⚠️ Warning: This is a draft ⚠️

This means it might contain formatting issues, incorrect code, conceptual problems, or other severe issues.

If you want to help to improve and eventually enable this page, please fork RosettaGit's repository and open a merge request on GitHub.

{{task}} Numbrix puzzles are similar to [[Solve a Hidato puzzle|Hidato]]. The most important difference is that it is only possible to move 1 node left, right, up, or down (sometimes referred to as the [[wp:Von Neumann neighborhood|Von Neumann neighborhood]]). Published puzzles also tend not to have holes in the grid and may not always indicate the end node. Two examples follow:

;Example 1 Problem.

```
0  0  0  0  0  0  0  0  0
0  0 46 45  0 55 74  0  0
0 38  0  0 43  0  0 78  0
0 35  0  0  0  0  0 71  0
0  0 33  0  0  0 59  0  0
0 17  0  0  0  0  0 67  0
0 18  0  0 11  0  0 64  0
0  0 24 21  0  1  2  0  0
0  0  0  0  0  0  0  0  0

```

Solution.

```
49 50 51 52 53 54 75 76 81
48 47 46 45 44 55 74 77 80
37 38 39 40 43 56 73 78 79
36 35 34 41 42 57 72 71 70
31 32 33 14 13 58 59 68 69
30 17 16 15 12 61 60 67 66
29 18 19 20 11 62 63 64 65
28 25 24 21 10  1  2  3  4
27 26 23 22  9  8  7  6  5

```

;Example 2 Problem.

```
0  0  0  0  0  0  0  0  0
0 11 12 15 18 21 62 61  0
0  6  0  0  0  0  0 60  0
0 33  0  0  0  0  0 57  0
0 32  0  0  0  0  0 56  0
0 37  0  1  0  0  0 73  0
0 38  0  0  0  0  0 72  0
0 43 44 47 48 51 76 77  0
0  0  0  0  0  0  0  0  0

```

Solution.

```
9 10 13 14 19 20 63 64 65
8 11 12 15 18 21 62 61 66
7  6  5 16 17 22 59 60 67
34 33  4  3 24 23 58 57 68
35 32 31  2 25 54 55 56 69
36 37 30  1 26 53 74 73 70
39 38 29 28 27 52 75 72 71
40 43 44 47 48 51 76 77 78
41 42 45 46 49 50 81 80 79

```

;Task Write a program to solve puzzles of this ilk, demonstrating your program by solving the above examples. Extra credit for other interesting examples.

• [[A* search algorithm]]
• [[Solve a Holy Knight's tour]]
• [[Knight's tour]]
• [[N-queens problem]]
• [[Solve a Hidato puzzle]]
• [[Solve a Holy Knight's tour]]
• [[Solve a Hopido puzzle]]
• [[Solve the no connection puzzle]]

## AutoHotkey

```SolveNumbrix(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 SolveNumbrix(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 SolveNumbrix(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] := 0
}
;--------------------------------
;--------------------------------
;--------------------------------
Neighbor(row,col){
return row-1 ":" col
. "," row+1 ":" col
. "," row ":" col+1
. "," row ":" col-1
}
;--------------------------------
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 := [[0,	0,	0,	0,	0,	0,	0,	0,	0]
,[0,	0,	46,	45,	0,	55,	74,	0,	0]
,[0,	38,	0,	0,	43,	0,	0,	78,	0]
,[0,	35,	0,	0,	0,	0,	0,	71,	0]
,[0,	0,	33,	0,	0,	0,	59,	0,	0]
,[0,	17,	0,	0,	0,	0,	0,	67,	0]
,[0,	18,	0,	0,	11,	0,	0,	64,	0]
,[0,	0,	24,	21,	0,	1,	2,	0,	0]
,[0,	0,	0,	0,	0,	0,	0,	0,	0]]
;--------------------------------
; find locked cells, find row and col of first value "1" and max value
Locked := []
max := 1
for i, line in Grid
for j, element in line
{
max ++
if element = 1
row :=i , col := j
if (element > 0)
Locked[element] := i ":" j "," Neighbor(i, j)	; save locked elements position and neighbors

}
;--------------------------------
MsgBox, 262144, ,% SolveNumbrix(Grid, Locked, Max, row, col)
return

```

Outputs:

```49	50	51	52	53	54	75	76	81
48	47	46	45	44	55	74	77	80
37	38	39	40	43	56	73	78	79
36	35	34	41	42	57	72	71	70
31	32	33	14	13	58	59	68	69
30	17	16	15	12	61	60	67	66
29	18	19	20	11	62	63	64	65
28	25	24	21	10	1	2	3	4
27	26	23	22	9	8	7	6	5
```

