Knight's tour: Difference between revisions

Content added Content deleted
m (→‎{{header|Raku}}: auto-vivification pretty reliable lately)
m (syntax highlighting fixup automation)
Line 25: Line 25:
{{trans|Python}}
{{trans|Python}}


<lang 11l>V _kmoves = [(2, 1), (1, 2), (-1, 2), (-2, 1), (-2, -1), (-1, -2), (1, -2), (2, -1)]
<syntaxhighlight lang="11l">V _kmoves = [(2, 1), (1, 2), (-1, 2), (-2, 1), (-2, -1), (-1, -2), (1, -2), (2, -1)]


F chess2index(=chess, boardsize)
F chess2index(=chess, boardsize)
Line 81: Line 81:
V board = knights_tour(start, boardsize)
V board = knights_tour(start, boardsize)
print(boardstring(board, boardsize' boardsize))
print(boardstring(board, boardsize' boardsize))
print()</lang>
print()</syntaxhighlight>


{{out}}
{{out}}
Line 124: Line 124:
=={{header|360 Assembly}}==
=={{header|360 Assembly}}==
{{trans|BBC PASIC}}
{{trans|BBC PASIC}}
<lang 360asm>* Knight's tour 20/03/2017
<syntaxhighlight lang="360asm">* Knight's tour 20/03/2017
KNIGHT CSECT
KNIGHT CSECT
USING KNIGHT,R13 base registers
USING KNIGHT,R13 base registers
Line 378: Line 378:
PG DC CL128' ' buffer
PG DC CL128' ' buffer
YREGS
YREGS
END KNIGHT</lang>
END KNIGHT</syntaxhighlight>
{{out}}
{{out}}
<pre>
<pre>
Line 396: Line 396:
First, we specify a naive implementation the package Knights_Tour with naive backtracking. It is a bit more general than required for this task, by providing a mechanism '''not''' to visit certain coordinates. This mechanism is actually useful for the task [[Solve a Holy Knight's tour#Ada]], which also uses the package Knights_Tour.
First, we specify a naive implementation the package Knights_Tour with naive backtracking. It is a bit more general than required for this task, by providing a mechanism '''not''' to visit certain coordinates. This mechanism is actually useful for the task [[Solve a Holy Knight's tour#Ada]], which also uses the package Knights_Tour.


<lang Ada>generic
<syntaxhighlight lang="ada">generic
Size: Integer;
Size: Integer;
package Knights_Tour is
package Knights_Tour is
Line 417: Line 417:
-- writes The_Tour to the output using Ada.Text_IO;
-- writes The_Tour to the output using Ada.Text_IO;
end Knights_Tour;</lang>
end Knights_Tour;</syntaxhighlight>


Here is the implementation:
Here is the implementation:


<lang Ada>with Ada.Text_IO, Ada.Integer_Text_IO;
<syntaxhighlight lang="ada">with Ada.Text_IO, Ada.Integer_Text_IO;
package body Knights_Tour is
package body Knights_Tour is
Line 505: Line 505:
end Tour_IO;
end Tour_IO;
end Knights_Tour;</lang>
end Knights_Tour;</syntaxhighlight>


Here is the main program:
Here is the main program:


<lang Ada>with Knights_Tour, Ada.Command_Line;
<syntaxhighlight lang="ada">with Knights_Tour, Ada.Command_Line;


procedure Test_Knight is
procedure Test_Knight is
Line 519: Line 519:
begin
begin
KT.Tour_IO(KT.Get_Tour(1, 1));
KT.Tour_IO(KT.Get_Tour(1, 1));
end Test_Knight;</lang>
end Test_Knight;</syntaxhighlight>


For small sizes, this already works well (< 1 sec for size 8). Sample output:
For small sizes, this already works well (< 1 sec for size 8). Sample output:
Line 533: Line 533:


For larger sizes we'll use Warnsdorff's heuristic (without any thoughtful tie breaking). We enhance the specification adding a function Warnsdorff_Get_Tour. This enhancement of the package Knights_Tour will also be used for the task [[Solve a Holy Knight's tour#Ada]]. The specification of Warnsdorff_Get_Tour is the following.
For larger sizes we'll use Warnsdorff's heuristic (without any thoughtful tie breaking). We enhance the specification adding a function Warnsdorff_Get_Tour. This enhancement of the package Knights_Tour will also be used for the task [[Solve a Holy Knight's tour#Ada]]. The specification of Warnsdorff_Get_Tour is the following.
<syntaxhighlight lang="ada">
<lang Ada>
function Warnsdorff_Get_Tour(Start_X, Start_Y: Index; Scene: Tour := Empty)
function Warnsdorff_Get_Tour(Start_X, Start_Y: Index; Scene: Tour := Empty)
return Tour;
return Tour;
-- uses Warnsdorff heurisitic to find a tour faster
-- uses Warnsdorff heurisitic to find a tour faster
-- same interface as Get_Tour</lang>
-- same interface as Get_Tour</syntaxhighlight>


Its implementation is as follows.
Its implementation is as follows.


<lang Ada> function Warnsdorff_Get_Tour(Start_X, Start_Y: Index; Scene: Tour := Empty)
<syntaxhighlight lang="ada"> function Warnsdorff_Get_Tour(Start_X, Start_Y: Index; Scene: Tour := Empty)
return Tour is
return Tour is
Done: Boolean;
Done: Boolean;
Line 626: Line 626:
end if;
end if;
return Visited;
return Visited;
end Warnsdorff_Get_Tour;</lang>
end Warnsdorff_Get_Tour;</syntaxhighlight>


The modification for the main program is trivial:
The modification for the main program is trivial:
<lang Ada>with Knights_Tour, Ada.Command_Line;
<syntaxhighlight lang="ada">with Knights_Tour, Ada.Command_Line;


procedure Test_Fast is
procedure Test_Fast is
Line 639: Line 639:
begin
begin
KT.Tour_IO(KT.Warnsdorff_Get_Tour(1, 1));
KT.Tour_IO(KT.Warnsdorff_Get_Tour(1, 1));
end Test_Fast;</lang>
end Test_Fast;</syntaxhighlight>


This works still well for somewhat larger sizes:
This works still well for somewhat larger sizes:
Line 670: Line 670:
=={{header|ALGOL 68}}==
=={{header|ALGOL 68}}==
{{works with|ALGOL 68G|Any - tested with release 2.8.win32}}
{{works with|ALGOL 68G|Any - tested with release 2.8.win32}}
<lang algol68># Non-recursive Knight's Tour with Warnsdorff's algorithm #
<syntaxhighlight lang="algol68"># Non-recursive Knight's Tour with Warnsdorff's algorithm #
# If there are multiple choices, backtrack if the first choice doesn't #
# If there are multiple choices, backtrack if the first choice doesn't #
# find a solution #
# find a solution #
Line 957: Line 957:
FI
FI


)</lang>
)</syntaxhighlight>
{{out}}
{{out}}
<pre>
<pre>
Line 979: Line 979:
ANSI BASIC doesn't allow function parameters to be passed by reference so X and Y were made global variables.
ANSI BASIC doesn't allow function parameters to be passed by reference so X and Y were made global variables.


<lang ANSI Standard BASIC>100 DECLARE EXTERNAL FUNCTION choosemove
<syntaxhighlight lang="ansi standard basic">100 DECLARE EXTERNAL FUNCTION choosemove
110 !
110 !
120 RANDOMIZE
120 RANDOMIZE
Line 1,053: Line 1,053:
820 IF X<0 OR X>7 OR Y<0 OR Y>7 THEN EXIT FUNCTION
820 IF X<0 OR X>7 OR Y<0 OR Y>7 THEN EXIT FUNCTION
830 IF Board(X,Y)=FALSE THEN LET validmove = TRUE
830 IF Board(X,Y)=FALSE THEN LET validmove = TRUE
840 END FUNCTION</lang>
840 END FUNCTION</syntaxhighlight>


=={{header|ATS}}==
=={{header|ATS}}==
<lang ats>(*
<syntaxhighlight lang="ats">(*
Find Knight’s Tours.
Find Knight’s Tours.


