# Solve a Hidato puzzle

(Redirected from Hidato)
Solve a Hidato puzzle
You are encouraged to solve this task according to the task description, using any language you may know.

The task is to write a program which solves Hidato (aka Hidoku) puzzles.

The rules are:

• You are given a grid with some numbers placed in it. The other squares in the grid will be blank.
• The grid is not necessarily rectangular.
• The grid may have holes in it.
• The grid is always connected.
• The number “1” is always present, as is another number that is equal to the number of squares in the grid. Other numbers are present so as to force the solution to be unique.
• It may be assumed that the difference between numbers present on the grid is not greater than lucky 13.
• The aim is to place a natural number in each blank square so that in the sequence of numbered squares from “1” upwards, each square is in the wp:Moore neighborhood of the squares immediately before and after it in the sequence (except for the first and last squares, of course, which only have one-sided constraints).
• Thus, if the grid was overlaid on a chessboard, a king would be able to make legal moves along the path from first to last square in numerical order.
• A square may only contain one number.
• In a proper Hidato puzzle, the solution is unique.

For example the following problem

has the following solution, with path marked on it:

## AutoHotkey

`SolveHidato(Grid, Locked, Max, row, col, num:=1, R:="", C:=""){	if (R&&C)							; if neighbors (not first iteration)	{		Grid[R, C] := ">" num 					; place num in current neighbor and mark it visited ">"		row:=R, col:=C						; move to current neighbor	} 	num++								; increment num	if (num=max)							; if reached end		return map(Grid)					; return solution 	if locked[num]							; if current num is a locked value	{		row := StrSplit((StrSplit(locked[num], ",").1) , ":").1	; find row of num		col := StrSplit((StrSplit(locked[num], ",").1) , ":").2	; find col of num		if SolveHidato(Grid, Locked, Max, row, col, num)	; solve for current location and value			return map(Grid)				; if solved, return solution	}	else	{		for each, value in StrSplit(Neighbor(row,col), ",")		{			R := StrSplit(value, ":").1			C := StrSplit(value, ":").2 			if (Grid[R,C] = "")				; a hole or out of bounds			|| InStr(Grid[R, C], ">")			; visited			|| Locked[num+1] && !(Locked[num+1]~= "\b" R ":" C "\b") ; not neighbor of locked[num+1]			|| Locked[num-1] && !(Locked[num-1]~= "\b" R ":" C "\b") ; not neighbor of locked[num-1]			|| Locked[num]					; locked value			|| Locked[Grid[R, C]]				; locked cell				continue 			if SolveHidato(Grid, Locked, Max, row, col, num, R, C)	; solve for current location, neighbor and value				return map(Grid)			; if solved, return solution		}	}	num--								; step back	for i, line in Grid		for j, element in line			if InStr(element, ">") && (StrReplace(element, ">") >= num)				Grid[i, j] := "Y"};--------------------------------;--------------------------------;--------------------------------Neighbor(row,col){	R := row-1	loop, 9	{		DeltaC := Mod(A_Index, 3) ? Mod(A_Index, 3)-2	: 1		res .= (R=row && !DeltaC) ? "" : R ":" col+DeltaC ","		R := Mod(A_Index, 3) ? R : R+1	}	return Trim(res, ",")};--------------------------------map(Grid){	for i, row in Grid	{		for j, element in row			line .= (A_Index > 1 ? "`t" : "") . element 		map .= (map<>""?"`n":"") line		line := ""	}	return StrReplace(map, ">")}`
Examples:
`;--------------------------------Grid := [[ "Y"	, 33	, 35	, "Y"	, "Y"]	,[ "Y"	, "Y"	, 24	, 22	, "Y"]	,[ "Y"	, "Y"	, "Y"	, 21	, "Y"	, "Y"]	,[ "Y"	, 26	, "Y"	, 13	, 40	, 11 ]	,[ 27	, "Y"	, "Y"	, "Y"	, 9	, "Y"	, 1  ]	,[ ""	, ""	, "Y"	, "Y"	, 18	, "Y"	, "Y"]	,[ ""	, ""	, ""	, ""	, "Y"	, 7	, "Y"	, "Y"]	,[ ""	, ""	, ""	, ""	, ""	, ""	, 5	, "Y"]] ;--------------------------------; find locked cells, find row and col of first value "1" and max value Locked := []for i, line in Grid	for j, element in line	{		if element = 1			row :=i , col := j		if element is integer			Locked[element] := i ":" j "," Neighbor(i, j)	; save locked elements position and neighbors			, max := element > max ? element : max		; find max value	};--------------------------------MsgBox, 262144, ,% SolveHidato(Grid, Locked, Max, row, col)return`
Outputs:
```32	33	35	36	37
31	34	24	22	38
30	25	23	21	12	39
29	26	20	13	40	11
27	28	14	19	9	10	1
15	16	18	8	2
17	7	6	3
5	4
```

## Bracmat

`(  ( hidato  =     Line solve lowest Ncells row column rpad      , Board colWidth maxDigits start curCol curRow      , range head line cellN solution output tail    .   out\$!arg      & @(!arg:? ((%@:>" ") ?:?arg))      & 0:?row:?column      & :?Board      & ( Line        =   token          .   whl            ' ( @(!arg:?token [3 ?arg)              & (   (   @(!token:? "_" ?)                      & :?token                    | @(!token:? #?token (|" " ?))                    )                  & (!token.!row.!column) !Board:?Board                |                 )              & 1+!column:?column              )        )      &   whl        ' ( @(!arg:?line \n ?arg)          & Line\$!line          & 1+!row:?row          & 0:?column          )      & Line\$!arg      & ( range        =   hi lo          .   (!arg+1:?hi)+-2:?lo            & '(\$lo|\$arg|\$hi)        )      & ( solve        =     ToDo cellN row column head tail remainder            , candCell Solved rowCand colCand pattern recurse          .   !arg:(?ToDo.?cellN.?row.?column)            & range\$!row:(=?row)            & range\$!column:(=?column)            &                     ' (     ?head (\$cellN.?rowCand.?colCand) ?tail                      & (!rowCand.!colCand):(\$row.\$column)                      & !recurse                    |   ?head                        (.(\$row.\$column):(?rowCand.?colCand))                        (?tail&!recurse)                  .     ((!rowCand.!colCand).\$cellN)                      : ?candCell                    &   (   !head !tail:                          & out\$found!                          & !candCell                        |       solve                              \$ ( !head !tail                                . \$cellN+1                                . !rowCand                                . !colCand                                )                            : ?remainder                          & !candCell+!remainder                        )                      : ?Solved                  )              : (=?pattern.?recurse)            & !ToDo:!pattern            & !Solved        )      & infinity:?lowest      & (   !Board          : ? (<!lowest:#%?lowest.?start) (?&~)        | solve\$(!Board.!lowest.!start):?solution        )      & :?output      & 0:?curCol      & !solution:((?curRow.?).?)+?+[?Ncells      & @(!Ncells:? [?maxDigits)      & 1+!maxDigits:?colWidth      & ( rpad        =   len          .   !arg:(?arg.?len)            & @(str\$(!arg "    "):?arg [!len ?)            & !arg        )      &   whl        ' ( !solution:((?row.?column).?cellN)+?solution          & (   !row:>!curRow:?curRow              & !output \n:?output              & 0:?curCol            |             )          &   whl            ' ( !curCol+1:~>!column:?curCol              & !output rpad\$(.!colWidth):?output              )          &   !output rev\$(rpad\$(rev\$(str\$(!cellN " ")).!colWidth))            : ?output          & !curCol+1:?curCol          )      & str\$!output  )&   " __ 33 35 __ __          __ __ 24 22 __          __ __ __ 21 __ __       __ 26 __ 13 40 11       27 __ __ __  9 __  1          __ __ 18 __ __                __  7 __ __                    5 __"  : ?board& out\$(hidato\$!board));`

Output:

``` __ 33 35 __ __
__ __ 24 22 __
__ __ __ 21 __ __
__ 26 __ 13 40 11
27 __ __ __  9 __  1
__ __ 18 __ __
__  7 __ __
5 __
found!
32 33 35 36 37
31 34 24 22 38
30 25 23 21 12 39
29 26 20 13 40 11
27 28 14 19  9 10  1
15 16 18  8  2
17  7  6  3
5  4```

## C

Depth-first graph, with simple connectivity check to reject some impossible situations early. The checks slow down simpler puzzles significantly, but can make some deep recursions backtrack much earilier.

`#include <stdio.h>#include <stdlib.h>#include <string.h>#include <ctype.h> int *board, *flood, *known, top = 0, w, h; static inline int idx(int y, int x) { return y * w + x; } int neighbors(int c, int *p)/*@c cell@p list of neighbours@return amount of neighbours*/{	int i, j, n = 0;	int y = c / w, x = c % w; 	for (i = y - 1; i <= y + 1; i++) {		if (i < 0 || i >= h) continue;		for (j = x - 1; j <= x + 1; j++)			if (!(j < 0 || j >= w				|| (j == x && i == y)				|| board[ p[n] = idx(i,j) ] == -1))				n++;	} 	return n;} void flood_fill(int c)/*fill all free cells around @c with “1” and write output to variable “flood”@c cell*/{	int i, n[8], nei; 	nei = neighbors(c, n);	for (i = 0; i < nei; i++) { // for all neighbours		if (board[n[i]] || flood[n[i]]) continue; // if cell is not free, choose another neighbour 		flood[n[i]] = 1;		flood_fill(n[i]);	}} /* Check all empty cells are reachable from higher known cells.   Should really do more checks to make sure cell_x and cell_x+1   share enough reachable empty cells; I'm lazy. Will implement   if a good counter example is presented. */int check_connectity(int lowerbound){	int c;	memset(flood, 0, sizeof(flood[0]) * w * h);	for (c = lowerbound + 1; c <= top; c++)		if (known[c]) flood_fill(known[c]); // mark all free cells around known cells 	for (c = 0; c < w * h; c++)		if (!board[c] && !flood[c]) // if there are free cells which could not be reached from flood_fill			return 0; 	return 1;} void make_board(int x, int y, const char *s){	int i; 	w = x, h = y;        top = 0;	x = w * h;         known = calloc(x + 1, sizeof(int));        board = calloc(x,     sizeof(int));        flood = calloc(x,     sizeof(int)); 	while (x--) board[x] = -1; 	for (y = 0; y < h; y++)	for (x = 0; x < w; x++) {		i = idx(y, x); 		while (isspace(*s)) s++; 		switch (*s) {		case '_':	board[i] = 0;		case '.':	break;		default:			known[ board[i] = strtol(s, 0, 10) ] = i;			if (board[i] > top) top = board[i];		} 		while (*s && !isspace(*s)) s++;	}} void show_board(const char *s){	int i, j, c; 	printf("\n%s:\n", s); 	for (i = 0; i < h; i++, putchar('\n'))	for (j = 0; j < w; j++) {		c = board[ idx(i, j) ];		printf(!c ? " __" : c == -1 ? "   " : " %2d", c);	}} int fill(int c, int n){	int i, nei, p[8], ko, bo; 	if ((board[c] && board[c] != n) || (known[n] && known[n] != c))		return 0; 	if (n == top) return 1; 	ko = known[n];	bo = board[c];	board[c] = n; 	if (check_connectity(n)) {		nei = neighbors(c, p);		for (i = 0; i < nei; i++)			if (fill(p[i], n + 1))				return 1;	} 	board[c] = bo;	known[n] = ko;	return 0;} int main(){	make_board(#define USE_E 0#if (USE_E == 0)		8,8,	" __ 33 35 __ __ .. .. .."			" __ __ 24 22 __ .. .. .."			" __ __ __ 21 __ __ .. .."			" __ 26 __ 13 40 11 .. .."			" 27 __ __ __  9 __  1 .."			" .   . __ __ 18 __ __ .."			" .  ..  .  . __  7 __ __"			" .  .. .. ..  .  .  5 __"#elif (USE_E == 1)	3, 3,	" . 4 ."		" _ 7 _"		" 1 _ _"#else	50, 3,	" 1 _ _ . . _ _ . . _ _ . . _ _ . . _ _ . . _ _ . . _ _ . . _ _ . . _ _ . . _ _ . . _ _ . . _ _ . . 74"	" . . _ . _ . _ . _ . _ . _ . _ . _ . _ . _ . _ . _ . _ . _ . _ . _ . _ . _ . _ . _ . _ . _ . _ . _ ."	" . . . _ _ . . _ _ . . _ _ . . _ _ . . _ _ . . _ _ . . _ _ . . _ _ . . _ _ . . _ _ . . _ _ . . _ _ ."#endif	); 	show_board("Before");	fill(known[1], 1);	show_board("After"); /* "40 lbs in two weeks!" */ 	return 0;}`
Output:
``` Before:
__ 33 35 __ __
__ __ 24 22 __
__ __ __ 21 __ __
__ 26 __ 13 40 11
27 __ __ __  9 __  1
__ __ 18 __ __
__  7 __ __
5 __

After:
32 33 35 36 37
31 34 24 22 38
30 25 23 21 12 39
29 26 20 13 40 11
27 28 14 19  9 10  1
15 16 18  8  2
17  7  6  3
5  4```

## C++

` #include <iostream>#include <sstream>#include <iterator>#include <vector> //------------------------------------------------------------------------------using namespace std; //------------------------------------------------------------------------------struct node{    int val;    unsigned char neighbors;};//------------------------------------------------------------------------------class hSolver{public:    hSolver()    {	dx[0] = -1; dx[1] = 0; dx[2] = 1; dx[3] = -1; dx[4] = 1; dx[5] = -1; dx[6] = 0; dx[7] = 1;	dy[0] = -1; dy[1] = -1; dy[2] = -1; dy[3] = 0; dy[4] = 0; dy[5] = 1; dy[6] = 1; dy[7] = 1;    }     void solve( vector<string>& puzz, int max_wid )    {	if( puzz.size() < 1 ) return;	wid = max_wid; hei = static_cast<int>( puzz.size() ) / wid;	int len = wid * hei, c = 0; max = 0;	arr = new node[len]; memset( arr, 0, len * sizeof( node ) );	weHave = new bool[len + 1]; memset( weHave, 0, len + 1 ); 	for( vector<string>::iterator i = puzz.begin(); i != puzz.end(); i++ )	{	    if( ( *i ) == "*" ) {    arr[c++].val = -1; continue; }	    arr[c].val = atoi( ( *i ).c_str() );	    if( arr[c].val > 0 ) weHave[arr[c].val] = true;	    if( max < arr[c].val ) max = arr[c].val;	    c++;	} 	solveIt(); c = 0;	for( vector<string>::iterator i = puzz.begin(); i != puzz.end(); i++ )	{	    if( ( *i ) == "." )	    {		ostringstream o; o << arr[c].val;		( *i ) = o.str();	    }	    c++;	}	delete [] arr;	delete [] weHave;    } private:    bool search( int x, int y, int w )    {	if( w == max ) return true; 	node* n = &arr[x + y * wid];	n->neighbors = getNeighbors( x, y );	if( weHave[w] )	{	    for( int d = 0; d < 8; d++ )	    {		if( n->neighbors & ( 1 << d ) )		{		    int a = x + dx[d], b = y + dy[d];		    if( arr[a + b * wid].val == w )		    if( search( a, b, w + 1 ) ) return true;		}	    }	    return false;	} 	for( int d = 0; d < 8; d++ )	{	    if( n->neighbors & ( 1 << d ) )	    {		int a = x + dx[d], b = y + dy[d];		if( arr[a + b * wid].val == 0 )		{		    arr[a + b * wid].val = w;		    if( search( a, b, w + 1 ) ) return true;		    arr[a + b * wid].val = 0;		}	    }	}	return false;    }     unsigned char getNeighbors( int x, int y )    {	unsigned char c = 0; int m = -1, a, b;	for( int yy = -1; yy < 2; yy++ )	    for( int xx = -1; xx < 2; xx++ )	    {		if( !yy && !xx ) continue;		m++; a = x + xx, b = y + yy;		if( a < 0 || b < 0 || a >= wid || b >= hei ) continue;		if( arr[a + b * wid].val > -1 ) c |= ( 1 << m );	    }	return c;    }     void solveIt()    {	int x, y; findStart( x, y );	if( x < 0 ) { cout << "\nCan't find start point!\n"; return; }	search( x, y, 2 );    }     void findStart( int& x, int& y )    {	for( int b = 0; b < hei; b++ )	    for( int a = 0; a < wid; a++ )		if( arr[a + wid * b].val == 1 ) { x = a; y = b; return; }	x = y = -1;    }     int wid, hei, max, dx[8], dy[8];    node* arr;    bool* weHave;};//------------------------------------------------------------------------------int main( int argc, char* argv[] ){    int wid;    string p = ". 33 35 . . * * * . . 24 22 . * * * . . . 21 . . * * . 26 . 13 40 11 * * 27 . . . 9 . 1 * * * . . 18 . . * * * * * . 7 . . * * * * * * 5 ."; wid = 8;    //string p = "54 . 60 59 . 67 . 69 . . 55 . . 63 65 . 72 71 51 50 56 62 . * * * * . . . 14 * * 17 . * 48 10 11 * 15 . 18 . 22 . 46 . * 3 . 19 23 . . 44 . 5 . 1 33 32 . . 43 7 . 36 . 27 . 31 42 . . 38 . 35 28 . 30"; wid = 9;    //string p = ". 58 . 60 . . 63 66 . 57 55 59 53 49 . 65 . 68 . 8 . . 50 . 46 45 . 10 6 . * * * . 43 70 . 11 12 * * * 72 71 . . 14 . * * * 30 39 . 15 3 17 . 28 29 . . 40 . . 19 22 . . 37 36 . 1 20 . 24 . 26 . 34 33"; wid = 9;     istringstream iss( p ); vector<string> puzz;    copy( istream_iterator<string>( iss ), istream_iterator<string>(), back_inserter<vector<string> >( puzz ) );    hSolver s; s.solve( puzz, wid );     int c = 0;    for( vector<string>::iterator i = puzz.begin(); i != puzz.end(); i++ )    {	if( ( *i ) != "*" && ( *i ) != "." )	{	    if( atoi( ( *i ).c_str() ) < 10 ) cout << "0";	    cout << ( *i ) << " ";	}	else cout << "   ";	if( ++c >= wid ) { cout << endl; c = 0; }    }    cout << endl << endl;    return system( "pause" );}//-------------------------------------------------------------------------------------------------- `

Output:

```32 33 35 36 37
31 34 24 22 38
30 25 23 21 12 39
29 26 20 13 40 11
27 28 14 19 09 10 01
15 16 18 08 02
17 07 06 03
05 04

56 58 54 60 61 62 63 66 67
57 55 59 53 49 47 65 64 68
09 08 52 51 50 48 46 45 69
10 06 07          44 43 70
05 11 12          72 71 42
04 14 13          30 39 41
15 03 17 18 28 29 38 31 40
02 16 19 22 23 27 37 36 32
01 20 21 24 25 26 35 34 33
```

## Curry

Works with: PAKCS

Probably not efficient.