## C++

```
#include <vector>
#include <sstream>
#include <iostream>
#include <iterator>
#include <cstdlib>
#include <string>
#include <bitset>

using namespace std;
typedef bitset<4> hood_t;

struct node
{
int val;
hood_t neighbors;
};

class nSolver
{
public:

void solve(vector<string>& puzz, int max_wid)
{
if (puzz.size() < 1) return;
wid = max_wid;
hei = static_cast<int>(puzz.size()) / wid;
max = wid * hei;
int len = max, c = 0;
arr = vector<node>(len, node({ 0, 0 }));
weHave = vector<bool>(len + 1, false);

for (const auto& s : puzz)
{
if (s == "*") { max--; arr[c++].val = -1; continue; }
arr[c].val = atoi(s.c_str());
if (arr[c].val > 0) weHave[arr[c].val] = true;
c++;
}

solveIt(); c = 0;
for (auto&& s : puzz)
{
if (s == ".")
s = std::to_string(arr[c].val);
c++;
}
}

private:
bool search(int x, int y, int w, int dr)
{
if ((w > max && dr > 0) || (w < 1 && dr < 0) || (w == max && weHave[w])) return true;

node& n = arr[x + y * wid];
n.neighbors = getNeighbors(x, y);
if (weHave[w])
{
for (int d = 0; d < 4; d++)
{
if (n.neighbors[d])
{
int a = x + dx[d], b = y + dy[d];
if (arr[a + b * wid].val == w)
if (search(a, b, w + dr, dr))
return true;
}
}
return false;
}

for (int d = 0; d < 4; d++)
{
if (n.neighbors[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 + dr, dr))
return true;
arr[a + b * wid].val = 0;
}
}
}
return false;
}

hood_t getNeighbors(int x, int y)
{
hood_t retval;
for (int xx = 0; xx < 4; xx++)
{
int a = x + dx[xx], b = y + dy[xx];
if (a < 0 || b < 0 || a >= wid || b >= hei)
continue;
if (arr[a + b * wid].val > -1)
retval.set(xx);
}
return retval;
}

void solveIt()
{
int x, y, z; findStart(x, y, z);
if (z == 99999) { cout << "\nCan't find start point!\n"; return; }
search(x, y, z + 1, 1);
if (z > 1) search(x, y, z - 1, -1);
}

void findStart(int& x, int& y, int& z)
{
z = 99999;
for (int b = 0; b < hei; b++)
for (int a = 0; a < wid; a++)
if (arr[a + wid * b].val > 0 && arr[a + wid * b].val < z)
{
x = a; y = b;
z = arr[a + wid * b].val;
}

}

vector<int> dx = vector<int>({ -1, 1, 0, 0 });
vector<int> dy = vector<int>({ 0, 0, -1, 1 });
int wid, hei, max;
vector<node> arr;
vector<bool> weHave;
};

//------------------------------------------------------------------------------
int main(int argc, char* argv[])
{
int wid; string p;
//p = ". . . . . . . . . . . 46 45 . 55 74 . . . 38 . . 43 . . 78 . . 35 . . . . . 71 . . . 33 . . . 59 . . . 17 . . . . . 67 . . 18 . . 11 . . 64 . . . 24 21 . 1  2 . . . . . . . . . . ."; wid = 9;
//p = ". . . . . . . . . . 11 12 15 18 21 62 61 . .  6 . . . . . 60 . . 33 . . . . . 57 . . 32 . . . . . 56 . . 37 .  1 . . . 73 . . 38 . . . . . 72 . . 43 44 47 48 51 76 77 . . . . . . . . . ."; wid = 9;
p = "17 . . . 11 . . . 59 . 15 . . 6 . . 61 . . . 3 . . .  63 . . . . . . 66 . . . . 23 24 . 68 67 78 . 54 55 . . . . 72 . . . . . . 35 . . . 49 . . . 29 . . 40 . . 47 . 31 . . . 39 . . . 45"; wid = 9;

istringstream iss(p); vector<string> puzz;
copy(istream_iterator<string>(iss), istream_iterator<string>(), back_inserter<vector<string> >(puzz));
nSolver s; s.solve(puzz, wid);

int c = 0;
for (const auto& s : puzz)
{
if (s != "*" && s != ".")
{
if (atoi(s.c_str()) < 10) cout << "0";
cout << s << " ";
}
else cout << "   ";
if (++c >= wid) { cout << endl; c = 0; }
}
cout << endl << endl;
return system("pause");
}

```

{{Out}}

```
49 50 51 52 53 54 75 76 81
48 47 46 45 44 55 74 77 80
37 38 39 40 43 56 73 78 79
36 35 34 41 42 57 72 71 70
31 32 33 14 13 58 59 68 69
30 17 16 15 12 61 60 67 66
29 18 19 20 11 62 63 64 65
28 25 24 21 10 01 02 03 04
27 26 23 22 09 08 07 06 05

09 10 13 14 19 20 63 64 65
08 11 12 15 18 21 62 61 66
07 06 05 16 17 22 59 60 67
34 33 04 03 24 23 58 57 68
35 32 31 02 25 54 55 56 69
36 37 30 01 26 53 74 73 70
39 38 29 28 27 52 75 72 71
40 43 44 47 48 51 76 77 78
41 42 45 46 49 50 81 80 79

17 16 13 12 11 10 09 60 59
18 15 14 05 06 07 08 61 58
19 20 03 04 65 64 63 62 57
22 21 02 01 66 79 80 81 56
23 24 69 68 67 78 77 54 55
26 25 70 71 72 75 76 53 52
27 28 35 36 73 74 49 50 51
30 29 34 37 40 41 48 47 46
31 32 33 38 39 42 43 44 45

```

## C#

The same solver can solve Hidato, Holy Knight's Tour, Hopido and Numbrix puzzles.
The input can be an array of strings if each cell is one character. The length of the first row must be the number of columns in the puzzle.
Any non-numeric value indicates a no-go.
If there are cells that require more characters, then a 2-dimensional array of ints must be used. Any number < 0 indicates a no-go.

```using System.Collections;
using System.Collections.Generic;
using static System.Console;
using static System.Math;
using static System.Linq.Enumerable;

public class Solver
{
private static readonly (int dx, int dy)[]
//other puzzle types elided
numbrixMoves = {(1,0),(0,1),(-1,0),(0,-1)};

private (int dx, int dy)[] moves;

public static void Main()
{
var numbrixSolver = new Solver(numbrixMoves);
Print(numbrixSolver.Solve(false, new [,] {
{  0,  0,  0,  0,  0,  0,  0,  0,  0 },
{  0,  0, 46, 45,  0, 55, 74,  0,  0 },
{  0, 38,  0,  0, 43,  0,  0, 78,  0 },
{  0, 35,  0,  0,  0,  0,  0, 71,  0 },
{  0,  0, 33,  0,  0,  0, 59,  0,  0 },
{  0, 17,  0,  0,  0,  0,  0, 67,  0 },
{  0, 18,  0,  0, 11,  0,  0, 64,  0 },
{  0,  0, 24, 21,  0,  1,  2,  0,  0 },
{  0,  0,  0,  0,  0,  0,  0,  0,  0 },
}));

Print(numbrixSolver.Solve(false, new [,] {
{  0,  0,  0,  0,  0,  0,  0,  0,  0 },
{  0, 11, 12, 15, 18, 21, 62, 61,  0 },
{  0,  6,  0,  0,  0,  0,  0, 60,  0 },
{  0, 33,  0,  0,  0,  0,  0, 57,  0 },
{  0, 32,  0,  0,  0,  0,  0, 56,  0 },
{  0, 37,  0,  1,  0,  0,  0, 73,  0 },
{  0, 38,  0,  0,  0,  0,  0, 72,  0 },
{  0, 43, 44, 47, 48, 51, 76, 77,  0 },
{  0,  0,  0,  0,  0,  0,  0,  0,  0 },
}));
}

public Solver(params (int dx, int dy)[] moves) => this.moves = moves;

public int[,] Solve(bool circular, params string[] puzzle)
{
var (board, given, count) = Parse(puzzle);
return Solve(board, given, count, circular);
}

public int[,] Solve(bool circular, int[,] puzzle)
{
var (board, given, count) = Parse(puzzle);
return Solve(board, given, count, circular);
}

private int[,] Solve(int[,] board, BitArray given, int count, bool circular)
{
var (height, width) = (board.GetLength(0), board.GetLength(1));
bool solved = false;
for (int x = 0; x < height && !solved; x++) {
solved = Range(0, width).Any(y => Solve(board, given, circular, (height, width), (x, y), count, (x, y), 1));
if (solved) return board;
}
return null;
}

private bool Solve(int[,] board, BitArray given, bool circular,
(int h, int w) size, (int x, int y) start, int last, (int x, int y) current, int n)
{
var (x, y) = current;
if (x < 0 || x >= size.h || y < 0 || y >= size.w) return false;
if (board[x, y] < 0) return false;
if (given[n - 1]) {
if (board[x, y] != n) return false;
} else if (board[x, y] > 0) return false;
board[x, y] = n;
if (n == last) {
if (!circular || AreNeighbors(start, current)) return true;
}
for (int i = 0; i < moves.Length; i++) {
var move = moves[i];
if (Solve(board, given, circular, size, start, last, (x + move.dx, y + move.dy), n + 1)) return true;
}
if (!given[n - 1]) board[x, y] = 0;
return false;

bool AreNeighbors((int x, int y) p1, (int x, int y) p2) => moves.Any(m => (p2.x + m.dx, p2.y + m.dy).Equals(p1));
}

private static (int[,] board, BitArray given, int count) Parse(string[] input)
{
(int height, int width) = (input.Length, input[0].Length);
int[,] board = new int[height, width];
int count = 0;
for (int x = 0; x < height; x++) {
string line = input[x];
for (int y = 0; y < width; y++) {
board[x, y] = y < line.Length && char.IsDigit(line[y]) ? line[y] - '0' : -1;
if (board[x, y] >= 0) count++;
}
}
BitArray given = Scan(board, count, height, width);
return (board, given, count);
}

private static (int[,] board, BitArray given, int count) Parse(int[,] input)
{
(int height, int width) = (input.GetLength(0), input.GetLength(1));
int[,] board = new int[height, width];
int count = 0;
for (int x = 0; x < height; x++)
for (int y = 0; y < width; y++)
if ((board[x, y] = input[x, y]) >= 0) count++;
BitArray given = Scan(board, count, height, width);
return (board, given, count);
}

private static BitArray Scan(int[,] board, int count, int height, int width)
{
var given = new BitArray(count + 1);
for (int x = 0; x < height; x++)
for (int y = 0; y < width; y++)
if (board[x, y] > 0) given[board[x, y] - 1] = true;
return given;
}

private static void Print(int[,] board)
{
if (board == null) {
WriteLine("No solution");
} else {
int w = board.Cast<int>().Where(i => i > 0).Max(i => (int?)Ceiling(Log10(i+1))) ?? 1;
string e = new string('-', w);
foreach (int x in Range(0, board.GetLength(0)))
WriteLine(string.Join(" ", Range(0, board.GetLength(1))
.Select(y => board[x, y] < 0 ? e : board[x, y].ToString().PadLeft(w, ' '))));
}
WriteLine();
}

}
```