Line 1,782: Line 1,782:
val _ = make_and_fprint_tours (stdout_ref, 8, 8, i, j, max_tours,
val _ = make_and_fprint_tours (stdout_ref, 8, 8, i, j, max_tours,
closed_only)
closed_only)
}</lang>
}</syntaxhighlight>


{{out}}
{{out}}
Line 1,845: Line 1,845:
=={{header|AutoHotkey}}==
=={{header|AutoHotkey}}==
{{libheader|GDIP}}
{{libheader|GDIP}}
<lang AutoHotkey>#SingleInstance, Force
<syntaxhighlight lang="autohotkey">#SingleInstance, Force
#NoEnv
#NoEnv
SetBatchLines, -1
SetBatchLines, -1
Line 1,940: Line 1,940:
If (A_Gui = 1)
If (A_Gui = 1)
PostMessage, 0xA1, 2
PostMessage, 0xA1, 2
}</lang>
}</syntaxhighlight>
{{out}}
{{out}}
For start at b3
For start at b3
Line 1,947: Line 1,947:


=={{header|AWK}}==
=={{header|AWK}}==
<syntaxhighlight lang="awk">
<lang AWK>
# syntax: GAWK -f KNIGHTS_TOUR.AWK [-v sr=x] [-v sc=x]
# syntax: GAWK -f KNIGHTS_TOUR.AWK [-v sr=x] [-v sc=x]
#
#
Line 2,016: Line 2,016:
}
}
}
}
</syntaxhighlight>
</lang>
<p>output:</p>
<p>output:</p>
<pre>
<pre>
Line 2,033: Line 2,033:
{{works with|BBC BASIC for Windows}}
{{works with|BBC BASIC for Windows}}
[[Image:knights_tour_bbc.gif|right]]
[[Image:knights_tour_bbc.gif|right]]
<lang bbcbasic> VDU 23,22,256;256;16,16,16,128
<syntaxhighlight lang="bbcbasic"> VDU 23,22,256;256;16,16,16,128
VDU 23,23,4;0;0;0;
VDU 23,23,4;0;0;0;
OFF
OFF
Line 2,092: Line 2,092:
DEF FNvalidmove(X%,Y%)
DEF FNvalidmove(X%,Y%)
IF X%<0 OR X%>7 OR Y%<0 OR Y%>7 THEN = FALSE
IF X%<0 OR X%>7 OR Y%<0 OR Y%>7 THEN = FALSE
= NOT(Board%(X%,Y%))</lang>
= NOT(Board%(X%,Y%))</syntaxhighlight>


=={{header|Bracmat}}==
=={{header|Bracmat}}==
<lang bracmat> ( knightsTour
<syntaxhighlight lang="bracmat"> ( knightsTour
= validmoves WarnsdorffSort algebraicNotation init solve
= validmoves WarnsdorffSort algebraicNotation init solve
, x y fieldsToVisit
, x y fieldsToVisit
Line 2,199: Line 2,199:
$ (algebraicNotation$(solve$((!x.!y).!fieldsToVisit)))
$ (algebraicNotation$(solve$((!x.!y).!fieldsToVisit)))
)
)
& out$(knightsTour$a1);</lang>
& out$(knightsTour$a1);</syntaxhighlight>


<pre>a1 b3 a5 b7 d8 f7 h8 g6 f8 h7 g5 h3 g1 e2 c1 a2 b4 a6 b8 c6 a7 c8 e7 g8 h6 g4 h2 f1 d2 b1 a3 c2 e1 f3 h4 g2 e3 d1 b2 a4 c3 b5 d4 f5 d6 c4 e5 d3 f2 h1 g3 e4 c5 d7 b6 a8 c7 d5 f4 e6 g7 e8 f6 h5</pre>
<pre>a1 b3 a5 b7 d8 f7 h8 g6 f8 h7 g5 h3 g1 e2 c1 a2 b4 a6 b8 c6 a7 c8 e7 g8 h6 g4 h2 f1 d2 b1 a3 c2 e1 f3 h4 g2 e3 d1 b2 a4 c3 b5 d4 f5 d6 c4 e5 d3 f2 h1 g3 e4 c5 d7 b6 a8 c7 d5 f4 e6 g7 e8 f6 h5</pre>
Line 2,207: Line 2,207:


The following draws on console the progress of the horsie. Specify board size on commandline, or use default 8.
The following draws on console the progress of the horsie. Specify board size on commandline, or use default 8.
<lang c>#include <stdio.h>
<syntaxhighlight lang="c">#include <stdio.h>
#include <stdlib.h>
#include <stdlib.h>
#include <string.h>
#include <string.h>
Line 2,309: Line 2,309:


return 0;
return 0;
}</lang>
}</syntaxhighlight>


=={{header|C sharp}}==
=={{header|C sharp}}==
<lang csharp>using System;
<syntaxhighlight lang="csharp">using System;
using System.Collections.Generic;
using System.Collections.Generic;


Line 2,395: Line 2,395:
}
}
}
}
}</lang>
}</syntaxhighlight>


=={{header|C++}}==
=={{header|C++}}==
Line 2,402: Line 2,402:
Uses Warnsdorff's rule and (iterative) backtracking if that fails.
Uses Warnsdorff's rule and (iterative) backtracking if that fails.


<lang cpp>#include <iostream>
<syntaxhighlight lang="cpp">#include <iostream>
#include <iomanip>
#include <iomanip>
#include <array>
#include <array>
Line 2,545: Line 2,545:
cout << b3 << endl;
cout << b3 << endl;
return 0;
return 0;
}</lang>
}</syntaxhighlight>


Output:
Output:
Line 2,605: Line 2,605:


For some reason, the interactive part does not work with sbcl, but it works fine wit clisp.
For some reason, the interactive part does not work with sbcl, but it works fine wit clisp.
<lang lisp>;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
<syntaxhighlight lang="lisp">;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;; Solving the knight's tour. ;;;
;;; Solving the knight's tour. ;;;
;;; Warnsdorff's rule with random tie break. ;;;
;;; Warnsdorff's rule with random tie break. ;;;
Line 2,792: Line 2,792:


(prompt)
(prompt)
(main)</lang>
(main)</syntaxhighlight>
{{out}}
{{out}}
<pre>Starting case (leave blank for random)? a8
<pre>Starting case (leave blank for random)? a8
Line 2,811: Line 2,811:
=={{header|Clojure}}==
=={{header|Clojure}}==
Using warnsdorff's rule
Using warnsdorff's rule
<syntaxhighlight lang="clojure">
<lang Clojure>
(defn isin? [x li]
(defn isin? [x li]
(not= [] (filter #(= x %) li)))
(not= [] (filter #(= x %) li)))
Line 2,837: Line 2,837:
(let [np (next-move mov pmoves n)]
(let [np (next-move mov pmoves n)]
(recur (conj mov np) (inc x)))))))
(recur (conj mov np) (inc x)))))))
</syntaxhighlight>
</lang>
{{out}}
{{out}}
<pre>
<pre>
Line 2,854: Line 2,854:
=={{header|CoffeeScript}}==
=={{header|CoffeeScript}}==
This algorithm finds 100,000 distinct solutions to the 8x8 problem in about 30 seconds. It precomputes knight moves up front, so it turns into a pure graph traversal problem. The program uses iteration and backtracking to find solutions.
This algorithm finds 100,000 distinct solutions to the 8x8 problem in about 30 seconds. It precomputes knight moves up front, so it turns into a pure graph traversal problem. The program uses iteration and backtracking to find solutions.
<lang coffeescript>
<syntaxhighlight lang="coffeescript">
graph_tours = (graph, max_num_solutions) ->
graph_tours = (graph, max_num_solutions) ->
# graph is an array of arrays
# graph is an array of arrays
Line 2,969: Line 2,969:
illustrate_knights_tour tours[0], BOARD_WIDTH
illustrate_knights_tour tours[0], BOARD_WIDTH
illustrate_knights_tour tours.pop(), BOARD_WIDTH
illustrate_knights_tour tours.pop(), BOARD_WIDTH
</syntaxhighlight>
</lang>


output
output
<lang>
<syntaxhighlight lang="text">
> time coffee knight.coffee
> time coffee knight.coffee
100000 tours found (showing first and last)
100000 tours found (showing first and last)
Line 2,999: Line 2,999:
user 0m25.656s
user 0m25.656s
sys 0m0.253s
sys 0m0.253s
</syntaxhighlight>
</lang>


=={{header|D}}==
=={{header|D}}==
===Fast Version===
===Fast Version===
{{trans|C++}}
{{trans|C++}}
<lang d>import std.stdio, std.algorithm, std.random, std.range,
<syntaxhighlight lang="d">import std.stdio, std.algorithm, std.random, std.range,
std.conv, std.typecons, std.typetuple;
std.conv, std.typecons, std.typetuple;