`import CLPFDimport Constraint (andC, anyC)import Findall (unpack)import Integer (abs)  hidato :: [[Int]] -> Successhidato path =    test path inner  & domain inner 1 40  & allDifferent inner  & andFD [x `near` y | x <- cells, y <- cells]  & labeling [] (concat path)  where    andFD = solve . foldr1 (#/\#)    cells = enumerate path    inner free near :: (Int,Int,Int) -> (Int,Int,Int) -> Constraint(x,rx,cx) `near` (y,ry,cy) =  x #<=# y  #/\#  dist (y -# x)                        #\/#  x #>#  y  #/\#  dist (x -# y)                        #\/#  x #=#  0                        #\/#  y #=#  0  where    dist d =  abs (rx - ry) #<=# d        #/\#  abs (cx - cy) #<=# d enumerate :: [[Int]] -> [(Int,Int,Int)]enumerate xss = [(x,row,col) | (xs,row) <- xss `zip` [1..]                             , (x ,col) <- xs  `zip` [1..]                ] test [[ 0,  0,  0,  0,  0,  0,  0, 0, 0, 0]     ,[ 0,  A, 33, 35,  B,  C,  0, 0, 0, 0]     ,[ 0,  D,  E, 24, 22,  F,  0, 0, 0, 0]     ,[ 0,  G,  H,  I, 21,  J,  K, 0, 0, 0]     ,[ 0,  L, 26,  M, 13, 40, 11, 0, 0, 0]     ,[ 0, 27,  N,  O,  P,  9,  Q, 1, 0, 0]     ,[ 0,  0,  0,  R,  S, 18,  T, U, 0, 0]     ,[ 0,  0,  0,  0,  0,  V,  7, W, X, 0]     ,[ 0,  0,  0,  0,  0,  0,  0, 5, Y, 0]     ,[ 0,  0,  0,  0,  0,  0,  0, 0, 0, 0]     ]     [ A, 33, 35,  B,  C     , D,  E, 24, 22,  F        , G,  H,  I, 21,  J,  K        , L, 26,  M, 13, 40, 11           , 27,  N,  O,  P,  9, Q, 1           ,  R,  S, 18,  T,  U               ,  V,  7,  W,  X                       ,  5,  Y     ] = success main = unpack hidato`
Output:
```Execution time: 1440 msec. / elapsed: 2270 msec.
[[0,0,0,0,0,0,0,0,0,0],[0,32,33,35,36,37,0,0,0,0],[0,31,34,24,22,38,0,0,0,0],[0,30,25,23,21,12,39,0,0,0],[0,29,26,20,13,40,11,0,0,0],[0,27,28,14,19,9,10,1,0,0],[0,0,0,15,16,18,8,2,0,0],[0,0,0,0,0,17,7,6,3,0],[0,0,0,0,0,0,0,5,4,0],[0,0,0,0,0,0,0,0,0,0]]
More values? [y(es)/N(o)/a(ll)]```

## D

### More C-Style Version

This version retains some of the characteristics of the original C version. It uses global variables, it doesn't enforce immutability and purity. This style is faster to write for prototypes, short programs or less important code, but in larger programs you usually want more strictness to avoid some bugs and increase long-term maintainability.

Translation of: C
`import std.stdio, std.array, std.conv, std.algorithm, std.string; int[][] board;int[] given, start; void setup(string s) {    auto lines = s.splitLines;    auto cols = lines[0].split.length;    auto rows = lines.length;    given.length = 0;     board = new int[][](rows + 2, cols + 2);    foreach (row; board)        row[] = -1;     foreach (r, row; lines) {        foreach (c, cell; row.split) {            switch (cell) {                case "__":                    board[r + 1][c + 1] = 0;                    break;                case ".":                    break;                default:                    int val = cell.to!int;                    board[r + 1][c + 1] = val;                    given ~= val;                    if (val == 1)                        start = [r + 1, c + 1];            }        }    }    given.sort();} bool solve(int r, int c, int n, int next = 0) {    if (n > given.back)        return true;     if (board[r][c] && board[r][c] != n)        return false;     if (board[r][c] == 0 && given[next] == n)        return false;     int back = board[r][c];     board[r][c] = n;    foreach (i; -1 .. 2)        foreach (j; -1 .. 2)            if (solve(r + i, c + j, n + 1, next + (back == n)))                return true;     board[r][c] = back;    return false;} void printBoard() {    foreach (row; board) {        foreach (c; row)            writef(c == -1 ? " . " : c ? "%2d " : "__ ", c);        writeln;    }} void main() {    auto hi = "__ 33 35 __ __  .  .  .                __ __ 24 22 __  .  .  .                __ __ __ 21 __ __  .  .                __ 26 __ 13 40 11  .  .                27 __ __ __  9 __  1  .                 .  . __ __ 18 __ __  .                 .  .  .  . __  7 __ __                 .  .  .  .  .  .  5 __";     hi.setup;    printBoard;    "\nFound:".writeln;    solve(start[0], start[1], 1);    printBoard;}`
Output:
``` .  .  .  .  .  .  .  .  .  .
. __ 33 35 __ __  .  .  .  .
. __ __ 24 22 __  .  .  .  .
. __ __ __ 21 __ __  .  .  .
. __ 26 __ 13 40 11  .  .  .
. 27 __ __ __  9 __  1  .  .
.  .  . __ __ 18 __ __  .  .
.  .  .  .  . __  7 __ __  .
.  .  .  .  .  .  .  5 __  .
.  .  .  .  .  .  .  .  .  .

Found:
.  .  .  .  .  .  .  .  .  .
. 32 33 35 36 37  .  .  .  .
. 31 34 24 22 38  .  .  .  .
. 30 25 23 21 12 39  .  .  .
. 29 26 20 13 40 11  .  .  .
. 27 28 14 19  9 10  1  .  .
.  .  . 15 16 18  8  2  .  .
.  .  .  .  . 17  7  6  3  .
.  .  .  .  .  .  .  5  4  .
.  .  .  .  .  .  .  .  .  . ```

### Stronger Version

Translation of: C

This version uses a little stronger typing, performs tests a run-time with contracts, it doesn't use global variables, it enforces immutability and purity where possible, and produces a correct text output for both larger ad small boards. This style is more fit for larger programs, or when you want the code to be less bug-prone or a little more efficient.

With this coding style the changes in the code become less bug-prone, but also more laborious. This version is also faster, its total runtime is about 0.02 seconds or less.

`import std.stdio, std.conv, std.ascii, std.array, std.string,       std.algorithm, std.exception, std.range, std.typetuple; struct Hidato {    // alias Cell = RangedValue!(int, -1, int.max);    alias Cell = int;    alias Pos = size_t;    enum : Cell { emptyCell = -1, unknownCell = 0 }     immutable Cell boardMax;    immutable size_t nCols, nRows;    Cell[] board;    Pos[] known;    bool[] flood;     this(in string input) pure @safe    in {        assert(!input.strip.empty);    } out {        assert(nCols > 0 && nRows > 0);        immutable size = nCols * nRows;        assert(board.length == size);        assert(known.length == size + 1);        assert(flood.length == size);        assert(boardMax > 0 && boardMax <= size);        assert(board.reduce!max == boardMax);        assert(board.canFind(1) && board.canFind(boardMax));        assert(flood.all!(f => f == 0));        assert(known.all!(rc => rc >= 0 && rc < size));         foreach (immutable i, immutable cell; board) {            assert(cell == Hidato.emptyCell ||                   cell == Hidato.unknownCell ||                   (cell >= 1 && cell <= size));            if (cell > 0)                assert(i == known[size_t(cell)]);        }    } body {        bool[Cell] pathSeen; // A set.        immutable lines = input.splitLines;        this.nRows = lines.length;        this.nCols = lines[0].split.length;         immutable size = nCols * nRows;        this.board.length = size;        this.board[] = emptyCell;        this.known.length = size + 1;        this.flood.length = size;         auto boardMaxMutable = Cell.min;        Pos i = 0;         foreach (immutable row; lines) {            assert(row.split.length == nCols,                   text("Wrong cols n.: ", row.split.length));             foreach (immutable cell; row.split) {                switch (cell) {                    case "_":                        this.board[i] = Hidato.unknownCell;                        break;                    case ".":                        this.board[i] = Hidato.emptyCell;                        break;                    default: // Known.                        immutable val = cell.to!Cell;                        enforce(val > 0, "Path numbers must be > 0.");                        enforce(val !in pathSeen,                                text("Duplicated path number: ", val));                        pathSeen[val] = true;                        this.board[i] = val;                        this.known[val] = i;                        boardMaxMutable = max(boardMaxMutable, val);                }                i++;            }        }         this.boardMax = boardMaxMutable;    }      private Pos idx(in size_t r, in size_t c) const pure nothrow @safe @nogc {        return r * nCols + c;    }     private uint nNeighbors(in Pos pos, ref Pos[8] neighbours)    const pure nothrow @safe @nogc {        immutable r = pos / nCols;        immutable c = pos % nCols;        typeof(return) n = 0;         foreach (immutable sr; TypeTuple!(-1, 0, 1)) {            immutable size_t i = r + sr; // Can wrap-around.            if (i >= nRows)                continue;            foreach (immutable sc; TypeTuple!(-1, 0, 1)) {                immutable size_t j = c + sc; // Can wrap-around.                if ((sc != 0 || sr != 0) && j < nCols) {                    immutable pos2 = idx(i, j);                    neighbours[n] = pos2;                    if (board[pos2] != Hidato.emptyCell)                        n++;                }            }        }         return n;    }     /// Fill all free cells around 'cell' with true and write    /// output to variable "flood".    private void floodFill(in Pos pos) pure nothrow @safe @nogc {        Pos[8] n = void;         // For all neighbours.        foreach (immutable i; 0 .. nNeighbors(pos, n)) {            // If pos is not free, choose another neighbour.            if (board[n[i]] || flood[n[i]])                continue;            flood[n[i]] = true;            floodFill(n[i]);        }    }     /// Check all empty cells are reachable from higher known cells.    private bool checkConnectity(in uint lowerBound) pure nothrow @safe @nogc {        flood[] = false;         foreach (immutable i; lowerBound + 1 .. boardMax + 1)            if (known[i])                floodFill(known[i]);         foreach (immutable i; 0 .. nCols * nRows)            // If there are free cells which could not be            // reached from floodFill.            if (!board[i] && !flood[i])                return false;        return true;    }     private bool fill(in Pos pos, in uint n) pure nothrow @safe @nogc {        if ((board[pos] && board[pos] != n) ||            (known[n] && known[n] != pos))            return false;         if (n == boardMax)            return true;         immutable ko = known[n];        immutable bo = board[pos];        board[pos] = n;         Pos[8] p = void;        if (checkConnectity(n))            foreach (immutable i; 0 .. nNeighbors(pos, p))                if (fill(p[i], n + 1))                    return true;         board[pos] = bo;        known[n] = ko;        return false;    }     void solve() pure nothrow @safe @nogc    in {        assert(!known.empty);    } body {        fill(known[1], 1);    }     string toString() const pure {        immutable d = [Hidato.emptyCell: ".",                       Hidato.unknownCell: "_"];        immutable form = "%" ~ text(boardMax.text.length + 1) ~ "s";         string result;        foreach (immutable r; 0 .. nRows) {            foreach (immutable c; 0 .. nCols) {                immutable cell = board[idx(r, c)];                result ~= format(form, d.get(cell, cell.text));            }            result ~= "\n";        }        return result;    }} void solveHidato(in string problem) {    auto game = problem.Hidato;    writeln("Problem:\n", game);    game.solve;    writeln("Solution:\n", game);} void main() {    solveHidato(" _ 33 35  _  _  .  .  .                  _  _ 24 22  _  .  .  .                  _  _  _ 21  _  _  .  .                  _ 26  _ 13 40 11  .  .                 27  _  _  _  9  _  1  .                  .  .  _  _ 18  _  _  .                  .  .  .  .  _  7  _  _                  .  .  .  .  .  .  5  _");     solveHidato(". 4 .                 _ 7 _                 1 _ _");     solveHidato("1 _ _ . . _ _ . . _ _ . . _ _ . . _ _ . . _ _ . . _ _ . . _ _ . . _ _ . . _ _ . . _ _ . . _ _ . . 74 . . _ . _ . _ . _ . _ . _ . _ . _ . _ . _ . _ . _ . _ . _ . _ . _ . _ . _ . _ . _ . _ . _ . _ . _ . . . . _ _ . . _ _ . . _ _ . . _ _ . . _ _ . . _ _ . . _ _ . . _ _ . . _ _ . . _ _ . . _ _ . . _ _ ."    );}`
Output:
```Problem:
_ 33 35  _  _  .  .  .
_  _ 24 22  _  .  .  .
_  _  _ 21  _  _  .  .
_ 26  _ 13 40 11  .  .
27  _  _  _  9  _  1  .
.  .  _  _ 18  _  _  .
.  .  .  .  _  7  _  _
.  .  .  .  .  .  5  _

Solution:
32 33 35 36 37  .  .  .
31 34 24 22 38  .  .  .
30 25 23 21 12 39  .  .
29 26 20 13 40 11  .  .
27 28 14 19  9 10  1  .
.  . 15 16 18  8  2  .
.  .  .  . 17  7  6  3
.  .  .  .  .  .  5  4

Problem:
. 4 .
_ 7 _
1 _ _

Solution:
. 4 .
3 7 5
1 2 6

Problem:
1  _  _  .  .  _  _  .  .  _  _  .  .  _  _  .  .  _  _  .  .  _  _  .  .  _  _  .  .  _  _  .  .  _  _  .  .  _  _  .  .  _  _  .  .  _  _  .  . 74
.  .  _  .  _  .  _  .  _  .  _  .  _  .  _  .  _  .  _  .  _  .  _  .  _  .  _  .  _  .  _  .  _  .  _  .  _  .  _  .  _  .  _  .  _  .  _  .  _  .
.  .  .  _  _  .  .  _  _  .  .  _  _  .  .  _  _  .  .  _  _  .  .  _  _  .  .  _  _  .  .  _  _  .  .  _  _  .  .  _  _  .  .  _  _  .  .  _  _  .

Solution:
1  2  3  .  .  8  9  .  . 14 15  .  . 20 21  .  . 26 27  .  . 32 33  .  . 38 39  .  . 44 45  .  . 50 51  .  . 56 57  .  . 62 63  .  . 68 69  .  . 74
.  .  4  .  7  . 10  . 13  . 16  . 19  . 22  . 25  . 28  . 31  . 34  . 37  . 40  . 43  . 46  . 49  . 52  . 55  . 58  . 61  . 64  . 67  . 70  . 73  .
.  .  .  5  6  .  . 11 12  .  . 17 18  .  . 23 24  .  . 29 30  .  . 35 36  .  . 41 42  .  . 47 48  .  . 53 54  .  . 59 60  .  . 65 66  .  . 71 72  .```

## Elixir

Translation of: Ruby
`# Solve a Hidato Like Puzzle with Warnsdorff like logic applied#defmodule HLPsolver do  defmodule Cell do    defstruct value: -1, used: false, adj: []  end   def solve(str, adjacent, print_out\\true) do    board = setup(str)    if print_out, do: print(board, "Problem:")    {start, _} = Enum.find(board, fn {_,cell} -> cell.value==1 end)    board = set_adj(board, adjacent)    zbl = for %Cell{value: n} <- Map.values(board), into: %{}, do: {n, true}    try do      solve(board, start, 1, zbl, map_size(board))      IO.puts "No solution"    catch      {:ok, result} -> if print_out, do: print(result, "Solution:"),                                   else: result    end  end   defp solve(board, position, seq_num, zbl, goal) do    value = board[position].value    cond do      value > 0 and value != seq_num -> nil      value == 0 and zbl[seq_num] -> nil      true ->        cell = %Cell{board[position] | value: seq_num, used: true}        board = %{board | position => cell}        if seq_num == goal, do: throw({:ok, board})        Enum.each(wdof(board, cell.adj), fn pos ->          solve(board, pos, seq_num+1, zbl, goal)        end)    end  end   defp setup(str) do    lines = String.strip(str) |> String.split(~r/(\n|\r\n|\r)/) |> Enum.with_index    for {line,i} <- lines, {char,j} <- Enum.with_index(String.split(line)),        :error != Integer.parse(char), into: %{} do          {n,_} = Integer.parse(char)          {{i,j}, %Cell{value: n}}        end  end   defp set_adj(board, adjacent) do    Enum.reduce(Map.keys(board), board, fn {x,y},map ->      adj = Enum.map(adjacent, fn {i,j} -> {x+i, y+j} end)            |> Enum.reduce([], fn pos,acc -> if board[pos], do: [pos | acc], else: acc end)      Map.update!(map, {x,y}, fn cell -> %Cell{cell | adj: adj} end)    end)  end   defp wdof(board, adj) do              # Warnsdorf's rule    Enum.reject(adj, fn pos -> board[pos].used end)    |> Enum.sort_by(fn pos ->         Enum.count(board[pos].adj, fn p -> not board[p].used end)       end)  end   def print(board, title) do    IO.puts "\n#{title}"    {xmin, xmax} = Map.keys(board) |> Enum.map(fn {x,_} -> x end) |> Enum.min_max    {ymin, ymax} = Map.keys(board) |> Enum.map(fn {_,y} -> y end) |> Enum.min_max    len = map_size(board) |> to_char_list |> length    space = String.duplicate(" ", len)    Enum.each(xmin..xmax, fn x ->      Enum.map_join(ymin..ymax, " ", fn y ->        case Map.get(board, {x,y}) do          nil  -> space          cell -> to_string(cell.value) |> String.rjust(len)        end      end)      |> IO.puts    end)  endend`

Test:

`adjacent = [{-1, -1}, {-1, 0}, {-1, 1}, {0, -1}, {0, 1}, {1, -1}, {1, 0}, {1, 1}] """  .  4  0  7  0  1  0  0"""|> HLPsolver.solve(adjacent) """  0 33 35  0  0  0  0 24 22  0  0  0  0 21  0  0  0 26  0 13 40 11 27  0  0  0  9  0  1  .  .  0  0 18  0  0  .  .  .  .  0  7  0  0  .  .  .  .  .  .  5  0"""|> HLPsolver.solve(adjacent) """  1  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  .  0  .  .  0  0  0  .  0  0  0  .  0  0  0  .  0  0  0  .  0  0  0  .  0  0  0  .  0"""|> HLPsolver.solve(adjacent)`
Output:
```Problem:
4
0 7 0
1 0 0

