 0 2)@$:@<:) @. * NB. tacit using anonymous recursion
- Example use:
H 3
0 2
0 1
2 1
0 2
1 2
1 0
2 0
The result is a 2-column table; a row i,j is interpreted as: move a disk (the top disk) from peg i to peg j . Or, using explicit rather than implicit code:
H1=: monad define NB. explicit equivalent of H
if. y do.
({&0 2 1 , 0 2 , {&1 0 2) H1 y-1
else.
i.0 2
end.
)
The usage here is the same:
H1 2 0 1 0 2 1 2
- Alternative solution
If a textual display is desired, similar to some of the other solutions here (counting from 1 instead of 0, tracking which disk is on the top of the stack, and of course formatting the result for a human reader instead of providing a numeric result):
hanoi=: monad define
moves=. H y
disks=. $~` ((],[,]) $:@<:) @.* y
('move disk ';' from peg ';' to peg ');@,."1 ":&.>disks,.1+moves
)
- Demonstration:
hanoi 3
move disk 1 from peg 1 to peg 3
move disk 2 from peg 1 to peg 2
move disk 1 from peg 3 to peg 2
move disk 3 from peg 1 to peg 3
move disk 1 from peg 2 to peg 1
move disk 2 from peg 2 to peg 3
move disk 1 from peg 1 to peg 3
Java
public void move(int n, int from, int to, int via) {
if (n == 1) {
System.out.println("Move disk from pole " + from + " to pole " + to);
} else {
move(n - 1, from, via, to);
move(1, from, to, via);
move(n - 1, via, to, from);
}
}
Where n is the number of disks to move and from, to, and via are the poles.
- Example use:
move(3, 1, 2, 3);
- Output:
Move disk from pole 1 to pole 2
Move disk from pole 1 to pole 3
Move disk from pole 2 to pole 3
Move disk from pole 1 to pole 2
Move disk from pole 3 to pole 1
Move disk from pole 3 to pole 2
Move disk from pole 1 to pole 2
JavaScript
ES5
function move(n, a, b, c) {
if (n > 0) {
move(n-1, a, c, b);
console.log("Move disk from " + a + " to " + c);
move(n-1, b, a, c);
}
}
move(4, "A", "B", "C");
Or, as a functional expression, rather than a statement with side effects:
(function () {
// hanoi :: Int -> String -> String -> String -> [[String, String]]
function hanoi(n, a, b, c) {
return n ? hanoi(n - 1, a, c, b)
.concat([
[a, b]
])
.concat(hanoi(n - 1, c, b, a)) : [];
}
return hanoi(3, 'left', 'right', 'mid')
.map(function (d) {
return d[0] + ' -> ' + d[1];
});
})();
- Output:
["left -> right", "left -> mid",
"right -> mid", "left -> right",
"mid -> left", "mid -> right",
"left -> right"]
ES6
(() => {
"use strict";
// ----------------- TOWERS OF HANOI -----------------
// hanoi :: Int -> String -> String ->
// String -> [[String, String]]
const hanoi = n =>
(a, b, c) => {
const go = hanoi(n - 1);
return n
? [
...go(a, c, b),
[a, b],
...go(c, b, a)
]
: [];
};
// ---------------------- TEST -----------------------
return hanoi(3)("left", "right", "mid")
.map(d => `${d[0]} -> ${d[1]}`)
.join("\n");
})();
- Output:
left -> right left -> mid right -> mid left -> right mid -> left mid -> right left -> right
Joy
DEFINE hanoi == [[rolldown] infra] dip
[[[null] [pop pop] ]
[[dup2 [[rotate] infra] dip pred]
[[dup rest put] dip
[[swap] infra] dip pred]
[]]]
condnestrec.Using it (5 is the number of disks.)
[source destination temp] 5 hanoi.jq
The algorithm used here is used elsewhere on this page but it is worthwhile pointing out that it can also be read as a proof that:
(a) move(n;"A";"B";"C") will logically succeed for n>=0; and
(b) move(n;"A";"B";"C") will generate the sequence of moves, assuming sufficient computing resources.
The proof of (a) is by induction:
- As explained in the comments, the algorithm establishes that move(n;x;y;z) is possible for all n>=0 and distinct x,y,z if move(n-1;x;y;z)) is possible;
- Since move(0;x;y;z) evidently succeeds, (a) is established by induction.
The truth of (b) follows from the fact that the algorithm emits an instruction of what to do when moving a single disk.
# n is the number of disks to move from From to To
def move(n; From; To; Via):
if n > 0 then
# move all but the largest at From to Via (according to the rules):
move(n-1; From; Via; To),
# ... so the largest disk at From is now free to move to its final destination:
"Move disk from \(From) to \(To)",
# Move the remaining disks at Via to To:
move(n-1; Via; To; From)
else empty
end;Example:
move(5; "A"; "B"; "C")
Jsish
From Javascript ES5 entry.
/* Towers of Hanoi, in Jsish */
function move(n, a, b, c) {
if (n > 0) {
move(n-1, a, c, b);
puts("Move disk from " + a + " to " + c);
move(n-1, b, a, c);
}
}
if (Interp.conf('unitTest')) move(4, "A", "B", "C");
/*
=!EXPECTSTART!=
Move disk from A to B
Move disk from A to C
Move disk from B to C
Move disk from A to B
Move disk from C to A
Move disk from C to B
Move disk from A to B
Move disk from A to C
Move disk from B to C
Move disk from B to A
Move disk from C to A
Move disk from B to C
Move disk from A to B
Move disk from A to C
Move disk from B to C
=!EXPECTEND!=
*/
- Output:
prompt$ jsish -u towersOfHanoi.jsi [PASS] towersOfHanoi.jsi
Julia
function solve(n::Integer, from::Integer, to::Integer, via::Integer)
if n == 1
println("Move disk from $from to $to")
else
solve(n - 1, from, via, to)
solve(1, from, to, via)
solve(n - 1, via, to, from)
end
end
solve(4, 1, 2, 3)
- Output:
Move disk from 1 to 3 Move disk from 1 to 2 Move disk from 3 to 2 Move disk from 1 to 3 Move disk from 2 to 1 Move disk from 2 to 3 Move disk from 1 to 3 Move disk from 1 to 2 Move disk from 3 to 2 Move disk from 3 to 1 Move disk from 2 to 1 Move disk from 3 to 2 Move disk from 1 to 3 Move disk from 1 to 2 Move disk from 3 to 2
K
h:{[n;a;b;c]if[n>0;_f[n-1;a;c;b];`0:,//$($n,":",$a,"->",$b,"\n");_f[n-1;c;b;a]]}
h[4;1;2;3]
1:1->3
2:1->2
1:3->2
3:1->3
1:2->1
2:2->3
1:1->3
4:1->2
1:3->2
2:3->1
1:2->1
3:3->2
1:1->3
2:1->2
1:3->2
The disk to move in the i'th step is the same as the position of the leftmost 1 in the binary representation of 1..2^n.
s:();{[n;a;b;c]if[n>0;_f[n-1;a;c;b];s,:n;_f[n-1;c;b;a]]}[4;1;2;3];s
1 2 1 3 1 2 1 4 1 2 1 3 1 2 1
1_{*1+&|x}'a:(2_vs!_2^4)
1 2 1 3 1 2 1 4 1 2 1 3 1 2 1
Klingphix
include ..\Utilitys.tlhy
:moveDisc %B !B %C !C %A !A %n !n { n A C B }
$n [
$n 1 - $A $B $C moveDisc
( "Move disc " $n " from pole " $A " to pole " $C ) lprint nl
$n 1 - $B $C $A moveDisc
] if
;
{ Move disc 3 from pole 1 to pole 3, with pole 2 as spare }
3 1 3 2 moveDisc
" " input- Output:
Move disc 1 from pole 1 to pole 3 Move disc 2 from pole 1 to pole 2 Move disc 1 from pole 3 to pole 2 Move disc 3 from pole 1 to pole 3 Move disc 1 from pole 2 to pole 1 Move disc 2 from pole 2 to pole 3 Move disc 1 from pole 1 to pole 3
Kotlin
// version 1.1.0
class Hanoi(disks: Int) {
private var moves = 0
init {
println("Towers of Hanoi with $disks disks:\n")
move(disks, 'L', 'C', 'R')
println("\nCompleted in $moves moves\n")
}
private fun move(n: Int, from: Char, to: Char, via: Char) {
if (n > 0) {
move(n - 1, from, via, to)
moves++
println("Move disk $n from $from to $to")
move(n - 1, via, to, from)
}
}
}
fun main(args: Array<String>) {
Hanoi(3)
Hanoi(4)
}
- Output:
Towers of Hanoi with 3 disks: Move disk 1 from L to C Move disk 2 from L to R Move disk 1 from C to R Move disk 3 from L to C Move disk 1 from R to L Move disk 2 from R to C Move disk 1 from L to C Completed in 7 moves Towers of Hanoi with 4 disks: Move disk 1 from L to R Move disk 2 from L to C Move disk 1 from R to C Move disk 3 from L to R Move disk 1 from C to L Move disk 2 from C to R Move disk 1 from L to R Move disk 4 from L to C Move disk 1 from R to C Move disk 2 from R to L Move disk 1 from C to L Move disk 3 from R to C Move disk 1 from L to R Move disk 2 from L to C Move disk 1 from R to C Completed in 15 moves
Lambdatalk
PSEUDO-CODE:
hanoi disks from A to B via C
if no disks
then stop
else hanoi upper disks from A to C via B
move lower disk from A to B
hanoi upper disks from C to B via A
CODE:
{def hanoi
{lambda {:disks :a :b :c}
{if {A.empty? :disks}
then
else {hanoi {A.rest :disks} :a :c :b}
{div > move {A.first :disks} from :a to :b}
{hanoi {A.rest :disks} :c :b :a} }}}
-> hanoi
{hanoi {A.new ==== === == =} A B C}
->
> move = from A to C
> move == from A to B
> move = from C to B
> move === from A to C
> move = from B to A
> move == from B to C
> move = from A to C
> move ==== from A to B
> move = from C to B
> move == from C to A
> move = from B to A
> move === from C to B
> move = from A to C
> move == from A to B
> move = from C to B
Lasso
#!/usr/bin/lasso9
define towermove(
disks::integer,
a,b,c
) => {
if(#disks > 0) => {
towermove(#disks - 1, #a, #c, #b )
stdoutnl("Move disk from " + #a + " to " + #c)
towermove(#disks - 1, #b, #a, #c )
}
}
towermove((integer($argv -> second || 3)), "A", "B", "C")
Called from command line:
./towers
- Output:
Move disk from A to C Move disk from A to B Move disk from C to B Move disk from A to C Move disk from B to A Move disk from B to C Move disk from A to C
Called from command line:
./towers 4
- Output:
Move disk from A to B Move disk from A to C Move disk from B to C Move disk from A to B Move disk from C to A Move disk from C to B Move disk from A to B Move disk from A to C Move disk from B to C Move disk from B to A Move disk from C to A Move disk from B to C Move disk from A to B Move disk from A to C Move disk from B to C
Liberty BASIC
This looks much better with a GUI interface.
source$ ="A"
via$ ="B"
target$ ="C"
call hanoi 4, source$, target$, via$ ' ie call procedure to move legally 4 disks from peg A to peg C via peg B
wait
sub hanoi numDisks, source$, target$, via$
if numDisks =0 then
exit sub
else
call hanoi numDisks -1, source$, via$, target$
print " Move disk "; numDisks; " from peg "; source$; " to peg "; target$
call hanoi numDisks -1, via$, target$, source$
end if
end sub
endLingo
on hanoi (n, a, b, c)
if n > 0 then
hanoi(n-1, a, c, b)
put "Move disk from" && a && "to" && c
hanoi(n-1, b, a, c)
end if
endhanoi(3, "A", "B", "C")
-- "Move disk from A to C"
-- "Move disk from A to B"
-- "Move disk from C to B"
-- "Move disk from A to C"
-- "Move disk from B to A"
-- "Move disk from B to C"
-- "Move disk from A to C"Logo
to move :n :from :to :via
if :n = 0 [stop]
move :n-1 :from :via :to
(print [Move disk from] :from [to] :to)
move :n-1 :via :to :from
end
move 4 "left "middle "rightLogtalk
:- object(hanoi).
:- public(run/1).
:- mode(run(+integer), one).
:- info(run/1, [
comment is 'Solves the towers of Hanoi problem for the specified number of disks.',
argnames is ['Disks']]).
run(Disks) :-
move(Disks, left, middle, right).
move(1, Left, _, Right):-
!,
report(Left, Right).
move(Disks, Left, Aux, Right):-
Disks2 is Disks - 1,
move(Disks2, Left, Right, Aux),
report(Left, Right),
move(Disks2, Aux, Left, Right).
report(Pole1, Pole2):-
write('Move a disk from '),
writeq(Pole1),
write(' to '),
writeq(Pole2),
write('.'),
nl.
:- end_object.
LOLCODE
HAI 1.2
HOW IZ I HANOI YR N AN YR SRC AN YR DST AN YR VIA
BTW VISIBLE SMOOSH "HANOI N=" N " SRC=" SRC " DST=" DST " VIA=" VIA MKAY
BOTH SAEM N AN 0, O RLY?
YA RLY
BTW VISIBLE "Done."
