Solve a Holy Knight's tour: Difference between revisions
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{{trans|Python}}
<
[-1, -2], [1, -2], [-1, 2], [1, 2],
[-2, -1], [-2, 1], [2, -1], [2, 1]
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find_solution(‘.xxx.....x.xx....xxxxxxxxxx..x.xx.x..xxxsxxxxxx...xx.x.....xxx..’, 8)
print()
find_solution(‘.....s.x..........x.x.........xxxxx.........xxx.......x..x.x..x..xxxxx...xxxxx..xx.....xx..xxxxx...xxxxx..x..x.x..x.......xxx.........xxxxx.........x.x..........x.x.....’, 13)</
{{out}}
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This solution uses the package Knights_Tour from [[Knight's Tour#Ada]]. The board is quadratic, the size of the board is read from the command line and the board itself is read from the standard input. For the board itself, Space and Minus indicate a no-go (i.e., a coin on the board), all other characters represent places the knight must visit. A '1' represents the start point. Ill-formatted input will crash the program.
<
procedure Holy_Knight is
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Ada.Text_IO.Put_Line("Tour:");
KT.Tour_IO(KT.Warnsdorff_Get_Tour(Start_X, Start_Y, Board));
end Holy_Knight;</
{{out}}
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=={{header|ALGOL 68}}==
Uses a modified version of the [[Knight's Tour#ALGOL 68]] solution.
<
INT nne = 1, ne = 2, se = 3, sse = 4;
INT ssw = 5, sw = 6, nw = 7, nnw = 8;
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FI;
print( ( iterations, " iterations, ", backtracks, " backtracks", newline ) )
)</
{{out}}
<pre>
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This solution can handle different input formats: the widths of the first and the other columns are computed. The cell were to start from should have a unique value, but this value is not prescribed. Non-empty cells (such as the start cell) should contain a character that is different from '-', '.' or white space.
The puzzle solver itself is only a few lines long.
<
= begin colWidth crumbs non-empty pairs path parseLine
, display isolateStartCell minDistance numberElementsAndSort
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& whl'(!boards:%?board ?boards&Holy-Knight$!board)
& done
);</
Output:
<pre>
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If there are cells that require more characters, then a 2-dimensional array of ints must be used. Any number < 0 indicates a no-go.<br/>
The puzzle can be made circular (the end cell must connect to the start cell). In that case, no start cell needs to be given.
<
using System.Collections.Generic;
using static System.Console;
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}
}</
{{out}}
<pre>
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=={{header|C++}}==
<
#include <vector>
#include <sstream>
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return system( "pause" );
}
</syntaxhighlight>
{{out}}
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{{trans|C++}}
From the refactored C++ version with more precise typing, and some optimizations. The HolyKnightPuzzle struct is created at compile-time, so its pre-conditions can catch most malformed puzzles at compile-time.
<
std.typecons, std.typetuple;
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writefln("One solution:\n%(%-(%2s %)\n%)\n", solution);
}
}</
{{out}}
<pre>One solution:
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{{trans|Ruby}}
This solution uses HLPsolver from [[Solve_a_Hidato_puzzle#Elixir | here]]
<
adjacent = [{-1,-2},{-2,-1},{-2,1},{-1,2},{1,2},{2,1},{2,-1},{1,-2}]
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_ _ _ _ _ 0 _ 0
"""
|> HLPsolver.solve(adjacent)</
{{out}}
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=={{header|Go}}==
{{trans|Python}}
<
import "fmt"
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fmt.Println()
findSolution(board2, 13)
}</
{{out}}
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=={{header|Haskell}}==
<
(Array, (//), (!), assocs, elems, bounds, listArray)
import Data.Foldable (forM_)
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case solveKnightTour $ toBoard board of
Nothing -> putStrLn "No solution.\n"
Just solution -> putStrLn $ showBoard solution ++ "\n")</
{{out}}
<pre> 19 26 17
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17 15 </pre>
As requested, in an attempt to make this solution faster, the following is a version that replaces the Array with an STUArray (unboxed and mutable), and yields a speedup of 4.2. No speedups were gained until move validation was inlined with the logic in `solve'. This seems to point to the list consing as the overhead for time and allocation, although profiling did show that about 25% of the time in the immutable version was spent creating arrays. Perhaps a more experienced Haskeller could provide insight on how to further optimize this or what optimizations were frivolous (barring a different algorithm or search heuristic, and jumping into C, unless those are the only way).