{{out}}

```
49 50 51 52 53 54 75 76 81
48 47 46 45 44 55 74 77 80
37 38 39 40 43 56 73 78 79
36 35 34 41 42 57 72 71 70
31 32 33 14 13 58 59 68 69
30 17 16 15 12 61 60 67 66
29 18 19 20 11 62 63 64 65
28 25 24 21 10  1  2  3  4
27 26 23 22  9  8  7  6  5

9 10 13 14 19 20 63 64 65
8 11 12 15 18 21 62 61 66
7  6  5 16 17 22 59 60 67
34 33  4  3 24 23 58 57 68
35 32 31  2 25 54 55 56 69
36 37 30  1 26 53 74 73 70
39 38 29 28 27 52 75 72 71
40 43 44 47 48 51 76 77 78
41 42 45 46 49 50 81 80 79

```

## D

From the refactored C++ version with more precise typing. The NumbrixPuzzle struct is created at compile-time, so its asserts and exceptions can catch most malformed puzzles at compile-time. {{trans|C++}}

```import std.stdio, std.conv, std.string, std.range, std.array, std.typecons, std.algorithm;

struct  {
alias BitSet8 = ubyte; // A set of 8 bits.
alias Cell = uint;
enum : string { unavailableInCell = "#", availableInCell = "." }
enum : Cell { unavailableCell = Cell.max, availableCell = 0 }

this(in string inPuzzle) pure @safe {
const rawPuzzle = inPuzzle.splitLines.map!(row => row.split).array;
assert(!rawPuzzle.empty);
assert(!rawPuzzle[0].empty);
assert(rawPuzzle.all!(row => row.length == rawPuzzle[0].length)); // Is rectangular.

gridWidth = rawPuzzle[0].length;
gridHeight = rawPuzzle.length;
immutable nMaxCells = gridWidth * gridHeight;
grid = new Cell[nMaxCells];
auto knownMutable = new bool[nMaxCells + 1];
uint nAvailableMutable = nMaxCells;
bool[Cell] seenCells; // To avoid duplicate input numbers.

uint i = 0;
foreach (const piece; rawPuzzle.join) {
if (piece == unavailableInCell) {
nAvailableMutable--;
grid[i++] = unavailableCell;
continue;
} else if (piece == availableInCell) {
grid[i] = availableCell;
} else {
immutable cell = piece.to!Cell;
assert(cell > 0 && cell <= nMaxCells);
assert(cell !in seenCells);
seenCells[cell] = true;
knownMutable[cell] = true;
grid[i] = cell;
}

i++;
}

known = knownMutable.idup;
nAvailable = nAvailableMutable;
}

@disable this();

auto solve() pure nothrow @safe @nogc
out(result) {
if (!result.isNull) {
// Can't verify 'result' here because it's const.
// assert(!result.get.join.canFind(availableCell.text));

assert(!grid.canFind(availableCell));
auto values = grid.filter!(c => c != unavailableCell);
auto interval = iota(reduce!min(values.front, values.dropOne),
reduce!max(values.front, values.dropOne) + 1);
assert(values.walkLength == interval.length);
assert(interval.all!(c => values.count(c) == 1)); // Quadratic.
}
} body {
auto result = grid
.map!(c => (c == unavailableCell) ? unavailableInCell : c.text)
.chunks(gridWidth);
alias OutRange = Nullable!(typeof(result));

const start = findStart;
if (start.isNull)
return OutRange();

search(start.r, start.c, start.cell + 1, 1);
if (start.cell > 1) {
immutable direction = -1;
search(start.r, start.c, start.cell + direction, direction);
}

if (grid.any!(c => c == availableCell))
return OutRange();
else
return OutRange(result);
}

private:

bool search(in uint r, in uint c, in Cell cell, in int direction)
pure nothrow @safe @nogc {
if ((cell > nAvailable && direction > 0) || (cell == 0 && direction < 0) ||
(cell == nAvailable && known[cell]))
return true; // One solution found.

immutable neighbors = getNeighbors(r, c);

if (known[cell]) {
foreach (immutable i, immutable rc; shifts) {
if (neighbors & (1u << i)) {
immutable c2 = c + rc[0],
r2 = r + rc[1];
if (grid[r2 * gridWidth + c2] == cell)
if (search(r2, c2, cell + direction, direction))
return true;
}
}
return false;
}

foreach (immutable i, immutable rc; shifts) {
if (neighbors & (1u << i)) {
immutable c2 = c + rc[0],
r2 = r + rc[1],
pos = r2 * gridWidth + c2;
if (grid[pos] == availableCell) {
grid[pos] = cell;          // Try.
if (search(r2, c2, cell + direction, direction))
return true;
grid[pos] = availableCell; // Restore.
}
}
}
return false;
}

BitSet8 getNeighbors(in uint r, in uint c) const pure nothrow @safe @nogc {
typeof(return) usable = 0;

foreach (immutable i, immutable rc; shifts) {
immutable c2 = c + rc[0],
r2 = r + rc[1];
if (c2 >= gridWidth || r2 >= gridHeight)
continue;
if (grid[r2 * gridWidth + c2] != unavailableCell)
usable |= (1u << i);
}

return usable;
}

auto findStart() const pure nothrow @safe @nogc {
alias Triple = Tuple!(uint,"r", uint,"c", Cell,"cell");
Nullable!Triple result;

auto cell = Cell.max;
foreach (immutable r; 0 .. gridHeight) {
foreach (immutable c; 0 .. gridWidth) {
immutable pos = gridWidth * r + c;
if (grid[pos] != availableCell &&
grid[pos] != unavailableCell && grid[pos] < cell) {
cell = grid[pos];
result = Triple(r, c, cell);
}
}
}

return result;
}

static immutable int[2][4] shifts = [[0, -1], [0, 1], [-1, 0], [1, 0]];
immutable uint gridWidth, gridHeight;
immutable int nAvailable;
immutable bool[] known; // Given known cells of the puzzle.
Cell[] grid;  // Flattened mutable game grid.
}

void main() {
// enum NumbrixPuzzle to catch malformed puzzles at compile-time.
enum puzzle1 = ".  .  .  .  .  .  .  .  .
.  . 46 45  . 55 74  .  .
. 38  .  . 43  .  . 78  .
. 35  .  .  .  .  . 71  .
.  . 33  .  .  . 59  .  .
. 17  .  .  .  .  . 67  .
. 18  .  . 11  .  . 64  .
.  . 24 21  .  1  2  .  .
.  .  .  .  .  .  .  .  .".NumbrixPuzzle;

enum puzzle2 = ".  .  .  .  .  .  .  .  .
. 11 12 15 18 21 62 61  .
.  6  .  .  .  .  . 60  .
. 33  .  .  .  .  . 57  .
. 32  .  .  .  .  . 56  .
. 37  .  1  .  .  . 73  .
. 38  .  .  .  .  . 72  .
. 43 44 47 48 51 76 77  .
.  .  .  .  .  .  .  .  .".NumbrixPuzzle;

enum puzzle3 = "17  .  .  . 11  .  .  . 59
. 15  .  .  6  .  . 61  .
.  .  3  .  .  . 63  .  .
.  .  .  . 66  .  .  .  .
23 24  . 68 67 78  . 54 55
.  .  .  . 72  .  .  .  .
.  . 35  .  .  . 49  .  .
. 29  .  . 40  .  . 47  .
31  .  .  . 39  .  .  . 45".NumbrixPuzzle;

foreach (puzzle; [puzzle1, puzzle2, puzzle3]) {
auto solution = puzzle.solve; // Solved at run-time.
if (solution.isNull)
writeln("No solution found for puzzle.\n");
else
writefln("One solution:\n%(%-(%2s %)\n%)\n", solution);
}
}
```