Solution:
4
3 7 5
1 2 6

Problem:
0 33 35  0  0
0  0 24 22  0
0  0  0 21  0  0
0 26  0 13 40 11
27  0  0  0  9  0  1
0  0 18  0  0
0  7  0  0
5  0

Solution:
32 33 35 36 37
31 34 24 22 38
30 25 23 21 12 39
29 26 20 13 40 11
27 28 14 19  9 10  1
15 16 18  8  2
17  7  6  3
5  4

Problem:
1  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     0
0  0  0     0  0  0     0  0  0     0  0  0     0  0  0     0  0  0     0

Solution:
1  2  3     9 10 11    17 18 19    25 26 27    33 34 35    41 42 43    49 50 51
4     8    12    16    20    24    28    32    36    40    44    48    52
5  6  7    13 14 15    21 22 23    29 30 31    37 38 39    45 46 47    53
```

## Erlang

To simplify the code I start a new process for searching each potential path through the grid. This means that the default maximum number of processes had to be raised ("erl +P 50000" works for me). The task takes about 1-2 seconds on a low level Mac mini. If faster times are needed, or even less performing hardware is used, some optimisation should be done.

` -module( solve_hidato_puzzle ). -export( [create/2, solve/1, task/0] ). -compile({no_auto_import,[max/2]}). create( Grid_list, Number_list ) ->        Squares = lists:flatten( [create_column(X, Y) || {X, Y} <- Grid_list] ),	lists:foldl( fun store/2, dict:from_list(Squares), Number_list ). print( Grid_list ) when is_list(Grid_list) -> print( create(Grid_list, []) );print( Grid_dict ) ->    Max_x = max_x( Grid_dict ),    Max_y = max_y( Grid_dict ),    Print_row = fun (Y) -> [print(X, Y, Grid_dict) || X <- lists:seq(1, Max_x)], io:nl() end,    [Print_row(Y) || Y <- lists:seq(1, Max_y)]. solve( Dict ) ->    {find_start, [Start]} = {find_start, dict:fold( fun start/3, [], Dict )},    Max = dict:size( Dict ),    {stop_ok, {Max, Max, [Stop]}} = {stop_ok, dict:fold( fun stop/3, {Max, 0, []}, Dict )},    My_pid = erlang:self(),    erlang:spawn( fun() -> path(Start, Stop, Dict, My_pid, []) end ),    receive    {grid, Grid, path, Path} -> {Grid, Path}    end. task() ->    %% Square is {X, Y}, N}. N = 0 for empty square. These are created if not present.    %% Leftmost column is X=1. Top row is Y=1.    %% Optimised for the example, grid is a list of {X, {Y_min, Y_max}}.    %% When there are holes, X is repeated as many times as needed with two new Y values each time.    Start = {{7,5}, 1},    Stop = {{5,4}, 40},    Grid_list = [{1, {1,5}}, {2, {1,5}}, {3, {1,6}}, {4, {1,6}}, {5, {1,7}}, {6, {3,7}}, {7, {5,8}}, {8, {7,8}}],    Number_list = [Start, Stop, {{1,5}, 27}, {{2,1}, 33}, {{2,4}, 26}, {{3,1}, 35}, {{3,2}, 24},                {{4,2}, 22}, {{4,3}, 21}, {{4,4}, 13}, {{5,5}, 9}, {{5,6}, 18}, {{6,4}, 11}, {{6,7}, 7}, {{7,8}, 5}],    Grid = create( Grid_list, Number_list ),    io:fwrite( "Start grid~n" ),    print( Grid ),    {New_grid, Path} = solve( create(Grid_list, Number_list) ),    io:fwrite( "Start square ~p, Stop square ~p.~nPath ~p~n", [Start, Stop, Path] ),    print( New_grid ).  create_column( X, {Y_min, Y_max} ) -> [{{X, Y}, 0} || Y <- lists:seq(Y_min, Y_max)]. is_filled( Dict ) -> [] =:= dict:fold( fun keep_0_square/3, [], Dict ). keep_0_square( Key, 0, Acc ) -> [Key | Acc];keep_0_square(  _Key, _Value, Acc ) -> Acc. max( Position, Keys ) ->    [Square | _T] = lists:reverse( lists:keysort(Position, Keys) ),    Square. max_x( Dict ) ->    {X, _Y} = max( 1, dict:fetch_keys(Dict) ),    X. max_y( Dict ) ->    {_X, Y} = max( 2, dict:fetch_keys(Dict) ),    Y.  neighbourhood( Square, Dict ) ->        Potentials = neighbourhood_potential_squares( Square ),	neighbourhood_squares( dict:find(Square, Dict), Potentials, Dict ). neighbourhood_potential_squares( {X, Y} ) -> [{Sx, Sy} || Sx <- [X-1, X, X+1], Sy <- [Y-1, Y, Y+1], {X, Y} =/= {Sx, Sy}]. neighbourhood_squares( {ok, Value}, Potentials, Dict ) ->        Square_values = lists:flatten( [neighbourhood_square_value(X, dict:find(X, Dict)) || X <- Potentials] ),        Next_value = Value + 1,        neighbourhood_squares_next_value( lists:keyfind(Next_value, 2, Square_values), Square_values, Next_value ). neighbourhood_squares_next_value( {Square, Value}, _Square_values, Value ) -> [{Square, Value}];neighbourhood_squares_next_value( false, Square_values, Value ) -> [{Square, Value} || {Square, Y} <- Square_values, Y =:= 0]. neighbourhood_square_value( Square, {ok, Value} ) -> [{Square, Value}];neighbourhood_square_value( _Square, error ) -> []. path( Square, Square, Dict, Pid, Path ) -> path_correct( is_filled(Dict), Pid, [Square | Path], Dict );path( Square, Stop, Dict, Pid, Path ) ->    Reversed_path = [Square | Path],    Neighbours = neighbourhood( Square, Dict ),    [erlang:spawn( fun() -> path(Next_square, Stop, dict:store(Next_square, Value, Dict), Pid, Reversed_path) end ) || {Next_square, Value} <- Neighbours]. path_correct( true, Pid, Path, Dict ) -> Pid ! {grid, Dict, path, lists:reverse( Path )};path_correct( false, _Pid, _Path, _Dict ) -> dead_end. print( X, Y, Dict ) -> print_number( dict:find({X, Y}, Dict) ). print_number( {ok, 0} ) -> io:fwrite( "~3s", ["."] ); % . is less distracting than 0print_number( {ok, Value} ) -> io:fwrite( "~3b", [Value] );print_number( error ) -> io:fwrite( "~3s", [" "] ). start( Key, 1, Acc ) -> [Key | Acc]; % Allow check that we only have one key with value 1.start( _Key, _Value, Acc ) -> Acc. stop( Key, Max, {Max, Max_found, Stops} ) -> {Max, erlang:max(Max, Max_found), [Key | Stops]}; % Allow check that we only have one key with value Max.stop( _Key, Value, {Max, Max_found, Stops} ) -> {Max, erlang:max(Value, Max_found), Stops}. % Allow check that Max is Max. store( {Key, Value}, Dict ) -> dict:store( Key, Value, Dict ). `
Output:
```2> solve_hidato_puzzle:task().
Start grid
. 33 35  .  .
.  . 24 22  .
.  .  . 21  .  .
. 26  . 13 40 11
27  .  .  .  9  .  1
.  . 18  .  .
.  7  .  .
5  .
Start square {{7,5},1}, Stop square {{5,4},40}.
Path [{7,5}, {7,6}, {8,7}, {8,8}, {7,8}, {7,7}, {6,7}, {6,6}, {5,5}, {6,5}, {6,4}, {5,3}, {4,4}, {3,5}, {3,6}, {4,6}, {5,7}, {5,6}, {4,5}, {3,4},
{4,3}, {4,2}, {3,3}, {3,2}, {2,3}, {2,4}, {1,5},{2,5}, {1,4}, {1,3}, {1,2}, {1,1}, {2,1}, {2,2}, {3,1}, {4,1}, {5,1}, {5,2}, {6,3}, {5,4}]
32 33 35 36 37
31 34 24 22 38
30 25 23 21 12 39
29 26 20 13 40 11
27 28 14 19  9 10  1
15 16 18  8  2
17  7  6  3
5  4
```

## Go

Translation of: Java
`package main import (    "fmt"    "sort"    "strconv"    "strings") var board [][]intvar start, given []int func setup(input []string) {    /* This task is not about input validation, so       we're going to trust the input to be valid */    puzzle := make([][]string, len(input))    for i := 0; i < len(input); i++ {        puzzle[i] = strings.Fields(input[i])    }    nCols := len(puzzle[0])    nRows := len(puzzle)    list := make([]int, nRows*nCols)    board = make([][]int, nRows+2)    for i := 0; i < nRows+2; i++ {        board[i] = make([]int, nCols+2)        for j := 0; j < nCols+2; j++ {            board[i][j] = -1        }    }    for r := 0; r < nRows; r++ {        row := puzzle[r]        for c := 0; c < nCols; c++ {            switch cell := row[c]; cell {            case "_":                board[r+1][c+1] = 0            case ".":                break            default:                val, _ := strconv.Atoi(cell)                board[r+1][c+1] = val                list = append(list, val)                if val == 1 {                    start = append(start, r+1, c+1)                }            }        }    }    sort.Ints(list)    given = make([]int, len(list))    for i := 0; i < len(given); i++ {        given[i] = list[i]    }} func solve(r, c, n, next int) bool {    if n > given[len(given)-1] {        return true    }     back := board[r][c]    if back != 0 && back != n {        return false    }     if back == 0 && given[next] == n {        return false    }     if back == n {        next++    }     board[r][c] = n    for i := -1; i < 2; i++ {        for j := -1; j < 2; j++ {            if solve(r+i, c+j, n+1, next) {                return true            }        }    }     board[r][c] = back    return false} func printBoard() {    for _, row := range board {        for _, c := range row {            switch {            case c == -1:                fmt.Print(" . ")            case c > 0:                fmt.Printf("%2d ", c)            default:                fmt.Print("__ ")            }        }        fmt.Println()    }} func main() {    input := []string{        "_ 33 35 _ _ . . .",        "_ _ 24 22 _ . . .",        "_ _ _ 21 _ _ . .",        "_ 26 _ 13 40 11 . .",        "27 _ _ _ 9 _ 1 .",        ". . _ _ 18 _ _ .",        ". . . . _ 7 _ _",        ". . . . . . 5 _",    }    setup(input)    printBoard()    fmt.Println("\nFound:")    solve(start[0], start[1], 1, 0)    printBoard()}`
Output:
``` .  .  .  .  .  .  .  .  .  .
. __ 33 35 __ __  .  .  .  .
. __ __ 24 22 __  .  .  .  .
. __ __ __ 21 __ __  .  .  .
. __ 26 __ 13 40 11  .  .  .
. 27 __ __ __  9 __  1  .  .
.  .  . __ __ 18 __ __  .  .
.  .  .  .  . __  7 __ __  .
.  .  .  .  .  .  .  5 __  .
.  .  .  .  .  .  .  .  .  .