<
import Control.Monad (forM_)
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case solveKnightTour $ toBoard board of
Nothing -> putStrLn "No solution.\n"
Just solution -> putStrLn $ showBoard solution ++ "\n")</
This version is similar to the previous one but:
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This results in 117x speedup over the very first version. This speed up comes from a smarter traversal rather than from minor code optimisations.
<syntaxhighlight lang="haskell">
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE LambdaCase #-}
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Just solution -> putStrLn $ showBoard solution ++ "\n")
</syntaxhighlight>
==Icon and {{header|Unicon}}==
This is a Unicon-specific solution:
<
record Pos(r,c)
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QMouse(puzzle, visit(loc.r+1,loc.c-2), self, val)
QMouse(puzzle, visit(loc.r-1,loc.c-2), self, val)
end</
Sample run:
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The simplest J implementation here uses a breadth first search - but that can be memory inefficient so it's worth representing the boards as characters (several orders of magnitude space improvement) and it's worth capping how much memory we allow J to use (2^34 is 16GB):
<
unpack=:verb define
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moves=. (#~ (0{a.)={&y) moves
moves y adverb def (':';'y x} m')"0 (x+1){a.
)</
Letting that cook:
<
48422 8 8</
That's 48422 solutions. Here's one of them:
<
__ 11 28 13 __ __ __ __
__ 22 __ 10 29 __ __ __
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1 24 3 34 5 18 7 __
__ __ 36 19 __ 33 __ __
__ __ __ 4 35 6 __ __</
and here's a couple more:
<
__ 5 8 31 __ __ __ __
__ 32 __ 6 9 __ __ __
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1 36 17 30 27 4 23 __
__ __ 2 21 __ 29 __ __
__ __ __ 28 3 22 __ __</
This is something of a problem, however, because finding all those solutions is slow. And even having to be concerned about a 16GB memory limit for this small of a problem is troubling (and using 64 bit integers, instead of 8 bit characters, to represent board squares, would exceed that limit). Also, you'd get bored, inspecting 48422 boards.
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So, let's just find one solution:
<
mask=. +./' '~:y
board=. __ 0 1 {~ {.@:>:@:"."0 mask#"1 y
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moves=. (#~ 0={&y) moves
moves y adverb def (':';'y x} m')"0 x+1
)</
Here, we break our problem space up into blocks of no more than 10 boards each, and use recursion to investigate each batch of boards. When we find a solution, we stop there (for each iteration at each level of recursion):
<
__ 11 28 13 __ __ __ __
__ 22 __ 10 29 __ __ __
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1 24 3 34 5 18 7 __
__ __ 36 19 __ 33 __ __
__ __ __ 4 35 6 __ __</
[Why ten boards and not just one board? Because 10 is a nice compromise between amortizing the overhead of each attempt and not trying too much at one time. Most individual attempts will fail, but by splitting up the workload after exceeding 10 possibilities, instead of investigating each possibility individually, we increase the chances that we are investigating something useful. Also, J implementations penalize the performance of algorithms which are overly serial in structure.]
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With this tool in hand, we can now attempt bigger problems:
<
1 0
0 0
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0 0
0 0
)</
Finding a solution for this looks like:
<
__ __ __ __ __ 1 __ 5 __ __ __ __ __
__ __ __ __ __ 6 __ 46 __ __ __ __ __
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__ __ __ __ 24 21 26 17 28 __ __ __ __
__ __ __ __ __ 18 __ 20 __ __ __ __ __
__ __ __ __ __ 25 __ 27 __ __ __ __ __</
=={{header|Java}}==
{{works with|Java|8}}
<
public class HolyKnightsTour {
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}
}
}</
<pre> 19 26 21
28 18 25
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===ES6===
By composition of generic functions, cacheing degree-sorted moves for each node.
<
'use strict';
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// TEST -------------------------------------------------------------------
return unlines(map(solutionString, problems));
})();</
{{Out}}
(Executed in Atom editor, using 'Script' package).
