lambdaspeech :: hanoi

_img https://upload.wikimedia.org/wikipedia/commons/thumb/0/07/Tower_of_Hanoi.jpeg/260px-Tower_of_Hanoi.jpeg

_h1 towers of hanoï

{pre
A     B     C   A2B   A     B     C   A2C   A     B     C   B2C   A     B     C   A2B
[-    |     ]    .    [     |     ]    .    [     |     ]    .    [     |     ]
[--   |     ]    .    [--   |     ]    .    [     |     ]    .    [     |     ]-
[---  |     ]    .    [---  |-    ]    .    [---  |-    ]--  .    [---  |     ]--

A     B     C   C2A   A     B     C   C2B   A     B     C   A2B   A     B     C
[     |     ]    .    [     |     ]    .    [     |     ]    .    [     |-    ]
[     |     ]-   .    [     |     ]    .    [     |--   ]    .    [     |--   ]
[     |---  ]--  .    [-    |---  ]--  .    [-    |---  ]    .    [     |---  ]
}

_h2 1) '{lambda speech}
{pre {@ style="box-shadow:0 0 8px #000"}
'{def move
 {lambda {:n :from :to :via}
  {if {<= :n 0}
   then >
   else {move {- :n 1} :from :via :to}
         move disk from :from to :to {br}
        {move {- :n 1} :via :to :from} }}}
-> {def move
 {lambda {:n :from :to :via}
  {if {<= :n 0}
   then >
   else {move {- :n 1} :from :via :to}
         move disk from :from to :to {br}
        {move {- :n 1} :via :to :from} }}}
}

{pre
'{move 2 A B C}
}
{move 2 A B C}

{pre
'{move 3 A B C}
}
{move 3 A B C}

{pre
'{move 4 A B C}
}
{move 4 A B C}

_h2 2) other languages

_p Following [[https://rosettacode.org/wiki/Towers_of_Hanoi|https://rosettacode.org/wiki/Towers_of_Hanoi]]

_h3 newLisp
{pre
(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 3 1 2 3)
}

_h3 picoLisp
{pre
(de move (N A B C)
   (unless (=0 N)
      (move (dec N) A C B)
      (println 'Move 'disk 'from A 'to B)
      (move (dec N) C B A) ) )

(move 3 'left 'center 'right)
}

_h3 Racket
{pre
#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 3 'left 'middle 'right)
}

_h3 Scheme
{pre
(define (hanoi n a b c)
  (if (> n 0)
    (begin
      (hanoi (- n 1) a c b)
      (display "Move disk from pole ")
      (display a)
      (display " to pole ")
      (display b)
      (newline)
      (hanoi (- n 1) c b a))))
 
(hanoi 3 1 2 3)
}

_h3 Python

{pre
def hanoi(ndisks, startPeg=1, endPeg=3):
    if ndisks:
        hanoi(ndisks-1, startPeg, 6-startPeg-endPeg)
        print "Move disk %d from peg %d to peg %d" % (ndisks, startPeg, endPeg)
        hanoi(ndisks-1, 6-startPeg-endPeg, endPeg)
 
hanoi(ndisks=4)
}

_h3 C

{pre

#include <stdio.h>
 
void move(int n, int from, int to, int 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);
  }
}

int main() '{
  move(4, 1,2,3);
  return 0;
}
}