Line 3,080: Line 3,080:
writeln();
writeln();
}
}
}</lang>
}</syntaxhighlight>
{{out}}
{{out}}
<pre>23 16 11 6 21
<pre>23 16 11 6 21
Line 3,131: Line 3,131:
===Shorter Version===
===Shorter Version===
{{trans|Haskell}}
{{trans|Haskell}}
<lang d>import std.stdio, std.math, std.algorithm, std.range, std.typecons;
<syntaxhighlight lang="d">import std.stdio, std.math, std.algorithm, std.range, std.typecons;


alias Square = Tuple!(int,"x", int,"y");
alias Square = Tuple!(int,"x", int,"y");
Line 3,157: Line 3,157:
const board = iota(1, 9).cartesianProduct(iota(1, 9)).map!Square.array;
const board = iota(1, 9).cartesianProduct(iota(1, 9)).map!Square.array;
writefln("%(%-(%s -> %)\n%)", board.knightTour([sq]).map!toAlg.chunks(8));
writefln("%(%-(%s -> %)\n%)", board.knightTour([sq]).map!toAlg.chunks(8));
}</lang>
}</syntaxhighlight>
{{out}}
{{out}}
<pre>e5 -> d7 -> b8 -> a6 -> b4 -> a2 -> c1 -> b3
<pre>e5 -> d7 -> b8 -> a6 -> b4 -> a2 -> c1 -> b3
Line 3,171: Line 3,171:


The algorithm uses iterative backtracking and Warnsdorff's heuristic. It can output closed or non-closed tours.
The algorithm uses iterative backtracking and Warnsdorff's heuristic. It can output closed or non-closed tours.
<lang lisp>
<syntaxhighlight lang="lisp">
(require 'plot)
(require 'plot)
(define *knight-moves*
(define *knight-moves*
Line 3,240: Line 3,240:
(play starter 0 starter (dim n) wants-open)
(play starter 0 starter (dim n) wants-open)
(catch (hit mess) (show-steps n wants-open))))
(catch (hit mess) (show-steps n wants-open))))
</syntaxhighlight>
</lang>




{{out}}
{{out}}
<lang lisp>
<syntaxhighlight lang="lisp">
(k-tour 8 0 #f)
(k-tour 8 0 #f)
♞-closed-tour: 66 tries.
♞-closed-tour: 66 tries.
Line 3,278: Line 3,278:
79 76 83 18 91 74 137 16 169 72 153 14 167 70 157 12 63 68 55 10
79 76 83 18 91 74 137 16 169 72 153 14 167 70 157 12 63 68 55 10
82 19 80 75 84 17 92 73 152 15 168 71 154 13 62 69 54 11 52 67
82 19 80 75 84 17 92 73 152 15 168 71 154 13 62 69 54 11 52 67
</syntaxhighlight>
</lang>


;Plotting:
;Plotting:
64 shades of gray. We plot the move sequence in shades of gray, from black to white. The starting square is red. The ending square is green. One can observe that the squares near the border are played first (dark squares).
64 shades of gray. We plot the move sequence in shades of gray, from black to white. The starting square is red. The ending square is green. One can observe that the squares near the border are played first (dark squares).
<lang lisp>
<syntaxhighlight lang="lisp">
(define (step-color x y n last-one)
(define (step-color x y n last-one)
(letrec ((sq (square (floor x) (floor y) n))
(letrec ((sq (square (floor x) (floor y) n))
Line 3,292: Line 3,292:
(define ( k-plot n)
(define ( k-plot n)
(plot-rgb (lambda (x y) (step-color x y n (dim n))) (- n epsilon) (- n epsilon)))
(plot-rgb (lambda (x y) (step-color x y n (dim n))) (- n epsilon) (- n epsilon)))
</syntaxhighlight>
</lang>




Line 3,301: Line 3,301:
=={{header|Elixir}}==
=={{header|Elixir}}==
{{trans|Ruby}}
{{trans|Ruby}}
<lang elixir>defmodule Board do
<syntaxhighlight lang="elixir">defmodule Board do
import Integer, only: [is_odd: 1]
import Integer, only: [is_odd: 1]
Line 3,364: Line 3,364:
Board.knight_tour(4,9,1,1)
Board.knight_tour(4,9,1,1)
Board.knight_tour(5,5,1,2)
Board.knight_tour(5,5,1,2)
Board.knight_tour(12,12,2,2)</lang>
Board.knight_tour(12,12,2,2)</syntaxhighlight>


{{out}}
{{out}}
Line 3,410: Line 3,410:


=={{header|Elm}}==
=={{header|Elm}}==
<lang elm>module Main exposing (main)
<syntaxhighlight lang="elm">module Main exposing (main)


import Browser exposing (element)
import Browser exposing (element)
Line 3,755: Line 3,755:
, subscriptions = subscriptions
, subscriptions = subscriptions
}
}
</syntaxhighlight>
</lang>


Link to live demo: https://dmcbane.github.io/knights-tour/
Link to live demo: https://dmcbane.github.io/knights-tour/
Line 3,761: Line 3,761:
=={{header|Erlang}}==
=={{header|Erlang}}==
Again I use backtracking. It seemed easier this time.
Again I use backtracking. It seemed easier this time.
<syntaxhighlight lang="erlang">
<lang Erlang>
-module( knights_tour ).
-module( knights_tour ).


Line 3,840: Line 3,840:
next_moves_row( 8 ) -> [6, 7];
next_moves_row( 8 ) -> [6, 7];
next_moves_row( N ) -> [N - 2, N - 1, N + 1, N + 2].
next_moves_row( N ) -> [N - 2, N - 1, N + 1, N + 2].
</syntaxhighlight>
</lang>
{{out}}
{{out}}
<pre>
<pre>
Line 3,866: Line 3,866:
=={{header|ERRE}}==
=={{header|ERRE}}==
Taken from ERRE distribution disk. Comments are in Italian.
Taken from ERRE distribution disk. Comments are in Italian.
<syntaxhighlight lang="erre">
<lang ERRE>
! **********************************************************************
! **********************************************************************
! * *
! * *
Line 4,076: Line 4,076:
UNTIL A$<>""
UNTIL A$<>""
END PROGRAM
END PROGRAM
</syntaxhighlight>
</lang>
{{out}}
{{out}}
<pre> *** LA GALOPPATA DEL CAVALIERE ***
<pre> *** LA GALOPPATA DEL CAVALIERE ***
Line 4,097: Line 4,097:


=={{header|FreeBASIC}}==
=={{header|FreeBASIC}}==
<lang freebasic>
<syntaxhighlight lang="freebasic">
Dim Shared As Integer tamano, xc, yc, nm
Dim Shared As Integer tamano, xc, yc, nm
Dim As Integer f, qm, nmov, n = 0
Dim As Integer f, qm, nmov, n = 0
Line 4,155: Line 4,155:
Sleep
Sleep
End
End
</syntaxhighlight>
</lang>
{{out}}
{{out}}
[https://www.dropbox.com/s/s3bpwechpoueum4/Knights%20Tour%20FreeBasic.png?dl=0 Knights Tour FreeBasic image]
[https://www.dropbox.com/s/s3bpwechpoueum4/Knights%20Tour%20FreeBasic.png?dl=0 Knights Tour FreeBasic image]
Line 4,191: Line 4,191:
{{works with|gfortran|11.2.1}}
{{works with|gfortran|11.2.1}}
{{works with|f2c}}
{{works with|f2c}}
<lang fortran>C-----------------------------------------------------------------------
<syntaxhighlight lang="fortran">C-----------------------------------------------------------------------
C
C
C Find Knight’s Tours.
C Find Knight’s Tours.
Line 4,841: Line 4,841:
end
end


C-----------------------------------------------------------------------</lang>
C-----------------------------------------------------------------------</syntaxhighlight>
{{out}}
{{out}}
$ echo "c5 2 T" | ./knights_tour
$ echo "c5 2 T" | ./knights_tour
Line 4,904: Line 4,904:
{{works with|gfortran|11.2.1}}
{{works with|gfortran|11.2.1}}
{{trans|ATS}}
{{trans|ATS}}
<lang fortran>!-----------------------------------------------------------------------
<syntaxhighlight lang="fortran">!-----------------------------------------------------------------------
!
!
! Find Knight’s Tours.
! Find Knight’s Tours.
Line 5,464: Line 5,464:
end program
end program


!-----------------------------------------------------------------------</lang>
!-----------------------------------------------------------------------</syntaxhighlight>


{{out}}
{{out}}
Line 5,528: Line 5,528:
{{works with|gfortran|11.2.1}}
{{works with|gfortran|11.2.1}}
(This one is ''not'' a translation of my ATS implementation. I wrote it earlier.)
(This one is ''not'' a translation of my ATS implementation. I wrote it earlier.)
<lang fortran>!!!
<syntaxhighlight lang="fortran">!!!
!!! Find a Knight’s Tour.
!!! Find a Knight’s Tour.
!!!
!!!
Line 5,853: Line 5,853:
end if
end if
end do
end do
end program knights_tour_main</lang>
end program knights_tour_main</syntaxhighlight>