{{out}}

```One solution:
49 50 51 52 53 54 75 76 81
48 47 46 45 44 55 74 77 80
37 38 39 40 43 56 73 78 79
36 35 34 41 42 57 72 71 70
31 32 33 14 13 58 59 68 69
30 17 16 15 12 61 60 67 66
29 18 19 20 11 62 63 64 65
28 25 24 21 10  1  2  3  4
27 26 23 22  9  8  7  6  5

One solution:
9 10 13 14 19 20 63 64 65
8 11 12 15 18 21 62 61 66
7  6  5 16 17 22 59 60 67
34 33  4  3 24 23 58 57 68
35 32 31  2 25 54 55 56 69
36 37 30  1 26 53 74 73 70
39 38 29 28 27 52 75 72 71
40 43 44 47 48 51 76 77 78
41 42 45 46 49 50 81 80 79

One solution:
17 16 13 12 11 10  9 60 59
18 15 14  5  6  7  8 61 58
19 20  3  4 65 64 63 62 57
22 21  2  1 66 79 80 81 56
23 24 69 68 67 78 77 54 55
26 25 70 71 72 75 76 53 52
27 28 35 36 73 74 49 50 51
30 29 34 37 40 41 48 47 46
31 32 33 38 39 42 43 44 45
```

## Elixir

{{trans|Ruby}} This solution uses HLPsolver from [[Solve_a_Hidato_puzzle#Elixir | here]]

```# require HLPsolver

adjacent = [{-1, 0}, {0, -1}, {0, 1}, {1, 0}]

board1 = """
0  0  0  0  0  0  0  0  0
0  0 46 45  0 55 74  0  0
0 38  0  0 43  0  0 78  0
0 35  0  0  0  0  0 71  0
0  0 33  0  0  0 59  0  0
0 17  0  0  0  0  0 67  0
0 18  0  0 11  0  0 64  0
0  0 24 21  0  1  2  0  0
0  0  0  0  0  0  0  0  0
"""

board2 = """
0  0  0  0  0  0  0  0  0
0 11 12 15 18 21 62 61  0
0  6  0  0  0  0  0 60  0
0 33  0  0  0  0  0 57  0
0 32  0  0  0  0  0 56  0
0 37  0  1  0  0  0 73  0
0 38  0  0  0  0  0 72  0
0 43 44 47 48 51 76 77  0
0  0  0  0  0  0  0  0  0
"""
```

{{out}}

```
Problem:
0  0  0  0  0  0  0  0  0
0  0 46 45  0 55 74  0  0
0 38  0  0 43  0  0 78  0
0 35  0  0  0  0  0 71  0
0  0 33  0  0  0 59  0  0
0 17  0  0  0  0  0 67  0
0 18  0  0 11  0  0 64  0
0  0 24 21  0  1  2  0  0
0  0  0  0  0  0  0  0  0

Solution:
49 50 51 52 53 54 75 76 81
48 47 46 45 44 55 74 77 80
37 38 39 40 43 56 73 78 79
36 35 34 41 42 57 72 71 70
31 32 33 14 13 58 59 68 69
30 17 16 15 12 61 60 67 66
29 18 19 20 11 62 63 64 65
28 25 24 21 10  1  2  3  4
27 26 23 22  9  8  7  6  5

Problem:
0  0  0  0  0  0  0  0  0
0 11 12 15 18 21 62 61  0
0  6  0  0  0  0  0 60  0
0 33  0  0  0  0  0 57  0
0 32  0  0  0  0  0 56  0
0 37  0  1  0  0  0 73  0
0 38  0  0  0  0  0 72  0
0 43 44 47 48 51 76 77  0
0  0  0  0  0  0  0  0  0

Solution:
9 10 13 14 19 20 63 64 65
8 11 12 15 18 21 62 61 66
7  6  5 16 17 22 59 60 67
34 33  4  3 24 23 58 57 68
35 32 31  2 25 54 55 56 69
36 37 30  1 26 53 74 73 70
39 38 29 28 27 52 75 72 71
40 43 44 47 48 51 76 77 78
41 42 45 46 49 50 81 80 79