GTFO
NO WAI
I HAS A LOWER ITZ DIFF OF N AN 1
I IZ HANOI YR LOWER AN YR SRC AN YR VIA AN YR DST MKAY
VISIBLE SMOOSH "Move disc " N " from " SRC " to " DST MKAY
I IZ HANOI YR LOWER AN YR VIA AN YR DST AN YR SRC MKAY
OIC
IF U SAY SO
I IZ HANOI YR 4 AN YR 1 AN YR 2 AN YR 3 MKAY
KTHXBYELua
function move(n, src, dst, via)
if n > 0 then
move(n - 1, src, via, dst)
print(src, 'to', dst)
move(n - 1, via, dst, src)
end
end
move(4, 1, 2, 3)
Template:More informative version
function move(n, src, via, dst)
if n > 0 then
move(n - 1, src, dst, via)
print('Disk ',n,' from ' ,src, 'to', dst)
move(n - 1, via, src, dst)
end
end
move(4, 1, 2, 3)
Hanoi Iterative
#!/usr/bin/env luajit
local function printf(fmt, ...) io.write(string.format(fmt, ...)) end
local runs=0
local function move(tower, from, to)
if #tower[from]==0
or (#tower[to]>0
and tower[from][#tower[from]]>tower[to][#tower[to]]) then
to,from=from,to
end
if #tower[from]>0 then
tower[to][#tower[to]+1]=tower[from][#tower[from]]
tower[from][#tower[from]]=nil
io.write(tower[to][#tower[to]],":",from, "→", to, " ")
end
end
local function hanoi(n)
local src,dst,via={},{},{}
local tower={src,dst,via}
for i=1,n do src[i]=n-i+1 end
local one,nxt,lst
if n%2==1 then -- odd
one,nxt,lst=1,2,3
else
one,nxt,lst=1,3,2
end
--repeat
::loop::
move(tower, one, nxt)
if #dst==n then return end
move(tower, one, lst)
one,nxt,lst=nxt,lst,one
goto loop
--until false
end
local num=arg[1] and tonumber(arg[1]) or 4
hanoi(num)
- Output:
> ./hanoi_iter.lua 5 1:1→2 2:1→3 1:2→3 3:1→2 1:3→1 2:3→2 1:1→2 4:1→3 1:2→3 2:2→1 1:3→1 3:2→3 1:1→2 2:1→3 1:2→3 5:1→2 1:3→1 2:3→2 1:1→2 3:3→1 1:2→3 2:2→1 1:3→1 4:3→2 1:1→2 2:1→3 1:2→3 3:1→2 1:3→1 2:3→2 1:1→2
Hanoi Bitwise Fast
#!/usr/bin/env luajit
-- binary solution
local bit=require"bit"
local band,bor=bit.band,bit.bor
local function hanoi(n)
local even=(n-1)%2
for m=1,2^n-1 do
io.write(m,":",band(m,m-1)%3+1, "→", (bor(m,m-1)+1)%3+1, " ")
end
end
local num=arg[1] and tonumber(arg[1]) or 4
hanoi(num)
- Output:
> ./hanoi_bit.lua 4 1:1→3 2:1→2 3:3→2 4:1→3 5:2→1 6:2→3 7:1→3 8:1→2 9:3→2 10:3→1 11:2→1 12:3→2 13:1→3 14:1→2 15:3→2 > time ./hanoi_bit.lua 30 >/dev/null ; on AMD FX-8350 @ 4 GHz ./hanoi_bit.lua 30 > /dev/null 297,40s user 1,39s system 99% cpu 4:59,01 total
M2000 Interpreter
Module Hanoi {
Rem HANOI TOWERS
Print "Three disks" : Print
move(3, 1, 2, 3)
Print
Print "Four disks" : Print
move(4, 1, 2, 3)
Sub move(n, from, to, via)
If n <=0 Then Exit Sub
move(n - 1, from, via, to)
Print "Move disk"; n; " from pole"; from; " to pole"; to
move(n - 1, via, to, from)
End Sub
}
Hanoi- Output:
same as in FreeBasic
MACRO-11
.TITLE HANOI
.MCALL .PRINT,.EXIT
HANOI:: MOV #4,R2
MOV #61,R3
MOV #62,R4
MOV #63,R5
JSR PC,MOVE
.EXIT
MOVE: DEC R2
BLT 1$
MOV R2,-(SP)
MOV R3,-(SP)
MOV R4,-(SP)
MOV R5,-(SP)
MOV R5,R0
MOV R4,R5
MOV R0,R4
JSR PC,MOVE
MOV (SP)+,R5
MOV (SP)+,R4
MOV (SP)+,R3
MOV (SP)+,R2
MOVB R3,3$
MOVB R4,4$
.PRINT #2$
MOV R3,R0
MOV R4,R3
MOV R5,R4
MOV R0,R5
BR MOVE
1$: RTS PC
2$: .ASCII /MOVE DISK FROM PEG /
3$: .ASCII /* TO PEG /
4$: .ASCIZ /*/
.EVEN
.END HANOI- Output:
MOVE DISK FROM PEG 1 TO PEG 3 MOVE DISK FROM PEG 1 TO PEG 2 MOVE DISK FROM PEG 2 TO PEG 3 MOVE DISK FROM PEG 1 TO PEG 3 MOVE DISK FROM PEG 3 TO PEG 1 MOVE DISK FROM PEG 3 TO PEG 2 MOVE DISK FROM PEG 2 TO PEG 1 MOVE DISK FROM PEG 1 TO PEG 2 MOVE DISK FROM PEG 2 TO PEG 3 MOVE DISK FROM PEG 2 TO PEG 1 MOVE DISK FROM PEG 1 TO PEG 3 MOVE DISK FROM PEG 2 TO PEG 3 MOVE DISK FROM PEG 3 TO PEG 2 MOVE DISK FROM PEG 3 TO PEG 1 MOVE DISK FROM PEG 1 TO PEG 2
MAD
NORMAL MODE IS INTEGER
DIMENSION LIST(100)
SET LIST TO LIST
VECTOR VALUES MOVFMT =
0 $20HMOVE DISK FROM POLE ,I1,S1,8HTO POLE ,I1*$
INTERNAL FUNCTION(DUMMY)
ENTRY TO MOVE.
LOOP NUM = NUM - 1
WHENEVER NUM.E.0
PRINT FORMAT MOVFMT,FROM,DEST
OTHERWISE
SAVE RETURN
SAVE DATA NUM,FROM,VIA,DEST
TEMP=DEST
DEST=VIA
VIA=TEMP
MOVE.(0)
RESTORE DATA NUM,FROM,VIA,DEST
RESTORE RETURN
PRINT FORMAT MOVFMT,FROM,DEST
TEMP=FROM
FROM=VIA
VIA=TEMP
TRANSFER TO LOOP
END OF CONDITIONAL
FUNCTION RETURN
END OF FUNCTION
NUM = 4
FROM = 1
VIA = 2
DEST = 3
MOVE.(0)
END OF PROGRAM- Output:
MOVE DISK FROM POLE 1 TO POLE 2 MOVE DISK FROM POLE 1 TO POLE 3 MOVE DISK FROM POLE 2 TO POLE 3 MOVE DISK FROM POLE 1 TO POLE 2 MOVE DISK FROM POLE 3 TO POLE 1 MOVE DISK FROM POLE 3 TO POLE 2 MOVE DISK FROM POLE 1 TO POLE 2 MOVE DISK FROM POLE 1 TO POLE 3 MOVE DISK FROM POLE 2 TO POLE 3 MOVE DISK FROM POLE 2 TO POLE 1 MOVE DISK FROM POLE 3 TO POLE 1 MOVE DISK FROM POLE 2 TO POLE 3 MOVE DISK FROM POLE 1 TO POLE 2 MOVE DISK FROM POLE 1 TO POLE 3 MOVE DISK FROM POLE 2 TO POLE 3
Maple
Hanoi := proc(n::posint,a,b,c)
if n = 1 then
printf("Move disk from tower %a to tower %a.\n",a,c);
else
Hanoi(n-1,a,c,b);
Hanoi(1,a,b,c);
Hanoi(n-1,b,a,c);
fi;
end:
printf("Moving 2 disks from tower A to tower C using tower B.\n");
Hanoi(2,A,B,C);- Output:
Moving 2 disks from tower A to tower C using tower B.
Move disk from tower A to tower B.
Move disk from tower A to tower C.
Move disk from tower B to tower C.
Mathematica/Wolfram Language
Hanoi[0, from_, to_, via_] := Null
Hanoi[n_Integer, from_, to_, via_] := (Hanoi[n-1, from, via, to];Print["Move disk from pole ", from, " to ", to, "."];Hanoi[n-1, via, to, from])
MATLAB
This is a direct translation from the Python example given in the Wikipedia entry for the Tower of Hanoi puzzle.
function towerOfHanoi(n,A,C,B)
if (n~=0)
towerOfHanoi(n-1,A,B,C);
disp(sprintf('Move plate %d from tower %d to tower %d',[n A C]));
towerOfHanoi(n-1,B,C,A);
end
end
- Sample output:
towerOfHanoi(3,1,3,2) Move plate 1 from tower 1 to tower 3 Move plate 2 from tower 1 to tower 2 Move plate 1 from tower 3 to tower 2 Move plate 3 from tower 1 to tower 3 Move plate 1 from tower 2 to tower 1 Move plate 2 from tower 2 to tower 3 Move plate 1 from tower 1 to tower 3
MiniScript
moveDisc = function(n, A, C, B)
if n == 0 then return
moveDisc n-1, A, B, C
print "Move disc " + n + " from pole " + A + " to pole " + C
moveDisc n-1, B, C, A
end function
// Move disc 3 from pole 1 to pole 3, with pole 2 as spare
moveDisc 3, 1, 3, 2
- Output:
Move disc 1 from pole 1 to pole 3 Move disc 2 from pole 1 to pole 2 Move disc 1 from pole 3 to pole 2 Move disc 3 from pole 1 to pole 3 Move disc 1 from pole 2 to pole 1 Move disc 2 from pole 2 to pole 3 Move disc 1 from pole 1 to pole 3
Miranda
main :: [sys_message]
main = [Stdout (lay (map showmove (move 4 1 2 3)))]
showmove :: (num,num)->[char]
showmove (src,dest)
= "Move disk from pole " ++ show src ++ " to pole " ++ show dest
move :: num->*->*->*->[(*,*)]
move n src via dest
= [], if n=0
= left ++ [(src,dest)] ++ right, otherwise
where left = move (n-1) src dest via
right = move (n-1) via src dest- Output:
Move disk from pole 1 to pole 2 Move disk from pole 1 to pole 3 Move disk from pole 2 to pole 3 Move disk from pole 1 to pole 2 Move disk from pole 3 to pole 1 Move disk from pole 3 to pole 2 Move disk from pole 1 to pole 2 Move disk from pole 1 to pole 3 Move disk from pole 2 to pole 3 Move disk from pole 2 to pole 1 Move disk from pole 3 to pole 1 Move disk from pole 2 to pole 3 Move disk from pole 1 to pole 2 Move disk from pole 1 to pole 3 Move disk from pole 2 to pole 3
MIPS Assembly
# Towers of Hanoi
# MIPS assembly implementation (tested with MARS)
# Source: https://stackoverflow.com/questions/50382420/hanoi-towers-recursive-solution-using-mips/50383530#50383530
.data
prompt: .asciiz "Enter a number: "
part1: .asciiz "\nMove disk "
part2: .asciiz " from rod "
part3: .asciiz " to rod "
.text
.globl main
main:
li $v0, 4 # print string
la $a0, prompt
syscall
li $v0, 5 # read integer
syscall
# parameters for the routine
add $a0, $v0, $zero # move to $a0
li $a1, 'A'
li $a2, 'B'
li $a3, 'C'
jal hanoi # call hanoi routine
li $v0, 10 # exit
syscall
hanoi:
#save in stack
addi $sp, $sp, -20
sw $ra, 0($sp)
sw $s0, 4($sp)
sw $s1, 8($sp)
sw $s2, 12($sp)
sw $s3, 16($sp)
add $s0, $a0, $zero
add $s1, $a1, $zero
add $s2, $a2, $zero
add $s3, $a3, $zero
addi $t1, $zero, 1
beq $s0, $t1, output
recur1:
addi $a0, $s0, -1
add $a1, $s1, $zero
add $a2, $s3, $zero
add $a3, $s2, $zero
jal hanoi
j output
recur2:
addi $a0, $s0, -1
add $a1, $s3, $zero
add $a2, $s2, $zero
add $a3, $s1, $zero
jal hanoi
exithanoi:
lw $ra, 0($sp) # restore registers from stack
lw $s0, 4($sp)
lw $s1, 8($sp)
lw $s2, 12($sp)
lw $s3, 16($sp)
addi $sp, $sp, 20 # restore stack pointer
jr $ra
output:
li $v0, 4 # print string
la $a0, part1
syscall
li $v0, 1 # print integer
add $a0, $s0, $zero
syscall
li $v0, 4 # print string
la $a0, part2
syscall
li $v0, 11 # print character
add $a0, $s1, $zero
syscall
li $v0, 4 # print string
la $a0, part3
syscall
li $v0, 11 # print character
add $a0, $s2, $zero
syscall
beq $s0, $t1, exithanoi
j recur2
МК-61/52
^ 2 x^y П0 <-> 2 / {x} x#0 16
3 П3 2 П2 БП 20 3 П2 2 П3
1 П1 ПП 25 КППB ПП 28 КППA ПП 31
КППB ПП 34 КППA ИП1 ИП3 КППC ИП1 ИП2 КППC
ИП3 ИП2 КППC ИП1 ИП3 КППC ИП2 ИП1 КППC ИП2
ИП3 КППC ИП1 ИП3 КППC В/О ИП1 ИП2 БП 62
ИП2 ИП1 КППC ИП1 ИП2 ИП3 П1 -> П3 ->
П2 В/О 1 0 / + С/П КИП0 ИП0 x=0
89 3 3 1 ИНВ ^ ВП 2 С/П В/О
Instruction: РA = 56; РB = 60; РC = 72; N В/О С/П, where 2 <= N <= 7.
Modula-2
MODULE Towers;
FROM FormatString IMPORT FormatString;
FROM Terminal IMPORT WriteString,ReadChar;
PROCEDURE Move(n,from,to,via : INTEGER);
VAR buf : ARRAY[0..63] OF CHAR;
BEGIN
IF n>0 THEN
Move(n-1, from, via, to);
FormatString("Move disk %i from pole %i to pole %i\n", buf, n, from, to);
WriteString(buf);
Move(n-1, via, to, from)
END
END Move;
BEGIN
Move(3, 1, 3, 2);
ReadChar
END Towers.
Modula-3
MODULE Hanoi EXPORTS Main;
FROM IO IMPORT Put;
FROM Fmt IMPORT Int;
PROCEDURE doHanoi(n, from, to, using: INTEGER) =
BEGIN
IF n > 0 THEN
doHanoi(n - 1, from, using, to);
Put("move " & Int(from) & " --> " & Int(to) & "\n");
doHanoi(n - 1, using, to, from);
END;
END doHanoi;
BEGIN
doHanoi(4, 1, 2, 3);
END Hanoi.Monte
def move(n, fromPeg, toPeg, viaPeg):
if (n > 0):
move(n.previous(), fromPeg, viaPeg, toPeg)
traceln(`Move disk $n from $fromPeg to $toPeg`)
move(n.previous(), viaPeg, toPeg, fromPeg)
move(3, "left", "right", "middle")
MoonScript
hanoi = (n, src, dest, via) ->
if n > 1
hanoi n-1, src, via, dest
print "#{src} -> #{dest}"
if n > 1
hanoi n-1, via, dest, src
hanoi 4,1,3,2
- Output:
1 -> 2 1 -> 3 2 -> 3 1 -> 2 3 -> 1 3 -> 2 1 -> 2 1 -> 3 2 -> 3 2 -> 1 3 -> 1 2 -> 3 1 -> 2 1 -> 3 2 -> 3
Nemerle
using System;
using System.Console;
module Towers
{
Hanoi(n : int, from = 1, to = 3, via = 2) : void
{
when (n > 0)
{
Hanoi(n - 1, from, via, to);
WriteLine("Move disk from peg {0} to peg {1}", from, to);
Hanoi(n - 1, via, to, from);
}
}
Main() : void
{
Hanoi(4)
}
}
NetRexx
/* NetRexx */
options replace format comments java crossref symbols binary
runSample(arg)
return
-- 09:02, 27 August 2022 (UTC)09:02, 27 August 2022 (UTC)09:02, 27 August 2022 (UTC)09:02, 27 August 2022 (UTC)09:02, 27 August 2022 (UTC)09:02, 27 August 2022 (UTC)09:02, 27 August 2022 (UTC)09:02, 27 August 2022 (UTC)09:02, 27 August 2022 (UTC)09:02, 27 August 2022 (UTC)09:02, 27 August 2022 (UTC)09:02, 27 August 2022 (UTC)09:02, 27 August 2022 (UTC)09:02, 27 August 2022 (UTC)09:02, 27 August 2022 (UTC)~~
method runSample(arg) private static
parse arg discs .
if discs = '', discs < 1 then discs = 4
say 'Minimum moves to solution:' 2 ** discs - 1
moves = move(discs)
say 'Solved in' moves 'moves.'
return
-- 09:02, 27 August 2022 (UTC)09:02, 27 August 2022 (UTC)09:02, 27 August 2022 (UTC)09:02, 27 August 2022 (UTC)09:02, 27 August 2022 (UTC)09:02, 27 August 2022 (UTC)09:02, 27 August 2022 (UTC)09:02, 27 August 2022 (UTC)09:02, 27 August 2022 (UTC)09:02, 27 August 2022 (UTC)09:02, 27 August 2022 (UTC)09:02, 27 August 2022 (UTC)09:02, 27 August 2022 (UTC)09:02, 27 August 2022 (UTC)09:02, 27 August 2022 (UTC)~~
method move(discs = int 4, towerFrom = int 1, towerTo = int 2, towerVia = int 3, moves = int 0) public static
if discs == 1 then do
moves = moves + 1
say 'Move disc from peg' towerFrom 'to peg' towerTo '- Move No:' Rexx(moves).right(5)
end
else do
moves = move(discs - 1, towerFrom, towerVia, towerTo, moves)
moves = move(1, towerFrom, towerTo, towerVia, moves)
moves = move(discs - 1, towerVia, towerTo, towerFrom, moves)
end
return moves- Output:
Minimum moves to solution: 15 Move disc from peg 1 to peg 3 - Move No: 1 Move disc from peg 1 to peg 2 - Move No: 2 Move disc from peg 3 to peg 2 - Move No: 3 Move disc from peg 1 to peg 3 - Move No: 4 Move disc from peg 2 to peg 1 - Move No: 5 Move disc from peg 2 to peg 3 - Move No: 6 Move disc from peg 1 to peg 3 - Move No: 7 Move disc from peg 1 to peg 2 - Move No: 8 Move disc from peg 3 to peg 2 - Move No: 9 Move disc from peg 3 to peg 1 - Move No: 10 Move disc from peg 2 to peg 1 - Move No: 11 Move disc from peg 3 to peg 2 - Move No: 12 Move disc from peg 1 to peg 3 - Move No: 13 Move disc from peg 1 to peg 2 - Move No: 14 Move disc from peg 3 to peg 2 - Move No: 15 Solved in 15 moves.