$ ./knights_tour a1 b2 c3
$ ./knights_tour a1 b2 c3
Line 5,885: Line 5,885:
=={{header|Go}}==
=={{header|Go}}==
===Warnsdorf's rule===
===Warnsdorf's rule===
<lang go>package main
<syntaxhighlight lang="go">package main


import (
import (
Line 5,992: Line 5,992:
}
}
return true
return true
}</lang>
}</syntaxhighlight>
{{out}}
{{out}}
<pre>
<pre>
Line 6,005: Line 6,005:
</pre>
</pre>
===Ant colony===
===Ant colony===
<lang go>/* Adapted from "Enumerating Knight's Tours using an Ant Colony Algorithm"
<syntaxhighlight lang="go">/* Adapted from "Enumerating Knight's Tours using an Ant Colony Algorithm"
by Philip Hingston and Graham Kendal,
by Philip Hingston and Graham Kendal,
PDF at http://www.cs.nott.ac.uk/~gxk/papers/cec05knights.pdf. */
PDF at http://www.cs.nott.ac.uk/~gxk/papers/cec05knights.pdf. */
Line 6,196: Line 6,196:
tourCh <- moves
tourCh <- moves
}
}
}</lang>
}</syntaxhighlight>
Output:
Output:
<pre>
<pre>
Line 6,212: Line 6,212:


=={{header|Haskell}}==
=={{header|Haskell}}==
<lang Haskell>import Data.Bifunctor (bimap)
<syntaxhighlight lang="haskell">import Data.Bifunctor (bimap)
import Data.Char (chr, ord)
import Data.Char (chr, ord)
import Data.List (intercalate, minimumBy, sort, (\\))
import Data.List (intercalate, minimumBy, sort, (\\))
Line 6,273: Line 6,273:
printTour tour = do
printTour tour = do
putStrLn $ intercalate " -> " $ take 8 tour
putStrLn $ intercalate " -> " $ take 8 tour
printTour $ drop 8 tour</lang>
printTour $ drop 8 tour</syntaxhighlight>
{{Out}}
{{Out}}
<pre>e5 -> f7 -> h8 -> g6 -> h4 -> g2 -> e1 -> f3
<pre>e5 -> f7 -> h8 -> g6 -> h4 -> g2 -> e1 -> f3
Line 6,291: Line 6,291:


The algorithm doesn't always generate a complete tour.
The algorithm doesn't always generate a complete tour.
<lang Icon>link printf
<syntaxhighlight lang="icon">link printf


procedure main(A)
procedure main(A)
Line 6,391: Line 6,391:
}
}
every write(hdr2|hdr1|&null)
every write(hdr2|hdr1|&null)
end</lang>
end</syntaxhighlight>


The following can be used when debugging to validate the board structure and to image the available moves on the board.
The following can be used when debugging to validate the board structure and to image the available moves on the board.
<lang Icon>procedure DumpBoard(B) #: Dump Board internals
<syntaxhighlight lang="icon">procedure DumpBoard(B) #: Dump Board internals
write("Board size=",B.N)
write("Board size=",B.N)
write("Available Moves at start of tour:", ImageMovesTo(B.movesto))
write("Available Moves at start of tour:", ImageMovesTo(B.movesto))
Line 6,404: Line 6,404:
every s ||:= " " || (!sort(movesto[k])|"\n")
every s ||:= " " || (!sort(movesto[k])|"\n")
return s
return s
end</lang>
end</syntaxhighlight>




Line 6,456: Line 6,456:
'''Solution:'''<br>
'''Solution:'''<br>
[[j:Essays/Knight's Tour|The Knight's tour essay on the Jwiki]] shows a couple of solutions including one using [[wp:Knight's_tour#Warnsdorff.27s_algorithm|Warnsdorffs algorithm]].
[[j:Essays/Knight's Tour|The Knight's tour essay on the Jwiki]] shows a couple of solutions including one using [[wp:Knight's_tour#Warnsdorff.27s_algorithm|Warnsdorffs algorithm]].
<lang j>NB. knight moves for each square of a (y,y) board
<syntaxhighlight lang="j">NB. knight moves for each square of a (y,y) board
kmoves=: monad define
kmoves=: monad define
t=. (>,{;~i.y) +"1/ _2]\2 1 2 _1 1 2 1 _2 _1 2 _1 _2 _2 1 _2 _1
t=. (>,{;~i.y) +"1/ _2]\2 1 2 _1 1 2 1 _2 _1 2 _1 _2 _2 1 _2 _1
Line 6,472: Line 6,472:
assert. ~:p
assert. ~:p
(,~y)$/:p
(,~y)$/:p
)</lang>
)</syntaxhighlight>


'''Example Use:'''
'''Example Use:'''
<lang j> ktourw 8 NB. solution for an 8 x 8 board
<syntaxhighlight lang="j"> ktourw 8 NB. solution for an 8 x 8 board
0 25 14 23 28 49 12 31
0 25 14 23 28 49 12 31
15 22 27 50 13 30 63 48
15 22 27 50 13 30 63 48
Line 6,496: Line 6,496:
555 558 553 778 563 570 775 780 785 772 1000...
555 558 553 778 563 570 775 780 785 772 1000...
100 551 556 561 102 777 572 771 104 781 57...
100 551 556 561 102 777 572 771 104 781 57...
557 554 101 552 571 562 103 776 573 770 10...</lang>
557 554 101 552 571 562 103 776 573 770 10...</syntaxhighlight>


=={{header|Java}}==
=={{header|Java}}==
{{Works with|Java|7}}
{{Works with|Java|7}}
<lang java>import java.util.*;
<syntaxhighlight lang="java">import java.util.*;


public class KnightsTour {
public class KnightsTour {
Line 6,597: Line 6,597:
}
}
}
}
}</lang>
}</syntaxhighlight>
<pre>34 17 20 3 36 7 22 5
<pre>34 17 20 3 36 7 22 5
19 2 35 40 21 4 37 8
19 2 35 40 21 4 37 8
Line 6,608: Line 6,608:
===More efficient non-trackback solution===
===More efficient non-trackback solution===
{{Works with|Java|8}}
{{Works with|Java|8}}
<lang>
<syntaxhighlight lang="text">
package com.knight.tour;
package com.knight.tour;
import java.util.ArrayList;
import java.util.ArrayList;
Line 6,767: Line 6,767:
}
}
}
}
</syntaxhighlight>
</lang>
<pre>
<pre>
Found a path for 8 X 8 chess board.
Found a path for 8 X 8 chess board.
Line 6,784: Line 6,784:
You can test it [http://paulo-jorente.de/webgames/repos/knightsTour/ here].
You can test it [http://paulo-jorente.de/webgames/repos/knightsTour/ here].


<lang javascript>
<syntaxhighlight lang="javascript">
class KnightTour {
class KnightTour {
constructor() {
constructor() {
Line 7,000: Line 7,000:
}
}
new KnightTour();
new KnightTour();
</syntaxhighlight>
</lang>
To test it, you'll need an index.html
To test it, you'll need an index.html
<pre>
<pre>
Line 7,070: Line 7,070:
A composition of values, drawing on generic abstractions:
A composition of values, drawing on generic abstractions:
{{Trans|Haskell}}
{{Trans|Haskell}}
<lang javascript>(() => {
<syntaxhighlight lang="javascript">(() => {
'use strict';
'use strict';


Line 7,363: Line 7,363:
// MAIN ---
// MAIN ---
return main();
return main();
})();</lang>
})();</syntaxhighlight>
{{Out}}
{{Out}}
<pre>(Board size 8*8)
<pre>(Board size 8*8)
Line 7,392: Line 7,392:
=={{header|Julia}}==
=={{header|Julia}}==
Uses the Hidato puzzle solver module, which has its source code listed [[Solve_a_Hidato_puzzle#Julia | here]] in the Hadato task.
Uses the Hidato puzzle solver module, which has its source code listed [[Solve_a_Hidato_puzzle#Julia | here]] in the Hadato task.
<lang julia>using .Hidato # Note that the . here means to look locally for the module rather than in the libraries
<syntaxhighlight lang="julia">using .Hidato # Note that the . here means to look locally for the module rather than in the libraries


const chessboard = """
const chessboard = """
Line 7,410: Line 7,410:
hidatosolve(board, maxmoves, knightmoves, fixed, starts[1][1], starts[1][2], 1)
hidatosolve(board, maxmoves, knightmoves, fixed, starts[1][1], starts[1][2], 1)
printboard(board)
printboard(board)
</lang>{{output}}<pre>
</syntaxhighlight>{{output}}<pre>
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
Line 7,433: Line 7,433:
{{trans|Haskell}}
{{trans|Haskell}}


<lang scala>data class Square(val x : Int, val y : Int)
<syntaxhighlight lang="scala">data class Square(val x : Int, val y : Int)


val board = Array(8 * 8, { Square(it / 8 + 1, it % 8 + 1) })
val board = Array(8 * 8, { Square(it / 8 + 1, it % 8 + 1) })
Line 7,461: Line 7,461:
col = (col + 1) % 8
col = (col + 1) % 8
}
}
}</lang>
}</syntaxhighlight>


{{out}}
{{out}}
Line 7,477: Line 7,477:
Influenced by the Python version, although computed tours are different.
Influenced by the Python version, although computed tours are different.