```

## Go

{{trans|Kotlin}}

```package main

import (
"fmt"
"sort"
"strconv"
"strings"
)

var example1 = []string{
"00,00,00,00,00,00,00,00,00",
"00,00,46,45,00,55,74,00,00",
"00,38,00,00,43,00,00,78,00",
"00,35,00,00,00,00,00,71,00",
"00,00,33,00,00,00,59,00,00",
"00,17,00,00,00,00,00,67,00",
"00,18,00,00,11,00,00,64,00",
"00,00,24,21,00,01,02,00,00",
"00,00,00,00,00,00,00,00,00",
}

var example2 = []string{
"00,00,00,00,00,00,00,00,00",
"00,11,12,15,18,21,62,61,00",
"00,06,00,00,00,00,00,60,00",
"00,33,00,00,00,00,00,57,00",
"00,32,00,00,00,00,00,56,00",
"00,37,00,01,00,00,00,73,00",
"00,38,00,00,00,00,00,72,00",
"00,43,44,47,48,51,76,77,00",
"00,00,00,00,00,00,00,00,00",
}

var moves = [][2]int{{1, 0}, {0, 1}, {-1, 0}, {0, -1}}

var (
grid        [][]int
clues       []int
totalToFill = 0
)

func solve(r, c, count, nextClue int) bool {
if count > totalToFill {
return true
}

back := grid[r][c]

if back != 0 && back != count {
return false
}

if back == 0 && nextClue < len(clues) && clues[nextClue] == count {
return false
}

if back == count {
nextClue++
}

grid[r][c] = count
for _, move := range moves {
if solve(r+move[1], c+move[0], count+1, nextClue) {
return true
}
}
grid[r][c] = back
return false
}

func printResult(n int) {
fmt.Println("Solution for example", n, "\b:")
for _, row := range grid {
for _, i := range row {
if i == -1 {
continue
}
fmt.Printf("%2d ", i)
}
fmt.Println()
}
}

func main() {
for n, board := range [2][]string{example1, example2} {
nRows := len(board) + 2
nCols := len(strings.Split(board[0], ",")) + 2
startRow, startCol := 0, 0
grid = make([][]int, nRows)
totalToFill = (nRows - 2) * (nCols - 2)
var lst []int

for r := 0; r < nRows; r++ {
grid[r] = make([]int, nCols)
for c := 0; c < nCols; c++ {
grid[r][c] = -1
}
if r >= 1 && r < nRows-1 {
row := strings.Split(board[r-1], ",")
for c := 1; c < nCols-1; c++ {
val, _ := strconv.Atoi(row[c-1])
if val > 0 {
lst = append(lst, val)
}
if val == 1 {
startRow, startCol = r, c
}
grid[r][c] = val
}
}
}

sort.Ints(lst)
clues = lst
if solve(startRow, startCol, 1, 0) {
printResult(n + 1)
}
}
}
```

{{out}}

```
Solution for example 1:

49 50 51 52 53 54 75 76 81
48 47 46 45 44 55 74 77 80
37 38 39 40 43 56 73 78 79
36 35 34 41 42 57 72 71 70
31 32 33 14 13 58 59 68 69
30 17 16 15 12 61 60 67 66
29 18 19 20 11 62 63 64 65
28 25 24 21 10  1  2  3  4
27 26 23 22  9  8  7  6  5

Solution for example 2:

9 10 13 14 19 20 63 64 65
8 11 12 15 18 21 62 61 66
7  6  5 16 17 22 59 60 67
34 33  4  3 24 23 58 57 68
35 32 31  2 25 54 55 56 69
36 37 30  1 26 53 74 73 70
39 38 29 28 27 52 75 72 71
40 43 44 47 48 51 76 77 78
41 42 45 46 49 50 81 80 79

```

This is a Unicon-specific solution, based on the Unicon Hidato problem solver:

```global nCells, cMap, best
record Pos(r,c)

procedure main(A)
QMouse(puzzle,findStart(puzzle),&null,0)
showPuzzle("Output", solvePuzzle(puzzle)) | write("No solution!")
end

p := []
nCells := maxCols := 0
every line := !&input do {
put(p,[: gencells(line) :])
maxCols <:= *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 p
end

procedure gencells(s)
static WS, NWS
initial {
NWS := ~(WS := " \t")
cMap := table()     # Map to/from internal model
cMap["_"] :=  0; 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 p
end

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] = (val|0)); end
method visit(r,c); return (/best, validPos(r,c), Pos(r,c)); end

method validPos(r,c)
v := val+1      # number we're looking for
xv := puzzle[r,c] | fail
if (xv ~= 0) & (xv != v) then fail
if xv = (0|v) then {
ancestor := self
while xl := (ancestor := \ancestor.getParent()).getLoc() do
if (xl.r = r) & (xl.c = c) then fail
return
}
end

initially
val := val+1
if atEnd() then return best := self
QMouse(puzzle, visit(loc.r-1,loc.c)  , self, val)   # North
QMouse(puzzle, visit(loc.r,  loc.c+1), self, val)   # East
QMouse(puzzle, visit(loc.r+1,loc.c),   self, val)   # South
QMouse(puzzle, visit(loc.r,  loc.c-1), self, val)   # West
end
```

{{Out}}Sample runs:

```
->numbrix <numbrix1.in
Input with 81 cells:

_  _  _  _  _  _  _  _  _
_  _ 46 45  _ 55 74  _  _
_ 38  _  _ 43  _  _ 78  _
_ 35  _  _  _  _  _ 71  _
_  _ 33  _  _  _ 59  _  _
_ 17  _  _  _  _  _ 67  _
_ 18  _  _ 11  _  _ 64  _
_  _ 24 21  _  1  2  _  _
_  _  _  _  _  _  _  _  _

Output with 81 cells:

49 50 51 52 53 54 75 76 81
48 47 46 45 44 55 74 77 80
37 38 39 40 43 56 73 78 79
36 35 34 41 42 57 72 71 70
31 32 33 14 13 58 59 68 69
30 17 16 15 12 61 60 67 66
29 18 19 20 11 62 63 64 65
28 25 24 21 10  1  2  3  4
27 26 23 22  9  8  7  6  5

->numbrix <numbrix2.in
Input with 81 cells:

_  _  _  _  _  _  _  _  _
_ 11 12 15 18 21 62 61  _
_  6  _  _  _  _  _ 60  _
_ 33  _  _  _  _  _ 57  _
_ 32  _  _  _  _  _ 56  _
_ 37  _  1  _  _  _ 73  _
_ 38  _  _  _  _  _ 72  _
_ 43 44 47 48 51 76 77  _
_  _  _  _  _  _  _  _  _

Output with 81 cells:

9 10 13 14 19 20 63 64 65
8 11 12 15 18 21 62 61 66
7  6  5 16 17 22 59 60 67
34 33  4  3 24 23 58 57 68
35 32 31  2 25 54 55 56 69
36 37 30  1 26 53 74 73 70
39 38 29 28 27 52 75 72 71
40 43 44 47 48 51 76 77 78
41 42 45 46 49 50 81 80 79

->