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=={{header|Julia}}==
Uses the Hidato puzzle solver module, which has its source code listed [[Solve_a_Hidato_puzzle#Julia | here]] in the Hadato task.
<
const holyknight = """
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hidatosolve(board, maxmoves, knightmoves, fixed, starts[1][1], starts[1][2], 1)
printboard(board)
</
0 0 0
0 0 0
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=={{header|Kotlin}}==
{{trans|Python}}
<
val moves = arrayOf(
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println()
findSolution(board2, 13)
}</
{{out}}
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=={{header|Lua}}==
<
local p1, p1W = ".xxx.....x.xx....xxxxxxxxxx..x.xx.x..xxxsxxxxxx...xx.x.....xxx..", 8
local p2, p2W = ".....s.x..........x.x.........xxxxx.........xxx.......x..x.x..x..xxxxx...xxxxx..xx.....xx..xxxxx...xxxxx..x..x.x..x.......xxx.........xxxxx.........x.x..........x.x.....", 13
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print( "\n\n" ); fill( p2, p2W );
if solve( sx, sy, 2 ) then printSolution() end
</syntaxhighlight>
{{out}}
<pre>
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=={{header|Mathematica}}/{{header|Wolfram Language}}==
Outputs coordinates and a visualization of the tour:
<
0 0 0
0 0 0 0 0 0 0
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e = VertexList[g];
order = FindShortestTour[g][[2]]
Graphics[{Red, Disk[#, 0.2] & /@ e, Black, BlockMap[Arrow, e[[order]], 2, 1]}]</
{{out}}
<pre>{{6,1},{4,2},{6,3},{8,4},{7,6},{6,4},{5,6},{3,5},{1,4},{2,2},{4,3},{5,1},{3,2},{2,4},{1,2},{3,3},{4,1},{6,2},{7,4},{8,6},{6,7},{4,8},{3,6},{5,7},{3,8},{4,6},{6,5},{5,3},{3,4},{1,3},{2,5},{3,7},{5,8},{6,6},{8,5},{7,3},{6,1}}
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In this version, the board is described as an array of strings rather than a string in the Go version (so, we don’t have to specify the size). The way to initialize is also different and even if the Moves where in the same order, the solution would be different. Changing the order of the Moves may have a great impact on performance, but there is no best order. The order we have chosen provides excellent performance with the two examples: less than 20 ms on our laptop. But with another order, it took more than 2 seconds!
<
const Moves = [[-1, -2], [1, -2], [-2, -1], [2, -1], [-2, 1], [2, 1], [-1, 2], [1, 2]]
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Board1.findSolution()
echo()
Board2.findSolution()</
{{out}}
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=={{header|Perl}}==
We perform a brute-force search. As an enhancement, we unroll the search by one level and use Parallel::ForkManager to search the top-level sub-trees concurrently, subject to the number of cores of course. We implement the search with explicit recursion, which impacts performance but improves readability and provides a use case for the "local" keyword.
<
# A sequence of locations on a 2-D board whose order might or might not
# matter. Suitable for representing a partial tour, a complete tour, or the
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$kt->find_tour();
return;
}</
{{out}}
The timings shown below were obtained on a Dell Optiplex 9020 with 4 cores.