NewLISP
(define (move n from to via)
(if (> n 0)
(move (- n 1) from via to
(print "move disk from pole " from " to pole " to "\n")
(move (- n 1) via to from))))
(move 4 1 2 3)Nim
proc hanoi(disks: int; fromTower, toTower, viaTower: string) =
if disks != 0:
hanoi(disks - 1, fromTower, viaTower, toTower)
echo("Move disk ", disks, " from ", fromTower, " to ", toTower)
hanoi(disks - 1, viaTower, toTower, fromTower)
hanoi(4, "1", "2", "3")- Output:
Move disk 1 from 1 to 3 Move disk 2 from 1 to 2 Move disk 1 from 3 to 2 Move disk 3 from 1 to 3 Move disk 1 from 2 to 1 Move disk 2 from 2 to 3 Move disk 1 from 1 to 3 Move disk 4 from 1 to 2 Move disk 1 from 3 to 2 Move disk 2 from 3 to 1 Move disk 1 from 2 to 1 Move disk 3 from 3 to 2 Move disk 1 from 1 to 3 Move disk 2 from 1 to 2 Move disk 1 from 3 to 2
Oberon-2
MODULE Hanoi;
IMPORT Out;
PROCEDURE Move(n,from,via,to:INTEGER);
BEGIN
IF n > 1 THEN
Move(n-1,from,to,via);
Out.String("Move disk from pole ");
Out.Int(from,0);
Out.String(" to pole ");
Out.Int(to,0);
Out.Ln;
Move(n-1,via,from,to);
ELSE
Out.String("Move disk from pole ");
Out.Int(from,0);
Out.String(" to pole ");
Out.Int(to,0);
Out.Ln;
END;
END Move;
BEGIN
Move(4,1,2,3);
END Hanoi.- Output:
Move disk from pole 1 to pole 2 Move disk from pole 1 to pole 3 Move disk from pole 2 to pole 3 Move disk from pole 1 to pole 2 Move disk from pole 3 to pole 1 Move disk from pole 3 to pole 2 Move disk from pole 1 to pole 2 Move disk from pole 1 to pole 3 Move disk from pole 2 to pole 3 Move disk from pole 2 to pole 1 Move disk from pole 3 to pole 1 Move disk from pole 2 to pole 3 Move disk from pole 1 to pole 2 Move disk from pole 1 to pole 3 Move disk from pole 2 to pole 3
Objeck
class Hanoi {
function : Main(args : String[]) ~ Nil {
Move(4, 1, 2, 3);
}
function: Move(n:Int, f:Int, t:Int, v:Int) ~ Nil {
if(n = 1) {
"Move disk from pole {$f} to pole {$t}"->PrintLine();
}
else {
Move(n - 1, f, v, t);
Move(1, f, t, v);
Move(n - 1, v, t, f);
};
}
}Objective-C
From here
It should be compatible with XCode/Cocoa on MacOS too.
The Interface - TowersOfHanoi.h:
#import <Foundation/NSObject.h>
@interface TowersOfHanoi: NSObject {
int pegFrom;
int pegTo;
int pegVia;
int numDisks;
}
-(void) setPegFrom: (int) from andSetPegTo: (int) to andSetPegVia: (int) via andSetNumDisks: (int) disks;
-(void) movePegFrom: (int) from andMovePegTo: (int) to andMovePegVia: (int) via andWithNumDisks: (int) disks;
@endThe Implementation - TowersOfHanoi.m:
#import "TowersOfHanoi.h"
@implementation TowersOfHanoi
-(void) setPegFrom: (int) from andSetPegTo: (int) to andSetPegVia: (int) via andSetNumDisks: (int) disks {
pegFrom = from;
pegTo = to;
pegVia = via;
numDisks = disks;
}
-(void) movePegFrom: (int) from andMovePegTo: (int) to andMovePegVia: (int) via andWithNumDisks: (int) disks {
if (disks == 1) {
printf("Move disk from pole %i to pole %i\n", from, to);
} else {
[self movePegFrom: from andMovePegTo: via andMovePegVia: to andWithNumDisks: disks-1];
[self movePegFrom: from andMovePegTo: to andMovePegVia: via andWithNumDisks: 1];
[self movePegFrom: via andMovePegTo: to andMovePegVia: from andWithNumDisks: disks-1];
}
}
@endTest code: TowersTest.m:
#import <stdio.h>
#import "TowersOfHanoi.h"
int main( int argc, const char *argv[] ) {
@autoreleasepool {
TowersOfHanoi *tower = [[TowersOfHanoi alloc] init];
int from = 1;
int to = 3;
int via = 2;
int disks = 3;
[tower setPegFrom: from andSetPegTo: to andSetPegVia: via andSetNumDisks: disks];
[tower movePegFrom: from andMovePegTo: to andMovePegVia: via andWithNumDisks: disks];
}
return 0;
}OCaml
let rec hanoi n a b c =
if n <> 0 then begin
hanoi (pred n) a c b;
Printf.printf "Move disk from pole %d to pole %d\n" a b;
hanoi (pred n) c b a
end
let () =
hanoi 4 1 2 3Octave
function hanoimove(ndisks, from, to, via)
if ( ndisks == 1 )
printf("Move disk from pole %d to pole %d\n", from, to);
else
hanoimove(ndisks-1, from, via, to);
hanoimove(1, from, to, via);
hanoimove(ndisks-1, via, to, from);
endif
endfunction
hanoimove(4, 1, 2, 3);Oforth
: move(n, from, to, via)
n 0 > ifTrue: [
move(n 1-, from, via, to)
System.Out "Move disk from " << from << " to " << to << cr
move(n 1-, via, to, from)
] ;
5 $left $middle $right) moveOz
declare
proc {TowersOfHanoi N From To Via}
if N > 0 then
{TowersOfHanoi N-1 From Via To}
{System.showInfo "Move from "#From#" to "#To}
{TowersOfHanoi N-1 Via To From}
end
end
in
{TowersOfHanoi 4 left middle right}PARI/GP
\\ Towers of Hanoi
\\ 8/19/2016 aev
\\ Where: n - number of disks, sp - start pole, ep - end pole.
HanoiTowers(n,sp,ep)={
if(n!=0,
HanoiTowers(n-1,sp,6-sp-ep);
print("Move disk ", n, " from pole ", sp," to pole ", ep);
HanoiTowers(n-1,6-sp-ep,ep);
);
}
\\ Testing n=3:
HanoiTowers(3,1,3);- Output:
> HanoiTower(3,1,3); Move disk 1 from pole 1 to pole 3 Move disk 2 from pole 1 to pole 2 Move disk 1 from pole 3 to pole 2 Move disk 3 from pole 1 to pole 3 Move disk 1 from pole 2 to pole 1 Move disk 2 from pole 2 to pole 3 Move disk 1 from pole 1 to pole 3
Pascal
I think it is standard pascal, except for the constant array "strPole". I am not sure if constant arrays are part of the standard. However, as far as I know, they are a "de facto" standard in every compiler.
program Hanoi;
type
TPole = (tpLeft, tpCenter, tpRight);
const
strPole:array[TPole] of string[6]=('left','center','right');
procedure MoveStack (const Ndisks : integer; const Origin,Destination,Auxiliary:TPole);
begin
if Ndisks >0 then begin
MoveStack(Ndisks - 1, Origin,Auxiliary, Destination );
Writeln('Move disk ',Ndisks ,' from ',strPole[Origin],' to ',strPole[Destination]);
MoveStack(Ndisks - 1, Auxiliary, Destination, origin);
end;
end;
begin
MoveStack(4,tpLeft,tpCenter,tpRight);
end.A little longer, but clearer for my taste
program Hanoi;
type
TPole = (tpLeft, tpCenter, tpRight);
const
strPole:array[TPole] of string[6]=('left','center','right');
procedure MoveOneDisk(const DiskNum:integer; const Origin,Destination:TPole);
begin
Writeln('Move disk ',DiskNum,' from ',strPole[Origin],' to ',strPole[Destination]);
end;
procedure MoveStack (const Ndisks : integer; const Origin,Destination,Auxiliary:TPole);
begin
if Ndisks =1 then
MoveOneDisk(1,origin,Destination)
else begin
MoveStack(Ndisks - 1, Origin,Auxiliary, Destination );
MoveOneDisk(Ndisks,origin,Destination);
MoveStack(Ndisks - 1, Auxiliary, Destination, origin);
end;
end;
begin
MoveStack(4,tpLeft,tpCenter,tpRight);
end.Perl
sub hanoi {
my ($n, $from, $to, $via) = (@_, 1, 2, 3);
if ($n == 1) {
print "Move disk from pole $from to pole $to.\n";
} else {
hanoi($n - 1, $from, $via, $to);
hanoi(1, $from, $to, $via);
hanoi($n - 1, $via, $to, $from);
};
};Phix
constant poles = {"left","middle","right"} enum left, middle, right sequence disks integer moves procedure showpegs(integer src, integer dest) string desc = sprintf("%s to %s:",{poles[src],poles[dest]}) disks[dest] &= disks[src][$] disks[src] = disks[src][1..$-1] for i=1 to length(disks) do printf(1,"%-16s | %s\n",{desc,join(sq_add(disks[i],'0'),' ')}) desc = "" end for printf(1,"\n") moves += 1 end procedure procedure hanoir(integer n, src=left, dest=right, via=middle) if n>0 then hanoir(n-1, src, via, dest) showpegs(src,dest) hanoir(n-1, via, dest, src) end if end procedure procedure hanoi(integer n) disks = {reverse(tagset(n)),{},{}} moves = 0 hanoir(n) printf(1,"completed in %d moves\n",{moves}) end procedure hanoi(3) -- (output of 4,5,6 also shown)
- Output:
left to right: | 3 2
|
| 1
left to middle: | 3
| 2
| 1
right to middle: | 3
| 2 1
|
left to right: |
| 2 1
| 3
middle to left: | 1
| 2
| 3
middle to right: | 1
|
| 3 2
left to right: |
|
| 3 2 1
completed in 7 moves
left to middle: | 4 3 2
| 1
|
left to right: | 4 3
| 1
| 2
middle to right: | 4 3
|
| 2 1
...
left to middle: | 2
| 1
| 4 3
left to right: |
| 1
| 4 3 2
middle to right: |
|
| 4 3 2 1
completed in 15 moves
left to right: | 5 4 3 2
|
| 1
left to middle: | 5 4 3
| 2
| 1
right to middle: | 5 4 3
| 2 1
|
...
middle to left: | 1
| 2
| 5 4 3
middle to right: | 1
|
| 5 4 3 2
left to right: |
|
| 5 4 3 2 1
completed in 31 moves
left to middle: | 6 5 4 3 2
| 1
|
left to right: | 6 5 4 3
| 1
| 2
middle to right: | 6 5 4 3
|
| 2 1
...
left to middle: | 2
| 1
| 6 5 4 3
left to right: |
| 1
| 6 5 4 3 2
middle to right: |
|
| 6 5 4 3 2 1
completed in 63 moves
PHL
module hanoi;
extern printf;
@Void move(@Integer n, @Integer from, @Integer to, @Integer via) [
if (n > 0) {
move(n - 1, from, via, to);
printf("Move disk from pole %d to pole %d\n", from, to);
move(n - 1, via, to, from);
}
]
@Integer main [
move(4, 1,2,3);
return 0;
]PHP
function move($n,$from,$to,$via) {
if ($n === 1) {
print("Move disk from pole $from to pole $to");
} else {
move($n-1,$from,$via,$to);
move(1,$from,$to,$via);
move($n-1,$via,$to,$from);
}
}Picat
main =>
hanoi(3, left, center, right).
hanoi(0, _From, _To, _Via) => true.
hanoi(N, From, To, Via) =>
hanoi(N - 1, From, Via, To),
printf("Move disk %w from pole %w to pole %w\n", N, From, To),
hanoi(N - 1, Via, To, From).- Output:
Move disk 1 from pole left to pole center Move disk 2 from pole left to pole right Move disk 1 from pole center to pole right Move disk 3 from pole left to pole center Move disk 1 from pole right to pole left Move disk 2 from pole right to pole center Move disk 1 from pole left to pole center count=7, theoretical=7
Fast counting
main =>
hanoi(64).
hanoi(N) =>
printf("N=%d\n", N),
Count = move(N, left, center, right) ,
printf("count=%w, theoretical=%w\n", Count, 2**N-1).
table
move(0, _From, _To, _Via) = 0.
move(N, From, To, Via) = Count =>
Count1 = move(N - 1, From, Via, To),
Count2 = move(N - 1, Via, To, From),
Count = Count1+Count2+1.- Output:
N=64 count=18446744073709551615, theoretical=18446744073709551615
PicoLisp
(de move (N A B C) # Use: (move 3 'left 'center 'right)
(unless (=0 N)
(move (dec N) A C B)
(println 'Move 'disk 'from A 'to B)
(move (dec N) C B A) ) )PL/I
tower: proc options (main);
call Move (4,1,2,3);
Move: procedure (ndiscs, from, to, via) recursive;
declare (ndiscs, from, to, via) fixed binary;
if ndiscs = 1 then
put skip edit ('Move disc from pole ', trim(from), ' to pole ',
trim(to) ) (a);
else
do;
call Move (ndiscs-1, from, via, to);
call Move (1, from, to, via);
call Move (ndiscs-1, via, to, from);
end;
end Move;
end tower;PL/M
Iterative solution as PL/M doesn't do recursion.