```

## Java

{{works with|Java|8}}

```import java.util.*;

public class Numbrix {

final static String[] board = {
"00,00,00,00,00,00,00,00,00",
"00,00,46,45,00,55,74,00,00",
"00,38,00,00,43,00,00,78,00",
"00,35,00,00,00,00,00,71,00",
"00,00,33,00,00,00,59,00,00",
"00,17,00,00,00,00,00,67,00",
"00,18,00,00,11,00,00,64,00",
"00,00,24,21,00,01,02,00,00",
"00,00,00,00,00,00,00,00,00"};

final static int[][] moves = {{1, 0}, {0, 1}, {-1, 0}, {0, -1}};

static int[][] grid;
static int[] clues;
static int totalToFill;

public static void main(String[] args) {
int nRows = board.length + 2;
int nCols = board[0].split(",").length + 2;
int startRow = 0, startCol = 0;

grid = new int[nRows][nCols];
totalToFill = (nRows - 2) * (nCols - 2);
List<Integer> lst = new ArrayList<>();

for (int r = 0; r < nRows; r++) {
Arrays.fill(grid[r], -1);

if (r >= 1 && r < nRows - 1) {

String[] row = board[r - 1].split(",");

for (int c = 1; c < nCols - 1; c++) {
int val = Integer.parseInt(row[c - 1]);
if (val > 0)
if (val == 1) {
startRow = r;
startCol = c;
}
grid[r][c] = val;
}
}
}

clues = lst.stream().sorted().mapToInt(i -> i).toArray();

if (solve(startRow, startCol, 1, 0))
printResult();
}

static boolean solve(int r, int c, int count, int nextClue) {
if (count > totalToFill)
return true;

if (grid[r][c] != 0 && grid[r][c] != count)
return false;

if (grid[r][c] == 0 && nextClue < clues.length)
if (clues[nextClue] == count)
return false;

int back = grid[r][c];
if (back == count)
nextClue++;

grid[r][c] = count;
for (int[] move : moves)
if (solve(r + move[1], c + move[0], count + 1, nextClue))
return true;

grid[r][c] = back;
return false;
}

static void printResult() {
for (int[] row : grid) {
for (int i : row) {
if (i == -1)
continue;
System.out.printf("%2d ", i);
}
System.out.println();
}
}
}
```
```49 50 51 52 53 54 75 76 81
48 47 46 45 44 55 74 77 80
37 38 39 40 43 56 73 78 79
36 35 34 41 42 57 72 71 70
31 32 33 14 13 58 59 68 69
30 17 16 15 12 61 60 67 66
29 18 19 20 11 62 63 64 65
28 25 24 21 10  1  2  3  4
27 26 23 22  9  8  7  6  5
```

=={{header|Julia}} See the Hidato module here.

```using .Hidato

const numbrixmoves = [[-1, 0], [0, -1], [0, 1], [1, 0]]

board, maxmoves, fixed, starts = hidatoconfigure(numbrix1)
printboard(board, " 0 ", "   ")
hidatosolve(board, maxmoves, numbrixmoves, fixed, starts[1][1], starts[1][2], 1)
printboard(board)

board, maxmoves, fixed, starts = hidatoconfigure(numbrix2)
printboard(board, " 0 ", "   ")
hidatosolve(board, maxmoves, numbrixmoves, fixed, starts[1][1], starts[1][2], 1)
printboard(board)

```

{{output}}

```
0  0  0  0  0  0  0  0  0
0  0 46 45  0 55 74  0  0
0 38  0  0 43  0  0 78  0
0 35  0  0  0  0  0 71  0
0  0 33  0  0  0 59  0  0
0 17  0  0  0  0  0 67  0
0 18  0  0 11  0  0 64  0
0  0 24 21  0  1  2  0  0
0  0  0  0  0  0  0  0  0

49 50 51 52 53 54 75 76 81
48 47 46 45 44 55 74 77 80
37 38 39 40 43 56 73 78 79
36 35 34 41 42 57 72 71 70
31 32 33 14 13 58 59 68 69
30 17 16 15 12 61 60 67 66
29 18 19 20 11 62 63 64 65
28 25 24 21 10  1  2  3  4
27 26 23 22  9  8  7  6  5

0  0  0  0  0  0  0  0  0
0 11 12 15 18 21 62 61  0
0  6  0  0  0  0  0 60  0
0 33  0  0  0  0  0 57  0
0 32  0  0  0  0  0 56  0
0 37  0  1  0  0  0 73  0
0 38  0  0  0  0  0 72  0
0 43 44 47 48 51 76 77  0
0  0  0  0  0  0  0  0  0

9 10 13 14 19 20 63 64 65
8 11 12 15 18 21 62 61 66
7  6  5 16 17 22 59 60 67
34 33  4  3 24 23 58 57 68
35 32 31  2 25 54 55 56 69
36 37 30  1 26 53 74 73 70
39 38 29 28 27 52 75 72 71
40 43 44 47 48 51 76 77 78
41 42 45 46 49 50 81 80 79

```

## Julia

Uses the Hidato puzzle solver module, which has its source code listed [[Solve_a_Hidato_puzzle#Julia | here]] in the Hadato task.

```using .Hidato       # Note that the . here means to look locally for the module rather than in the libraries

const numbrix1 = """
0  0  0  0  0  0  0  0  0
0  0 46 45  0 55 74  0  0
0 38  0  0 43  0  0 78  0
0 35  0  0  0  0  0 71  0
0  0 33  0  0  0 59  0  0
0 17  0  0  0  0  0 67  0
0 18  0  0 11  0  0 64  0
0  0 24 21  0  1  2  0  0
0  0  0  0  0  0  0  0  0 """

const numbrix2 = """
0  0  0  0  0  0  0  0  0
0 11 12 15 18 21 62 61  0
0  6  0  0  0  0  0 60  0
0 33  0  0  0  0  0 57  0
0 32  0  0  0  0  0 56  0
0 37  0  1  0  0  0 73  0
0 38  0  0  0  0  0 72  0
0 43 44 47 48 51 76 77  0
0  0  0  0  0  0  0  0  0 """

const numbrixmoves = [[-1, 0], [0, -1], [0, 1], [1, 0]]

board, maxmoves, fixed, starts = hidatoconfigure(numbrix1)
printboard(board, " 0 ", "   ")
hidatosolve(board, maxmoves, numbrixmoves, fixed, starts[1][1], starts[1][2], 1)
printboard(board)

board, maxmoves, fixed, starts = hidatoconfigure(numbrix2)
printboard(board, " 0 ", "   ")
hidatosolve(board, maxmoves, numbrixmoves, fixed, starts[1][1], starts[1][2], 1)
printboard(board)