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=={{header|Phix}}==
Tweaked the knights tour algorithm (to use a limit variable rather than size*size). Bit slow on the second one... (hence omitted under pwa/p2js)
<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">board</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">warnsdorffs</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">size</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">limit</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">nchars</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">fmt</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">blank</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">ROW</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">COL</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">moves</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{{-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">2</span><span style="color: #0000FF;">},{-</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">},{-</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">},{-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">2</span><span style="color: #0000FF;">}}</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">onboard</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">row</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">col</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">row</span><span style="color: #0000FF;">>=</span><span style="color: #000000;">1</span> <span style="color: #008080;">and</span> <span style="color: #000000;">row</span><span style="color: #0000FF;"><=</span><span style="color: #000000;">size</span> <span style="color: #008080;">and</span> <span style="color: #000000;">col</span><span style="color: #0000FF;">>=</span><span style="color: #000000;">nchars</span> <span style="color: #008080;">and</span> <span style="color: #000000;">col</span><span style="color: #0000FF;"><=</span><span style="color: #000000;">nchars</span><span style="color: #0000FF;">*</span><span style="color: #000000;">size</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">procedure</span> <span style="color: #000000;">init_warnsdorffs</span><span style="color: #0000FF;">()</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">row</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">size</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">col</span><span style="color: #0000FF;">=</span><span style="color: #000000;">nchars</span> <span style="color: #008080;">to</span> <span style="color: #000000;">nchars</span><span style="color: #0000FF;">*</span><span style="color: #000000;">size</span> <span style="color: #008080;">by</span> <span style="color: #000000;">nchars</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">move</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">moves</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">nrow</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">row</span><span style="color: #0000FF;">+</span><span style="color: #000000;">moves</span><span style="color: #0000FF;">[</span><span style="color: #000000;">move</span><span style="color: #0000FF;">][</span><span style="color: #000000;">ROW</span><span style="color: #0000FF;">],</span>
<span style="color: #000000;">ncol</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">col</span><span style="color: #0000FF;">+</span><span style="color: #000000;">moves</span><span style="color: #0000FF;">[</span><span style="color: #000000;">move</span><span style="color: #0000FF;">][</span><span style="color: #000000;">COL</span><span style="color: #0000FF;">]*</span><span style="color: #000000;">nchars</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">onboard</span><span style="color: #0000FF;">(</span><span style="color: #000000;">nrow</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ncol</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">warnsdorffs</span><span style="color: #0000FF;">[</span><span style="color: #000000;">nrow</span><span style="color: #0000FF;">][</span><span style="color: #000000;">ncol</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
<span style="color:
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">t0</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">(),</span>
<span style="color: #000000;">t1</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()+</span><span style="color: #000000;">1</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">tries</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">backtracks</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">solve</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">row</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">col</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()></span><span style="color: #000000;">t1</span> <span style="color: #008080;">and</span> <span style="color: #7060A8;">platform</span><span style="color: #0000FF;">()!=</span><span style="color: #004600;">JS</span> <span style="color: #008080;">then</span>
<span style="color: #0000FF;">?{</span><span style="color: #000000;">row</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">col</span><span style="color: #0000FF;">/</span><span style="color: #000000;">nchars</span><span style="color: #0000FF;">),</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">tries</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: #7060A8;">join</span><span style="color: #0000FF;">(</span><span style="color: #000000;">board</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\n"</span><span style="color: #0000FF;">)&</span><span style="color: #008000;">"\n"</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">t1</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()+</span><span style="color: #000000;">1</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">tries</span><span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">></span><span style="color: #000000;">limit</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #000000;">1</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">wmoves</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">nrow</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">ncol</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">move</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">moves</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">nrow</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">row</span><span style="color: #0000FF;">+</span><span style="color: #000000;">moves</span><span style="color: #0000FF;">[</span><span style="color: #000000;">move</span><span style="color: #0000FF;">][</span><span style="color: #000000;">ROW</span><span style="color: #0000FF;">]</span>