... under CP/M (or an emulator)
100H: /* ITERATIVE TOWERS OF HANOI; TRANSLATED FROM TINY BASIC (VIA ALGOL W) */
/* CP/M BDOS SYSTEM CALL */
BDOS: PROCEDURE( FN, ARG ); DECLARE FN BYTE, ARG ADDRESS; GOTO 5; END;
/* I/O ROUTINES */
PR$CHAR: PROCEDURE( C ); DECLARE C BYTE; CALL BDOS( 2, C ); END;
PR$STRING: PROCEDURE( S ); DECLARE S ADDRESS; CALL BDOS( 9, S ); END;
DECLARE ( D, N, X, S, T ) ADDRESS;
/* FIXED NUMBER OF DISCS: 4 */
N = 1;
DO D = 1 TO 4;
N = N + N;
END;
DO X = 1 TO N - 1;
/* AS IN ALGOL W, WE CAN USE PL/M'S BIT ABD MOD OPERATORS */
S = ( X AND ( X - 1 ) ) MOD 3;
T = ( ( X OR ( X - 1 ) ) + 1 ) MOD 3;
CALL PR$STRING( .'MOVE DISC ON PEG $' );
CALL PR$CHAR( '1' + S );
CALL PR$STRING( .' TO PEG $' );
CALL PR$CHAR( '1' + T );
CALL PR$STRING( .( 0DH, 0AH, '$' ) );
END;
EOF- Output:
MOVE DISC ON PEG 1 TO PEG 3 MOVE DISC ON PEG 1 TO PEG 2 MOVE DISC ON PEG 3 TO PEG 2 MOVE DISC ON PEG 1 TO PEG 3 MOVE DISC ON PEG 2 TO PEG 1 MOVE DISC ON PEG 2 TO PEG 3 MOVE DISC ON PEG 1 TO PEG 3 MOVE DISC ON PEG 1 TO PEG 2 MOVE DISC ON PEG 3 TO PEG 2 MOVE DISC ON PEG 3 TO PEG 1 MOVE DISC ON PEG 2 TO PEG 1 MOVE DISC ON PEG 3 TO PEG 2 MOVE DISC ON PEG 1 TO PEG 3 MOVE DISC ON PEG 1 TO PEG 2 MOVE DISC ON PEG 3 TO PEG 2
Plain TeX
\newcount\hanoidepth
\def\hanoi#1{%
\hanoidepth = #1
\move abc
}%
\def\move#1#2#3{%
\advance \hanoidepth by -1
\ifnum \hanoidepth > 0
\move #1#3#2
\fi
Move the upper disk from pole #1 to pole #3.\par
\ifnum \hanoidepth > 0
\move#2#1#3
\fi
\advance \hanoidepth by 1
}
\hanoi{5}
\endPop11
define hanoi(n, src, dst, via);
if n > 0 then
hanoi(n - 1, src, via, dst);
'Move disk ' >< n >< ' from ' >< src >< ' to ' >< dst >< '.' =>
hanoi(n - 1, via, dst, src);
endif;
enddefine;
hanoi(4, "left", "middle", "right");PostScript
A million-page document, each page showing one move.
%!PS-Adobe-3.0
%%BoundingBox: 0 0 300 300
/plate {
exch 100 mul 50 add exch th mul 10 add moveto
dup s mul neg 2 div 0 rmoveto
dup s mul 0 rlineto
0 th rlineto
s neg mul 0 rlineto
closepath gsave .5 setgray fill grestore 0 setgray stroke
} def
/drawtower {
0 1 2 { /x exch def /y 0 def
tower x get {
dup 0 gt { x y plate /y y 1 add def } {pop} ifelse
} forall
} for showpage
} def
/apop { [ exch aload pop /last exch def ] last } def
/apush{ [ 3 1 roll aload pop counttomark -1 roll ] } def
/hanoi {
0 dict begin /from /mid /to /h 5 -1 2 { -1 roll def } for
h 1 eq {
tower from get apop tower to get apush
tower to 3 -1 roll put
tower from 3 -1 roll put
drawtower
} {
/h h 1 sub def
from to mid h hanoi
from mid to 1 hanoi
mid from to h hanoi
} ifelse
end
} def
/n 12 def
/s 90 n div def
/th 180 n div def
/tower [ [n 1 add -1 2 { } for ] [] [] ] def
drawtower 0 1 2 n hanoi
%%EOFPowerShell
function hanoi($n, $a, $b, $c) {
if($n -eq 1) {
"$a -> $c"
} else{
hanoi ($n - 1) $a $c $b
hanoi 1 $a $b $c
hanoi ($n - 1) $b $a $c
}
}
hanoi 3 "A" "B" "C"Output:
A -> C A -> B C -> B A -> C B -> A B -> C A -> C
Prolog
From Programming in Prolog by W.F. Clocksin & C.S. Mellish
hanoi(N) :- move(N,left,center,right).
move(0,_,_,_) :- !.
move(N,A,B,C) :-
M is N-1,
move(M,A,C,B),
inform(A,B),
move(M,C,B,A).
inform(X,Y) :- write([move,a,disk,from,the,X,pole,to,Y,pole]), nl.Using DCGs and separating core logic from IO
hanoi(N, Src, Aux, Dest, Moves-NMoves) :-
NMoves is 2^N - 1,
length(Moves, NMoves),
phrase(move(N, Src, Aux, Dest), Moves).
move(1, Src, _, Dest) --> !,
[Src->Dest].
move(2, Src, Aux, Dest) --> !,
[Src->Aux,Src->Dest,Aux->Dest].
move(N, Src, Aux, Dest) -->
{ succ(N0, N) },
move(N0, Src, Dest, Aux),
move(1, Src, Aux, Dest),
move(N0, Aux, Src, Dest).PureBasic
Algorithm according to http://en.wikipedia.org/wiki/Towers_of_Hanoi
Procedure Hanoi(n, A.s, C.s, B.s)
If n
Hanoi(n-1, A, B, C)
PrintN("Move the plate from "+A+" to "+C)
Hanoi(n-1, B, C, A)
EndIf
EndProcedureFull program
Procedure Hanoi(n, A.s, C.s, B.s)
If n
Hanoi(n-1, A, B, C)
PrintN("Move the plate from "+A+" to "+C)
Hanoi(n-1, B, C, A)
EndIf
EndProcedure
If OpenConsole()
Define n=3
PrintN("Moving "+Str(n)+" pegs."+#CRLF$)
Hanoi(n,"Left Peg","Middle Peg","Right Peg")
PrintN(#CRLF$+"Press ENTER to exit."): Input()
EndIf- Output:
Moving 3 pegs. Move the plate from Left Peg to Middle Peg Move the plate from Left Peg to Right Peg Move the plate from Middle Peg to Right Peg Move the plate from Left Peg to Middle Peg Move the plate from Right Peg to Left Peg Move the plate from Right Peg to Middle Peg Move the plate from Left Peg to Middle Peg Press ENTER to exit.
Python
Recursive
def hanoi(ndisks, startPeg=1, endPeg=3):
if ndisks:
hanoi(ndisks-1, startPeg, 6-startPeg-endPeg)
print(f"Move disk {ndisks} from peg {startPeg} to peg {endPeg}")
hanoi(ndisks-1, 6-startPeg-endPeg, endPeg)
hanoi(4)- Output:
for ndisks=2
Move disk 1 from peg 1 to peg 2 Move disk 2 from peg 1 to peg 3 Move disk 1 from peg 2 to peg 3
Or, separating the definition of the data from its display:
'''Towers of Hanoi'''
# hanoi :: Int -> String -> String -> String -> [(String, String)]
def hanoi(n):
'''A list of (from, to) label pairs,
where a, b and c are labels for each of the
three Hanoi tower positions.'''
def go(n, a, b, c):
p = n - 1
return (
go(p, a, c, b) + [(a, b)] + go(p, c, b, a)
) if 0 < n else []
return lambda a: lambda b: lambda c: go(n, a, b, c)
# TEST ----------------------------------------------------
if __name__ == '__main__':
# fromTo :: (String, String) -> String
def fromTo(xy):
'''x -> y'''
x, y = xy
return x.rjust(5, ' ') + ' -> ' + y
print(__doc__ + ':\n\n' + '\n'.join(
map(fromTo, hanoi(4)('left')('right')('mid'))
))- Output:
Towers of Hanoi: left -> mid left -> right mid -> right left -> mid right -> left right -> mid left -> mid left -> right mid -> right mid -> left right -> left mid -> right left -> mid left -> right mid -> right
Graphic
Refactoring the version above to recursively generate a simple visualisation:
'''Towers of Hanoi'''
from itertools import accumulate, chain, repeat
from inspect import signature
import operator
# hanoi :: Int -> [(Int, Int)]
def hanoi(n):
'''A list of index pairs, representing disk moves
between indexed Hanoi positions.
'''
def go(n, a, b, c):
p = n - 1
return (
go(p, a, c, b) + [(a, b)] + go(p, c, b, a)
) if 0 < n else []
return go(n, 0, 2, 1)
# hanoiState :: ([Int],[Int],[Int], String) -> (Int, Int) ->
# ([Int],[Int],[Int], String)
def hanoiState(tpl, ab):
'''A new Hanoi tower state'''
a, b = ab
xs, ys = tpl[a], tpl[b]
w = 3 * (2 + (2 * max(map(max, filter(len, tpl[:-1])))))
def delta(i):
return tpl[i] if i not in ab else xs[1:] if (
i == a
) else [xs[0]] + ys
tkns = moveName(('left', 'mid', 'right'))(ab)
caption = ' '.join(tkns)
return tuple(map(delta, [0, 1, 2])) + (
(caption if tkns[0] != 'mid' else caption.rjust(w, ' ')),
)
# showHanoi :: ([Int],[Int],[Int], String) -> String
def showHanoi(tpl):
'''Captioned string representation of an updated Hanoi tower state.'''
def fullHeight(n):
return lambda xs: list(repeat('', n - len(xs))) + xs
mul = curry(operator.mul)
lt = curry(operator.lt)
rods = fmap(fmap(mul('__')))(
list(tpl[0:3])
)
h = max(map(len, rods))
w = 2 + max(
map(
compose(max)(fmap(len)),
filter(compose(lt(0))(len), rods)
)
)
xs = fmap(concat)(
transpose(fmap(
compose(fmap(center(w)(' ')))(
fullHeight(h)
)
)(rods))
)
return tpl[3] + '\n\n' + unlines(xs) + '\n' + ('___' * w)
# moveName :: (String, String, String) -> (Int, Int) -> [String]
def moveName(labels):
'''(from, to) index pair represented as an a -> b string.'''
def go(ab):
a, b = ab
return [labels[a], ' to ', labels[b]] if a < b else [
labels[b], ' from ', labels[a]
]
return lambda ab: go(ab)
# TEST ----------------------------------------------------
def main():
'''Visualisation of a Hanoi tower sequence for N discs.
'''
n = 3
print('Hanoi sequence for ' + str(n) + ' disks:\n')
print(unlines(
fmap(showHanoi)(
scanl(hanoiState)(
(enumFromTo(1)(n), [], [], '')
)(hanoi(n))
)
))
# GENERIC -------------------------------------------------
# center :: Int -> Char -> String -> String
def center(n):
'''String s padded with c to approximate centre,
fitting in but not truncated to width n.'''
return lambda c: lambda s: s.center(n, c)
# compose (<<<) :: (b -> c) -> (a -> b) -> a -> c
def compose(g):
'''Right to left function composition.'''
return lambda f: lambda x: g(f(x))
# concat :: [[a]] -> [a]
# concat :: [String] -> String
def concat(xs):
'''The concatenation of all the elements
in a list or iterable.'''
def f(ys):
zs = list(chain(*ys))
return ''.join(zs) if isinstance(ys[0], str) else zs
return (
f(xs) if isinstance(xs, list) else (
chain.from_iterable(xs)
)
) if xs else []
# curry :: ((a, b) -> c) -> a -> b -> c
def curry(f):
'''A curried function derived
from an uncurried function.'''
if 1 < len(signature(f).parameters):
return lambda x: lambda y: f(x, y)
else:
return f
# enumFromTo :: (Int, Int) -> [Int]
def enumFromTo(m):
'''Integer enumeration from m to n.'''
return lambda n: list(range(m, 1 + n))
# fmap :: (a -> b) -> [a] -> [b]
def fmap(f):
'''fmap over a list.
f lifted to a function over a list.
'''
return lambda xs: list(map(f, xs))
# scanl :: (b -> a -> b) -> b -> [a] -> [b]
def scanl(f):
'''scanl is like reduce, but returns a succession of
intermediate values, building from the left.
'''
return lambda a: lambda xs: (
accumulate(chain([a], xs), f)
)
# showLog :: a -> IO String
def showLog(*s):
'''Arguments printed with
intercalated arrows.'''
print(
' -> '.join(map(str, s))
)
# transpose :: Matrix a -> Matrix a
def transpose(m):
'''The rows and columns of the argument transposed.
(The matrix containers and rows can be lists or tuples).
'''
if m:
inner = type(m[0])
z = zip(*m)
return (type(m))(
map(inner, z) if tuple != inner else z
)
else:
return m
# unlines :: [String] -> String
def unlines(xs):
'''A single string derived by the intercalation
of a list of strings with the newline character.
'''
return '\n'.join(xs)
# TEST ----------------------------------------------------
if __name__ == '__main__':
main()Hanoi sequence for 3 disks:
__
____
______
________________________
left to right
____
______ __
________________________
left to mid
______ ____ __
________________________
mid from right
__
______ ____
________________________
left to right
__
____ ______
________________________
left from mid
__ ____ ______
________________________
mid to right
____
__ ______
________________________
left to right
__
____
______
________________________
There is a 3D hanoi-game in the examples that come with VPython, and at github.
Quackery
[ stack ] is rings ( --> [ )
[ rings share
depth share -
8 * times sp
emit sp emit sp
say 'move' cr ] is echomove ( c c --> )
[ dup rings put
depth put
char a char b char c
[ swap decurse
rot 2dup echomove
decurse
swap rot ]
3 times drop
depth release
rings release ] is hanoi ( n --> n )
say 'How to solve a three ring Towers of Hanoi puzzle:' cr cr
3 hanoi cr- Output:
How to solve a three ring Towers of Hanoi puzzle:
a c move
a b move
c b move
a c move
b a move
b c move
a c move
a b move
c b move
c a move
b a move
c b move
a c move
a b move
c b move
Quite BASIC
'This is implemented on the Quite BASIC website 'http://www.quitebasic.com/prj/puzzle/towers-of-hanoi/
1000 REM Towers of Hanoi
1010 REM Quite BASIC Puzzle Project
1020 CLS
1030 PRINT "Towers of Hanoi"
1040 PRINT
1050 PRINT "This is a recursive solution for seven discs."
1060 PRINT
1070 PRINT "See the REM statements in the program if you didn't think that recursion was possible in classic BASIC!"
1080 REM Yep, recursive GOSUB calls works in Quite BASIC!
1090 REM However, to actually write useful recursive algorithms, it helps to have variable scoping and parameters to subroutines -- something classic BASIC is lacking. In this case we have only one "parameter" -- the variable N. And subroutines are always called with N-1. This is lucky for us because we can keep track of the value by decrementing it when we enter subroutines and incrementing it back when we exit.
1100 REM If we had subroutine parameters we could have written a single subroutine for moving discs from peg P to peg Q where P and Q were subroutine parameters, but no such luck. Instead we have to write six different subroutines for moving from peg to peg. See Subroutines 4000, 5000, 6000, 7000, 8000, and 9000.