Found:
.  .  .  .  .  .  .  .  .  .
. 32 33 35 36 37  .  .  .  .
. 31 34 24 22 38  .  .  .  .
. 30 25 23 21 12 39  .  .  .
. 29 26 20 13 40 11  .  .  .
. 27 28 14 19  9 10  1  .  .
.  .  . 15 16 18  8  2  .  .
.  .  .  .  . 17  7  6  3  .
.  .  .  .  .  .  .  5  4  .
.  .  .  .  .  .  .  .  .  .
```

`{-# LANGUAGE TupleSections #-}{-# LANGUAGE Rank2Types #-} import qualified Data.IntMap as Iimport Data.IntMap (IntMap)import Data.Listimport Data.Maybeimport Data.Time.Clock data BoardProblem = Board  { cells :: IntMap (IntMap Int)  , endVal :: Int  , onePos :: (Int, Int)  , givens :: [Int]  } deriving (Show, Eq) tupIns x y v m = I.insert x (I.insert y v (I.findWithDefault I.empty x m)) m tupLookup x y m = I.lookup x m >>= I.lookup y makeBoard =  (\x ->      x      { givens = dropWhile (<= 1) \$ sort \$ givens x      }) .  foldl' --'    f    (Board I.empty 0 (0, 0) []) .  concatMap (zip [0 ..]) . zipWith (\y w -> map (y, ) \$ words w) [0 ..]  where    f bd (x, (y, v)) =      if v == "."        then bd        else Board               (tupIns x y (read v) (cells bd))               (if read v > endVal bd                  then read v                  else endVal bd)               (if v == "1"                  then (x, y)                  else onePos bd)               (read v : givens bd) hidato brd = listToMaybe \$ h 2 (cells brd) (onePos brd) (givens brd)  where    h nval pmap (x, y) gs      | nval == endVal brd = [pmap]      | nval == head gs =        if null nvalAdj          then []          else h (nval + 1) pmap (fst \$ head nvalAdj) (tail gs)      | not \$ null nvalAdj = h (nval + 1) pmap (fst \$ head nvalAdj) gs      | otherwise = hEmptyAdj      where        around =          [ (x - 1, y - 1)          , (x, y - 1)          , (x + 1, y - 1)          , (x - 1, y)          , (x + 1, y)          , (x - 1, y + 1)          , (x, y + 1)          , (x + 1, y + 1)          ]        lkdUp = map (\(x, y) -> ((x, y), tupLookup x y pmap)) around        nvalAdj = filter ((== Just nval) . snd) lkdUp        hEmptyAdj =          concatMap            (\((nx, ny), _) -> h (nval + 1) (tupIns nx ny nval pmap) (nx, ny) gs) \$          filter ((== Just 0) . snd) lkdUp printCellMap cellmap = putStrLn \$ concat strings  where    maxPos = xyBy I.findMax maximum    minPos = xyBy I.findMin minimum    xyBy :: (forall a. IntMap a -> (Int, a)) -> ([Int] -> Int) -> (Int, Int)    xyBy a b = (fst (a cellmap), b \$ map (fst . a . snd) \$ I.toList cellmap)    strings =      map        f        [ (x, y)        | y <- [snd minPos .. snd maxPos]         , x <- [fst minPos .. fst maxPos] ]    f (x, y) =      let z =            if x == fst maxPos              then "\n"              else " "      in case tupLookup x y cellmap of           Nothing -> "  " ++ z           Just n ->             (if n < 10                then ' ' : show n                else show n) ++             z main = do  let sampleBoard = makeBoard sample  printCellMap \$ cells sampleBoard  printCellMap \$ fromJust \$ hidato sampleBoard sample =  [ " 0 33 35  0  0"  , " 0  0 24 22  0"  , " 0  0  0 21  0  0"  , " 0 26  0 13 40 11"  , "27  0  0  0  9  0  1"  , ".  .   0  0 18  0  0"  , ".  .  .  .   0  7  0  0"  , ".  .  .  .  .  .   5  0"  ]`
Output:
``` 0 33 35  0  0
0  0 24 22  0
0  0  0 21  0  0
0 26  0 13 40 11
27  0  0  0  9  0  1
0  0 18  0  0
0  7  0  0
5  0

32 33 35 36 37
31 34 24 22 38
30 25 23 21 12 39
29 26 20 13 40 11
27 28 14 19  9 10  1
15 16 18  8  2
17  7  6  3
5  4
```

## Icon and Unicon

This is an Unicon-specific solution but could easily be adjusted to work in Icon.

`global nCells, cMap, bestrecord Pos(r,c) procedure main(A)    puzzle := showPuzzle("Input",readPuzzle())    QMouse(puzzle,findStart(puzzle),&null,0)    showPuzzle("Output", solvePuzzle(puzzle)) | write("No solution!")end procedure readPuzzle()    # Start with a reduced puzzle space    p := [[-1]]    nCells := maxCols := 0    every line := !&input do {        put(p,[: -1 | gencells(line) | -1 :])        maxCols <:= *p[-1]        }    put(p, [-1])    # Now normalize all rows to the same length    every i := 1 to *p do p[i] := [: !p[i] | (|-1\(maxCols - *p[i])) :]    return pend procedure gencells(s)    static WS, NWS    initial {        NWS := ~(WS := " \t")        cMap := table()     # Map to/from internal model        cMap["#"] := -1;  cMap["_"] :=  0        cMap[-1]  := " "; cMap[0]   := "_"        }     s ? while not pos(0) do {            w := (tab(many(WS))|"", tab(many(NWS))) | break            w := numeric(\cMap[w]|w)            if -1 ~= w then nCells +:= 1            suspend w            }end procedure showPuzzle(label, p)    write(label," with ",nCells," cells:")    every r := !p do {        every c := !r do writes(right((\cMap[c]|c),*nCells+1))        write()        }    return pend procedure findStart(p)    if \p[r := !*p][c := !*p[r]] = 1 then return Pos(r,c)end procedure solvePuzzle(puzzle)    if path := \best then {        repeat {            loc := path.getLoc()            puzzle[loc.r][loc.c] := path.getVal()            path := \path.getParent() | break            }        return puzzle        }end class QMouse(puzzle, loc, parent, val)    method getVal(); return val; end    method getLoc(); return loc; end    method getParent(); return parent; end    method atEnd(); return (nCells = val) = puzzle[loc.r][loc.c]; end    method goNorth(); return visit(loc.r-1,loc.c);   end    method goNE();    return visit(loc.r-1,loc.c+1); end    method goEast();  return visit(loc.r,  loc.c+1); end    method goSE();    return visit(loc.r+1,loc.c+1); end    method goSouth(); return visit(loc.r+1,loc.c);   end    method goSW();    return visit(loc.r+1,loc.c-1); end    method goWest();  return visit(loc.r,  loc.c-1); end    method goNW();    return visit(loc.r-1,loc.c-1); end     method visit(r,c)        if /best & validPos(r,c) then return Pos(r,c)    end     method validPos(r,c)        xv := puzzle[r][c]        if xv = (val+1) then return        if xv = 0 then {  # make sure this path hasn't already gone there            ancestor := self            while xl := (ancestor := \ancestor.getParent()).getLoc() do                if (xl.r = r) & (xl.c = c) then fail            return            }    end initially    val +:= 1    if atEnd() then return best := self    QMouse(puzzle, goNorth(), self, val)    QMouse(puzzle, goNE(),    self, val)    QMouse(puzzle, goEast(),  self, val)    QMouse(puzzle, goSE(),    self, val)    QMouse(puzzle, goSouth(), self, val)    QMouse(puzzle, goSW(),    self, val)    QMouse(puzzle, goWest(),  self, val)    QMouse(puzzle, goNW(),    self, val)end`

Sample run:

```->hd <hd.in
Input with 40 cells:

_ 33 35  _  _
_  _ 24 22  _
_  _  _ 21  _  _
_ 26  _ 13 40 11
27  _  _  _  9  _  1
_  _ 18  _  _
_  7  _  _
5  _

Output with 40 cells:

32 33 35 36 37
31 34 24 22 38
30 25 23 21 12 39
29 26 20 13 40 11
27 28 14 19  9 10  1
15 16 18  8  2
17  7  6  3
5  4

->
```

## Java

Translation of: D
Works with: Java version 7
`import java.util.ArrayList;import java.util.Collections;import java.util.List; public class Hidato {     private static int[][] board;    private static int[] given, start;     public static void main(String[] args) {        String[] input = {"_ 33 35 _ _ . . .",            "_ _ 24 22 _ . . .",            "_ _ _ 21 _ _ . .",            "_ 26 _ 13 40 11 . .",            "27 _ _ _ 9 _ 1 .",            ". . _ _ 18 _ _ .",            ". . . . _ 7 _ _",            ". . . . . . 5 _"};         setup(input);        printBoard();        System.out.println("\nFound:");        solve(start[0], start[1], 1, 0);        printBoard();    }     private static void setup(String[] input) {        /* This task is not about input validation, so           we're going to trust the input to be valid */         String[][] puzzle = new String[input.length][];        for (int i = 0; i < input.length; i++)            puzzle[i] = input[i].split(" ");         int nCols = puzzle[0].length;        int nRows = puzzle.length;         List<Integer> list = new ArrayList<>(nRows * nCols);         board = new int[nRows + 2][nCols + 2];        for (int[] row : board)            for (int c = 0; c < nCols + 2; c++)                row[c] = -1;         for (int r = 0; r < nRows; r++) {            String[] row = puzzle[r];            for (int c = 0; c < nCols; c++) {                String cell = row[c];                switch (cell) {                    case "_":                        board[r + 1][c + 1] = 0;                        break;                    case ".":                        break;                    default:                        int val = Integer.parseInt(cell);                        board[r + 1][c + 1] = val;                        list.add(val);                        if (val == 1)                            start = new int[]{r + 1, c + 1};                }            }        }        Collections.sort(list);        given = new int[list.size()];        for (int i = 0; i < given.length; i++)            given[i] = list.get(i);    }     private static boolean solve(int r, int c, int n, int next) {        if (n > given[given.length - 1])            return true;         if (board[r][c] != 0 && board[r][c] != n)            return false;         if (board[r][c] == 0 && given[next] == n)            return false;         int back = board[r][c];        if (back == n)            next++;         board[r][c] = n;        for (int i = -1; i < 2; i++)            for (int j = -1; j < 2; j++)                if (solve(r + i, c + j, n + 1, next))                    return true;         board[r][c] = back;        return false;    }     private static void printBoard() {        for (int[] row : board) {            for (int c : row) {                if (c == -1)                    System.out.print(" . ");                else                    System.out.printf(c > 0 ? "%2d " : "__ ", c);            }            System.out.println();        }    }}`

Output:

``` .  .  .  .  .  .  .  .  .  .
. __ 33 35 __ __  .  .  .  .
. __ __ 24 22 __  .  .  .  .
. __ __ __ 21 __ __  .  .  .
. __ 26 __ 13 40 11  .  .  .
. 27 __ __ __  9 __  1  .  .
.  .  . __ __ 18 __ __  .  .
.  .  .  .  . __  7 __ __  .
.  .  .  .  .  .  .  5 __  .
.  .  .  .  .  .  .  .  .  .

Found:
.  .  .  .  .  .  .  .  .  .
. 32 33 35 36 37  .  .  .  .
. 31 34 24 22 38  .  .  .  .
. 30 25 23 21 12 39  .  .  .
. 29 26 20 13 40 11  .  .  .
. 27 28 14 19  9 10  1  .  .
.  .  . 15 16 18  8  2  .  .
.  .  .  .  . 17  7  6  3  .
.  .  .  .  .  .  .  5  4  .
.  .  .  .  .  .  .  .  .  .```

## Julia

This solution utilizes a Hidato puzzle solver module which is also used for the Hopido and knight move tasks.

`module Hidato export hidatosolve, printboard, hidatoconfigure function hidatoconfigure(str)    lines = split(str, "\n")    nrows, ncols = length(lines), length(split(lines[1], r"\s+"))    board = fill(-1, (nrows, ncols))    presets = Vector{Int}()    starts = Vector{CartesianIndex{2}}()    maxmoves = 0    for (i, line) in enumerate(lines), (j, s) in enumerate(split(strip(line), r"\s+"))        c = s[1]        if c == '_' || (c == '0' && length(s) == 1)            board[i, j] = 0            maxmoves += 1        elseif c == '.'            continue        else # numeral, get 2 digits            board[i, j] = parse(Int, s)            push!(presets, board[i, j])            if board[i, j] == 1                push!(starts, CartesianIndex(i, j))            end            maxmoves += 1        end    end    board, maxmoves, sort!(presets), length(starts) == 1 ? starts : findall(x -> x == 0, board)end function hidatosolve(board, maxmoves, movematrix, fixed, row, col, sought)    if sought > maxmoves        return true    elseif (0 != board[row, col] != sought) || (board[row, col] == 0 && sought in fixed)        return false    end    backnum = board[row, col] == sought ? sought : 0    board[row, col] = sought # try board with this cell set to next number    for move in movematrix        i, j = row + move[1], col + move[2]        if (0 < i <= size(board)[1]) && (0 < j <= size(board)[2]) &&            hidatosolve(board, maxmoves, movematrix, fixed, i, j, sought + 1)            return true        end    end    board[row, col] = backnum # return board to original state    falseend function printboard(board, emptysquare= "__ ", blocked = "   ")    d = Dict(-1 => blocked, 0 => emptysquare, -2 => "\n")    map(x -> d[x] = rpad(lpad(string(x), 2), 3), 1:maximum(board))    println(join([d[i] for i in hcat(board, fill(-2, size(board)[1]))'], ""))end end  # module `
`using .Hidato hidat = """__ 33 35 __ __  .  .  .__ __ 24 22 __  .  .  .__ __ __ 21 __ __  .  .__ 26 __ 13 40 11  .  .27 __ __ __  9 __  1  . .  . __ __ 18 __ __  . .  .  .  . __  7 __ __ .  .  .  .  .  .  5 __""" const kingmoves = [[-1, -1], [-1, 0], [-1, 1], [0, -1], [0, 1], [1, -1], [1, 0], [1, 1]] board, maxmoves, fixed, starts = hidatoconfigure(hidat)printboard(board)hidatosolve(board, maxmoves, kingmoves, fixed, starts[1][1], starts[1][2], 1)printboard(board) `
Output:
```
__ 33 35 __ __
__ __ 24 22 __
__ __ __ 21 __ __
__ 26 __ 13 40 11
27 __ __ __  9 __  1
__ __ 18 __ __
__  7 __ __
5 __

32 33 35 36 37
31 34 24 22 38
30 25 23 21 12 39
29 26 20 13 40 11
27 28 14 19  9 10  1
15 16 18  8  2
17  7  6  3
5  4

```

## Kotlin

Translation of: Java
`// version 1.2.0 lateinit var board: List<IntArray>lateinit var given: IntArraylateinit var start: IntArray fun setUp(input: List<String>) {    val nRows = input.size    val puzzle = List(nRows) { input[it].split(" ") }    val nCols = puzzle[0].size    val list = mutableListOf<Int>()    board = List(nRows + 2) { IntArray(nCols + 2) { -1 } }    for (r in 0 until nRows) {        val row = puzzle[r]        for (c in 0 until nCols) {            val cell = row[c]            if (cell == "_") {                board[r + 1][c + 1] = 0            }            else if (cell != ".") {                val value = cell.toInt()                board[r + 1][c + 1] = value                list.add(value)                if (value == 1) start = intArrayOf(r + 1, c + 1)            }        }    }    list.sort()    given = list.toIntArray()} fun solve(r: Int, c: Int, n: Int, next: Int): Boolean {    if (n > given[given.lastIndex]) return true    val back = board[r][c]    if (back != 0 && back != n) return false    if (back == 0 && given[next] == n) return false    var next2 = next    if (back == n) next2++    board[r][c] = n    for (i in -1..1)        for (j in -1..1)            if (solve(r + i, c + j, n + 1, next2)) return true    board[r][c] = back    return false} fun printBoard() {    for (row in board) {        for (c in row) {            if (c == -1)                print(" . ")            else                print(if (c > 0) "%2d ".format(c) else "__ ")        }        println()    }} fun main(args: Array<String>) {    var input = listOf(        "_ 33 35 _ _ . . .",        "_ _ 24 22 _ . . .",        "_ _ _ 21 _ _ . .",        "_ 26 _ 13 40 11 . .",        "27 _ _ _ 9 _ 1 .",        ". . _ _ 18 _ _ .",        ". . . . _ 7 _ _",        ". . . . . . 5 _"    )    setUp(input)    printBoard()    println("\nFound:")    solve(start[0], start[1], 1, 0)    printBoard()}`
Output:
``` .  .  .  .  .  .  .  .  .  .
. __ 33 35 __ __  .  .  .  .
. __ __ 24 22 __  .  .  .  .
. __ __ __ 21 __ __  .  .  .
. __ 26 __ 13 40 11  .  .  .
. 27 __ __ __  9 __  1  .  .
.  .  . __ __ 18 __ __  .  .
.  .  .  .  . __  7 __ __  .
.  .  .  .  .  .  .  5 __  .
.  .  .  .  .  .  .  .  .  .

Found:
.  .  .  .  .  .  .  .  .  .
. 32 33 35 36 37  .  .  .  .
. 31 34 24 22 38  .  .  .  .
. 30 25 23 21 12 39  .  .  .
. 29 26 20 13 40 11  .  .  .
. 27 28 14 19  9 10  1  .  .
.  .  . 15 16 18  8  2  .  .
.  .  .  .  . 17  7  6  3  .
.  .  .  .  .  .  .  5  4  .
.  .  .  .  .  .  .  .  .  .
```

## Mathprog

`/*Hidato.mathprog, part of KuKu by Nigel Galloway   Find a solution to a Hidato problem   [email protected]  April 1st., 2011*/ param ZBLS;param ROWS;param COLS;param D := 1;set ROWSR := 1..ROWS;set COLSR := 1..COLS;set ROWSV := (1-D)..(ROWS+D);set COLSV := (1-D)..(COLS+D);param Iz{ROWSR,COLSR}, integer, default 0;set ZBLSV := 1..(ZBLS+1);set ZBLSR := 1..ZBLS; var BR{ROWSV,COLSV,ZBLSV}, binary; void0{r in ROWSV, z in ZBLSR,c in (1-D)..0}: BR[r,c,z] = 0;void1{r in ROWSV, z in ZBLSR,c in (COLS+1)..(COLS+D)}: BR[r,c,z] = 0;void2{c in COLSV, z in ZBLSR,r in (1-D)..0}: BR[r,c,z] = 0;void3{c in COLSV, z in ZBLSR,r in (ROWS+1)..(ROWS+D)}: BR[r,c,z] = 0;void4{r in ROWSV,c in (1-D)..0}: BR[r,c,ZBLS+1] = 1;void5{r in ROWSV,c in (COLS+1)..(COLS+D)}: BR[r,c,ZBLS+1] = 1;void6{c in COLSV,r in (1-D)..0}: BR[r,c,ZBLS+1] = 1;void7{c in COLSV,r in (ROWS+1)..(ROWS+D)}: BR[r,c,ZBLS+1] = 1; Izfree{r in ROWSR, c in COLSR, z in ZBLSR : Iz[r,c] = -1}: BR[r,c,z] = 0;Iz1{Izr in ROWSR, Izc in COLSR, r in ROWSR, c in COLSR, z in ZBLSR : Izr=r and Izc=c and Iz[Izr,Izc]=z}: BR[r,c,z] = 1; rule1{z in ZBLSR}: sum{r in ROWSR, c in COLSR} BR[r,c,z] = 1;rule2{r in ROWSR, c in COLSR}: sum{z in ZBLSV} BR[r,c,z] = 1;rule3{r in ROWSR, c in COLSR, z in ZBLSR}: BR[0,0,z+1] + BR[r-1,c-1,z+1] + BR[r-1,c,z+1] + BR[r-1,c+1,z+1] + BR[r,c-1,z+1] + BR[r,c+1,z+1] + BR[r+1,c-1,z+1] + BR[r+1,c,z+1] + BR[r+1,c+1,z+1] - BR[r,c,z] >= 0; solve; for {r in ROWSR} {    for {c in COLSR} {        printf " %2d", sum{z in ZBLSR} BR[r,c,z]*z;    }    printf "\n";}data; param ROWS := 8;param COLS := 8;param ZBLS := 40;paramIz: 1   2   3   4   5   6   7   8 := 1  .  33  35   .   .  -1  -1  -1 2  .   .  24  22   .  -1  -1  -1 3  .   .   .  21   .   .  -1  -1 4  .  26   .  13  40  11  -1  -1 5 27   .   .   .   9   .   1  -1  6 -1  -1   .   .  18   .   .  -1  7 -1  -1  -1  -1   .   7   .   . 8 -1  -1  -1  -1  -1  -1   5   .  ;  end;`