<span style="color: #000000;">ncol</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">col</span><span style="color: #0000FF;">+</span><span style="color: #000000;">moves</span><span style="color: #0000FF;">[</span><span style="color: #000000;">move</span><span style="color: #0000FF;">][</span><span style="color: #000000;">COL</span><span style="color: #0000FF;">]*</span><span style="color: #000000;">nchars</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">onboard</span><span style="color: #0000FF;">(</span><span style="color: #000000;">nrow</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ncol</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">and</span> <span style="color: #000000;">board</span><span style="color: #0000FF;">[</span><span style="color: #000000;">nrow</span><span style="color: #0000FF;">][</span><span style="color: #000000;">ncol</span><span style="color: #0000FF;">]=</span><span style="color: #008000;">' '</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">wmoves</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">wmoves</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">warnsdorffs</span><span style="color: #0000FF;">[</span><span style="color: #000000;">nrow</span><span style="color: #0000FF;">][</span><span style="color: #000000;">ncol</span><span style="color: #0000FF;">],</span><span style="color: #000000;">nrow</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ncol</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;">for</span>
<span style="color: #000000;">wmoves</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sort</span><span style="color: #0000FF;">(</span><span style="color: #000000;">wmoves</span><span style="color: #0000FF;">)</span>
<span style="color: #000080;font-style:italic;">-- avoid creating orphans</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">wmoves</span><span style="color: #0000FF;">)<</span><span style="color: #000000;">2</span> <span style="color: #008080;">or</span> <span style="color: #000000;">wmoves</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">][</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]></span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">m</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">wmoves</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #0000FF;">{?,</span><span style="color: #000000;">nrow</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ncol</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">wmoves</span><span style="color: #0000FF;">[</span><span style="color: #000000;">m</span><span style="color: #0000FF;">]</span>
<span style="color: #000000;">warnsdorffs</span><span style="color: #0000FF;">[</span><span style="color: #000000;">nrow</span><span style="color: #0000FF;">][</span><span style="color: #000000;">ncol</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">-=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">m</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">wmoves</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #0000FF;">{?,</span><span style="color: #000000;">nrow</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ncol</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">wmoves</span><span style="color: #0000FF;">[</span><span style="color: #000000;">m</span><span style="color: #0000FF;">]</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">scol</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ncol</span><span style="color: #0000FF;">-</span><span style="color: #000000;">nchars</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span>
<span style="color: #000000;">board</span><span style="color: #0000FF;">[</span><span style="color: #000000;">nrow</span><span style="color: #0000FF;">][</span><span style="color: #000000;">scol</span><span style="color: #0000FF;">..</span><span style="color: #000000;">ncol</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">fmt</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">solve</span><span style="color: #0000FF;">(</span><span style="color: #000000;">nrow</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ncol</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #000000;">1</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">backtracks</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
<span style="color: #000000;">board</span><span style="color: #0000FF;">[</span><span style="color: #000000;">nrow</span><span style="color: #0000FF;">][</span><span style="color: #000000;">scol</span><span style="color: #0000FF;">..</span><span style="color: #000000;">ncol</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">blank</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">m</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">wmoves</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #0000FF;">{?,</span><span style="color: #000000;">nrow</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ncol</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">wmoves</span><span style="color: #0000FF;">[</span><span style="color: #000000;">m</span><span style="color: #0000FF;">]</span>
<span style="color: #000000;">warnsdorffs</span><span style="color: #0000FF;">[</span><span style="color: #000000;">nrow</span><span style="color: #0000FF;">][</span><span style="color: #000000;">ncol</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">0</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">procedure</span> <span style="color: #000000;">holyknight</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">split</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span><span style="color: #008000;">'\n'</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">size</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">nchars</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">" %d"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">size</span><span style="color: #0000FF;">*</span><span style="color: #000000;">size</span><span style="color: #0000FF;">))</span>