```

{{output}}

```
0  0  0  0  0  0  0  0  0
0  0 46 45  0 55 74  0  0
0 38  0  0 43  0  0 78  0
0 35  0  0  0  0  0 71  0
0  0 33  0  0  0 59  0  0
0 17  0  0  0  0  0 67  0
0 18  0  0 11  0  0 64  0
0  0 24 21  0  1  2  0  0
0  0  0  0  0  0  0  0  0

49 50 51 52 53 54 75 76 81
48 47 46 45 44 55 74 77 80
37 38 39 40 43 56 73 78 79
36 35 34 41 42 57 72 71 70
31 32 33 14 13 58 59 68 69
30 17 16 15 12 61 60 67 66
29 18 19 20 11 62 63 64 65
28 25 24 21 10  1  2  3  4
27 26 23 22  9  8  7  6  5

0  0  0  0  0  0  0  0  0
0 11 12 15 18 21 62 61  0
0  6  0  0  0  0  0 60  0
0 33  0  0  0  0  0 57  0
0 32  0  0  0  0  0 56  0
0 37  0  1  0  0  0 73  0
0 38  0  0  0  0  0 72  0
0 43 44 47 48 51 76 77  0
0  0  0  0  0  0  0  0  0

9 10 13 14 19 20 63 64 65
8 11 12 15 18 21 62 61 66
7  6  5 16 17 22 59 60 67
34 33  4  3 24 23 58 57 68
35 32 31  2 25 54 55 56 69
36 37 30  1 26 53 74 73 70
39 38 29 28 27 52 75 72 71
40 43 44 47 48 51 76 77 78
41 42 45 46 49 50 81 80 79

```

## Kotlin

{{trans|Java}}

```// version 1.2.0

val example1 = listOf(
"00,00,00,00,00,00,00,00,00",
"00,00,46,45,00,55,74,00,00",
"00,38,00,00,43,00,00,78,00",
"00,35,00,00,00,00,00,71,00",
"00,00,33,00,00,00,59,00,00",
"00,17,00,00,00,00,00,67,00",
"00,18,00,00,11,00,00,64,00",
"00,00,24,21,00,01,02,00,00",
"00,00,00,00,00,00,00,00,00"
)

val example2 = listOf(
"00,00,00,00,00,00,00,00,00",
"00,11,12,15,18,21,62,61,00",
"00,06,00,00,00,00,00,60,00",
"00,33,00,00,00,00,00,57,00",
"00,32,00,00,00,00,00,56,00",
"00,37,00,01,00,00,00,73,00",
"00,38,00,00,00,00,00,72,00",
"00,43,44,47,48,51,76,77,00",
"00,00,00,00,00,00,00,00,00"
)

val moves = listOf(1 to 0, 0 to 1, -1 to 0, 0 to -1)

lateinit var board: List<String>
lateinit var grid: List<IntArray>
lateinit var clues: IntArray
var totalToFill = 0

fun solve(r: Int, c: Int, count: Int, nextClue: Int): Boolean {
if (count > totalToFill) return true
val back = grid[r][c]
if (back != 0 && back != count) return false
if (back == 0 && nextClue < clues.size && clues[nextClue] == count) {
return false
}
var nextClue2 = nextClue
if (back == count) nextClue2++
grid[r][c] = count
for (m in moves) {
if (solve(r + m.second, c + m.first, count + 1, nextClue2)) return true
}
grid[r][c] = back
return false
}

fun printResult(n: Int) {
println("Solution for example \$n:")
for (row in grid) {
for (i in row) {
if (i == -1) continue
print("%2d ".format(i))
}
println()
}
}

fun main(args: Array<String>) {
for ((n, ex) in listOf(example1, example2).withIndex()) {
board = ex
val nRows = board.size + 2
val nCols = board[0].split(",").size + 2
var startRow = 0
var startCol = 0
grid = List(nRows) { IntArray(nCols) { -1 } }
totalToFill = (nRows - 2) * (nCols - 2)
val lst = mutableListOf<Int>()
for (r in 0 until nRows) {
if (r in 1 until nRows - 1) {
val row = board[r - 1].split(",")
for (c in 1 until nCols - 1) {
val value = row[c - 1].toInt()
if (value == 1) {
startRow = r
startCol = c
}
grid[r][c] = value
}
}
}
lst.sort()
clues = lst.toIntArray()
if (solve(startRow, startCol, 1, 0)) printResult(n + 1)
}
}
```

{{out}}

```
Solution for example 1:

49 50 51 52 53 54 75 76 81
48 47 46 45 44 55 74 77 80
37 38 39 40 43 56 73 78 79
36 35 34 41 42 57 72 71 70
31 32 33 14 13 58 59 68 69
30 17 16 15 12 61 60 67 66
29 18 19 20 11 62 63 64 65
28 25 24 21 10  1  2  3  4
27 26 23 22  9  8  7  6  5

Solution for example 2:

9 10 13 14 19 20 63 64 65
8 11 12 15 18 21 62 61 66
7  6  5 16 17 22 59 60 67
34 33  4  3 24 23 58 57 68
35 32 31  2 25 54 55 56 69
36 37 30  1 26 53 74 73 70
39 38 29 28 27 52 75 72 71
40 43 44 47 48 51 76 77 78
41 42 45 46 49 50 81 80 79