1110 REM ===============================
2000 REM A, B, and C are arrays holding the discs
2010 REM We refer to the corresponding pegs as peg A, B, and C
2020 ARRAY A
2030 ARRAY B
2040 ARRAY C
2050 REM Fill peg A with seven discs
2060 FOR I = 0 TO 6
2070 LET A[I] = 7 - I
2080 NEXT I
2090 REM X, Y, Z hold the number of discs on pegs A, B, and C
2100 LET X = 7
2110 LET Y = 0
2120 LET Z = 0
2130 REM Disc colors
2140 ARRAY P
2150 LET P[1] = "cyan"
2160 LET P[2] = "blue"
2170 LET P[3] = "green"
2180 LET P[4] = "yellow"
2190 LET P[5] = "magenta"
2200 LET P[6] = "orange"
2210 LET P[7] = "red"
2220 REM Draw initial position -- all discs on the A peg
2230 FOR I = 0 TO 6
2240 FOR J = 8 - A[I] TO 8 + A[I]
2250 PLOT J, I, P[A[I]]
2260 NEXT J
2270 NEXT I
2280 REM N is the number of discs to move
2290 LET N = 7
2320 REM Move all discs from peg A to peg B
2310 GOSUB 6000
2320 END
3000 REM The subroutines 3400, 3500, 3600, 3700, 3800, 3900
3010 REM handle the drawing of the discs on the canvas as we
3020 REM move discs from one peg to another.
3030 REM These subroutines also update the variables X, Y, and Z
3040 REM which hold the number of discs on each peg.
3050 REM ==============================
3400 REM Subroutine -- Remove disc from peg A
3410 LET X = X - 1
3420 FOR I = 8 - A[X] TO 8 + A[X]
3430 PLOT I, X, "gray"
3440 NEXT I
3450 RETURN
3500 REM Subroutine -- Add disc to peg A
3510 FOR I = 8 - A[X] TO 8 + A[X]
3520 PLOT I, X, P[A[X]]
3530 NEXT I
3540 LET X = X + 1
3550 PAUSE 400 * (5 - LEVEL) + 10
3560 RETURN
3600 REM Subroutine -- Remove disc from peg B
3610 LET Y = Y - 1
3620 FOR I = 24 - B[Y] TO 24 + B[Y]
3630 PLOT I, Y, "gray"
3640 NEXT I
3650 RETURN
3700 REM Subroutine -- Add disc to peg B
3710 FOR I = 24 - B[Y] TO 24 + B[Y]
3720 PLOT I, Y, P[B[Y]]
3730 NEXT I
3740 LET Y = Y + 1
3750 PAUSE 400 * (5 - LEVEL) + 10
3760 RETURN
3800 REM Subroutine -- Remove disc from peg C
3810 LET Z = Z - 1
3820 FOR I = 40 - C[Z] TO 40 + C[Z]
3830 PLOT I, Z, "gray"
3840 NEXT I
3850 RETURN
3900 REM Subroutine -- Add disc to peg C
3910 FOR I = 40 - C[Z] TO 40 + C[Z]
3920 PLOT I, Z, P[C[Z]]
3930 NEXT I
3940 LET Z = Z + 1
3950 PAUSE 400 * (5 - LEVEL) + 10
3960 RETURN
4000 REM ======================================
4010 REM Recursive Subroutine -- move N discs from peg B to peg A
4020 REM First move N-1 discs from peg B to peg C
4030 LET N = N - 1
4040 IF N <> 0 THEN GOSUB 9000
4050 REM Then move one disc from peg B to peg A
4060 GOSUB 3600
4070 LET A[X] = B[Y]
4080 GOSUB 3500
4090 REM And finally move N-1 discs from peg C to peg A
4100 IF N <> 0 THEN GOSUB 5000
4110 REM Restore N before returning
4120 LET N = N + 1
4130 RETURN
5000 REM ======================================
5010 REM Recursive Subroutine -- Move N discs from peg C to peg A
5020 REM First move N-1 discs from peg C to peg B
5030 LET N = N - 1
5040 IF N <> 0 THEN GOSUB 8000
5050 REM Then move one disc from peg C to peg A
5060 GOSUB 3800
5070 LET A[X] = C[Z]
5080 GOSUB 3500
5090 REM And finally move N-1 discs from peg B to peg A
5100 IF N <> 0 THEN GOSUB 4000
5120 REM Restore N before returning
5130 LET N = N + 1
5140 RETURN
6000 REM ======================================
6000 REM Recursive Subroutine -- Move N discs from peg A to peg B
6010 REM First move N-1 discs from peg A to peg C
6020 LET N = N - 1
6030 IF N <> 0 THEN GOSUB 7000
6040 REM Then move one disc from peg A to peg B
6050 GOSUB 3400
6060 LET B[Y] = A[X]
6070 GOSUB 3700
6090 REM And finally move N-1 discs from peg C to peg B
6100 IF N <> 0 THEN GOSUB 8000
6110 REM Restore N before returning
6120 LET N = N + 1
6130 RETURN
7000 REM ======================================
7010 REM Recursive Subroutine -- Move N discs from peg A to peg C
7020 REM First move N-1 discs from peg A to peg B
7030 LET N = N - 1
7040 IF N <> 0 THEN GOSUB 6000
7050 REM Then move one disc from peg A to peg C
7060 GOSUB 3400
7070 LET C[Z] = A[X]
7080 GOSUB 3900
7090 REM And finally move N-1 discs from peg B to peg C
7100 IF N <> 0 THEN GOSUB 9000
7110 REM Restore N before returning
7120 LET N = N + 1
7130 RETURN
8000 REM ======================================
8010 REM Recursive Subroutine -- Move N discs from peg C to peg B
8020 REM First move N-1 discs from peg C to peg A
8030 LET N = N - 1
8040 IF N <> 0 THEN GOSUB 5000
8050 REM Then move one disc from peg C to peg B
8060 GOSUB 3800
8070 LET B[Y] = C[Z]
8080 GOSUB 3700
8090 REM And finally move N-1 discs from peg A to peg B
8100 IF N <> 0 THEN GOSUB 6000
8110 REM Restore N before returning
8120 LET N = N + 1
8130 RETURN
9000 REM ======================================
9010 REM Recursive Subroutine -- Move N discs from peg B to peg C
9020 REM First move N-1 discs from peg B to peg A
9030 LET N = N - 1
9040 IF N <> 0 THEN GOSUB 4000
9050 REM Then move one disc from peg B to peg C
9060 GOSUB 3600
9070 LET C[Z] = B[Y]
9080 GOSUB 3900
9090 REM And finally move N-1 discs from peg A to peg C
9100 IF N <> 0 THEN GOSUB 7000
9110 REM Restore N before returning
9120 LET N = N + 1
9130 RETURNR
hanoimove <- function(ndisks, from, to, via) {
if (ndisks == 1) {
cat("move disk from", from, "to", to, "\n")
} else {
hanoimove(ndisks - 1, from, via, to)
hanoimove(1, from, to, via)
hanoimove(ndisks - 1, via, to, from)
}
}
hanoimove(4, 1, 2, 3)Racket
#lang racket
(define (hanoi n a b c)
(when (> n 0)
(hanoi (- n 1) a c b)
(printf "Move ~a to ~a\n" a b)
(hanoi (- n 1) c b a)))
(hanoi 4 'left 'middle 'right)Raku
(formerly Perl 6)
subset Peg of Int where 1|2|3;
multi hanoi (0, Peg $a, Peg $b, Peg $c) { }
multi hanoi (Int $n, Peg $a = 1, Peg $b = 2, Peg $c = 3) {
hanoi $n - 1, $a, $c, $b;
say "Move $a to $b.";
hanoi $n - 1, $c, $b, $a;
}Rascal
public void hanoi(ndisks, startPeg, endPeg){
if(ndisks>0){
hanoi(ndisks-1, startPeg, 6 - startPeg - endPeg);
println("Move disk <ndisks> from peg <startPeg> to peg <endPeg>");
hanoi(ndisks-1, 6 - startPeg - endPeg, endPeg);
}
}- Output:
rascal>hanoi(4,1,3)
Move disk 1 from peg 1 to peg 2
Move disk 2 from peg 1 to peg 3
Move disk 1 from peg 2 to peg 3
Move disk 3 from peg 1 to peg 2
Move disk 1 from peg 3 to peg 1
Move disk 2 from peg 3 to peg 2
Move disk 1 from peg 1 to peg 2
Move disk 4 from peg 1 to peg 3
Move disk 1 from peg 2 to peg 3
Move disk 2 from peg 2 to peg 1
Move disk 1 from peg 3 to peg 1
Move disk 3 from peg 2 to peg 3
Move disk 1 from peg 1 to peg 2
Move disk 2 from peg 1 to peg 3
Move disk 1 from peg 2 to peg 3
okRaven
define hanoi use ndisks, startpeg, endpeg
ndisks 0 > if
6 startpeg - endpeg - startpeg ndisks 1 - hanoi
endpeg startpeg ndisks "Move disk %d from peg %d to peg %d\n" print
endpeg 6 startpeg - endpeg - ndisks 1 - hanoi
define dohanoi use ndisks
# startpeg=1, endpeg=3
3 1 ndisks hanoi
# 4 disks
4 dohanoi- Output:
raven hanoi.rv Move disk 1 from peg 1 to peg 2 Move disk 2 from peg 1 to peg 3 Move disk 1 from peg 2 to peg 3 Move disk 3 from peg 1 to peg 2 Move disk 1 from peg 3 to peg 1 Move disk 2 from peg 3 to peg 2 Move disk 1 from peg 1 to peg 2 Move disk 4 from peg 1 to peg 3 Move disk 1 from peg 2 to peg 3 Move disk 2 from peg 2 to peg 1 Move disk 1 from peg 3 to peg 1 Move disk 3 from peg 2 to peg 3 Move disk 1 from peg 1 to peg 2 Move disk 2 from peg 1 to peg 3 Move disk 1 from peg 2 to peg 3
REBOL
REBOL [
Title: "Towers of Hanoi"
URL: http://rosettacode.org/wiki/Towers_of_Hanoi
]
hanoi: func [
{Begin moving the golden disks from one pole to the next.
Note: when last disk moved, the world will end.}
disks [integer!] "Number of discs on starting pole."
/poles "Name poles."
from to via
][
if disks = 0 [return]
if not poles [from: 'left to: 'middle via: 'right]
hanoi/poles disks - 1 from via to
print [from "->" to]
hanoi/poles disks - 1 via to from
]
hanoi 4- Output:
left -> right left -> middle right -> middle left -> right middle -> left middle -> right left -> right left -> middle right -> middle right -> left middle -> left right -> middle left -> right left -> middle right -> middle
Refal
$ENTRY Go {
= <Move 4 1 2 3>;
};
Move {
0 e.X = ;
s.N s.Src s.Via s.Dest, <- s.N 1>: s.Next =
<Move s.Next s.Src s.Dest s.Via>
<Prout "Move disk from pole" s.Src "to pole" s.Dest>
<Move s.Next s.Via s.Src s.Dest>;
};- Output:
Move disk from pole 1 to pole 2 Move disk from pole 1 to pole 3 Move disk from pole 2 to pole 3 Move disk from pole 1 to pole 2 Move disk from pole 3 to pole 1 Move disk from pole 3 to pole 2 Move disk from pole 1 to pole 2 Move disk from pole 1 to pole 3 Move disk from pole 2 to pole 3 Move disk from pole 2 to pole 1 Move disk from pole 3 to pole 1 Move disk from pole 2 to pole 3 Move disk from pole 1 to pole 2 Move disk from pole 1 to pole 3 Move disk from pole 2 to pole 3
Retro
[[User:Wodan58|Wodan58]] ([[User talk:Wodan58|talk]])
{ 'Num 'From 'To 'Via } [ var ] a:for-each
:set !Via !To !From !Num ;
:display @To @From 'Move_a_ring_from_%n_to_%n\n s:format s:put ;
:hanoi (num,from,to,via-)
set @Num n:-zero?
[ @Num @From @To @Via
@Num n:dec @From @Via @To hanoi set display
@Num n:dec @Via @To @From hanoi ] if ;
#3 #1 #3 #2 hanoi nl
[[User:Wodan58|Wodan58]] ([[User talk:Wodan58|talk]])REXX
simple text moves
/*REXX program displays the moves to solve the Tower of Hanoi (with N disks). */
parse arg N . /*get optional number of disks from CL.*/
if N=='' | N=="," then N=3 /*Not specified? Then use the default.*/
#= 0 /*#: the number of disk moves (so far)*/
z= 2**N - 1 /*Z: " " " minimum # of moves.*/
call mov 1, 3, N /*move the top disk, then recurse ··· */
say /* [↓] Display the minimum # of moves.*/
say 'The minimum number of moves to solve a ' N"─disk Tower of Hanoi is " z
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
mov: procedure expose # z; parse arg @1,@2,@3; L= length(z)
if @3==1 then do; #= # + 1 /*bump the (disk) move counter by one. */
say 'step' right(#, L)": move disk on tower" @1 '───►' @2
end
else do; call mov @1, 6 -@1 -@2, @3 -1
call mov @1, @2, 1
call mov 6 - @1 - @2, @2, @3 -1
end
return /* [↑] this subroutine uses recursion.*/- output when using the default input:
step 1: move disk on tower 1 ───► 3 step 2: move disk on tower 1 ───► 2 step 3: move disk on tower 3 ───► 2 step 4: move disk on tower 1 ───► 3 step 5: move disk on tower 2 ───► 1 step 6: move disk on tower 2 ───► 3 step 7: move disk on tower 1 ───► 3 The minimum number of moves to solve a 3-disk Tower of Hanoi is 7
output when the following was entered (to solve with four disks): 4
step 1: move disk on tower 1 ───► 2 step 2: move disk on tower 1 ───► 3 step 3: move disk on tower 2 ───► 3 step 4: move disk on tower 1 ───► 2 step 5: move disk on tower 3 ───► 1 step 6: move disk on tower 3 ───► 2 step 7: move disk on tower 1 ───► 2 step 8: move disk on tower 1 ───► 3 step 9: move disk on tower 2 ───► 3 step 10: move disk on tower 2 ───► 1 step 11: move disk on tower 3 ───► 1 step 12: move disk on tower 2 ───► 3 step 13: move disk on tower 1 ───► 2 step 14: move disk on tower 1 ───► 3 step 15: move disk on tower 2 ───► 3 The minimum number of moves to solve a 4-disk Tower of Hanoi is 15
pictorial moves
This REXX version pictorially shows (via ASCII art) the moves for solving the Town of Hanoi.
Quite a bit of code has been dedicated to showing a "picture" of the towers with the disks, and the movement of the disk (for each move). "Coloring" of the disks is attempted with dithering.
In addition, it shows each move in a countdown manner (the last move is marked as #1).
It may not be obvious from the pictorial display of the moves, but whenever a disk is moved from one tower to another, it is always the top disk that is moved (to the target tower).
Also, since the pictorial showing of the moves may be voluminous (especially for a larger number of disks), the move counter is started with the maximum and is the count shown is decremented so the viewer can see how many moves are left to display.