<lang locobasic>10 mode 1:defint a-z
<syntaxhighlight lang="locobasic">10 mode 1:defint a-z
20 input "Board size: ",size
20 input "Board size: ",size
30 input "Start position: ",a$
30 input "Start position: ",a$
Line 7,523: Line 7,523:
450 ' skip this move
450 ' skip this move
460 next
460 next
470 return</lang>
470 return</syntaxhighlight>


[[File:Knights tour Locomotive Basic.png]]
[[File:Knights tour Locomotive Basic.png]]


=={{header|Lua}}==
=={{header|Lua}}==
<lang lua>N = 8
<syntaxhighlight lang="lua">N = 8


moves = { {1,-2},{2,-1},{2,1},{1,2},{-1,2},{-2,1},{-2,-1},{-1,-2} }
moves = { {1,-2},{2,-1},{2,1},{1,2},{-1,2},{-2,1},{-2,-1},{-1,-2} }
Line 7,578: Line 7,578:
print( string.format( "%s%d - %s%d", string.sub("ABCDEFGH",last[1],last[1]), last[2], string.sub("ABCDEFGH",lst[i][1],lst[i][1]), lst[i][2] ) )
print( string.format( "%s%d - %s%d", string.sub("ABCDEFGH",last[1],last[1]), last[2], string.sub("ABCDEFGH",lst[i][1],lst[i][1]), lst[i][2] ) )
last = lst[i]
last = lst[i]
end</lang>
end</syntaxhighlight>
=={{header|M2000 Interpreter}}==
=={{header|M2000 Interpreter}}==
<syntaxhighlight lang="m2000 interpreter">
<lang M2000 Interpreter>
Function KnightTour$(StartW=1, StartH=1){
Function KnightTour$(StartW=1, StartH=1){
def boolean swapH, swapV=True
def boolean swapH, swapV=True
Line 7,683: Line 7,683:
Clipboard ex$
Clipboard ex$
Report ex$
Report ex$
</syntaxhighlight>
</lang>
{{out}}
{{out}}
<pre>
<pre>
Line 7,730: Line 7,730:
Beware the program writes to a file ‘__random_number__’ in the working directory. (This can be avoided in GNU m4 by using ‘esyscmd’ instead of ‘syscmd’. I do not know how to avoid it in general.)
Beware the program writes to a file ‘__random_number__’ in the working directory. (This can be avoided in GNU m4 by using ‘esyscmd’ instead of ‘syscmd’. I do not know how to avoid it in general.)


<lang m4>divert(-1)
<syntaxhighlight lang="m4">divert(-1)


----------------------------------------------------------------------
----------------------------------------------------------------------
Line 7,908: Line 7,908:
find_tour(a1)
find_tour(a1)
find_tour(c5)
find_tour(c5)
find_tour(h8)</lang>
find_tour(h8)</syntaxhighlight>


{{out}}
{{out}}
Line 7,920: Line 7,920:
=={{header|Mathematica}}/{{header|Wolfram Language}}==
=={{header|Mathematica}}/{{header|Wolfram Language}}==
'''Solution'''
'''Solution'''
<lang Mathematica>knightsTourMoves[start_] :=
<syntaxhighlight lang="mathematica">knightsTourMoves[start_] :=
Module[{
Module[{
vertexLabels = (# -> ToString@c[[Quotient[# - 1, 8] + 1]] <> ToString[Mod[# - 1, 8] + 1]) & /@ Range[64], knightsGraph,
vertexLabels = (# -> ToString@c[[Quotient[# - 1, 8] + 1]] <> ToString[Mod[# - 1, 8] + 1]) & /@ Range[64], knightsGraph,
Line 7,927: Line 7,927:
hamiltonianCycle = ((FindHamiltonianCycle[knightsGraph] /. UndirectedEdge -> DirectedEdge) /. labels)[[1]];
hamiltonianCycle = ((FindHamiltonianCycle[knightsGraph] /. UndirectedEdge -> DirectedEdge) /. labels)[[1]];
end = Cases[hamiltonianCycle, (x_ \[DirectedEdge] start) :> x][[1]];
end = Cases[hamiltonianCycle, (x_ \[DirectedEdge] start) :> x][[1]];
FindShortestPath[g, start, end]]</lang>
FindShortestPath[g, start, end]]</syntaxhighlight>


'''Usage'''
'''Usage'''
<lang Mathematica>knightsTourMoves["d8"]
<syntaxhighlight lang="mathematica">knightsTourMoves["d8"]


(* out *)
(* out *)
Line 7,936: Line 7,936:
"c7", "a8", "b6", "c8", "d6", "e4", "d2", "f1", "e3", "d1", "f2", "h1", "g3", "e2", "c1", "d3", "e1", "g2", "h4", "f5", "e7", "d5", \
"c7", "a8", "b6", "c8", "d6", "e4", "d2", "f1", "e3", "d1", "f2", "h1", "g3", "e2", "c1", "d3", "e1", "g2", "h4", "f5", "e7", "d5", \
"f4", "h5", "g7", "e8", "f6", "g8", "h6", "g4", "h2", "f3", "g1", "h3", "g5", "h7", "f8", "d7", "e5", "g6", "h8", "f7"}
"f4", "h5", "g7", "e8", "f6", "g8", "h6", "g4", "h2", "f3", "g1", "h3", "g5", "h7", "f8", "d7", "e5", "g6", "h8", "f7"}
</syntaxhighlight>
</lang>


'''Analysis'''
'''Analysis'''


'''vertexLabels''' replaces the default vertex (i.e. square) names of the chessboard with the standard algebraic names "a1", "a2",...,"h8".
'''vertexLabels''' replaces the default vertex (i.e. square) names of the chessboard with the standard algebraic names "a1", "a2",...,"h8".
<syntaxhighlight lang="mathematica">
<lang Mathematica>
vertexLabels = (# -> ToString@c[[Quotient[# - 1, 8] + 1]] <> ToString[Mod[# - 1, 8] + 1]) & /@ Range[64]
vertexLabels = (# -> ToString@c[[Quotient[# - 1, 8] + 1]] <> ToString[Mod[# - 1, 8] + 1]) & /@ Range[64]


Line 7,952: Line 7,952:
41 -> "f1", 42 -> "f2", 43 -> "f3", 44 -> "f4", 45 -> "f5", 46 -> "f6", 47 -> "f7", 48 -> "f8",
41 -> "f1", 42 -> "f2", 43 -> "f3", 44 -> "f4", 45 -> "f5", 46 -> "f6", 47 -> "f7", 48 -> "f8",
49 -> "g1", 50 -> "g2", 51 -> "g3", 52 -> "g4", 53 -> "g5", 54 -> "g6",55 -> "g7", 56 -> "g8",
49 -> "g1", 50 -> "g2", 51 -> "g3", 52 -> "g4", 53 -> "g5", 54 -> "g6",55 -> "g7", 56 -> "g8",
57 -> "h1", 58 -> "h2", 59 -> "h3", 60 -> "h4", 61 -> "h5", 62 -> "h6", 63 -> "h7", 64 -> "h8"}</lang>
57 -> "h1", 58 -> "h2", 59 -> "h3", 60 -> "h4", 61 -> "h5", 62 -> "h6", 63 -> "h7", 64 -> "h8"}</syntaxhighlight>


'''knightsGraph''' creates a graph of the solution space.
'''knightsGraph''' creates a graph of the solution space.
<lang Mathematica>knightsGraph = KnightTourGraph[i, i, VertexLabels -> vertexLabels, ImagePadding -> 15];</lang>
<syntaxhighlight lang="mathematica">knightsGraph = KnightTourGraph[i, i, VertexLabels -> vertexLabels, ImagePadding -> 15];</syntaxhighlight>
[[File:KnightsTour-3.png]]
[[File:KnightsTour-3.png]]


Find a Hamiltonian cycle (a path that visits each square exactly one time.)
Find a Hamiltonian cycle (a path that visits each square exactly one time.)