Using the data in the model produces the following:

Output:
```>glpsol --minisat --math Hidato.mathprog
GLPSOL: GLPK LP/MIP Solver, v4.47
Parameter(s) specified in the command line:
--minisat --math Hidato.mathprog
Generating void0...
Generating void1...
Generating void2...
Generating void3...
Generating void4...
Generating void5...
Generating void6...
Generating void7...
Generating Izfree...
Generating Iz1...
Generating rule1...
Generating rule2...
Generating rule3...
Model has been successfully generated
Will search for ANY feasible solution
Translating to CNF-SAT...
Original problem has 5279 rows, 4100 columns, and 33359 non-zeros
2520 covering inequalities
2719 partitioning equalities
Solving CNF-SAT problem...
Instance has 7076 variables, 24047 clauses, and 77735 literals
==================================[MINISAT]===================================
| Conflicts |     ORIGINAL     |              LEARNT              | Progress |
|           | Clauses Literals |   Limit Clauses Literals  Lit/Cl |          |
==============================================================================
|         0 |   21432    75120 |    7144       0        0     0.0 |  0.000 % |
==============================================================================
SATISFIABLE
Objective value =  0.000000000e+000
Time used:   0.0 secs
Memory used: 14.5 Mb (15192264 bytes)
32 33 35 36 37  0  0  0
31 34 24 22 38  0  0  0
30 25 23 21 12 39  0  0
29 26 20 13 40 11  0  0
27 28 14 19  9 10  1  0
0  0 15 16 18  8  2  0
0  0  0  0 17  7  6  3
0  0  0  0  0  0  5  4
Model has been successfully processed
```

Modelling Evil Case 1:

```data;
param ROWS := 3;
param COLS := 3;
param ZBLS := 7;
param
Iz: 1   2   3 :=
1 -1   4  -1
2  .   7   .
3  1   .   .
;
end;
```

Produces:

```>glpsol --minisat --math Hidato.mathprog --data Evil1.data
GLPSOL: GLPK LP/MIP Solver, v4.47
Parameter(s) specified in the command line:
--minisat --math Hidato.mathprog --data Evil1.data
Hidato.mathprog:47: warning: data section ignored
Generating void0...
Generating void1...
Generating void2...
Generating void3...
Generating void4...
Generating void5...
Generating void6...
Generating void7...
Generating Izfree...
Generating Iz1...
Generating rule1...
Generating rule2...
Generating rule3...
Model has been successfully generated
Will search for ANY feasible solution
Translating to CNF-SAT...
Original problem has 256 rows, 200 columns, and 935 non-zeros
56 covering inequalities
193 partitioning equalities
Solving CNF-SAT problem...
Instance has 337 variables, 1237 clauses, and 4094 literals
==================================[MINISAT]===================================
| Conflicts |     ORIGINAL     |              LEARNT              | Progress |
|           | Clauses Literals |   Limit Clauses Literals  Lit/Cl |          |
==============================================================================
|         0 |    1060     3917 |     353       0        0     0.0 |  0.000 % |
==============================================================================
SATISFIABLE
Objective value =  0.000000000e+000
Time used:   0.0 secs
Memory used: 0.8 Mb (861188 bytes)
0  4  0
3  7  5
1  2  6
Model has been successfully processed
```

Modelling Evil Case 2 - The Snake in the Grass:

```data;
param ROWS := 3;
param COLS := 50;
param ZBLS := 74;
param
Iz:  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 :=
1   1  .  . -1 -1  .  . -1 -1  .  . -1 -1  .  . -1 -1  .  . -1 -1  .  . -1 -1  .  . -1 -1  .  . -1 -1  .  . -1 -1  .  . -1 -1  .  . -1 -1  .  . -1 -1 74
2  -1 -1  . -1  . -1  . -1  . -1  . -1  . -1  . -1  . -1  . -1  . -1  . -1  . -1  . -1  . -1  . -1  . -1  . -1  . -1  . -1  . -1  . -1  . -1  . -1  . -1
3  -1 -1 -1  .  . -1 -1  .  . -1 -1  .  . -1 -1  .  . -1 -1  .  . -1 -1  .  . -1 -1  .  . -1 -1  .  . -1 -1  .  . -1 -1  .  . -1 -1  .  . -1 -1  .  . -1
;
end;
```

Produces:

```G:\IAJAAR4.47>glpsol --minisat --math Hidato.mathprog --data Evil2.data
GLPSOL: GLPK LP/MIP Solver, v4.47
Parameter(s) specified in the command line:
--minisat --math Hidato.mathprog --data Evil2.data
Hidato.mathprog:47: warning: data section ignored
Evil2.data:11: warning: final NL missing before end of file
Generating void0...
Generating void1...
Generating void2...
Generating void3...
Generating void4...
Generating void5...
Generating void6...
Generating void7...
Generating Izfree...
Generating Iz1...
Generating rule1...
Generating rule2...
Generating rule3...
Model has been successfully generated
Will search for ANY feasible solution
Translating to CNF-SAT...
Original problem has 25500 rows, 19500 columns, and 147452 non-zeros
11026 covering inequalities
14400 partitioning equalities
Solving CNF-SAT problem...
Instance has 31338 variables, 98310 clauses, and 305726 literals
==================================[MINISAT]===================================
| Conflicts |     ORIGINAL     |              LEARNT              | Progress |
|           | Clauses Literals |   Limit Clauses Literals  Lit/Cl |          |
==============================================================================
|         0 |   84134   291550 |   28044       0        0     0.0 |  0.000 % |
|       101 |   31135   126809 |   30848      98     5496    56.1 | 65.521 % |
|       251 |   31135   126809 |   33933     244    12470    51.1 | 66.552 % |
|       476 |   27353   115512 |   37327     446    23819    53.4 | 68.160 % |
|       814 |   26574   113330 |   41059     770    42161    54.8 | 69.586 % |
|      1321 |   25432   110534 |   45165    1262    83658    66.3 | 70.056 % |
==============================================================================
SATISFIABLE
Objective value =  0.000000000e+000
Time used:   1.0 secs
Memory used: 60.9 Mb (63862624 bytes)
1  2  3  0  0  8  9  0  0 14 15  0  0 20 21  0  0 26 27  0  0 32 33  0  0 38 39  0  0 44 45  0  0 50 51  0  0 56 57  0  0 62 63  0  0 68 69  0  0 74
0  0  4  0  7  0 10  0 13  0 16  0 19  0 22  0 25  0 28  0 31  0 34  0 37  0 40  0 43  0 46  0 49  0 52  0 55  0 58  0 61  0 64  0 67  0 70  0 73  0
0  0  0  5  6  0  0 11 12  0  0 17 18  0  0 23 24  0  0 29 30  0  0 35 36  0  0 41 42  0  0 47 48  0  0 53 54  0  0 59 60  0  0 65 66  0  0 71 72  0
Model has been successfully processed
```

Modelling Evil Case 3 - A fatter snake in the Grass:

```data;
param ROWS := 4;
param COLS := 46;
param ZBLS := 82;
param
Iz:  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 :=
1   1  0 -1 -1 -1  0  0 -1 -1 -1  0  0 -1 -1 -1  0  0 -1 -1 -1  0  0 -1 -1 -1  0  0 -1 -1 -1  0  0 -1 -1 -1  0  0 -1 -1 -1  0  0 -1 -1 -1 82
2  -1 -1  0 -1  0 -1 -1  0 -1  0 -1 -1  0 -1  0 -1 -1  0 -1  0 -1 -1  0 -1  0 -1 -1  0 -1  0 -1 -1  0 -1  0 -1 -1  0 -1  0 -1 -1  0 -1  0 -1
3  -1  0 -1  0 -1 -1  0 -1  0 -1 -1  0 -1  0 -1 -1  0 -1  0 -1 -1  0 -1  0 -1 -1  0 -1  0 -1 -1  0 -1  0 -1 -1  0 -1  0 -1 -1  0 -1  0 -1 -1
4   0  0  0 -1 -1  0  0  0 -1 -1  0  0  0 -1 -1  0  0  0 -1 -1  0  0  0 -1 -1  0  0  0 -1 -1  0  0  0 -1 -1  0  0  0 -1 -1  0  0  0 -1 -1 -1
;
end;
```

Produces:

```>glpsol --minisat --math Hidato.mathprog --data Evil3.data
GLPSOL: GLPK LP/MIP Solver, v4.47
Parameter(s) specified in the command line:
--minisat --math Hidato.mathprog --data Evil3.data
Hidato.mathprog:47: warning: data section ignored
Generating void0...
Generating void1...
Generating void2...
Generating void3...
Generating void4...
Generating void5...
Generating void6...
Generating void7...
Generating Izfree...
Generating Iz1...
Generating rule1...
Generating rule2...
Generating rule3...
Model has been successfully generated
Will search for ANY feasible solution
Translating to CNF-SAT...
Original problem has 32684 rows, 23904 columns, and 198488 non-zeros
15006 covering inequalities
17596 partitioning equalities
Solving CNF-SAT problem...
Instance has 39792 variables, 130040 clauses, and 407222 literals
==================================[MINISAT]===================================
| Conflicts |     ORIGINAL     |              LEARNT              | Progress |
|           | Clauses Literals |   Limit Clauses Literals  Lit/Cl |          |
==============================================================================
|         0 |  112710   389892 |   37570       0        0     0.0 |  0.000 % |
==============================================================================
SATISFIABLE
Objective value =  0.000000000e+000
Time used:   0.0 secs
Memory used: 80.2 Mb (84067912 bytes)
1  2  0  0  0 10 11  0  0  0 19 20  0  0  0 28 29  0  0  0 37 38  0  0  0 46 47  0  0  0 55 56  0  0  0 64 65  0  0  0 73 74  0  0  0 82
0  0  3  0  9  0  0 12  0 18  0  0 21  0 27  0  0 30  0 36  0  0 39  0 45  0  0 48  0 54  0  0 57  0 63  0  0 66  0 72  0  0 75  0 81  0
0  4  0  8  0  0 13  0 17  0  0 22  0 26  0  0 31  0 35  0  0 40  0 44  0  0 49  0 53  0  0 58  0 62  0  0 67  0 71  0  0 76  0 80  0  0
5  6  7  0  0 14 15 16  0  0 23 24 25  0  0 32 33 34  0  0 41 42 43  0  0 50 51 52  0  0 59 60 61  0  0 68 69 70  0  0 77 78 79  0  0  0
Model has been successfully processed
```