<span style="color: #000000;">fmt</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">" %%%dd"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">nchars</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">blank</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #008000;">' '</span><span style="color: #0000FF;">,</span><span style="color: #000000;">nchars</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">board</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #008000;">' '</span><span style="color: #0000FF;">,</span><span style="color: #000000;">size</span><span style="color: #0000FF;">*</span><span style="color: #000000;">nchars</span><span style="color: #0000FF;">),</span><span style="color: #000000;">size</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">limit</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">sx</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">sy</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">size</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">y</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">nchars</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">size</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">ch</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">j</span><span style="color: #0000FF;">></span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">x</span><span style="color: #0000FF;">])?</span><span style="color: #008000;">'-'</span><span style="color: #0000FF;">:</span><span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">x</span><span style="color: #0000FF;">][</span><span style="color: #000000;">j</span><span style="color: #0000FF;">])</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">ch</span><span style="color: #0000FF;">=</span><span style="color: #008000;">' '</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">ch</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">'-'</span>
<span style="color: #008080;">elsif</span> <span style="color: #000000;">ch</span><span style="color: #0000FF;">=</span><span style="color: #008000;">'0'</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">ch</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">' '</span>
<span style="color: #000000;">limit</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">elsif</span> <span style="color: #000000;">ch</span><span style="color: #0000FF;">=</span><span style="color: #008000;">'1'</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">sx</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">x</span>
<span style="color: #000000;">sy</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">y</span>
<span style="color: #008080;">end</span>
<span style="color: #000000;">board</span><span style="color: #0000FF;">[</span><span style="color: #000000;">x</span><span style="color: #0000FF;">][</span><span style="color: #000000;">y</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ch</span>
<span style="color: #000000;">y</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">nchars</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000000;">warnsdorffs</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">size</span><span style="color: #0000FF;">*</span><span style="color: #000000;">nchars</span><span style="color: #0000FF;">),</span><span style="color: #000000;">size</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">init_warnsdorffs</span><span style="color: #0000FF;">()</span>
<span style="color: #000000;">t0</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()</span>
<span style="color: #000000;">tries</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #000000;">backtracks</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #000000;">t1</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()+</span><span style="color: #000000;">1</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">solve</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sx</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sy</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</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: #7060A8;">join</span><span style="color: #0000FF;">(</span><span style="color: #000000;">board</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\n"</span><span style="color: #0000FF;">))</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\nsolution found in %d tries, %d backtracks (%3.2fs)\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">tries</span><span style="color: #0000FF;">,</span><span style="color: #000000;">backtracks</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">time</span><span style="color: #0000FF;">()-</span><span style="color: #000000;">t0</span><span style="color: #0000FF;">})</span>
<span style="color: #008080;">else</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;">procedure</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">board1</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">"""
000
0
0000000
000 0 0
0 0 000
1000000
000"""</span>
<span style="color: #000000;">holyknight</span><span style="color: #0000FF;">(</span><span style="color: #000000;">board1</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">board2</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">"""
-----1-0-----
-----0-0-----
----00000----
-----000-----
--0--0-0--0--
00000---00000
--00--
--0--0-
--
--
-----0-0-----"""</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">platform</span><span style="color: #0000FF;">()!=</span><span style="color: #004600;">JS</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">holyknight</span><span style="color: #0000FF;">(</span><span style="color: #000000;">board2</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #0000FF;">{}</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">wait_key</span><span style="color: #0000FF;">()</span>
<!--</syntaxhighlight>-->
{{out}}
<pre>
Line 3,597 ⟶ 3,595:
- - - - - 27 - 29 - - - - -
solution found in 61341542 tries, 61341486 backtracks (180.56s)
</pre>
=={{header|Picat}}==
<syntaxhighlight lang="picat">import sat.
main =>
S = {".000....",
".0.00...",
".0000000",
"000..0.0",
"0.0..000",
"1000000.",
"..00.0..",
"...000.."},
MaxR = len(S),
MaxC = len(S[1]),
M = new_array(MaxR,MaxC),
StartR = _, % make StartR and StartC global
StartC = _,
foreach (R in 1..MaxR)
fill_row(R, S[R], M[R], 1, StartR, StartC)
end,
NZeros = len([1 : R in 1..MaxR, C in 1..MaxC, M[R,C] == 0]),
M :: 0..MaxR*MaxC-NZeros,
Vs = [{(R,C),1} : R in 1..MaxR, C in 1..MaxC, M[R,C] !== 0],
Es = [{(R,C),(R1,C1),_} : R in 1..MaxR, C in 1..MaxC, M[R,C] !== 0,
neibs(M,MaxR,MaxC,R,C,Neibs),
(R1,C1) in Neibs, M[R1,C1] !== 0],
hcp(Vs,Es),
foreach ({(R,C),(R1,C1),B} in Es)
B #/\ (R1 #!= StartR #\/ C1 #!= StartC) #=> M[R1,C1] #= M[R,C]+1
end,
solve(M),
foreach (R in 1..MaxR)
foreach (C in 1..MaxC)
if M[R,C] == 0 then
printf("%4c", '.')
else
printf("%4d", M[R,C])
end
end,
nl
end.
neibs(M,MaxR,MaxC,R,C,Neibs) =>
Connected = [(R+1, C+2),
(R+1, C-2),
(R-1, C+2),
(R-1, C-2),
(R+2, C+1),
(R+2, C-1),
(R-2, C+1),
(R-2, C-1)],
Neibs = [(R1,C1) : (R1,C1) in Connected,
R1 >= 1, R1 =< MaxR, C1 >= 1, C1 =< MaxC,
M[R1,C1] !== 0].
fill_row(_R, [], _Row, _C, _StartR, _StartC) => true.
fill_row(R, ['.'|Str], Row, C, StartR, StartC) =>
Row[C] = 0,
fill_row(R,Str, Row, C+1, StartR, StartC).
fill_row(R, ['0'|Str], Row, C, StartR, StartC) =>
fill_row(R, Str, Row, C+1, StartR, StartC).
fill_row(R, ['1'|Str], Row, C, StartR, StartC) =>
Row[C] = 1,
StartR = R,
StartC = C,
fill_row(R, Str, Row, C+1, StartR, StartC).