<lang Mathematica>hamiltonianCycle = ((FindHamiltonianCycle[knightsGraph] /. UndirectedEdge -> DirectedEdge) /. labels)[[1]];</lang>
<syntaxhighlight lang="mathematica">hamiltonianCycle = ((FindHamiltonianCycle[knightsGraph] /. UndirectedEdge -> DirectedEdge) /. labels)[[1]];</syntaxhighlight>


Find the end square:
Find the end square:


<lang Mathematica>end = Cases[hamiltonianCycle, (x_ \[DirectedEdge] start) :> x][[1]];</lang>
<syntaxhighlight lang="mathematica">end = Cases[hamiltonianCycle, (x_ \[DirectedEdge] start) :> x][[1]];</syntaxhighlight>


Find shortest path from the start square to the end square.
Find shortest path from the start square to the end square.


<lang Mathematica>FindShortestPath[g, start, end]]</lang>
<syntaxhighlight lang="mathematica">FindShortestPath[g, start, end]]</syntaxhighlight>


=={{header|Mathprog}}==
=={{header|Mathprog}}==
Line 7,977: Line 7,977:
2. It is possible to specify which square is used for any Knights Move.
2. It is possible to specify which square is used for any Knights Move.


<lang>
<syntaxhighlight lang="text">
/*Knights.mathprog
/*Knights.mathprog
Line 8,039: Line 8,039:
end;
end;
</syntaxhighlight>
</lang>


Produces:
Produces:


<lang>
<syntaxhighlight lang="text">
GLPSOL: GLPK LP/MIP Solver, v4.47
GLPSOL: GLPK LP/MIP Solver, v4.47
Parameter(s) specified in the command line:
Parameter(s) specified in the command line:
Line 8,089: Line 8,089:
23 10 21 16 25
23 10 21 16 25
Model has been successfully processed
Model has been successfully processed
</syntaxhighlight>
</lang>


and
and


<lang>
<syntaxhighlight lang="text">
/*Knights.mathprog
/*Knights.mathprog
Line 8,158: Line 8,158:
end;
end;
</syntaxhighlight>
</lang>


Produces:
Produces:


<lang>
<syntaxhighlight lang="text">
GLPSOL: GLPK LP/MIP Solver, v4.47
GLPSOL: GLPK LP/MIP Solver, v4.47
Parameter(s) specified in the command line:
Parameter(s) specified in the command line:
Line 8,227: Line 8,227:
10 55 20 57 12 37 40 1
10 55 20 57 12 37 40 1
Model has been successfully processed
Model has been successfully processed
</syntaxhighlight>
</lang>


=={{header|Nim}}==
=={{header|Nim}}==
Line 8,235: Line 8,235:
We have added a case to test the absence of solution. Note that, in this case, there is a lot of backtracking which considerably slows down the execution.
We have added a case to test the absence of solution. Note that, in this case, there is a lot of backtracking which considerably slows down the execution.


<lang Nim>import algorithm, options, random, parseutils, strutils, strformat
<syntaxhighlight lang="nim">import algorithm, options, random, parseutils, strutils, strformat


type
type
Line 8,336: Line 8,336:
#run[5]("c4") # No solution, so very slow compared to other cases.
#run[5]("c4") # No solution, so very slow compared to other cases.
run[8]("b5")
run[8]("b5")
run[31]("a1")</lang>
run[31]("a1")</syntaxhighlight>


{{out}}
{{out}}
Line 8,394: Line 8,394:
=={{header|ObjectIcon}}==
=={{header|ObjectIcon}}==
{{trans|ATS}}
{{trans|ATS}}
<lang objecticon>#
<syntaxhighlight lang="objecticon">#
# Find Knight’s Tours.
# Find Knight’s Tours.
#
#
Line 8,756: Line 8,756:
return (((i_diff = 2 & j_diff = 1) |
return (((i_diff = 2 & j_diff = 1) |
(i_diff = 1 & j_diff = 2)) & &yes) | fail
(i_diff = 1 & j_diff = 2)) & &yes) | fail
end</lang>
end</syntaxhighlight>


{{out}}
{{out}}
Line 8,819: Line 8,819:
=={{header|Perl}}==
=={{header|Perl}}==
Knight's tour using [[wp:Knight's_tour#Warnsdorff.27s_algorithm|Warnsdorffs algorithm]]
Knight's tour using [[wp:Knight's_tour#Warnsdorff.27s_algorithm|Warnsdorffs algorithm]]
<lang perl>use strict;
<syntaxhighlight lang="perl">use strict;
use warnings;
use warnings;
# Find a knight's tour
# Find a knight's tour
Line 8,905: Line 8,905:
return unless $square =~ /^([a-h])([1-8])$/;
return unless $square =~ /^([a-h])([1-8])$/;
return (8-$2, ord($1) - ord('a'));
return (8-$2, ord($1) - ord('a'));
}</lang>
}</syntaxhighlight>


Sample output (start square c3):
Sample output (start square c3):
Line 8,913: Line 8,913:
=={{header|Phix}}==
=={{header|Phix}}==
This is pretty fast (<<1s) up to size 48, before some sizes start to take quite some time to complete. It will even solve a 200x200 in 0.67s
This is pretty fast (<<1s) up to size 48, before some sizes start to take quite some time to complete. It will even solve a 200x200 in 0.67s
<!--<lang Phix>(phixonline)-->
<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">size</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">8</span><span style="color: #0000FF;">,</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">size</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">8</span><span style="color: #0000FF;">,</span>
Line 8,998: Line 8,998:
<span style="color: #7060A8;">puts</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"no solutions found\n"</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">puts</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"no solutions found\n"</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<!--</lang>-->
<!--</syntaxhighlight>-->
{{out}}
{{out}}
<pre>
<pre>
Line 9,014: Line 9,014:


=={{header|Picat}}==
=={{header|Picat}}==
<lang Picat>import cp.
<syntaxhighlight lang="picat">import cp.


main =>
main =>
Line 9,049: Line 9,049:
fill_output_matrix(N,OutputM,V,V[I],Count+1)
fill_output_matrix(N,OutputM,V,V[I],Count+1)
end.
end.
</syntaxhighlight>
</lang>


{{out}}
{{out}}
Line 9,064: Line 9,064:


=={{header|PicoLisp}}==
=={{header|PicoLisp}}==
<lang PicoLisp>(load "@lib/simul.l")
<syntaxhighlight lang="picolisp">(load "@lib/simul.l")


# Build board
# Build board
Line 9,093: Line 9,093:
(moves Tour) )
(moves Tour) )
(push 'Tour @) )
(push 'Tour @) )
(flip Tour) )</lang>
(flip Tour) )</syntaxhighlight>
Output:
Output:
<pre>-> (b1 a3 b5 a7 c8 b6 a8 c7 a6 b8 d7 f8 h7 g5 h3 g1 e2 c1 a2 b4 c2 a1 b3 a5 b7
<pre>-> (b1 a3 b5 a7 c8 b6 a8 c7 a6 b8 d7 f8 h7 g5 h3 g1 e2 c1 a2 b4 c2 a1 b3 a5 b7
Line 9,101: Line 9,101:
=={{header|PostScript}}==
=={{header|PostScript}}==
You probably shouldn't send this to a printer. Solution using Warnsdorffs algorithm.
You probably shouldn't send this to a printer. Solution using Warnsdorffs algorithm.
<lang postscript>%!PS-Adobe-3.0
<syntaxhighlight lang="postscript">%!PS-Adobe-3.0
%%BoundingBox: 0 0 300 300
%%BoundingBox: 0 0 300 300


Line 9,210: Line 9,210:
3 1 100 { solve } for
3 1 100 { solve } for


%%EOF</lang>
%%EOF</syntaxhighlight>


=={{header|Prolog}}==
=={{header|Prolog}}==
Line 9,216: Line 9,216:
Knights tour using [[wp:Knight's_tour#Warnsdorff.27s_algorithm|Warnsdorffs algorithm]]
Knights tour using [[wp:Knight's_tour#Warnsdorff.27s_algorithm|Warnsdorffs algorithm]]


<lang Prolog>% N is the number of lines of the chessboard
<syntaxhighlight lang="prolog">% N is the number of lines of the chessboard
knight(N) :-
knight(N) :-
Max is N * N,
Max is N * N,
Line 9,296: Line 9,296:
M1 is M + 1,
M1 is M + 1,
display(N, M1, T).
display(N, M1, T).
</syntaxhighlight>
</lang>


Output :
Output :
Line 9,335: Line 9,335:
===Alternative version===
===Alternative version===
{{Works with|GNU Prolog}}
{{Works with|GNU Prolog}}
<lang prolog>:- initialization(main).
<syntaxhighlight lang="prolog">:- initialization(main).