## Nim

`import strutils, algorithm var board: array[0..19, array[0..19, int]]var given, start: seq[int] = @[]var rows, cols: int = 0 proc setup(s: string) =    var lines = s.splitLines()    cols = lines[0].split().len()    rows = lines.len()     for i in 0 .. rows + 1:        for j in 0 .. cols + 1:           board[i][j] = -1     for r, row in pairs(lines):        for c, cell in pairs(row.split()):            case cell            of "__" :                 board[r + 1][c + 1] = 0                continue            of "." : continue            else :               var val = parseInt(cell)               board[r + 1][c + 1] = val               given.add(val)               if (val == 1):                    start.add(r + 1)                   start.add(c + 1)    given.sort(cmp[int], Ascending) proc solve(r, c, n: int, next: int = 0): bool =    if n > given[high(given)]:       return true    if board[r][c] < 0:        return false    if (board[r][c] > 0 and board[r][c] != n):        return false    if (board[r][c] == 0 and given[next] == n):        return false     var back = board[r][c]    board[r][c] = n    for i in -1 .. 1:        for j in -1 .. 1:            if back == n:                if (solve(r + i, c + j, n + 1, next + 1)):  return true            else:                if (solve(r + i, c + j, n + 1, next)): return true    board[r][c] = back    result = false  proc printBoard() =    for r in  0 .. rows + 1:        for cellid,c in pairs(board[r]):            if cellid > cols + 1: break            if c == -1:                write(stdout, " . ")            elif c == 0:                write(stdout, "__ ")            else:                write(stdout, "\$# " % align(\$c,2))        writeLine(stdout, "") var hi: string = """__ 33 35 __ __  .  .  .__ __ 24 22 __  .  .  .__ __ __ 21 __ __  .  .__ 26 __ 13 40 11  .  .27 __ __ __  9 __  1  ..  . __ __ 18 __ __  ..  .  .  . __  7 __ __.  .  .  .  .  .  5 __""" setup(hi)printBoard()echo("")echo("Found:")discard solve(start[0], start[1], 1)printBoard()`
Output:
``` .  .  .  .  .  .  .  .  .  .
. __ 33 35 __ __  .  .  .  .
. __ __ 24 22 __  .  .  .  .
. __ __ __ 21 __ __  .  .  .
. __ 26 __ 13 40 11  .  .  .
. 27 __ __ __  9 __  1  .  .
.  .  . __ __ 18 __ __  .  .
.  .  .  .  . __  7 __ __  .
.  .  .  .  .  .  .  5 __  .
.  .  .  .  .  .  .  .  .  .

Found:
.  .  .  .  .  .  .  .  .  .
. 32 33 35 36 37  .  .  .  .
. 31 34 24 22 38  .  .  .  .
. 30 25 23 21 12 39  .  .  .
. 29 26 20 13 40 11  .  .  .
. 27 28 14 19  9 10  1  .  .
.  .  . 15 16 18  8  2  .  .
.  .  .  .  . 17  7  6  3  .
.  .  .  .  .  .  .  5  4  .
.  .  .  .  .  .  .  .  .  . ```

## Perl

`use strict;use List::Util 'max'; our (@grid, @known, \$n); sub show_board {	for my \$r (@grid) {		print map(!defined(\$_)	? '   ' : \$_					? sprintf("%3d", \$_)					: ' __'			, @\$r), "\n"	}} sub parse_board {	@grid = map{[map(/^_/ ? 0 : /^\./ ? undef: \$_, split ' ')]}			split "\n", shift();	for my \$y (0 .. \$#grid) {		for my \$x (0 .. \$#{\$grid[\$y]}) {			\$grid[\$y][\$x] > 0				and \$known[\$grid[\$y][\$x]] = "\$y,\$x";		}	}	\$n = max(map { max @\$_ } @grid);} sub neighbors {	my (\$y, \$x) = @_;	my @out;	for (	[-1, -1], [-1, 0], [-1, 1],		[ 0, -1],	   [ 0, 1],		[ 1, -1], [ 1, 0], [ 1, 1])	{		my \$y1 = \$y + \$_->[0];		my \$x1 = \$x + \$_->[1];		next if \$x1 < 0 || \$y1 < 0;		next unless defined \$grid[\$y1][\$x1];		push @out, "\$y1,\$x1";	}	@out} sub try_fill {	my (\$v, \$coord) = @_;	return 1	if \$v > \$n; 	my (\$y, \$x) = split ',', \$coord;	my \$old = \$grid[\$y][\$x]; 	return	if \$old && \$old != \$v;	return	if exists \$known[\$v] and \$known[\$v] ne \$coord; 	\$grid[\$y][\$x] = \$v;	print "\033[0H";	show_board(); 	try_fill(\$v + 1, \$_) && return 1			for neighbors(\$y, \$x); 	\$grid[\$y][\$x] = \$old;	return} parse_board #	". 4 .#	 _ 7 _#	 1 _ _"; #	" 1 _ _ . . _ _ . . _ _ . . _ _ . . _ _ . . _ _ . . _ _ . . _ _ . . _ _ . . _ _ . . _ _ . . _ _ . . 74#	  . . _ . _ . _ . _ . _ . _ . _ . _ . _ . _ . _ . _ . _ . _ . _ . _ . _ . _ . _ . _ . _ . _ . _ . _#	  . . . _ _ . . _ _ . . _ _ . . _ _ . . _ _ . . _ _ . . _ _ . . _ _ . . _ _ . . _ _ . . _ _ . . _ _#	"; 	"__ 33 35 __ __ .. .. .. .	 __ __ 24 22 __ .. .. .. .	 __ __ __ 21 __ __ .. .. .	 __ 26 __ 13 40 11 .. .. .	 27 __ __ __  9 __  1 .. .	 .   . __ __ 18 __ __ .. .	 .  ..  .  . __  7 __ __ .	 .  .. .. ..  .  .  5 __ ."; print "\033[2J";try_fill(1, \$known[1]);`
Output:
```32 33 35 36 37
31 34 24 22 38
30 25 23 21 12 39
29 26 20 13 40 11
27 28 14 19  9 10  1
15 16 18  8  2
17  7  6  3
5  4
```

## Perl 6

This uses a Warnsdorff solver, which cuts down the number of tries by more than a factor of six over the brute force approach. This same solver is used in:

`my @adjacent = [-1, -1], [-1, 0], [-1, 1],               [ 0, -1],          [ 0, 1],               [ 1, -1], [ 1, 0], [ 1, 1]; solveboard q:to/END/;        __ 33 35 __ __ .. .. ..        __ __ 24 22 __ .. .. ..        __ __ __ 21 __ __ .. ..        __ 26 __ 13 40 11 .. ..        27 __ __ __  9 __  1 ..        .. .. __ __ 18 __ __ ..        .. .. .. .. __  7 __ __        .. .. .. .. .. ..  5 __        END sub solveboard(\$board) {    my \$max = +\$board.comb(/\w+/);    my \$width = \$max.chars;     my @grid;    my @known;    my @neigh;    my @degree;     @grid = \$board.lines.map: -> \$line {        [ \$line.words.map: { /^_/ ?? 0 !! /^\./ ?? Rat !! \$_ } ]    }     sub neighbors(\$y,\$x --> List) {        eager gather for @adjacent {            my \$y1 = \$y + .[0];            my \$x1 = \$x + .[1];            take [\$y1,\$x1] if defined @grid[\$y1][\$x1];        }    }     for ^@grid -> \$y {        for ^@grid[\$y] -> \$x {            if @grid[\$y][\$x] -> \$v {                @known[\$v] = [\$y,\$x];            }            if @grid[\$y][\$x].defined {                @neigh[\$y][\$x] = neighbors(\$y,\$x);                @degree[\$y][\$x] = +@neigh[\$y][\$x];            }        }    }    print "\e[0H\e[0J";     my \$tries = 0;     try_fill 1, @known[1];     sub try_fill(\$v, \$coord [\$y,\$x] --> Bool) {        return True if \$v > \$max;        \$tries++;         my \$old = @grid[\$y][\$x];         return False if +\$old and \$old != \$v;        return False if @known[\$v] and @known[\$v] !eqv \$coord;         @grid[\$y][\$x] = \$v;               # conjecture grid value         print "\e[0H";                    # show conjectured board        for @grid -> \$r {            say do for @\$r {                when Rat { ' ' x \$width }                when 0   { '_' x \$width }                default  { .fmt("%{\$width}d") }            }        }          my @neighbors = @neigh[\$y][\$x][];         my @degrees;        for @neighbors -> \n [\$yy,\$xx] {            my \$d = --@degree[\$yy][\$xx];  # conjecture new degrees            push @degrees[\$d], n;         # and categorize by degree        }         for @degrees.grep(*.defined) -> @ties {            for @ties.reverse {           # reverse works better for this hidato anyway                return True if try_fill \$v + 1, \$_;            }        }         for @neighbors -> [\$yy,\$xx] {            ++@degree[\$yy][\$xx];          # undo degree conjectures        }         @grid[\$y][\$x] = \$old;             # undo grid value conjecture        return False;    }     say "\$tries tries";}`

## Phix

`sequence board, warnsdorffs, knownx, knowny integer width, height, limit, nchars, triesstring fmt, blank constant ROW = 1, COL = 2constant moves = {{-1,-1},{-1,0},{-1,1},{0,-1},{0,1},{1,-1},{1,0},{1,1}} function onboard(integer row, integer col)    return row>=1 and row<=height and col>=nchars and col<=nchars*widthend function procedure init_warnsdorffs()integer nrow,ncol    for row=1 to height do        for col=nchars to nchars*width by nchars do            for move=1 to length(moves) do                nrow = row+moves[move][ROW]                ncol = col+moves[move][COL]*nchars                if onboard(nrow,ncol)                and board[nrow][ncol]='_' then                    warnsdorffs[nrow][ncol] += 1                end if            end for        end for    end forend procedure function solve(integer row, integer col, integer n)integer nrow, ncol    tries+= 1    if n>limit then return 1 end if    if knownx[n] then        for move=1 to length(moves) do            nrow = row+moves[move][ROW]            ncol = col+moves[move][COL]*nchars            if nrow = knownx[n]            and ncol = knowny[n] then                if solve(nrow,ncol,n+1) then return 1 end if                exit            end if        end for        return 0    end if    sequence wmoves = {}    for move=1 to length(moves) do        nrow = row+moves[move][ROW]        ncol = col+moves[move][COL]*nchars        if onboard(nrow,ncol)        and board[nrow][ncol]='_' then            wmoves = append(wmoves,{warnsdorffs[nrow][ncol],nrow,ncol})        end if    end for    wmoves = sort(wmoves)    -- avoid creating orphans    if length(wmoves)<2 or wmoves[2][1]>1 then        for m=1 to length(wmoves) do            {?,nrow,ncol} = wmoves[m]            warnsdorffs[nrow][ncol] -= 1        end for        for m=1 to length(wmoves) do            {?,nrow,ncol} = wmoves[m]            board[nrow][ncol-nchars+1..ncol] = sprintf(fmt,n)            if solve(nrow,ncol,n+1) then return 1 end if            board[nrow][ncol-nchars+1..ncol] = blank        end for        for m=1 to length(wmoves) do            {?,nrow,ncol} = wmoves[m]            warnsdorffs[nrow][ncol] += 1        end for    end if    return 0end function procedure Hidato(sequence s, integer w, integer h, integer lim)integer y, ch, ch2, katom t0 = time()    s = split(s,'\n')    width = w    height = h    nchars = length(sprintf(" %d",lim))    fmt = sprintf(" %%%dd",nchars-1)    blank = repeat('_',nchars)    board = repeat(repeat(' ',width*nchars),height)    knownx = repeat(0,lim)    knowny = repeat(0,lim)    limit = 0    for x=1 to height do        for y=nchars to width*nchars by nchars do            if y>length(s[x]) then                ch = '.'            else                ch = s[x][y]            end if            if ch='_' then                limit += 1            elsif ch!='.' then                k = ch-'0'                ch2 = s[x][y-1]                if ch2!=' ' then                    k += (ch2-'0')*10                    board[x][y-1] = ch2                end if                knownx[k] = x                knowny[k] = y                limit += 1            end if            board[x][y] = ch        end for    end for    warnsdorffs = repeat(repeat(0,width*nchars),height)    init_warnsdorffs()    tries = 0    if solve(knownx[1],knowny[1],2) then        puts(1,join(board,"\n"))        printf(1,"\nsolution found in %d tries (%3.2fs)\n",{tries,time()-t0})    else        puts(1,"no solutions found\n")    end ifend procedure constant board1 = """ __ 33 35 __ __ .. .. .. __ __ 24 22 __ .. .. .. __ __ __ 21 __ __ .. .. __ 26 __ 13 40 11 .. .. 27 __ __ __  9 __  1 .. .. .. __ __ 18 __ __ .. .. .. .. .. __  7 __ __ .. .. .. .. .. ..  5 __"""Hidato(board1,8,8,40) constant board2 = """ . 4 . _ 7 _ 1 _ _"""Hidato(board2,3,3,7) constant board3 = """  1  _  _  .  .  _  _  .  .  _  _  .  .  _  _  .  .  _  _  .  .  _  _  .  .  _  _  .  .  _  _  .  .  _  _  .  .  _  _  .  .  _  _  .  .  _  _  .  . 74  .  .  _  .  _  .  _  .  _  .  _  .  _  .  _  .  _  .  _  .  _  .  _  .  _  .  _  .  _  .  _  .  _  .  _  .  _  .  _  .  _  .  _  .  _  .  _  .  _  .  .  .  .  _  _  .  .  _  _  .  .  _  _  .  .  _  _  .  .  _  _  .  .  _  _  .  .  _  _  .  .  _  _  .  .  _  _  .  .  _  _  .  .  _  _  .  .  _  _  ."""Hidato(board3,50,3,74) constant board4 = """ 54 __ 60 59 __ 67 __ 69 __ __ 55 __ __ 63 65 __ 72 71 51 50 56 62 __ .. .. .. .. __ __ __ 14 .. .. 17 __ .. 48 10 11 .. 15 __ 18 __ 22 __ 46 __ ..  3 __ 19 23 __ __ 44 __  5 __  1 33 32 __ __ 43  7 __ 36 __ 27 __ 31 42 __ __ 38 __ 35 28 __ 30"""Hidato(board4,9,9,72) constant board5 = """ __ 58 __ 60 __ __ 63 66 __ 57 55 59 53 49 __ 65 __ 68 __  8 __ __ 50 __ 46 45 __ 10  6 __ .. .. .. __ 43 70 __ 11 12 .. .. .. 72 71 __ __ 14 __ .. .. .. 30 39 __ 15  3 17 __ 28 29 __ __ 40 __ __ 19 22 __ __ 37 36 __  1 20 __ 24 __ 26 __ 34 33"""Hidato(board5,9,9,72) constant board6 = """  1 __ .. .. .. __ __ .. .. .. __ __ .. .. .. __ __ .. .. .. __ __ .. .. .. __ __ .. .. .. __ __ .. .. .. __ __ .. .. .. __ __ .. .. .. 82 .. .. __ .. __ .. .. __ .. __ .. .. __ .. __ .. .. __ .. __ .. .. __ .. __ .. .. __ .. __ .. .. __ .. __ .. .. __ .. __ .. .. __ .. __ .. .. __ .. __ .. .. __ .. __ .. .. __ .. __ .. .. __ .. __ .. .. __ .. __ .. .. __ .. __ .. .. __ .. __ .. .. __ .. __ .. .. __ .. __ .. .. __ __ __ .. .. __ __ __ .. .. __ __ __ .. .. __ __ __ .. .. __ __ __ .. .. __ __ __ .. .. __ __ __ .. .. __ __ __ .. .. __ __ __ .. .. .."""Hidato(board6,46,4,82)`
Output:
``` 32 33 35 36 37  .  .  .
31 34 24 22 38  .  .  .
30 25 23 21 12 39  .  .
29 26 20 13 40 11  .  .
27 28 14 19  9 10  1  .
.  . 15 16 18  8  2  .
.  .  .  . 17  7  6  3
.  .  .  .  .  .  5  4
solution found in 760 tries (0.00s)
. 4 .
3 7 5
1 2 6
solution found in 10 tries (0.00s)
1  2  3  .  .  8  9  .  . 14 15  .  . 20 21  .  . 26 27  .  . 32 33  .  . 38 39  .  . 44 45  .  . 50 51  .  . 56 57  .  . 62 63  .  . 68 69  .  . 74
.  .  4  .  7  . 10  . 13  . 16  . 19  . 22  . 25  . 28  . 31  . 34  . 37  . 40  . 43  . 46  . 49  . 52  . 55  . 58  . 61  . 64  . 67  . 70  . 73  .
.  .  .  5  6  .  . 11 12  .  . 17 18  .  . 23 24  .  . 29 30  .  . 35 36  .  . 41 42  .  . 47 48  .  . 53 54  .  . 59 60  .  . 65 66  .  . 71 72  .
solution found in 74 tries (0.00s)
54 53 60 59 58 67 66 69 70
52 55 61 57 63 65 68 72 71
51 50 56 62 64  .  .  .  .
49 12 13 14  .  . 17 21  .
48 10 11  . 15 16 18 20 22
47 46  9  .  3  2 19 23 24
45 44  8  5  4  1 33 32 25
41 43  7  6 36 34 27 26 31
42 40 39 38 37 35 28 29 30
solution found in 106 tries (0.00s)
56 58 54 60 61 62 63 66 67
57 55 59 53 49 47 65 64 68
9  8 52 51 50 48 46 45 69
10  6  7  .  .  . 44 43 70
5 11 12  .  .  . 72 71 42
4 14 13  .  .  . 30 39 41
15  3 17 18 28 29 38 31 40
2 16 19 22 25 27 37 36 32
1 20 21 24 23 26 35 34 33
solution found in 495 tries (0.00s)
1  2  .  .  . 10 11  .  .  . 19 20  .  .  . 28 29  .  .  . 37 38  .  .  . 46 47  .  .  . 55 56  .  .  . 64 65  .  .  . 73 74  .  .  . 82
.  .  3  .  9  .  . 12  . 18  .  . 21  . 27  .  . 30  . 36  .  . 39  . 45  .  . 48  . 54  .  . 57  . 63  .  . 66  . 72  .  . 75  . 81  .
.  4  .  8  .  . 13  . 17  .  . 22  . 26  .  . 31  . 35  .  . 40  . 44  .  . 49  . 53  .  . 58  . 62  .  . 67  . 71  .  . 76  . 80  .  .
5  6  7  .  . 14 15 16  .  . 23 24 25  .  . 32 33 34  .  . 41 42 43  .  . 50 51 52  .  . 59 60 61  .  . 68 69 70  .  . 77 78 79  .  .  .
solution found in 82 tries (0.02s)
```

## PicoLisp

`(load "@lib/simul.l") (de hidato (Lst)   (let Grid (grid (length (maxi length Lst)) (length Lst))      (mapc         '((G L)            (mapc               '((This Val)                  (nond                     (Val                        (with (: 0 1 1) (con (: 0 1)))    # Cut off west                        (with (: 0 1 -1) (set (: 0 1)))   # east                        (with (: 0 -1 1) (con (: 0 -1)))  # south                        (with (: 0 -1 -1) (set (: 0 -1))) # north                        (set This) )                     ((=T Val) (=: val Val)) ) )               G L ) )         Grid         (apply mapcar (reverse Lst) list) )      (let Todo         (by '((This) (: val)) sort            (mapcan '((Col) (filter '((This) (: val)) Col))               Grid ) )         (let N 1            (with (pop 'Todo)               (recur (N Todo)                  (unless (> (inc 'N) (; Todo 1 val))                     (find                        '((Dir)                           (with (Dir This)                              (cond                                 ((= N (: val))                                    (if (cdr Todo) (recurse N @) T) )                                 ((not (: val))                                    (=: val N)                                    (or (recurse N Todo) (=: val NIL)) ) ) ) )                        (quote                           west east south north                           ((X) (or (south (west X)) (west (south X))))                           ((X) (or (north (west X)) (west (north X))))                           ((X) (or (south (east X)) (east (south X))))                           ((X) (or (north (east X)) (east (north X)))) ) ) ) ) ) ) )      (disp Grid 0         '((This)            (if (: val) (align 3 @) "   ") ) ) ) )`

Test:

`(hidato   (quote      (T   33  35  T   T)      (T   T   24  22  T)      (T   T   T   21  T   T)      (T   26  T   13  40  11)      (27  T   T   T   9   T   1)      (NIL NIL T   T   18  T   T)      (NIL NIL NIL NIL T   7   T  T)      (NIL NIL NIL NIL NIL NIL 5  T) ) )`

Output:

```   +---+---+---+---+---+---+---+---+
8 | 32  33  35  36  37|   |   |   |
+   +   +   +   +   +---+---+---+
7 | 31  34  24  22  38|   |   |   |
+   +   +   +   +   +---+---+---+
6 | 30  25  23  21  12  39|   |   |
+   +   +   +   +   +   +---+---+
5 | 29  26  20  13  40  11|   |   |
+   +   +   +   +   +   +---+---+
4 | 27  28  14  19   9  10   1|   |
+---+---+   +   +   +   +   +---+
3 |   |   | 15  16  18   8   2|   |
+---+---+---+---+   +   +   +---+
2 |   |   |   |   | 17   7   6   3|
+---+---+---+---+---+---+   +   +
1 |   |   |   |   |   |   |  5   4|
+---+---+---+---+---+---+---+---+
a   b   c   d   e   f   g   h```

## Prolog

Works with SWI-Prolog and library(clpfd) written by Markus Triska.
Puzzle solved is from the Wilkipedia page : http://en.wikipedia.org/wiki/Hidato