/*REXX program displays the moves to solve the Tower of Hanoi (with N disks). */
parse arg N . /*get optional number of disks from CL.*/
if N=='' | N=="," then N=3 /*Not specified? Then use the default.*/
sw= 80; wp= sw%3 - 1; blanks= left('', wp) /*define some default REXX variables. */
c.1= sw % 3 % 2 /* [↑] SW: assume default Screen Width*/
c.2= sw % 2 - 1 /* ◄─── C.1 C.2 C.2 are the positions*/
c.3= sw - 2 - c.1 /* of the 3 columns.*/
#= 0; z= 2**N - 1; moveK= z /*#moves; min# of moves; where to move.*/
@abc= 'abcdefghijklmnopqrstuvwxyN' /*dithering chars when many disks used.*/
ebcdic= ('f2'x==2) /*determine if EBCDIC or ASCII machine.*/
if ebcdic then do; bar= 'bf'x; ar= "df"x; dither= 'db9f9caf'x; down= "9a"x
tr= 'bc'x; bl= "ab"x; br= 'bb'x; vert= "fa"x; tl= 'ac'x
end
else do; bar= 'c4'x; ar= "10"x; dither= 'b0b1b2db'x; down= "19"x
tr= 'bf'x; bl= "c0"x; br= 'd9'x; vert= "b3"x; tl= 'da'x
end
verts= vert || vert; Tcorners= tl || tr; box = left(dither, 1)
downs= down || down; Bcorners= bl || br; boxChars= dither || @abc
$.= 0; $.1= N; k= N; kk= k + k
do j=1 for N; @.3.j= blanks; @.2.j= blanks; @.1.j= center( copies(box, kk), wp)
if N<=length(boxChars) then @.1.j= translate( @.1.j, , substr( boxChars, kk%2, 1), box)
kk= kk - 2
end /*j*/ /*populate the tower of Hanoi spindles.*/
call showTowers; call mov 1,3,N; say
say 'The minimum number of moves to solve a ' N"-disk Tower of Hanoi is " z
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
dsk: parse arg from dest; #= # + 1; pp=
if from==1 then do; pp= overlay(bl, pp, c.1)
pp= overlay(bar, pp, c.1+1, c.dest-c.1-1, bar) || tr
end
if from==2 then do
if dest==1 then do; pp= overlay(tl, pp, c.1)
pp= overlay(bar, pp, c.1+1, c.2-c.1-1,bar)||br
end
if dest==3 then do; pp= overlay(bl, pp, c.2)
pp= overlay(bar, pp, c.2+1, c.3-c.2-1,bar)||tr
end
end
if from==3 then do; pp= overlay(br, pp, c.3)
pp= overlay(bar, pp, c.dest+1, c.3-c.dest-1, bar)
pp= overlay(tl, pp, c.dest)
end
say translate(pp, downs, Bcorners || Tcorners || bar); say overlay(moveK, pp, 1)
say translate(pp, verts, Tcorners || Bcorners || bar)
say translate(pp, downs, Tcorners || Bcorners || bar); moveK= moveK - 1
$.from= $.from - 1; $.dest= $.dest + 1; _f= $.from + 1; _t= $.dest
@.dest._t= @.from._f; @.from._f= blanks; call showTowers
return
/*──────────────────────────────────────────────────────────────────────────────────────*/
mov: if arg(3)==1 then call dsk arg(1) arg(2)
else do; call mov arg(1), 6 -arg(1) -arg(2), arg(3) -1
call mov arg(1), arg(2), 1
call mov 6 -arg(1) -arg(2), arg(2), arg(3) -1
end /* [↑] The MOV subroutine is recursive, */
return /*it uses no variables, is uses BIFs instead*/
/*──────────────────────────────────────────────────────────────────────────────────────*/
showTowers: do j=N by -1 for N; _=@.1.j @.2.j @.3.j; if _\='' then say _; end; return- output when using the default input:
░░
▒▒▒▒
▓▓▓▓▓▓
↓
7 └───────────────────────────────────────────────────┐
│
↓
▒▒▒▒
▓▓▓▓▓▓ ░░
↓
6 └─────────────────────────┐
│
↓
▓▓▓▓▓▓ ▒▒▒▒ ░░
↓
5 ┌─────────────────────────┘
│
↓
░░
▓▓▓▓▓▓ ▒▒▒▒
↓
4 └───────────────────────────────────────────────────┐
│
↓
░░
▒▒▒▒ ▓▓▓▓▓▓
↓
3 ┌─────────────────────────┘
│
↓
░░ ▒▒▒▒ ▓▓▓▓▓▓
↓
2 └─────────────────────────┐
│
↓
▒▒▒▒
░░ ▓▓▓▓▓▓
↓
1 └───────────────────────────────────────────────────┐
│
↓
░░
▒▒▒▒
▓▓▓▓▓▓
The minimum number of moves to solve a 3-disk Tower of Hanoi is 7
Ring
move(4, 1, 2, 3)
func move n, src, dst, via
if n > 0 move(n - 1, src, via, dst)
see "" + src + " to " + dst + nl
move(n - 1, via, dst, src) okRPL
≪ → ndisks start end
≪ IF ndisks THEN
ndisks 1 - start 6 start - end - HANOI
start →STR " → " + end →STR +
ndisks 1 - 6 start - end - end HANOI
END
≫ ≫ 'HANOI' STO
3 1 3 HANOI
- Output:
7: "1 → 3" 6: "1 → 2" 5: "3 → 2" 4: "1 → 3" 3: "2 → 1" 2: "2 → 3" 1: "1 → 3"
Ruby
version 1
def move(num_disks, start=0, target=1, using=2)
if num_disks == 1
@towers[target] << @towers[start].pop
puts "Move disk from #{start} to #{target} : #{@towers}"
else
move(num_disks-1, start, using, target)
move(1, start, target, using)
move(num_disks-1, using, target, start)
end
end
n = 5
@towers = [[*1..n].reverse, [], []]
move(n)- Output:
Move disk from 0 to 1 : [[5, 4, 3, 2], [1], []] Move disk from 0 to 2 : [[5, 4, 3], [1], [2]] Move disk from 1 to 2 : [[5, 4, 3], [], [2, 1]] Move disk from 0 to 1 : [[5, 4], [3], [2, 1]] Move disk from 2 to 0 : [[5, 4, 1], [3], [2]] Move disk from 2 to 1 : [[5, 4, 1], [3, 2], []] Move disk from 0 to 1 : [[5, 4], [3, 2, 1], []] Move disk from 0 to 2 : [[5], [3, 2, 1], [4]] Move disk from 1 to 2 : [[5], [3, 2], [4, 1]] Move disk from 1 to 0 : [[5, 2], [3], [4, 1]] Move disk from 2 to 0 : [[5, 2, 1], [3], [4]] Move disk from 1 to 2 : [[5, 2, 1], [], [4, 3]] Move disk from 0 to 1 : [[5, 2], [1], [4, 3]] Move disk from 0 to 2 : [[5], [1], [4, 3, 2]] Move disk from 1 to 2 : [[5], [], [4, 3, 2, 1]] Move disk from 0 to 1 : [[], [5], [4, 3, 2, 1]] Move disk from 2 to 0 : [[1], [5], [4, 3, 2]] Move disk from 2 to 1 : [[1], [5, 2], [4, 3]] Move disk from 0 to 1 : [[], [5, 2, 1], [4, 3]] Move disk from 2 to 0 : [[3], [5, 2, 1], [4]] Move disk from 1 to 2 : [[3], [5, 2], [4, 1]] Move disk from 1 to 0 : [[3, 2], [5], [4, 1]] Move disk from 2 to 0 : [[3, 2, 1], [5], [4]] Move disk from 2 to 1 : [[3, 2, 1], [5, 4], []] Move disk from 0 to 1 : [[3, 2], [5, 4, 1], []] Move disk from 0 to 2 : [[3], [5, 4, 1], [2]] Move disk from 1 to 2 : [[3], [5, 4], [2, 1]] Move disk from 0 to 1 : [[], [5, 4, 3], [2, 1]] Move disk from 2 to 0 : [[1], [5, 4, 3], [2]] Move disk from 2 to 1 : [[1], [5, 4, 3, 2], []] Move disk from 0 to 1 : [[], [5, 4, 3, 2, 1], []]
version 2
# solve(source, via, target)
# Example:
# solve([5, 4, 3, 2, 1], [], [])
# Note this will also solve randomly placed disks,
# "place all disk in target with legal moves only".
def solve(*towers)
# total number of disks
disks = towers.inject(0){|sum, tower| sum+tower.length}
x=0 # sequence number
p towers # initial trace
# have we solved the puzzle yet?
while towers.last.length < disks do
x+=1 # assume the next step
from = (x&x-1)%3
to = ((x|(x-1))+1)%3
# can we actually take from tower?
if top = towers[from].last
bottom = towers[to].last
# is the move legal?
if !bottom || bottom > top
# ok, do it!
towers[to].push(towers[from].pop)
p towers # trace
end
end
end
end
solve([5, 4, 3, 2, 1], [], [])- Output:
[[5, 4, 3, 2, 1], [], []] [[5, 4, 3, 2], [], [1]] [[5, 4, 3], [2], [1]] [[5, 4, 3], [2, 1], []] [[5, 4], [2, 1], [3]] [[5, 4, 1], [2], [3]] [[5, 4, 1], [], [3, 2]] [[5, 4], [], [3, 2, 1]] [[5], [4], [3, 2, 1]] [[5], [4, 1], [3, 2]] [[5, 2], [4, 1], [3]] [[5, 2, 1], [4], [3]] [[5, 2, 1], [4, 3], []] [[5, 2], [4, 3], [1]] [[5], [4, 3, 2], [1]] [[5], [4, 3, 2, 1], []] [[], [4, 3, 2, 1], [5]] [[1], [4, 3, 2], [5]] [[1], [4, 3], [5, 2]] [[], [4, 3], [5, 2, 1]] [[3], [4], [5, 2, 1]] [[3], [4, 1], [5, 2]] [[3, 2], [4, 1], [5]] [[3, 2, 1], [4], [5]] [[3, 2, 1], [], [5, 4]] [[3, 2], [], [5, 4, 1]] [[3], [2], [5, 4, 1]] [[3], [2, 1], [5, 4]] [[], [2, 1], [5, 4, 3]] [[1], [2], [5, 4, 3]] [[1], [], [5, 4, 3, 2]] [[], [], [5, 4, 3, 2, 1]]
Run BASIC
a = move(4, "1", "2", "3")
function move(n, a$, b$, c$)
if n > 0 then
a = move(n-1, a$, c$, b$)
print "Move disk from " ; a$ ; " to " ; c$
a = move(n-1, b$, a$, c$)
end if
end functionMove disk from 1 to 3 Move disk from 1 to 2 Move disk from 3 to 2 Move disk from 1 to 3 Move disk from 2 to 1 Move disk from 2 to 3 Move disk from 1 to 3 Move disk from 1 to 2 Move disk from 3 to 2 Move disk from 3 to 1 Move disk from 2 to 1 Move disk from 3 to 2 Move disk from 1 to 3 Move disk from 1 to 2 Move disk from 3 to 2
Rust
fn move_(n: i32, from: i32, to: i32, via: i32) {
if n > 0 {
move_(n - 1, from, via, to);
println!("Move disk from pole {} to pole {}", from, to);
move_(n - 1, via, to, from);
}
}
fn main() {
move_(4, 1,2,3);
}SASL
Copied from SAL manual, Appendix II, answer (3)
hanoi 8 ‘abc"
WHERE
hanoi 0 (a,b,c,) = ()
hanoi n ( a,b,c) = hanoi (n-1) (a,c,b) ,
‘move a disc from " , a , ‘ to " , b , NL ,
hanoi (n-1) (c,b,a)
?Sather
class MAIN is
move(ndisks, from, to, via:INT) is
if ndisks = 1 then
#OUT + "Move disk from pole " + from + " to pole " + to + "\n";
else
move(ndisks-1, from, via, to);
move(1, from, to, via);
move(ndisks-1, via, to, from);
end;
end;
main is
move(4, 1, 2, 3);
end;
end;Scala
def move(n: Int, from: Int, to: Int, via: Int) : Unit = {
if (n == 1) {
Console.println("Move disk from pole " + from + " to pole " + to)
} else {
move(n - 1, from, via, to)
move(1, from, to, via)
move(n - 1, via, to, from)
}
}This next example is from http://gist.github.com/66925 it is a translation to Scala of a Prolog solution and solves the problem at compile time
object TowersOfHanoi {
import scala.reflect.Manifest
def simpleName(m:Manifest[_]):String = {
val name = m.toString
name.substring(name.lastIndexOf('$')+1)
}
trait Nat
final class _0 extends Nat
final class Succ[Pre<:Nat] extends Nat
type _1 = Succ[_0]
type _2 = Succ[_1]
type _3 = Succ[_2]
type _4 = Succ[_3]
case class Move[N<:Nat,A,B,C]()
implicit def move0[A,B,C](implicit a:Manifest[A],b:Manifest[B]):Move[_0,A,B,C] = {
System.out.println("Move from "+simpleName(a)+" to "+simpleName(b));null
}
implicit def moveN[P<:Nat,A,B,C](implicit m1:Move[P,A,C,B],m2:Move[_0,A,B,C],m3:Move[P,C,B,A])
:Move[Succ[P],A,B,C] = null
def run[N<:Nat,A,B,C](implicit m:Move[N,A,B,C]) = null
case class Left()
case class Center()
case class Right()
def main(args:Array[String]){
run[_2,Left,Right,Center]
}
}Scheme
Recursive Process
(define (towers-of-hanoi n from to spare)
(define (print-move from to)
(display "Move[")
(display from)
(display ", ")
(display to)
(display "]")
(newline))
(cond ((= n 0) "done")
(else
(towers-of-hanoi (- n 1) from spare to)
(print-move from to)
(towers-of-hanoi (- n 1) spare to from))))
(towers-of-hanoi 3 "A" "B" "C")- Output:
Move[A, B] Move[A, C] Move[B, C] Move[A, B] Move[C, A] Move[C, B] Move[A, B] "done"
Seed7
const proc: hanoi (in integer: disk, in string: source, in string: dest, in string: via) is func
begin
if disk > 0 then
hanoi(pred(disk), source, via, dest);
writeln("Move disk " <& disk <& " from " <& source <& " to " <& dest);
hanoi(pred(disk), via, dest, source);
end if;
end func;SETL
program hanoi;
loop for [src, dest] in move(4, 1, 2, 3) do
print("Move disk from pole " + src + " to pole " + dest);
end loop;
proc move(n, src, via, dest);
if n=0 then return []; end if;
return move(n-1, src, dest, via)
+ [[src, dest]]
+ move(n-1, via, src, dest);
end proc;
end program;- Output:
Move disk from pole 1 to pole 2 Move disk from pole 1 to pole 3 Move disk from pole 2 to pole 3 Move disk from pole 1 to pole 2 Move disk from pole 3 to pole 1 Move disk from pole 3 to pole 2 Move disk from pole 1 to pole 2 Move disk from pole 1 to pole 3 Move disk from pole 2 to pole 3 Move disk from pole 2 to pole 1 Move disk from pole 3 to pole 1 Move disk from pole 2 to pole 3 Move disk from pole 1 to pole 2 Move disk from pole 1 to pole 3 Move disk from pole 2 to pole 3
Sidef
func hanoi(n, from=1, to=2, via=3) {
if (n == 1) {
say "Move disk from pole #{from} to pole #{to}.";
} else {
hanoi(n-1, from, via, to);
hanoi( 1, from, to, via);
hanoi(n-1, via, to, from);
}
}
hanoi(4);SNOBOL4
* # Note: count is global
define('hanoi(n,src,trg,tmp)') :(hanoi_end)
hanoi hanoi = eq(n,0) 1 :s(return)
hanoi(n - 1, src, tmp, trg)
count = count + 1
output = count ': Move disc from ' src ' to ' trg
hanoi(n - 1, tmp, trg, src) :(return)
hanoi_end
* # Test with 4 discs
hanoi(4,'A','C','B')
end- Output:
1: Move disc from A to B 2: Move disc from A to C 3: Move disc from B to C 4: Move disc from A to B 5: Move disc from C to A 6: Move disc from C to B 7: Move disc from A to B 8: Move disc from A to C 9: Move disc from B to C 10: Move disc from B to A 11: Move disc from C to A 12: Move disc from B to C 13: Move disc from A to B 14: Move disc from A to C 15: Move disc from B to C
SparForte
As a structured script.