Line 9,391: Line 9,391:




main :- make_graph, hamiltonian(5*3,Pn), show_path(Pn), halt.</lang>
main :- make_graph, hamiltonian(5*3,Pn), show_path(Pn), halt.</syntaxhighlight>
{{Output}}
{{Output}}
<pre> 5 18 35 22 3 16 55 24
<pre> 5 18 35 22 3 16 55 24
Line 9,405: Line 9,405:
=={{header|Python}}==
=={{header|Python}}==
Knights tour using [[wp:Knight's_tour#Warnsdorff.27s_algorithm|Warnsdorffs algorithm]]
Knights tour using [[wp:Knight's_tour#Warnsdorff.27s_algorithm|Warnsdorffs algorithm]]
<lang python>import copy
<syntaxhighlight lang="python">import copy


boardsize=6
boardsize=6
Line 9,469: Line 9,469:
start = input('Start position: ')
start = input('Start position: ')
board = knights_tour(start, boardsize)
board = knights_tour(start, boardsize)
print(boardstring(board, boardsize=boardsize))</lang>
print(boardstring(board, boardsize=boardsize))</syntaxhighlight>


;Sample runs
;Sample runs
Line 9,550: Line 9,550:
Based on a slight modification of [[wp:Knight%27s_tour#Warnsdorff.27s_rule|Warnsdorff's algorithm]], in that if a dead-end is reached, the program backtracks to the next best move.
Based on a slight modification of [[wp:Knight%27s_tour#Warnsdorff.27s_rule|Warnsdorff's algorithm]], in that if a dead-end is reached, the program backtracks to the next best move.


<lang r>#!/usr/bin/Rscript
<syntaxhighlight lang="r">#!/usr/bin/Rscript
# M x N Chess Board.
# M x N Chess Board.
Line 9,618: Line 9,618:
# Begin tour.
# Begin tour.
setboard(position, 1); knightTour(position, 2)</lang>
setboard(position, 1); knightTour(position, 2)</syntaxhighlight>


Output:
Output:
Line 9,636: Line 9,636:


=={{header|Racket}}==
=={{header|Racket}}==
<lang racket>
<syntaxhighlight lang="racket">
#lang racket
#lang racket
(define N 8)
(define N 8)
Line 9,661: Line 9,661:
" "))))
" "))))
(draw (tour (random N) (random N)))
(draw (tour (random N) (random N)))
</syntaxhighlight>
</lang>
{{out}}
{{out}}
<pre>
<pre>
Line 9,677: Line 9,677:
(formerly Perl 6)
(formerly Perl 6)
{{trans|Perl}}
{{trans|Perl}}
<lang perl6>my @board;
<syntaxhighlight lang="raku" line>my @board;


my $I = 8;
my $I = 8;
Line 9,749: Line 9,749:
sub from_algebraic($square where /^ (<[a..z]>) (\d+) $/) {
sub from_algebraic($square where /^ (<[a..z]>) (\d+) $/) {
$I - $1, ord(~$0) - ord('a');
$I - $1, ord(~$0) - ord('a');
}</lang>
}</syntaxhighlight>
(Output identical to Perl's above.)
(Output identical to Perl's above.)


Line 9,755: Line 9,755:
{{trans|ATS}}
{{trans|ATS}}
For use with the public domain ratfor77 translator and a FORTRAN 77 compiler.
For use with the public domain ratfor77 translator and a FORTRAN 77 compiler.
<lang ratfor>#-----------------------------------------------------------------------
<syntaxhighlight lang="ratfor">#-----------------------------------------------------------------------
#
#
# Find Knight’s Tours.
# Find Knight’s Tours.
Line 10,404: Line 10,404:
end
end


#-----------------------------------------------------------------------</lang>
#-----------------------------------------------------------------------</syntaxhighlight>


{{out}}
{{out}}
Line 10,474: Line 10,474:


This is an &nbsp; ''open tour'' &nbsp; solution. &nbsp; (See this task's &nbsp; ''discussion'' &nbsp; page for an explanation, the section is &nbsp; ''The 7x7 problem''.)
This is an &nbsp; ''open tour'' &nbsp; solution. &nbsp; (See this task's &nbsp; ''discussion'' &nbsp; page for an explanation, the section is &nbsp; ''The 7x7 problem''.)
<lang rexx>/*REXX program solves the knight's tour problem for a (general) NxN chessboard.*/
<syntaxhighlight lang="rexx">/*REXX program solves the knight's tour problem for a (general) NxN chessboard.*/
parse arg N sRank sFile . /*obtain optional arguments from the CL*/
parse arg N sRank sFile . /*obtain optional arguments from the CL*/
if N=='' | N=="," then N=8 /*No boardsize specified? Use default.*/
if N=='' | N=="," then N=8 /*No boardsize specified? Use default.*/
Line 10,511: Line 10,511:
end /*try different move. */
end /*try different move. */
end /*t*/ /* [↑] all moves tried.*/
end /*t*/ /* [↑] all moves tried.*/
return 0 /*tour is not possible. */</lang>
return 0 /*tour is not possible. */</syntaxhighlight>
'''output''' &nbsp; when using the default input:
'''output''' &nbsp; when using the default input:
<pre>
<pre>
Line 10,537: Line 10,537:
=={{header|Ruby}}==
=={{header|Ruby}}==
Knights tour using [[wp:Knight's_tour#Warnsdorff.27s_rule|Warnsdorffs rule]]
Knights tour using [[wp:Knight's_tour#Warnsdorff.27s_rule|Warnsdorffs rule]]
<lang ruby>class Board
<syntaxhighlight lang="ruby">class Board
Cell = Struct.new(:value, :adj) do
Cell = Struct.new(:value, :adj) do
def self.end=(end_val)
def self.end=(end_val)
Line 10,608: Line 10,608:
knight_tour(5,5,0,1)
knight_tour(5,5,0,1)


knight_tour(12,12,1,1)</lang>
knight_tour(12,12,1,1)</syntaxhighlight>
Which produces:
Which produces:
<pre>
<pre>
Line 10,654: Line 10,654:


=={{header|Rust}}==
=={{header|Rust}}==
<lang rust>use std::fmt;
<syntaxhighlight lang="rust">use std::fmt;


const SIZE: usize = 8;
const SIZE: usize = 8;
Line 10,764: Line 10,764:
None => println!("Fail!"),
None => println!("Fail!"),
}
}
}</lang>
}</syntaxhighlight>
{{out}}
{{out}}
<pre>
<pre>
Line 10,780: Line 10,780:


=={{header|Scala}}==
=={{header|Scala}}==
<syntaxhighlight lang="scala">
<lang Scala>
val b=Seq.tabulate(8,8,8,8)((x,y,z,t)=>(1L<<(x*8+y),1L<<(z*8+t),f"${97+z}%c${49+t}%c",(x-z)*(x-z)+(y-t)*(y-t)==5)).flatten.flatten.flatten.filter(_._4).groupBy(_._1)
val b=Seq.tabulate(8,8,8,8)((x,y,z,t)=>(1L<<(x*8+y),1L<<(z*8+t),f"${97+z}%c${49+t}%c",(x-z)*(x-z)+(y-t)*(y-t)==5)).flatten.flatten.flatten.filter(_._4).groupBy(_._1)
def f(p:Long,s:Long,v:Any){if(-1L!=s)b(p).foreach(x=>if((s&x._2)==0)f(x._2,s|x._2,v+x._3))else println(v)}
def f(p:Long,s:Long,v:Any){if(-1L!=s)b(p).foreach(x=>if((s&x._2)==0)f(x._2,s|x._2,v+x._3))else println(v)}
f(1,1,"a1")
f(1,1,"a1")
</syntaxhighlight>
</lang>
<pre>
<pre>
a1b3a5b7c5a4b2c4a3b1c3a2b4a6b8c6a7b5c7a8b6c8d6e4d2f1e3c2d4e2c1d3e1g2f4d5e7g8h6f5h4g6h8f7d8e6f8d7e5g4h2f3g1h3g5h7f6e8g7h5g3h1f2d1
a1b3a5b7c5a4b2c4a3b1c3a2b4a6b8c6a7b5c7a8b6c8d6e4d2f1e3c2d4e2c1d3e1g2f4d5e7g8h6f5h4g6h8f7d8e6f8d7e5g4h2f3g1h3g5h7f6e8g7h5g3h1f2d1
Line 10,790: Line 10,790:


=={{header|Scheme}}==
=={{header|Scheme}}==
<lang scheme>
<syntaxhighlight lang="scheme">
;;/usr/bin/petite
;;/usr/bin/petite
;;encoding:utf-8
;;encoding:utf-8
Line 10,837: Line 10,837:
(display (map (lambda(x) (decode x)) result)))
(display (map (lambda(x) (decode x)) result)))
(go (renew position))))
(go (renew position))))
</syntaxhighlight>
</lang>
{{out}}
{{out}}
<pre>
<pre>
Line 10,846: Line 10,846:
=={{header|SequenceL}}==
=={{header|SequenceL}}==
Knights tour using [[wp:Knight's_tour#Warnsdorff.27s_rule|Warnsdorffs rule]] (No Backtracking)
Knights tour using [[wp:Knight's_tour#Warnsdorff.27s_rule|Warnsdorffs rule]] (No Backtracking)
<syntaxhighlight lang="sequencel">
<lang sequenceL>
import <Utilities/Sequence.sl>;
import <Utilities/Sequence.sl>;
import <Utilities/Conversion.sl>;
import <Utilities/Conversion.sl>;
Line 10,897: Line 10,897:
value when x = i and y = j else
value when x = i and y = j else
board[i,j] foreach i within 1 ... size(board), j within 1 ... size(board[1]);
board[i,j] foreach i within 1 ... size(board), j within 1 ... size(board[1]);
</syntaxhighlight>
</lang>
{{out}}
{{out}}
8 X 8 board:
8 X 8 board:
Line 10,936: Line 10,936:
=={{header|Sidef}}==
=={{header|Sidef}}==
{{trans|Raku}}
{{trans|Raku}}
<lang ruby>var board = []
<syntaxhighlight lang="ruby">var board = []
var I = 8
var I = 8
var J = 8
var J = 8
Line 10,996: Line 10,996:
}
}
print "\n"
print "\n"
}</lang>
}</syntaxhighlight>


=={{header|Swift}}==
=={{header|Swift}}==
Line 11,002: Line 11,002:
{{trans|Rust}}
{{trans|Rust}}


<lang swift>public struct CPoint {
<syntaxhighlight lang="swift">public struct CPoint {
public var x: Int
public var x: Int
public var y: Int
public var y: Int
Line 11,131: Line 11,131:
}
}


b.printBoard()</lang>
b.printBoard()</syntaxhighlight>


{{out}}
{{out}}
Line 11,146: Line 11,146:


=={{header|Tcl}}==
=={{header|Tcl}}==
<lang tcl>package require Tcl 8.6; # For object support, which makes coding simpler
<syntaxhighlight lang="tcl">package require Tcl 8.6; # For object support, which makes coding simpler


oo::class create KnightsTour {
oo::class create KnightsTour {
Line 11,252: Line 11,252:
expr {$a in [my ValidMoves $b]}
expr {$a in [my ValidMoves $b]}
}
}
}</lang>
}</syntaxhighlight>
Demonstrating:
Demonstrating:
<lang tcl>set kt [KnightsTour new]
<syntaxhighlight lang="tcl">set kt [KnightsTour new]
$kt constructRandom
$kt constructRandom
$kt print
$kt print
Line 11,261: Line 11,261:
} else {
} else {
puts "This is an open tour"
puts "This is an open tour"
}</lang>
}</syntaxhighlight>
Sample output:
Sample output:
<pre>
<pre>
Line 11,273: Line 11,273:
</pre>
</pre>
The above code supports other sizes of boards and starting from nominated locations:
The above code supports other sizes of boards and starting from nominated locations:
<lang tcl>set kt [KnightsTour new 7 7]
<syntaxhighlight lang="tcl">set kt [KnightsTour new 7 7]
$kt constructFrom {0 0}
$kt constructFrom {0 0}
$kt print
$kt print
Line 11,280: Line 11,280:
} else {
} else {
puts "This is an open tour"
puts "This is an open tour"
}</lang>
}</syntaxhighlight>
Which could produce this output:
Which could produce this output:
<pre>
<pre>
Line 11,293: Line 11,293:
=={{header|Wren}}==
=={{header|Wren}}==
{{trans|Kotlin}}
{{trans|Kotlin}}
<lang ecmascript>class Square {
<syntaxhighlight lang="ecmascript">class Square {
construct new(x, y) {
construct new(x, y) {
_x = x
_x = x
Line 11,350: Line 11,350:
System.write((col == 7) ? "\n" : " ")
System.write((col == 7) ? "\n" : " ")
col = (col + 1) % 8
col = (col + 1) % 8
}</lang>
}</syntaxhighlight>


{{out}}
{{out}}
Line 11,365: Line 11,365:


=={{header|XPL0}}==
=={{header|XPL0}}==
<lang XPL0>int Board(8+2+2, 8+2+2); \board array with borders
<syntaxhighlight lang="xpl0">int Board(8+2+2, 8+2+2); \board array with borders
int LegalX, LegalY; \arrays of legal moves
int LegalX, LegalY; \arrays of legal moves
def IntSize=4; \number of bytes in an integer (4 or 2)
def IntSize=4; \number of bytes in an integer (4 or 2)
Line 11,415: Line 11,415:
]
]
else Text(0, "No Solution.^M^J");
else Text(0, "No Solution.^M^J");
]</lang>
]</syntaxhighlight>


Example output:
Example output:
Line 11,434: Line 11,434:


First we build a generic package for solving any kind of tour over the chess board. Here it is…
First we build a generic package for solving any kind of tour over the chess board. Here it is…
<lang>
<syntaxhighlight lang="text">
<xsl:package xsl:version="3.0"
<xsl:package xsl:version="3.0"
xmlns:xsl="http://www.w3.org/1999/XSL/Transform"
xmlns:xsl="http://www.w3.org/1999/XSL/Transform"
Line 11,491: Line 11,491:
</xsl:package>
</xsl:package>
</syntaxhighlight>
</lang>


And now for the style-sheet to solve the Knight’s tour…
And now for the style-sheet to solve the Knight’s tour…


<lang>
<syntaxhighlight lang="text">
<xsl:stylesheet version="3.0"
<xsl:stylesheet version="3.0"
xmlns:xsl="http://www.w3.org/1999/XSL/Transform"
xmlns:xsl="http://www.w3.org/1999/XSL/Transform"
Line 11,534: Line 11,534:
</xsl:stylesheet>
</xsl:stylesheet>
</syntaxhighlight>
</lang>


So an input like this…
So an input like this…


<lang>
<syntaxhighlight lang="text">
<tt>
<tt>
<knight>
<knight>
Line 11,544: Line 11,544:
</knight>
</knight>
</tt>
</tt>
</syntaxhighlight>
</lang>


…should be transformed in something like this…
…should be transformed in something like this…


<lang>
<syntaxhighlight lang="text">
<tt>
<tt>
<knight>
<knight>
Line 11,557: Line 11,557:
</knight>
</knight>
</tt>
</tt>
</syntaxhighlight>
</lang>


=={{header|zkl}}==
=={{header|zkl}}==
<lang zkl> // Use Warnsdorff's rule to perform a knights tour of a 8x8 board in
<syntaxhighlight lang="zkl"> // Use Warnsdorff's rule to perform a knights tour of a 8x8 board in
// linear time.
// linear time.
// See Pohl, Ira (July 1967),
// See Pohl, Ira (July 1967),
Line 11,607: Line 11,607:
fcn(ns){ vm.arglist.apply("%2s".fmt).concat(",")+"\n" });
fcn(ns){ vm.arglist.apply("%2s".fmt).concat(",")+"\n" });
}
}
}</lang>
}</syntaxhighlight>


<lang zkl>b:=Board(); b.knightsTour(3,3);
<syntaxhighlight lang="zkl">b:=Board(); b.knightsTour(3,3);
b.println();</lang>
b.println();</syntaxhighlight>
{{out}}
{{out}}
<pre>
<pre>
Line 11,623: Line 11,623:
</pre>
</pre>
Check that a solution for all squares is found:
Check that a solution for all squares is found:
<lang zkl>[[(x,y); [0..7]; [0..7];
<syntaxhighlight lang="zkl">[[(x,y); [0..7]; [0..7];
{ b:=Board(); n:=b.knightsTour(x,y); if(n!=64) b.println(">>>",x,",",y) } ]];</lang>
{ b:=Board(); n:=b.knightsTour(x,y); if(n!=64) b.println(">>>",x,",",y) } ]];</syntaxhighlight>
{{out}}Nada
{{out}}Nada