`:- use_module(library(clpfd)). hidato :-	init1(Li),	% skip first blank line	init2(1, 1, 10, Li),	my_write(Li).  init1(Li) :-	Li = [  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,		0,  A, 33, 35,  B,  C,  0,  0,  0,  0,	        0,  D,  E, 24, 22,  F,  0,  0,  0,  0,	        0,  G,  H,  I, 21,  J,  K,  0,  0,  0,	        0,  L, 26,  M, 13, 40, 11,  0,  0,  0,	        0, 27,  N,  O,  P,  9,  Q,  1,  0,  0,	        0,  0,  0,  R,  S, 18,  T,  U,  0,  0,	        0,  0,  0,  0,  0,  V,  7,  W,  X,  0,	        0,  0,  0,  0,  0,  0,  0,  5,  Y,  0,	        0,  0,  0,  0,  0,  0,  0,  0,  0,  0], 	LV = [  A, 33, 35,  B,  C,	        D,  E, 24, 22,  F,	        G,  H,  I, 21,  J,  K,	        L, 26,  M, 13, 40, 11,	       27,  N,  O,  P,  9,  Q,  1,	                R,  S, 18,  T,  U,	                        V,  7,  W,  X,					5,  Y],  	LV ins 1..40,	all_distinct(LV). % give the constraints% Stop before the last line init2(_N, Col, Max_Col, _L) :-	Col is Max_Col - 1. % skip zerosinit2(N, Lig, Col, L) :-	I is N + Lig * Col,	element(I, L, 0),	!,	V is N+1,	(   V > Col -> N1 = 1, Lig1 is Lig + 1; N1 = V, Lig1 = Lig),	init2(N1, Lig1, Col, L).  % skip first columninit2(1, Lig, Col, L) :-	!,	init2(2, Lig, Col, L) . % skip last columninit2(Col, Lig, Col, L) :-	!,	Lig1 is Lig+1,	init2(1, Lig1, Col, L). % V5 V3 V6% V1  V V2% V7 V4 V8% general caseinit2(N, Lig, Col, L) :-	I is N + Lig * Col,	element(I, L, V), 	I1 is I  - 1, I2 is I  + 1, I3 is I  - Col, I4 is I  + Col,	I5 is I3 - 1, I6 is I3 + 1, I7 is I4 - 1,   I8 is I4 + 1, 	maplist(compute_BI(L, V), [I1,I2,I3,I4,I5,I6,I7,I8], VI, BI), 	sum(BI, #=, SBI), 	(  ((V #=  1 #\/ V #=  40) #/\ SBI #= 1) #\/	    (V #\= 1 #/\ V #\= 40  #/\ SBI #= 2)) #<==> 1, 	labeling([ffc, enum], [V | VI]), 	N1 is N+1,	init2(N1, Lig, Col, L). compute_BI(L, V, I, VI, BI) :-	element(I, L, VI),	VI #= 0 #==> BI #= 0,	( VI #\= 0 #/\ (V - VI #= 1 #\/ VI - V #= 1))  #<==> BI. % display the resultmy_write([0, A, B, C, D, E, F, G, H, 0 | T]) :-	maplist(my_write_1, [A, B, C, D, E, F, G, H]), nl,	my_write(T). my_write([]). my_write_1(0) :-	write('   '). my_write_1(X) :-	writef('%3r', [X]).`
Output:
```?- hidato.
32 33 35 36 37
31 34 24 22 38
30 25 23 21 12 39
29 26 20 13 40 11
27 28 14 19  9 10  1
15 16 18  8  2
17  7  6  3
5  4
true ```

## Python

`board = []given = []start = None def setup(s):    global board, given, start    lines = s.splitlines()    ncols = len(lines[0].split())    nrows = len(lines)    board = [[-1] * (ncols + 2) for _ in xrange(nrows + 2)]     for r, row in enumerate(lines):        for c, cell in enumerate(row.split()):            if cell == "__" :                board[r + 1][c + 1] = 0                continue            elif cell == ".":                continue # -1            else:                val = int(cell)                board[r + 1][c + 1] = val                given.append(val)                if val == 1:                    start = (r + 1, c + 1)    given.sort() def solve(r, c, n, next=0):    if n > given[-1]:        return True    if board[r][c] and board[r][c] != n:        return False    if board[r][c] == 0 and given[next] == n:        return False     back = 0    if board[r][c] == n:        next += 1        back = n     board[r][c] = n    for i in xrange(-1, 2):        for j in xrange(-1, 2):            if solve(r + i, c + j, n + 1, next):                return True    board[r][c] = back    return False def print_board():    d = {-1: "  ", 0: "__"}    bmax = max(max(r) for r in board)    form = "%" + str(len(str(bmax)) + 1) + "s"    for r in board[1:-1]:        print "".join(form % d.get(c, str(c)) for c in r[1:-1]) hi = """\__ 33 35 __ __  .  .  .__ __ 24 22 __  .  .  .__ __ __ 21 __ __  .  .__ 26 __ 13 40 11  .  .27 __ __ __  9 __  1  . .  . __ __ 18 __ __  . .  .  .  . __  7 __ __ .  .  .  .  .  .  5 __""" setup(hi)print_board()solve(start[0], start[1], 1)printprint_board()`
Output:
``` __ 33 35 __ __
__ __ 24 22 __
__ __ __ 21 __ __
__ 26 __ 13 40 11
27 __ __ __  9 __  1
__ __ 18 __ __
__  7 __ __
5 __

32 33 35 36 37
31 34 24 22 38
30 25 23 21 12 39
29 26 20 13 40 11
27 28 14 19  9 10  1
15 16 18  8  2
17  7  6  3
5  4```

## Racket

### Standalone

Algorithm is depth first search for each number, repeating for all numbers in ascending order. It currently runs slowish due to temporary shortcomings in untyped Racket's array indexing, but finished immediately when tested with custom 2d vector library.

` #lang racket(require math/array) ;#f = not a legal position, #t = blank position(define board  (array   #[#[#t 33 35 #t #t #f #f #f]     #[#t #t 24 22 #t #f #f #f]     #[#t #t #t 21 #t #t #f #f]     #[#t 26 #t 13 40 11 #f #f]     #[27 #t #t #t  9 #t  1 #f]     #[#f #f #t #t 18 #t #t #f]     #[#f #f #f #f #t  7 #t #t]     #[#f #f #f #f #f #f  5 #t]])) ;filters elements with the predicate, returning the element and its indices(define (array-indices-of a f)  (for*/list ([i (range 0 (vector-ref (array-shape a) 0))]              [j (range 0 (vector-ref (array-shape a) 1))]              #:when (f (array-ref a (vector i j))))    (list (array-ref a (vector i j)) i j))) ;returns a list, each element is a list of the number followed by i and j indices;sorted ascending by number(define (goal-list v) (sort (array-indices-of v number?) (λ (a b) (< (car a) (car b))))) ;every direction + start position that's on the board(define (legal-moves a i0 j0)  (for*/list ([i (range (sub1 i0) (+ i0 2))]              [j (range (sub1 j0) (+ j0 2))]              ;cartesian product -1..1 and -1..1, except 0 0              #:when (and (not (and (= i i0) (= j j0)))                          ;make sure it's on the board                          (<= 0 i (sub1 (vector-ref (array-shape a) 0)))                          (<= 0 j (sub1 (vector-ref (array-shape a) 1)))                          ;make sure it's an actual position too (the real board isn't square)                          (array-ref a (vector i j))))    (cons i j))) ;find path through array, returning list of coords from start to finish(define (hidato-path a)  ;get starting position as first goal  (match-let ([(cons (list n i j) goals) (goal-list a)])    (let hidato ([goals goals] [n n] [i i] [j j] [path '()])      (match goals        ;no more goals, return path        ['() (reverse (cons (cons i j) path))]        ;get next goal        [(cons (list n-goal i-goal j-goal) _)         (let ([move (cons i j)])           ;already visiting a spot or taking too many moves to reach the next goal is no good           (cond [(or (member move path) (> n n-goal)) #f]                 ;taking the right number of moves to be at the goal square is good                 ;so go to the next goal                 [(and (= n n-goal) (= i i-goal) (= j j-goal))                  (hidato (cdr goals) n i j path)]                 ;depth first search using every legal move to find next goal                 [else (ormap (λ (m) (hidato goals (add1 n) (car m) (cdr m) (cons move path)))                              (legal-moves a i j))]))])))) ;take a path and insert it into the array(define (put-path a path)  (let ([a (array->mutable-array a)])    (for ([n (range 1 (add1 (length path)))] [move path])      (array-set! a (vector (car move) (cdr move)) n))    a)) ;main function(define (hidato board) (put-path board (hidato-path board))) `
Output:
```> (hidato board)
(mutable-array
#[#[32 33 35 36 37 #f #f #f]
#[31 34 24 22 38 #f #f #f]
#[30 25 23 21 12 39 #f #f]
#[29 26 20 13 40 11 #f #f]
#[27 28 14 19 9 10 1 #f]
#[#f #f 15 16 18 8 2 #f]
#[#f #f #f #f 17 7 6 3]
#[#f #f #f #f #f #f 5 4]])
```

### Using Hidato Family Solver from Numbrix

This solution uses the module "hidato-family-solver.rkt" from Solve a Numbrix puzzle#Racket. The difference between the two is essentially the neighbourhood function.

`#lang racket(require "hidato-family-solver.rkt") (define moore-neighbour-offsets  '((+1 0) (-1 0) (0 +1) (0 -1) (+1 +1) (-1 -1) (-1 +1) (+1 -1))) (define solve-hidato (solve-hidato-family moore-neighbour-offsets)) (displayln (puzzle->string  (solve-hidato   #(#( 0 33 35  0  0)     #( 0  0 24 22  0)     #( 0  0  0 21  0  0)     #( 0 26  0 13 40 11)     #(27  0  0  0  9  0  1)     #( _  _  0  0 18  0  0)     #( _  _  _  _  0  7  0  0)     #( _  _  _  _  _  _  5  0))))) `
Output:
```32 33 35 36 37  _  _  _
31 34 24 22 38  _  _  _
30 25 23 21 12 39  _  _
29 26 20 13 40 11  _  _
27 28 14 19  9 10  1  _
_  _ 15 16 18  8  2  _
_  _  _  _ 17  7  6  3
_  _  _  _  _  _  5  4```

## REXX

Programming note:   the coördinates for the cells used are the same as an   X Y   grid, that is,
the bottom left-most cell is   1 1   and the tenth cell on row 2 is   2 10
If any marker is negative, then it's assumed to be a Numbrix puzzle (and the absolute value is used).
Over half of the REXX program deals with validating the input and displaying the puzzle.

Hidato   and   Numbrix   are registered trademarks.

`/*REXX program solves a  Numbrix (R) puzzle, it also displays the puzzle and solution.  */maxR=0;    maxC=0;    maxX=0;     minR=9e9;      minC=9e9;    minX=9e9;    cells=0;    @.=parse arg xxx;        PZ='Hidato puzzle'         /*get the cell definitions from the CL.*/xxx=translate(xxx, , "/\;:_", ',')               /*also allow other characters as comma.*/                do  while xxx\='';  parse var  xxx    r c   marks  ','  xxx                   do  while marks\='';          [email protected].r.c                   parse var marks  x  marks                   if datatype(x,'N')  then do;  x=x/1                     /*normalize X*/                                                 if x<0  then PZ= 'Numbrix puzzle'                                                 x=abs(x)                  /*use  │x│   */                                            end                   minR=min(minR,r);  maxR=max(maxR,r); minC=min(minC,c); maxC=max(maxC,c)                   if x==1   then do;  !r=r;  !c=c;  end              /*the START cell. */                   if _\=='' then call err "cell at" r c 'is already occupied with:'  _                   @.r.c=x;   c=c+1;    cells=cells+1                 /*assign a mark.  */                   if x==.              then iterate                  /*is a hole?  Skip*/                   if \datatype(x,'W')  then call err 'illegal marker specified:' x                   minX=min(minX,x);    maxX=max(maxX,x)              /*min and max  X. */                   end   /*while marks¬='' */               end       /*while xxx  ¬='' */call show                                        /* [↓]  is used for making fast moves. */Nr = '0  1   0  -1    -1   1   1  -1'            /*possible  row     for the next move. */Nc = '1  0  -1   0     1  -1   1  -1'            /*   "      column   "   "    "    "   */pMoves=words(Nr) -4*(left(PZ,1)=='N')            /*is this to be a Numbrix puzzle ?     */  do i=1  for pMoves;   Nr.i=word(Nr,i);   Nc.i=word(Nc,i);   end     /*for fast moves. */if \next(2,!r,!c)  then call err  'No solution possible for this'   PZ    "puzzle."say 'A solution for the'   PZ    "exists.";      say;                     call showexit                                             /*stick a fork in it,  we're all done. *//*──────────────────────────────────────────────────────────────────────────────────────*/err:  say;    say '***error*** (from' PZ"): "    arg(1);        say;          exit 13/*──────────────────────────────────────────────────────────────────────────────────────*/next: procedure expose @. Nr. Nc. cells pMoves;  parse arg #,r,c;   ##=#+1           do t=1  for pMoves                                   /* [↓]  try some moves. */           parse value  r+Nr.t c+Nc.t  with nr nc               /*next move coördinates.*/           if @.nr.nc==.  then do;                @.nr.nc=#     /*let's try this move.  */                               if #==cells        then leave    /*is this the last move?*/                               if next(##,nr,nc)  then return 1                               @.nr.nc=.                        /*undo the above move.  */                               iterate                          /*go & try another move.*/                               end           if @.nr.nc==#  then do                               /*this a fill-in move ? */                               if #==cells        then return 1 /*this is the last move.*/                               if next(##,nr,nc)  then return 1 /*a fill-in move.       */                               end           end   /*t*/      return 0                                                  /*this ain't working.   *//*──────────────────────────────────────────────────────────────────────────────────────*/show: if maxR<1 | maxC<1  then call err  'no legal cell was specified.'      if minX<1           then call err  'no  1  was specified for the puzzle start'      w=max(2,length(cells));  do    r=maxR  to minR  by -1; _=                                  do c=minC  to maxC;        _=_ right(@.r.c,w); end /*c*/                               say _                               end   /*r*/      say;    return`

output   when using the following as input:
1 7 5 .\2 5 . 7 . .\3 3 . . 18 . .\4 1 27 . . . 9 . 1\5 1 . 26 . 13 40 11\6 1 . . . 21 . .\7 1 . . 24 22 .\8 1 . 33 35 . .

```  . 33 35  .  .
.  . 24 22  .
.  .  . 21  .  .
. 26  . 13 40 11
27  .  .  .  9  .  1
.  . 18  .  .
.  7  .  .
5  .

A solution for the Hidato puzzle exists.