#!/usr/local/bin/spar
pragma annotate( summary, "hanoi" )
@( description, "Solve the Towers of Hanoi problem with recursion." )
@( see_also, "https://rosettacode.org/wiki/Towers_of_Hanoi" )
@( author, "Ken O. Burtch" );
pragma license( unrestricted );
pragma restriction( no_external_commands );
procedure hanoi is
type pegs is (left, center, right);
-- Determine the moves
procedure solve( num_disks : natural; start_peg : pegs; end_peg : pegs; via_peg : pegs ) is
begin
if num_disks > 0 then
solve( num_disks - 1, start_peg, via_peg, end_peg );
put( "Move disk" )@( num_disks )@( " from " )@( start_peg )@( " to " )@( end_peg );
new_line;
solve( num_disks - 1, via_peg, end_peg, start_peg );
end if;
end solve;
begin
-- solve with 4 disks at the left
--solve( 4, left, right, center );
solve( 4, left, right, center );
put_line( "Towers of Hanoi puzzle completed" );
end hanoi;Standard ML
fun hanoi(0, a, b, c) = [] |
hanoi(n, a, b, c) = hanoi(n-1, a, c, b) @ [(a,b)] @ hanoi(n-1, c, b, a);
Stata
function hanoi(n, a, b, c) {
if (n>0) {
hanoi(n-1, a, c, b)
printf("Move from %f to %f\n", a, b)
hanoi(n-1, c, b, a)
}
}
hanoi(3, 1, 2, 3)
Move from 1 to 2
Move from 1 to 3
Move from 2 to 3
Move from 1 to 2
Move from 3 to 1
Move from 3 to 2
Move from 1 to 2Swift
func hanoi(n:Int, a:String, b:String, c:String) {
if (n > 0) {
hanoi(n - 1, a, c, b)
println("Move disk from \(a) to \(c)")
hanoi(n - 1, b, a, c)
}
}
hanoi(4, "A", "B", "C")Swift 2.1
func hanoi(n:Int, a:String, b:String, c:String) {
if (n > 0) {
hanoi(n - 1, a: a, b: c, c: b)
print("Move disk from \(a) to \(c)")
hanoi(n - 1, a: b, b: a, c: c)
}
}
hanoi(4, a:"A", b:"B", c:"C")Tcl
The use of interp alias shown is a sort of closure: keep track of the number of moves required
interp alias {} hanoi {} do_hanoi 0
proc do_hanoi {count n {from A} {to C} {via B}} {
if {$n == 1} {
interp alias {} hanoi {} do_hanoi [incr count]
puts "$count: move from $from to $to"
} else {
incr n -1
hanoi $n $from $via $to
hanoi 1 $from $to $via
hanoi $n $via $to $from
}
}
hanoi 4- Output:
1: move from A to B 2: move from A to C 3: move from B to C 4: move from A to B 5: move from C to A 6: move from C to B 7: move from A to B 8: move from A to C 9: move from B to C 10: move from B to A 11: move from C to A 12: move from B to C 13: move from A to B 14: move from A to C 15: move from B to C
TI-83 BASIC
TI-83 BASIC lacks recursion, so technically this task is impossible, however here is a version that uses an iterative method.
PROGRAM:TOHSOLVE
0→A
1→B
0→C
0→D
0→M
1→R
While A<1 or A>7
Input "No. of rings=?",A
End
randM(A+1,3)→[C]
[[1,2][1,3][2,3]]→[E]
Fill(0,[C])
For(I,1,A,1)
I?[C](I,1)
End
ClrHome
While [C](1,3)≠1 and [C](1,2)≠1
For(J,1,3)
For(I,1,A)
If [C](I,J)≠0:Then
Output(I+1,3J,[C](I,J))
End
End
End
While C=0
Output(1,3B," ")
1→I
[E](R,2)→J
While [C](I,J)=0 and I≤A
I+1→I
End
[C](I,J)→D
1→I
[E](R,1)→J
While [C](I,J)=0 and I≤A
I+1→I
End
If (D<[C](I,J) and D≠0) or [C](I,J)=0:Then
[E](R,2)→B
Else
[E](R,1)→B
End
1→I
While [C](I,B)=0 and I≤A
I+1→I
End
If I≤A:Then
[C](I,B)→C
0→[C](I,B)
Output(I+1,3B," ")
End
Output(1,3B,"V")
End
While C≠0
Output(1,3B," ")
If B=[E](R,2):Then
[E](R,1)→B
Else
[E](R,2)→B
End
1→I
While [C](I,B)=0 and I≤A
I+1→I
End
If [C](I,B)=0 or [C](I,B)>C:Then
C→[C](I-1,B)
0→C
M+1→M
End
End
Output(1,3B,"V")
R+1→R
If R=4:Then:1→R:End
EndTiny BASIC
Tiny BASIC does not have recursion, so only an iterative solution is possible... and it has no arrays, so actually keeping track of individual discs is not feasible.
But as if by magic, it turns out that the source and destination pegs on iteration number n are given by (n&n-1) mod 3 and ((n|n-1) + 1) mod 3 respectively, where & and | are the bitwise and and or operators. Line 40 onward is dedicated to implementing those bitwise operations, since Tiny BASIC hasn't got them natively.
5 PRINT "How many disks?"
INPUT D
IF D < 1 THEN GOTO 5
IF D > 10 THEN GOTO 5
LET N = 1
10 IF D = 0 THEN GOTO 20
LET D = D - 1
LET N = 2*N
GOTO 10
20 LET X = 0
30 LET X = X + 1
IF X = N THEN END
GOSUB 40
LET S = S - 3*(S/3)
GOSUB 50
LET T = T + 1
LET T = T - 3*(T/3)
PRINT "Move disc on peg ",S+1," to peg ",T+1
GOTO 30
40 LET B = X - 1
LET A = X
LET S = 0
LET Z = 2048
45 LET C = 0
IF B >= Z THEN LET C = 1
IF A >= Z THEN LET C = C + 1
IF C = 2 THEN LET S = S + Z
IF A >= Z THEN LET A = A - Z
IF B >= Z THEN LET B = B - Z
LET Z = Z / 2
IF Z = 0 THEN RETURN
GOTO 45
50 LET B = X - 1
LET A = X
LET T = 0
LET Z = 2048
55 LET C = 0
IF B >= Z THEN LET C = 1
IF A >= Z THEN LET C = C + 1
IF C > 0 THEN LET T = T + Z
IF A >= Z THEN LET A = A - Z
IF B >= Z THEN LET B = B - Z
LET Z = Z / 2
IF Z = 0 THEN RETURN
GOTO 55- Output:
How many discs? 4 Move disc on peg 1 to peg 3 Move disc on peg 1 to peg 2 Move disc on peg 3 to peg 2 Move disc on peg 1 to peg 3 Move disc on peg 2 to peg 1 Move disc on peg 2 to peg 3 Move disc on peg 1 to peg 3 Move disc on peg 1 to peg 2 Move disc on peg 3 to peg 2 Move disc on peg 3 to peg 1 Move disc on peg 2 to peg 1 Move disc on peg 3 to peg 2 Move disc on peg 1 to peg 3 Move disc on peg 1 to peg 2 Move disc on peg 3 to peg 2
Toka
value| sa sb sc n |
[ to sc to sb to sa to n ] is vars!
[ ( num from to via -- )
vars!
n 0 <>
[
n sa sb sc
n 1- sa sc sb recurse
vars!
." Move a ring from " sa . ." to " sb . cr
n 1- sc sb sa recurse
] ifTrue
] is hanoi
True BASIC
DECLARE SUB hanoi
SUB hanoi(n, desde , hasta, via)
IF n > 0 THEN
CALL hanoi(n - 1, desde, via, hasta)
PRINT "Mover disco"; n; "desde posición"; desde; "hasta posición"; hasta
CALL hanoi(n - 1, via, hasta, desde)
END IF
END SUB
PRINT "Tres discos"
PRINT
CALL hanoi(3, 1, 2, 3)
PRINT
PRINT "Cuatro discos"
PRINT
CALL hanoi(4, 1, 2, 3)
PRINT
PRINT "Pulsa un tecla para salir"
END
TSE SAL
// library: program: run: towersofhanoi: recursive: sub <description></description> <version>1.0.0.0.0</version> <version control></version control> (filenamemacro=runprrsu.s) [kn, ri, tu, 07-02-2012 19:54:23]
PROC PROCProgramRunTowersofhanoiRecursiveSub( INTEGER totalDiskI, STRING fromS, STRING toS, STRING viaS, INTEGER bufferI )
IF ( totalDiskI == 0 )
RETURN()
ENDIF
PROCProgramRunTowersofhanoiRecursiveSub( totalDiskI - 1, fromS, viaS, toS, bufferI )
AddLine( Format( "Move disk", " ", totalDiskI, " ", "from peg", " ", "'", fromS, "'", " ", "to peg", " ", "'", toS, "'" ), bufferI )
PROCProgramRunTowersofhanoiRecursiveSub( totalDiskI - 1, viaS, toS, fromS, bufferI )
END
// library: program: run: towersofhanoi: recursive <description></description> <version>1.0.0.0.6</version> <version control></version control> (filenamemacro=runprtre.s) [kn, ri, tu, 07-02-2012 19:40:45]
PROC PROCProgramRunTowersofhanoiRecursive( INTEGER totalDiskI, STRING fromS, STRING toS, STRING viaS )
INTEGER bufferI = 0
PushPosition()
bufferI = CreateTempBuffer()
PopPosition()
PROCProgramRunTowersofhanoiRecursiveSub( totalDiskI, fromS, toS, viaS, bufferI )
GotoBufferId( bufferI )
END
PROC Main()
STRING s1[255] = "4"
IF ( NOT ( Ask( "program: run: towersofhanoi: recursive: totalDiskI = ", s1, _EDIT_HISTORY_ ) ) AND ( Length( s1 ) > 0 ) ) RETURN() ENDIF
PROCProgramRunTowersofhanoiRecursive( Val( s1 ), "source", "target", "via" )
ENDuBasic/4tH
Proc _Move(4, 1,2,3) ' 4 disks, 3 poles
End
_Move Param(4)
If (a@ > 0) Then
Proc _Move (a@ - 1, b@, d@, c@)
Print "Move disk from pole ";b@;" to pole ";c@
Proc _Move (a@ - 1, d@, c@, b@)
EndIf
ReturnUiua
F ← |1.0 (
⟨
&p ⊏[1 2] &pf "Move disc [from to]: "
| F⍜(⊡0|-1)⍜(⊏[2 3]|⇌).
F⍜(⊡0|1◌).
F⍜(⊡0|-1)⍜(⊏[1 3]|⇌)
⟩≠1⊢.
)
F [4 1 2 3]- Output:
Move disc [from to]: [1 3] Move disc [from to]: [1 2] Move disc [from to]: [3 2] Move disc [from to]: [1 3] Move disc [from to]: [2 1] Move disc [from to]: [2 3] Move disc [from to]: [1 3] Move disc [from to]: [1 2] Move disc [from to]: [3 2] Move disc [from to]: [3 1] Move disc [from to]: [2 1] Move disc [from to]: [3 2] Move disc [from to]: [1 3] Move disc [from to]: [1 2] Move disc [from to]: [3 2]
UNIX Shell
function move {
typeset -i n=$1
typeset from=$2
typeset to=$3
typeset via=$4
if (( n )); then
move $(( n - 1 )) "$from" "$via" "$to"
echo "Move disk from pole $from to pole $to"
move $(( n - 1 )) "$via" "$to" "$from"
fi
}
move "$@"A strict POSIX (or just really old) shell has no subprogram capability, but scripts are naturally reentrant, so:
#!/bin/sh
if [ "$1" -gt 0 ]; then
"$0" "`expr $1 - 1`" "$2" "$4" "$3"
echo "Move disk from pole $2 to pole $3"
"$0" "`expr $1 - 1`" "$4" "$3" "$2"
fiOutput from any of the above:
- Output:
$ hanoi 4 1 3 2 Move disk from pole 1 to pole 2 Move disk from pole 1 to pole 3 Move disk from pole 2 to pole 3 Move disk from pole 1 to pole 2 Move disk from pole 3 to pole 1 Move disk from pole 3 to pole 2 Move disk from pole 1 to pole 2 Move disk from pole 1 to pole 3 Move disk from pole 2 to pole 3 Move disk from pole 2 to pole 1 Move disk from pole 3 to pole 1 Move disk from pole 2 to pole 3 Move disk from pole 1 to pole 2 Move disk from pole 1 to pole 3 Move disk from pole 2 to pole 3
Ursala
#import nat
move = ~&al^& ^rlPlrrPCT/~&arhthPX ^|W/~& ^|G/predecessor ^/~&htxPC ~&zyxPC
#show+
main = ^|T(~&,' -> '--)* move/4 <'start','end','middle'>- Output:
start -> middle start -> end middle -> end start -> middle end -> start end -> middle start -> middle start -> end middle -> end middle -> start end -> start middle -> end start -> middle start -> end middle -> end
Uxntal
|10 @Console &vector $2 &read $1 &pad $4 &type $1 &write $1 &error $1
|0100 ( -> )
#0102 [ LIT2 03 &count 04 ] hanoi
POP2 POP2 BRK
@hanoi ( from spare to count -: from spare to count )
( moving 0 disks is no-op )
DUP ?{ JMP2r }
( move disks 1..count-1 to the spare peg )
#01 SUB ROT SWP hanoi
( from to spare count-1 )
( print the current move )
;dict/move print-str
INCk #30 ORA .Console/write DEO
STH2
;dict/from print-str
OVR #30 ORA .Console/write DEO
;dict/to print-str
DUP #30 ORA .Console/write DEO
[ LIT2 0a -Console/write ] DEO
STH2r
( move disks 1..count-1 from the spare peg to the goal peg )
STH ROT ROT STHr hanoi
( restore original parameters for convenient recursion )
STH2 SWP STH2r INC
JMP2r
@print-str
&loop
LDAk .Console/write DEO
INC2 LDAk ?&loop
POP2 JMP2r
@dict
&move "Move 20 "disk 2000
&from 20 "from 20 "pole 2000
&to 20 "to 20 "pole 2000VBScript
Derived from the BASIC256 version.
Sub Move(n,fromPeg,toPeg,viaPeg)
If n > 0 Then
Move n-1, fromPeg, viaPeg, toPeg
WScript.StdOut.Write "Move disk from " & fromPeg & " to " & toPeg
WScript.StdOut.WriteBlankLines(1)
Move n-1, viaPeg, toPeg, fromPeg
End If
End Sub
Move 4,1,2,3
WScript.StdOut.Write("Towers of Hanoi puzzle completed!")- Output:
Move disk from 1 to 3 Move disk from 1 to 2 Move disk from 3 to 2 Move disk from 1 to 3 Move disk from 2 to 1 Move disk from 2 to 3 Move disk from 1 to 3 Move disk from 1 to 2 Move disk from 3 to 2 Move disk from 3 to 1 Move disk from 2 to 1 Move disk from 3 to 2 Move disk from 1 to 3 Move disk from 1 to 2 Move disk from 3 to 2 Towers of Hanoi puzzle completed!