</syntaxhighlight>
{{out}}
<pre>
. 7 4 25 . . . .
. 26 . 8 5 . . .
. 29 6 3 24 9 18 11
27 2 23 . . 12 . 16
30 . 28 . . 17 10 19
1 22 31 34 13 20 15 .
. . 36 21 . 33 . .
. . . 32 35 14 . .
</pre>
=={{header|Python}}==
<
from sys import stdout
moves = [
Line 3,655 ⟶ 3,733:
print()
find_solution(".....s.x..........x.x.........xxxxx.........xxx.......x..x.x..x..xxxxx...xxxxx..xx.....xx..xxxxx...xxxxx..x..x.x..x.......xxx.........xxxxx.........x.x..........x.x.....", 13)
</syntaxhighlight>
{{out}}<pre>
17 14 29
Line 3,689 ⟶ 3,767:
It solves the tasked problem, as well as the "extra credit" from [[#Ada]].
<
(require "hidato-family-solver.rkt")
Line 3,726 ⟶ 3,804:
#(- - - - 0 0 0 0 0 - - - -)
#(- - - - - 0 - 0 - - - - -)
#(- - - - - 0 - 0 - - - - -)))))</
{{out}}
Line 3,763 ⟶ 3,841:
* [[Solve the no connection puzzle#Raku|Solve the no connection puzzle]]
<syntaxhighlight lang="raku"
[ -2, -1], [ -2, 1],
[-1,-2], [-1,+2],
Line 3,864 ⟶ 3,942:
say "$tries tries";
}</
{{out}}
Line 3,883 ⟶ 3,961:
This is an ''open tour'' solution. (See this task's ''discussion'' page for an explanation [in the first section]).
<
blank=pos('//', space(arg(1), 0))\==0 /*see if the pennies are to be shown. */
parse arg ops '/' cent /*obtain the options and the pennies. */
Line 3,946 ⟶ 4,024:
end /*try a different move. */
end /*t*/ /* [↑] all moves tried.*/
return 0 /*tour isn't possible. */</
'''output''' when the following is used for input:
<br><tt> , 3 1 /1,1 3 /1,7 2 /2,1 2 /2,5 /2,7 2 /3,8 /4,2 /4,4 2 /5,4 2 /5,7 /6,1 /7,1 /7,3 /7,6 3 /8,1 /8,5 4 </tt>
Line 3,998 ⟶ 4,076:
=={{header|Ruby}}==
This solution uses HLPsolver from [[Solve_a_Hidato_puzzle#With_Warnsdorff | here]]
<
ADJACENT = [[-1,-2],[-2,-1],[-2,1],[-1,2],[1,2],[2,1],[2,-1],[1,-2]]
Line 4,014 ⟶ 4,092:
t0 = Time.now
HLPsolver.new(boardy).solve
puts " #{Time.now - t0} sec"</
Which produces:
Line 4,044 ⟶ 4,122:
=={{header|Tcl}}==
{{works with|Tcl|8.6}}
<
oo::class create HKTSolver {
Line 4,141 ⟶ 4,219:
HKTSolver create hkt $puzzle
hkt solve
showPuzzle [hkt solution] "Output"</
{{out}}
<pre>
Line 4,167 ⟶ 4,245:
{{trans|Kotlin}}
{{libheader|Wren-fmt}}
<
var moves = [ [-1, -2], [1, -2], [-1, 2], [1, 2], [-2, -1], [-2, 1], [2, -1], [2, 1] ]
Line 4,251 ⟶ 4,329:
findSolution.call(board1, 8)
System.print()
findSolution.call(board2, 13)</
{{out}}
|