32 33 35 36 37
31 34 24 22 38
30 25 23 21 12 39
29 26 20 13 40 11
27 28 14 19  9 10  1
15 16 18  8  2
17  7  6  3
5  4
```

## Ruby

### Without Warnsdorff

The following class provides functionality for solving a hidato problem:

`# Solve a Hidato Puzzle#class Hidato  Cell = Struct.new(:value, :used, :adj)  ADJUST = [[-1, -1], [-1, 0], [-1, 1], [0, -1], [0, 1], [1, -1], [1, 0], [1, 1]]   def initialize(board, pout=true)    @board = []    board.each_line do |line|      @board << line.split.map{|n| Cell[Integer(n), false] rescue nil} + [nil]    end    @board << []                                # frame (Sentinel value : nil)    @board.each_with_index do |row, x|      row.each_with_index do |cell, y|        if cell          @sx, @sy = x, y  if cell.value==1     # start position          cell.adj = ADJUST.map{|dx,dy| [x+dx,y+dy]}.select{|xx,yy| @board[xx][yy]}        end      end    end    @xmax = @board.size - 1    @ymax = @board.map(&:size).max - 1    @end  = @board.flatten.compact.size    puts to_s('Problem:')  if pout  end   def solve    @zbl = Array.new(@end+1, false)    @board.flatten.compact.each{|cell| @zbl[cell.value] = true}    puts (try(@board[@sx][@sy], 1) ? to_s('Solution:') : "No solution")  end   def try(cell, seq_num)    return true  if seq_num > @end    return false if cell.used    value = cell.value    return false if value > 0 and value != seq_num    return false if value == 0 and @zbl[seq_num]    cell.used = true    cell.adj.each do |x, y|      if try(@board[x][y], seq_num+1)        cell.value = seq_num        return true      end    end    cell.used = false  end   def to_s(msg=nil)    str = (0[email protected]).map do |x|      (0[email protected]).map{|y| "%3s" % (([email protected][x][y]) ? c.value : c)}.join    end    (msg ? [msg] : []) + str + [""]  endend`

Test:

`# Which may be used as follows to solve Evil Case 1:board1 = <<EOS  .  4  0  7  0  1  0  0EOSHidato.new(board1).solve # Which may be used as follows to solve this tasks example:board2 = <<EOS  0 33 35  0  0  0  0 24 22  0  0  0  0 21  0  0  0 26  0 13 40 11 27  0  0  0  9  0  1  .  .  0  0 18  0  0  .  .  .  .  0  7  0  0  .  .  .  .  .  .  5  0EOSHidato.new(board2).solve # Which may be used as follows to solve The Snake in the Grass:board3 = <<EOS  1  0  0  .  .  0  0  .  .  0  0  .  .  0  0  .  .  0  0  .  .  0  0  .  .  0  0  .  .  0  0  .  .  0  0  .  .  0  0  .  .  0  0  .  .  0  0  .  . 74  .  .  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  .  .  0  0  .  .  0  0  .  .  0  0  .  .  0  0  .  .  0  0  .  .  0  0  .  .  0  0  .  .  0  0  .EOSt0 = Time.nowHidato.new(board3).solveputs " #{Time.now - t0} sec"`
Output:
```Problem:
4
0  7  0
1  0  0

Solution:
4
3  7  5
1  2  6

Problem:
0 33 35  0  0
0  0 24 22  0
0  0  0 21  0  0
0 26  0 13 40 11
27  0  0  0  9  0  1
0  0 18  0  0
0  7  0  0
5  0

Solution:
32 33 35 36 37
31 34 24 22 38
30 25 23 21 12 39
29 26 20 13 40 11
27 28 14 19  9 10  1
15 16 18  8  2
17  7  6  3
5  4

Problem:
1  0  0        0  0        0  0        0  0        0  0        0  0        0  0        0  0        0  0        0  0        0  0        0  0       74
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        0  0        0  0        0  0        0  0        0  0        0  0        0  0        0  0

Solution:
1  2  3        8  9       14 15       20 21       26 27       32 33       38 39       44 45       50 51       56 57       62 63       68 69       74
4     7    10    13    16    19    22    25    28    31    34    37    40    43    46    49    52    55    58    61    64    67    70    73
5  6       11 12       17 18       23 24       29 30       35 36       41 42       47 48       53 54       59 60       65 66       71 72

40.198299 sec
```

### With Warnsdorff

I modify method as follows to implement Warnsdorff like

`# Solve a Hidato Like Puzzle with Warnsdorff like logic applied#class HLPsolver  attr_reader :board  Cell = Struct.new(:value, :used, :adj)   def initialize(board, pout=true)    @board = []    frame = ADJACENT.flatten.map(&:abs).max    board.each_line do |line|      @board << line.split.map{|n| Cell[Integer(n), false] rescue nil} + [nil]*frame    end    frame.times {@board << []}                  # frame (Sentinel value : nil)    @board.each_with_index do |row, x|      row.each_with_index do |cell, y|        if cell          @sx, @sy = x, y  if cell.value==1     # start position          cell.adj = ADJACENT.map{|dx,dy| [x+dx,y+dy]}.select{|xx,yy| @board[xx][yy]}        end      end    end    @xmax = @board.size - frame    @ymax = @board.map(&:size).max - frame    @end  = @board.flatten.compact.size    @format = " %#{@end.to_s.size}s"    puts to_s('Problem:')  if pout  end   def solve    @zbl = Array.new(@end+1, false)    @board.flatten.compact.each{|cell| @zbl[cell.value] = true}    puts (try(@board[@sx][@sy], 1) ? to_s('Solution:') : "No solution")  end   def try(cell, seq_num)    value = cell.value    return false if value > 0 and value != seq_num    return false if value == 0 and @zbl[seq_num]    cell.used = true    if seq_num == @end      cell.value = seq_num      return true    end    a = []    cell.adj.each_with_index do |(x, y), n|      cl = @board[x][y]      a << [wdof(cl.adj)*10+n, x, y]  unless cl.used    end    a.sort.each do |key, x, y|      if try(@board[x][y], seq_num+1)        cell.value = seq_num        return true      end    end    cell.used = false  end   def wdof(adj)    adj.count {|x,y| not @board[x][y].used}  end   def to_s(msg=nil)    str = (0[email protected]).map do |x|      (0[email protected]).map{|y| @format % (([email protected][x][y]) ? c.value : c)}.join    end    (msg ? [msg] : []) + str + [""]  endend`

Which may be used as follows to solve Hidato Puzzles:

`require 'HLPsolver' ADJACENT = [[-1, -1], [-1, 0], [-1, 1], [0, -1], [0, 1], [1, -1], [1, 0], [1, 1]] # solve Evil Case 1:board1 = <<EOS  .  4  0  7  0  1  0  0EOSHLPsolver.new(board1).solve boardx = <<EOS  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  1  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  0  0  0  0  0  0EOSHLPsolver.new(boardx).solve # solve this tasks example:board2 = <<EOS  0 33 35  0  0  0  0 24 22  0  0  0  0 21  0  0  0 26  0 13 40 11 27  0  0  0  9  0  1  .  .  0  0 18  0  0  .  .  .  .  0  7  0  0  .  .  .  .  .  .  5  0EOSHLPsolver.new(board2).solve #solve The Snake in the Grass:board3 = <<EOS  1  0  0  .  .  0  0  .  .  0  0  .  .  0  0  .  .  0  0  .  .  0  0  .  .  0  0  .  .  0  0  .  .  0  0  .  .  0  0  .  .  0  0  .  .  0  0  .  . 74  .  .  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  .  .  0  0  .  .  0  0  .  .  0  0  .  .  0  0  .  .  0  0  .  .  0  0  .  .  0  0  .  .  0  0  .EOSt0 = Time.nowHLPsolver.new(board3).solveputs " #{Time.now - t0} sec"`

Which produces:

```Problem:
4
0 7 0
1 0 0

Solution:
4
3 7 5
1 2 6

Problem:
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  1  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  0  0  0  0  0  0

Solution:
33 34 36 37 41 42 43 44
32 35 38 40 56 55 46 45
2 31 39 57 59 60 54 47
3  1 30 58 61 62 53 48
4  6 18 29 63 64 52 49
5  7 17 19 28 51 50 25
8 11 13 16 20 27 26 24
9 10 12 14 15 21 22 23

Problem:
0 33 35  0  0
0  0 24 22  0
0  0  0 21  0  0
0 26  0 13 40 11
27  0  0  0  9  0  1
0  0 18  0  0
0  7  0  0
5  0

Solution:
32 33 35 36 37
31 34 24 22 38
30 25 23 21 12 39
29 26 20 13 40 11
27 28 14 19  9 10  1
15 16 18  8  2
17  7  6  3
5  4

Problem:
1  0  0        0  0        0  0        0  0        0  0        0  0        0  0        0  0        0  0        0  0        0  0        0  0       74
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        0  0        0  0        0  0        0  0        0  0        0  0        0  0        0  0

Solution:
1  2  3        8  9       14 15       20 21       26 27       32 33       38 39       44 45       50 51       56 57       62 63       68 69       74
4     7    10    13    16    19    22    25    28    31    34    37    40    43    46    49    52    55    58    61    64    67    70    73
5  6       11 12       17 18       23 24       29 30       35 36       41 42       47 48       53 54       59 60       65 66       71 72

0.003001 sec
```

HLPsolver may be used to solve Knight's tour:

## Seed7

`\$ include "seed7_05.s7i"; var set of integer: given is {};var array array integer: board is 0 times 0 times 0;var integer: startRow is 0;var integer: startColumn is 0; const proc: setup (in array string: input) is func  local    var integer: r is 0;    var integer: c is 0;    var array string: row is 0 times "";    var string: cell is "";    var integer: value is 0;  begin    board := (length(input) + 2) times 0 times 0;    for key r range input do      row := split(input[r], " ");      board[r + 1] := (length(row) + 2) times - 1;      for key c range row do        cell := row[c];        if cell = "_" then          board[r + 1][c + 1] := 0;        elsif cell[1] in {'0' .. '9'} then          value := integer parse cell;          board[r + 1][c + 1] := value;          incl(given, value);          if value = 1 then            startRow := r + 1;            startColumn := c + 1;          end if;        end if;      end for;    end for;    board[1] := (length(row) + 2) times - 1;    board[length(input) + 2] := (length(row) + 2) times - 1;  end func; const func boolean: solve (in integer: r, in integer: c, in integer: n) is func  result    var boolean: solved is FALSE;  local    var integer: back is 0;    var integer: i is 0;    var integer: j is 0;  begin    if n > max(given) then      solved := TRUE;    elsif board[r][c] = 0 and n not in given or board[r][c] = n then      back := board[r][c];      board[r][c] := n;      for i range -1 to 1 until solved do        for j range -1 to 1 until solved do          solved := solve(r + i, c + j, n + 1);        end for;      end for;      if not solved then        board[r][c] := back;      end if;    end if;  end func; const proc: printBoard is func  local    var integer: r is 0;    var integer: c is 0;  begin    for key r range board do      for c range board[r] do        if c = -1 then          write(" . ");        elsif c > 0 then          write(c lpad 2 <& " ");        else          write("__ ");        end if;      end for;      writeln;    end for;  end func; const proc: main is func  local    const array string: input is [] ("_ 33 35 _ _ . . .",                                     "_ _ 24 22 _ . . .",                                     "_ _ _ 21 _ _ . .",                                     "_ 26 _ 13 40 11 . .",                                     "27 _ _ _ 9 _ 1 .",                                     ". . _ _ 18 _ _ .",                                     ". . . . _ 7 _ _",                                     ". . . . . . 5 _");  begin    setup(input);    printBoard;    writeln;    if solve(startRow, startColumn, 1) then      writeln("Found:");      printBoard;    end if;  end func;`
Output:
``` .  .  .  .  .  .  .  .  .  .
. __ 33 35 __ __  .  .  .  .
. __ __ 24 22 __  .  .  .  .
. __ __ __ 21 __ __  .  .  .
. __ 26 __ 13 40 11  .  .  .
. 27 __ __ __  9 __  1  .  .
.  .  . __ __ 18 __ __  .  .
.  .  .  .  . __  7 __ __  .
.  .  .  .  .  .  .  5 __  .
.  .  .  .  .  .  .  .  .  .

Found:
.  .  .  .  .  .  .  .  .  .
. 32 33 35 36 37  .  .  .  .
. 31 34 24 22 38  .  .  .  .
. 30 25 23 21 12 39  .  .  .
. 29 26 20 13 40 11  .  .  .
. 27 28 14 19  9 10  1  .  .
.  .  . 15 16 18  8  2  .  .
.  .  .  .  . 17  7  6  3  .
.  .  .  .  .  .  .  5  4  .
.  .  .  .  .  .  .  .  .  .
```

## Tcl

`proc init {initialConfiguration} {    global grid max filled    set max 1    set y 0    foreach row [split [string trim \$initialConfiguration "\n"] "\n"] {	set x 0	set rowcontents {}	foreach cell \$row {	    if {![string is integer -strict \$cell]} {set cell -1}	    lappend rowcontents \$cell	    set max [expr {max(\$max, \$cell)}]	    if {\$cell > 0} {		dict set filled \$cell [list \$y \$x]	    }	    incr x	}	lappend grid \$rowcontents	incr y    }} proc findseps {} {    global max filled    set result {}    for {set i 1} {\$i < \$max-1} {incr i} {	if {[dict exists \$filled \$i]} {	    for {set j [expr {\$i+1}]} {\$j <= \$max} {incr j} {		if {[dict exists \$filled \$j]} {		    if {\$j-\$i > 1} {			lappend result [list \$i \$j [expr {\$j-\$i}]]		    }		    break		}	    }	}    }    return [lsort -integer -index 2 \$result]} proc makepaths {sep} {    global grid filled    lassign \$sep from to len    lassign [dict get \$filled \$from] y x    set result {}    foreach {dx dy} {-1 -1  -1 0  -1 1  0 -1  0 1  1 -1  1 0  1 1} {	discover [expr {\$x+\$dx}] [expr {\$y+\$dy}] [expr {\$from+1}] \$to \	    [list [list \$from \$x \$y]] \$grid    }    return \$result}proc discover {x y n limit path model} {    global filled    # Check for illegal    if {[lindex \$model \$y \$x] != 0} return    upvar 1 result result    lassign [dict get \$filled \$limit] ly lx    # Special case    if {\$n == \$limit-1} {	if {abs(\$x-\$lx)<=1 && abs(\$y-\$ly)<=1 && !(\$lx==\$x && \$ly==\$y)} {	    lappend result [lappend path [list \$n \$x \$y] [list \$limit \$lx \$ly]]	}	return    }    # Check for impossible    if {abs(\$x-\$lx) > \$limit-\$n || abs(\$y-\$ly) > \$limit-\$n} return    # Recursive search    lappend path [list \$n \$x \$y]    lset model \$y \$x \$n    incr n    foreach {dx dy} {-1 -1  -1 0  -1 1  0 -1  0 1  1 -1  1 0  1 1} {	discover [expr {\$x+\$dx}] [expr {\$y+\$dy}] \$n \$limit \$path \$model    }} proc applypath {path} {    global grid filled    puts "Found unique path for [lindex \$path 0 0] -> [lindex \$path end 0]"    foreach cell [lrange \$path 1 end-1] {	lassign \$cell n x y	lset grid \$y \$x \$n	dict set filled \$n [list \$y \$x]    }} proc printgrid {} {    global grid max    foreach row \$grid {	foreach cell \$row {	    puts -nonewline [format " %*s" [string length \$max] [expr {		\$cell==-1 ? "." : \$cell	    }]]	}	puts ""    }} proc solveHidato {initialConfiguration} {    init \$initialConfiguration    set limit [llength [findseps]]    while {[llength [set seps [findseps]]] && [incr limit -1]>=0} {	foreach sep \$seps {	    if {[llength [set paths [makepaths \$sep]]] == 1} {		applypath [lindex \$paths 0]		break	    }	}    }    puts ""    printgrid}`

Demonstrating (dots are “outside” the grid, and zeroes are the cells to be filled in):

`solveHidato "     0  33  35   0   0   .   .   .     0   0  24  22   0   .   .   .     0   0   0  21   0   0   .   .     0  26   0  13  40  11   .   .    27   0   0   0   9   0   1   .     .   .   0   0  18   0   0   .     .   .   .   .   0   7   0   0      .   .   .   .   .   .   5   0 "`
Output:
```Found unique path for 5 -> 7
Found unique path for 7 -> 9
Found unique path for 9 -> 11
Found unique path for 11 -> 13
Found unique path for 33 -> 35
Found unique path for 18 -> 21
Found unique path for 1 -> 5
Found unique path for 35 -> 40
Found unique path for 22 -> 24
Found unique path for 24 -> 26
Found unique path for 27 -> 33
Found unique path for 13 -> 18

32 33 35 36 37  .  .  .
31 34 24 22 38  .  .  .
30 25 23 21 12 39  .  .
29 26 20 13 40 11  .  .
27 28 14 19  9 10  1  .
.  . 15 16 18  8  2  .
.  .  .  . 17  7  6  3
.  .  .  .  .  .  5  4
```

More complex cases are solvable with an extended version of this code, though that has more onerous version requirements.

## zkl

Translation of: Python
`hi:=  // 0==empty cell, X==not a cell#<<< "0  33  35   0   0   X   X   X  0   0  24  22   0   X   X   X  0   0   0  21   0   0   X   X  0  26   0  13  40  11   X   X 27   0   0   0   9   0   1   X  X   X   0   0  18   0   0   X  X   X   X   X   0   7   0   0  X   X   X   X   X   X   5   0";#<<< board,given,start:=setup(hi);print_board(board);solve(board,given, start.xplode(), 1);println();print_board(board);`
`fcn print_board(board){   d:=D(-1,"  ", 0,"__");   foreach r in (board[1,-1]){      r[1,-1].pump(String,'wrap(c){ "%2s ".fmt(d.find(c,c)) }).println();   }}fcn setup(s){   lines:=s.split("\n");   ncols,nrows:=lines[0].split().len(),lines.len();   board:=(nrows+2).pump(List(), (ncols+2).pump(List(),-1).copy);   given,start:=List(),Void;   foreach r,row in (lines.enumerate()){      foreach c,cell in (row.split().enumerate()){         if(cell=="X") continue;   // X == not in play, leave at -1	 val:=cell.toInt();	 board[r+1][c+1]=val;	 given.append(val);	 if(val==1) start=T(r+1,c+1);      }   }   return(board,given.filter().sort(),start);}fcn solve(board,given, r,c,n, next=0){   if(n>given[-1])                       return(True);   if(board[r][c] and board[r][c]!=n)    return(False);   if(board[r][c]==0 and given[next]==n) return(False);    back:=0;   if(board[r][c]==n){ next+=1; back=n; }    board[r][c]=n;   foreach i,j in ([-1..1],[-1..1]){      if(solve(board,given, r+i,c+j,n+1, next)) return(True);   }   board[r][c]=back;   False}`
Output:
```__ 33 35 __ __
__ __ 24 22 __
__ __ __ 21 __ __
__ 26 __ 13 40 11
27 __ __ __  9 __  1
__ __ 18 __ __
__  7 __ __
5 __

32 33 35 36 37
31 34 24 22 38
30 25 23 21 12 39
29 26 20 13 40 11
27 28 14 19  9 10  1
15 16 18  8  2
17  7  6  3
5  4
```