Vedit macro language
This implementation outputs the results in current edit buffer.
#1=1; #2=2; #3=3; #4=4 // move 4 disks from 1 to 2
Call("MOVE_DISKS")
Return
// Move disks
// #1 = from, #2 = to, #3 = via, #4 = number of disks
//
:MOVE_DISKS:
if (#4 > 0) {
Num_Push(1,4)
#9=#2; #2=#3; #3=#9; #4-- // #1 to #3 via #2
Call("MOVE_DISKS")
Num_Pop(1,4)
Ins_Text("Move a disk from ") // move one disk
Num_Ins(#1, LEFT+NOCR)
Ins_Text(" to ")
Num_Ins(#2, LEFT)
Num_Push(1,4)
#9=#1; #1=#3; #3 = #9; #4-- // #3 to #2 via #1
Call("MOVE_DISKS")
Num_Pop(1,4)
}
ReturnVim Script
function TowersOfHanoi(n, from, to, via)
if (a:n > 1)
call TowersOfHanoi(a:n-1, a:from, a:via, a:to)
endif
echom("Move a disc from " . a:from . " to " . a:to)
if (a:n > 1)
call TowersOfHanoi(a:n-1, a:via, a:to, a:from)
endif
endfunction
call TowersOfHanoi(4, 1, 3, 2)- Output:
Move a disc from 1 to 2 Move a disc from 1 to 3 Move a disc from 2 to 3 Move a disc from 1 to 2 Move a disc from 3 to 1 Move a disc from 3 to 2 Move a disc from 1 to 2 Move a disc from 1 to 3 Move a disc from 2 to 3 Move a disc from 2 to 1 Move a disc from 3 to 1 Move a disc from 2 to 3 Move a disc from 1 to 2 Move a disc from 1 to 3 Move a disc from 2 to 3
Visual Basic .NET
Module TowersOfHanoi
Sub MoveTowerDisks(ByVal disks As Integer, ByVal fromTower As Integer, ByVal toTower As Integer, ByVal viaTower As Integer)
If disks > 0 Then
MoveTowerDisks(disks - 1, fromTower, viaTower, toTower)
System.Console.WriteLine("Move disk {0} from {1} to {2}", disks, fromTower, toTower)
MoveTowerDisks(disks - 1, viaTower, toTower, fromTower)
End If
End Sub
Sub Main()
MoveTowerDisks(4, 1, 2, 3)
End Sub
End ModuleV (Vlang)
fn main() {
hanoi(4, "A", "B", "C")
}
fn hanoi(n u64, a string, b string, c string) {
if n > 0 {
hanoi(n - 1, a, c, b)
println("Move disk from ${a} to ${c}")
hanoi(n - 1, b, a, c)
}
}- Output:
Move disk from A to B Move disk from A to C Move disk from B to C Move disk from A to B Move disk from C to A Move disk from C to B Move disk from A to B Move disk from A to C Move disk from B to C Move disk from B to A Move disk from C to A Move disk from B to C Move disk from A to B Move disk from A to C Move disk from B to C
VTL-2
VTL-2 doesn't have procedure parameters, so this stacks and unstacks the return line number and parameters as reuired. The "move" routune starts at line 2000, the routine at 4000 stacks the return line number and parameters for "move" and the routine at 5000 unstacks the return line number and parameters.
1000 N=4
1010 F=1
1020 T=2
1030 V=3
1040 S=0
1050 #=2000
1060 #=9999
2000 R=!
2010 #=N<1*2210
2020 #=4000
2030 N=N-1
2040 A=T
2050 T=V
2060 V=A
2070 #=2000
2080 #=5000
2090 ?="Move disk from peg: ";
2100 ?=F
2110 ?=" to peg: ";
2120 ?=T
2130 ?=""
2140 #=4000
2150 N=N-1
2160 A=F
2170 F=V
2180 V=A
2190 #=2000
2200 #=5000
2210 #=R
4000 S=S+1
4010 :S)=R
4020 S=S+1
4030 :S)=N
4040 S=S+1
4050 :S)=F
4060 S=S+1
4070 :S)=V
4080 S=S+1
4090 :S)=T
4100 #=!
5000 T=:S)
5010 S=S-1
5020 V=:S)
5030 S=S-1
5040 F=:S)
5050 S=S-1
5060 N=:S)
5070 S=S-1
5080 R=:S)
5090 S=S-1
5100 #=!- Output:
Move disk from peg: 1 to peg: 3 Move disk from peg: 1 to peg: 2 Move disk from peg: 3 to peg: 2 Move disk from peg: 1 to peg: 3 Move disk from peg: 2 to peg: 1 Move disk from peg: 2 to peg: 3 Move disk from peg: 1 to peg: 3 Move disk from peg: 1 to peg: 2 Move disk from peg: 3 to peg: 2 Move disk from peg: 3 to peg: 1 Move disk from peg: 2 to peg: 1 Move disk from peg: 3 to peg: 2 Move disk from peg: 1 to peg: 3 Move disk from peg: 1 to peg: 2 Move disk from peg: 3 to peg: 2
Wren
class Hanoi {
construct new(disks) {
_moves = 0
System.print("Towers of Hanoi with %(disks) disks:\n")
move(disks, "L", "C", "R")
System.print("\nCompleted in %(_moves) moves\n")
}
move(n, from, to, via) {
if (n > 0) {
move(n - 1, from, via, to)
_moves = _moves + 1
System.print("Move disk %(n) from %(from) to %(to)")
move(n - 1, via, to, from)
}
}
}
Hanoi.new(3)
Hanoi.new(4)- Output:
Towers of Hanoi with 3 disks: Move disk 1 from L to C Move disk 2 from L to R Move disk 1 from C to R Move disk 3 from L to C Move disk 1 from R to L Move disk 2 from R to C Move disk 1 from L to C Completed in 7 moves Towers of Hanoi with 4 disks: Move disk 1 from L to R Move disk 2 from L to C Move disk 1 from R to C Move disk 3 from L to R Move disk 1 from C to L Move disk 2 from C to R Move disk 1 from L to R Move disk 4 from L to C Move disk 1 from R to C Move disk 2 from R to L Move disk 1 from C to L Move disk 3 from R to C Move disk 1 from L to R Move disk 2 from L to C Move disk 1 from R to C Completed in 15 moves
XBasic
PROGRAM "Hanoi"
VERSION "0.0000"
DECLARE FUNCTION Entry ()
DECLARE FUNCTION Hanoi(n, desde , hasta, via)
FUNCTION Entry ()
PRINT "Three disks\n"
Hanoi (3, 1, 2, 3)
PRINT "\nFour discks\n"
Hanoi (4, 1, 2, 3)
PRINT "\nTowers of Hanoi puzzle completed!"
END FUNCTION
FUNCTION Hanoi (n, desde , hasta, via)
IF n > 0 THEN
Hanoi (n - 1, desde, via, hasta)
PRINT "Move disk"; n; " from pole"; desde; " to pole"; hasta
Hanoi (n - 1, via, hasta, desde)
END IF
END FUNCTION
END PROGRAM- Output:
Same as FreeBASIC entry.
XPL0
code Text=12;
proc MoveTower(Discs, From, To, Using);
int Discs, From, To, Using;
[if Discs > 0 then
[MoveTower(Discs-1, From, Using, To);
Text(0, "Move from "); Text(0, From);
Text(0, " peg to "); Text(0, To); Text(0, " peg.^M^J");
MoveTower(Discs-1, Using, To, From);
];
];
MoveTower(3, "left", "right", "center")- Output:
Move from left peg to right peg. Move from left peg to center peg. Move from right peg to center peg. Move from left peg to right peg. Move from center peg to left peg. Move from center peg to right peg. Move from left peg to right peg.
XQuery
declare function local:hanoi($disk as xs:integer, $from as xs:integer,
$to as xs:integer, $via as xs:integer) as element()*
{
if($disk > 0)
then (
local:hanoi($disk - 1, $from, $via, $to),
<move disk='{$disk}'><from>{$from}</from><to>{$to}</to></move>,
local:hanoi($disk - 1, $via, $to, $from)
)
else ()
};
<hanoi>
{
local:hanoi(4, 1, 2, 3)
}
</hanoi>- Output:
<?xml version="1.0" encoding="UTF-8"?>
<hanoi>
<move disk="1">
<from>1</from>
<to>3</to>
</move>
<move disk="2">
<from>1</from>
<to>2</to>
</move>
<move disk="1">
<from>3</from>
<to>2</to>
</move>
<move disk="3">
<from>1</from>
<to>3</to>
</move>
<move disk="1">
<from>2</from>
<to>1</to>
</move>
<move disk="2">
<from>2</from>
<to>3</to>
</move>
<move disk="1">
<from>1</from>
<to>3</to>
</move>
<move disk="4">
<from>1</from>
<to>2</to>
</move>
<move disk="1">
<from>3</from>
<to>2</to>
</move>
<move disk="2">
<from>3</from>
<to>1</to>
</move>
<move disk="1">
<from>2</from>
<to>1</to>
</move>
<move disk="3">
<from>3</from>
<to>2</to>
</move>
<move disk="1">
<from>1</from>
<to>3</to>
</move>
<move disk="2">
<from>1</from>
<to>2</to>
</move>
<move disk="1">
<from>3</from>
<to>2</to>
</move>
</hanoi>XSLT
<xsl:template name="hanoi">
<xsl:param name="n"/>
<xsl:param name="from">left</xsl:param>
<xsl:param name="to">middle</xsl:param>
<xsl:param name="via">right</xsl:param>
<xsl:if test="$n > 0">
<xsl:call-template name="hanoi">
<xsl:with-param name="n" select="$n - 1"/>
<xsl:with-param name="from" select="$from"/>
<xsl:with-param name="to" select="$via"/>
<xsl:with-param name="via" select="$to"/>
</xsl:call-template>
<fo:block>
<xsl:text>Move disk from </xsl:text>
<xsl:value-of select="$from"/>
<xsl:text> to </xsl:text>
<xsl:value-of select="$to"/>
</fo:block>
<xsl:call-template name="hanoi">
<xsl:with-param name="n" select="$n - 1"/>
<xsl:with-param name="from" select="$via"/>
<xsl:with-param name="to" select="$to"/>
<xsl:with-param name="via" select="$from"/>
</xsl:call-template>
</xsl:if>
</xsl:template><xsl:call-template name="hanoi"><xsl:with-param name="n" select="4"/></xsl:call-template>
Yabasic
sub hanoi(ndisks, startPeg, endPeg)
if ndisks then
hanoi(ndisks-1, startPeg, 6-startPeg-endPeg)
//print "Move disk ", ndisks, " from ", startPeg, " to ", endPeg
hanoi(ndisks-1, 6-startPeg-endPeg, endPeg)
end if
end sub
print "Be patient, please.\n\n"
print "Hanoi 1 ellapsed ... ";
t1 = peek("millisrunning")
hanoi(22, 1, 3)
t2 = peek("millisrunning")
print t2-t1, " ms"
sub hanoi2(n, from, to_, via)
if n = 1 then
//print "Move from ", from, " to ", to_
else
hanoi2(n - 1, from, via , to_ )
hanoi2(1 , from, to_ , via )
hanoi2(n - 1, via , to_ , from)
end if
end sub
print "Hanoi 2 ellapsed ... ";
hanoi2(22, 1, 3, 2)
print peek("millisrunning") - t2, " ms"Z80 Assembly
Use the /S8 switch on the ZSM4 assembler for 8 significant characters for labels and names
;
; Towers of Hanoi using Z80 assembly language
;
; Runs under CP/M 3.1 on YAZE-AG-2.51.2 Z80 emulator
; Assembled with zsm4 on same emulator/OS, uses macro capabilities of said assembler
; Created with vim under Windows
;
; 2023-05-29 Xorph
;
;
; Useful definitions
;
bdos equ 05h ; Call to CP/M BDOS function
strdel equ 6eh ; Set string delimiter
wrtstr equ 09h ; Write string to console
nul equ 00h ; ASCII control characters
cr equ 0dh
lf equ 0ah
cnull equ '0' ; ASCII character constants
ca equ 'A'
cb equ 'B'
cc equ 'C'
disks equ 4 ; Number of disks to move
;
; Macros for BDOS calls
;
setdel macro char ; Set string delimiter to char
ld c,strdel
ld e,char
call bdos
endm
print macro msg ; Output string to console
ld c,wrtstr
ld de,msg
call bdos
endm
pushall macro ; Save required registers to stack
push af
push bc
push de
endm
popall macro ; Recall required registers from stack
pop de
pop bc
pop af
endm
;
; =====================
; Start of main program
; =====================
;
cseg
setdel nul ; Set string delimiter to 00h
ld a,disks ; Initialization:
ld b,ca ; Tower A is source
ld c,cb ; Tower B is target
ld d,cc ; Tower C is intermediate
hanoi:
;
; Parameters in registers:
; Move a disks from b (source) to c (target) via d (intermediate)
;
or a ; If 0 disks to move, return
ret z
dec a ; Move all but lowest disk from source to intermediate via target
pushall ; Save registers
ld e,c ; Exchange c and d (target and intermediate)
ld c,d
ld d,e
call hanoi ; First recursion
popall ; Restore registers
ld hl,source ; Print move of lowest disk from source to target, save registers during BDOS call
ld (hl),b ; Source is still in b
ld hl,target
ld (hl),c ; Target is back in c due to popall
pushall
print movement
popall
ld e,b ; Now move stack from intermediate to target via source
ld b,d ; Source is still in b, target in c and intermediate in d
ld d,e
jr hanoi ; Optimize tail recursion
;
; ================
; Data definitions
; ================
;
dseg
movement:
defb 'Move disk from tower '
source:
defs 1
defb ' to tower '
target:
defs 1
crlf:
defb cr,lf,nul- Output:
E>hanoi Move disk from tower A to tower C Move disk from tower A to tower B Move disk from tower C to tower B Move disk from tower A to tower C Move disk from tower B to tower A Move disk from tower B to tower C Move disk from tower A to tower C Move disk from tower A to tower B Move disk from tower C to tower B Move disk from tower C to tower A Move disk from tower B to tower A Move disk from tower C to tower B Move disk from tower A to tower C Move disk from tower A to tower B Move disk from tower C to tower B E>
Zig
const std = @import("std");
pub fn print(from: u32, to: u32) void {
std.log.info("Moving disk from rod {} to rod {}", .{ from, to });
}
pub fn move(n: u32, from: u32, via: u32, to: u32) void {
if (n > 1) {
move(n - 1, from, to, via);
print(from, to);
move(n - 1, via, from, to);
} else {
print(from, to);
}
}
pub fn main() !void {
move(4, 1, 2, 3);
}zkl
fcn move(n, from,to,via){
if (n>0){
move(n-1, from,via,to);
println("Move disk from pole %d to pole %d".fmt(from, to));
move(n-1, via,to,from);
}
}
move(3, 1,2,3);- Output:
Move disk from pole 1 to pole 2 Move disk from pole 1 to pole 3 Move disk from pole 2 to pole 3 Move disk from pole 1 to pole 2 Move disk from pole 3 to pole 1 Move disk from pole 3 to pole 2 Move disk from pole 1 to pole 2
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