```

## Perl

Tested on perl v5.26.1

```#!/usr/bin/perl

use strict;
use warnings;

\$_ = <<END;
0  0  0  0  0  0  0  0  0
0  0 46 45  0 55 74  0  0
0 38  0  0 43  0  0 78  0
0 35  0  0  0  0  0 71  0
0  0 33  0  0  0 59  0  0
0 17  0  0  0  0  0 67  0
0 18  0  0 11  0  0 64  0
0  0 24 21  0  1  2  0  0
0  0  0  0  0  0  0  0  0
END

my \$gap = /.\n/ * \$-[0];
print;
s/ (?=\d\b)/0/g;
my \$max = sprintf "%02d", tr/0-9// / 2;

solve( '01', \$_ );

sub solve
{
my (\$have, \$in) = @_;
\$have eq \$max and exit !print "solution\n", \$in =~ s/\b0/ /gr;
if( \$in =~ ++(my \$want = \$have) )
{
\$in =~ /(\$have|\$want)( |.{\$gap})(\$have|\$want)/s and solve(\$want, \$in);
}
else
{
(\$_ = \$in) =~ s/\$have \K00/\$want/          and solve( \$want, \$_ ); # R
(\$_ = \$in) =~ s/\$have.{\$gap}\K00/\$want/s   and solve( \$want, \$_ ); # D
(\$_ = \$in) =~ s/00(?= \$have)/\$want/        and solve( \$want, \$_ ); # L
(\$_ = \$in) =~ s/00(?=.{\$gap}\$have)/\$want/s and solve( \$want, \$_ ); # U
}
}
```

{{out|case=Example 1}}

``` 0  0  0  0  0  0  0  0  0
0  0 46 45  0 55 74  0  0
0 38  0  0 43  0  0 78  0
0 35  0  0  0  0  0 71  0
0  0 33  0  0  0 59  0  0
0 17  0  0  0  0  0 67  0
0 18  0  0 11  0  0 64  0
0  0 24 21  0  1  2  0  0
0  0  0  0  0  0  0  0  0
solution
49 50 51 52 53 54 75 76 81
48 47 46 45 44 55 74 77 80
37 38 39 40 43 56 73 78 79
36 35 34 41 42 57 72 71 70
31 32 33 14 13 58 59 68 69
30 17 16 15 12 61 60 67 66
29 18 19 20 11 62 63 64 65
28 25 24 21 10  1  2  3  4
27 26 23 22  9  8  7  6  5

```

## 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:

• [[Solve a Hidato puzzle#Perl_6|Solve a Hidato puzzle]]
• [[Solve a Hopido puzzle#Perl_6|Solve a Hopido puzzle]]
• [[Solve a Holy Knight's tour#Perl_6|Solve a Holy Knight's tour]]
• [[Solve a Numbrix puzzle#Perl_6|Solve a Numbrix puzzle]]
• [[Solve the no connection puzzle#Perl_6|Solve the no connection puzzle]]
```my @adjacent =           [-1, 0],
[ 0, -1],          [ 0, 1],
[ 1, 0];
put "\n" xx 60;

solveboard q:to/END/;
__ __ __ __ __ __ __ __ __
__ __ 46 45 __ 55 74 __ __
__ 38 __ __ 43 __ __ 78 __
__ 35 __ __ __ __ __ 71 __
__ __ 33 __ __ __ 59 __ __
__ 17 __ __ __ __ __ 67 __
__ 18 __ __ 11 __ __ 64 __
__ __ 24 21 __  1  2 __ __
__ __ __ __ __ __ __ __ __
END

# And
put "\n" xx 60;

solveboard q:to/END/;
0  0  0  0  0  0  0  0  0
0 11 12 15 18 21 62 61  0
0  6  0  0  0  0  0 60  0
0 33  0  0  0  0  0 57  0
0 32  0  0  0  0  0 56  0
0 37  0  1  0  0  0 73  0
0 38  0  0  0  0  0 72  0
0 43 44 47 48 51 76 77  0
0  0  0  0  0  0  0  0  0
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) {
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";
}

```

{{out}}

```49 50 51 52 53 54 75 76 81
48 47 46 45 44 55 74 77 80
37 38 39 40 43 56 73 78 79
36 35 34 41 42 57 72 71 70
31 32 33 14 13 58 59 68 69
30 17 16 15 12 61 60 67 66
29 18 19 20 11 62 63 64 65
28 25 24 21 10  1  2  3  4
27 26 23 22  9  8  7  6  5
1275 tries

9 10 13 14 19 20 63 64 65
8 11 12 15 18 21 62 61 66
7  6  5 16 17 22 59 60 67
34 33  4  3 24 23 58 57 68
35 32 31  2 25 54 55 56 69
36 37 30  1 26 53 74 73 70
39 38 29 28 27 52 75 72 71
40 43 44 47 48 51 76 77 78
41 42 45 46 49 50 81 80 79
4631 tries
```

Oddly, reversing the tiebreaker rule that makes hidato run twice as fast causes this last example to run four times slower. Go figure...

## Phix

```sequence board, knownx, knowny

integer size, limit, nchars, tries
string fmt, blank

constant ROW = 1, COL = 2
constant moves = {{-1,0},{0,-1},{0,1},{1,0}}

function onboard(integer row, integer col)
return row>=1 and row<=size and col>=nchars and col<=nchars*size
end function

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
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 if
end for
return 0
end function

procedure Numbrix(sequence s)
integer y, ch, ch2, k
atom t0 = time()
s = split(s,'\n')
size = length(s)
limit = size*size
nchars = length(sprintf(" %d",limit))
fmt = sprintf(" %%%dd",nchars-1)
blank = repeat('.',nchars)
board = repeat(repeat(' ',size*nchars),size)
knownx = repeat(0,limit)
knowny = repeat(0,limit)
for x=1 to size do
for y=nchars to size*nchars by nchars do
ch = s[x][y]
if 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
end if
board[x][y] = ch
end for
end for
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 if
end procedure

constant board1 = """
.  .  .  .  .  .  .  .  .
.  . 46 45  . 55 74  .  .
. 38  .  . 43  .  . 78  .
. 35  .  .  .  .  . 71  .
.  . 33  .  .  . 59  .  .
. 17  .  .  .  .  . 67  .
. 18  .  . 11  .  . 64  .
.  . 24 21  .  1  2  .  .
.  .  .  .  .  .  .  .  ."""
Numbrix(board1)

constant board2 = """
.  .  .  .  .  .  .  .  .
. 11 12 15 18 21 62 61  .
.  6  .  .  .  .  . 60  .
. 33  .  .  .  .  . 57  .
. 32  .  .  .  .  . 56  .
. 37  .  1  .  .  . 73  .
. 38  .  .  .  .  . 72  .
. 43 44 47 48 51 76 77  .
.  .  .  .  .  .  .  .  ."""
Numbrix(board2)
```

{{out}}

```
49 50 51 52 53 54 75 76 81
48 47 46 45 44 55 74 77 80
37 38 39 40 43 56 73 78 79
36 35 34 41 42 57 72 71 70
31 32 33 14 13 58 59 68 69
30 17 16 15 12 61 60 67 66
29 18 19 20 11 62 63 64 65
28 25 24 21 10  1  2  3  4
27 26 23 22  9  8  7  6  5
solution found in 580 tries (0.00s)
9 10 13 14 19 20 63 64 65
8 11 12 15 18 21 62 61 66
7  6  5 16 17 22 59 60 67
34 33  4  3 24 23 58 57 68
35 32 31  2 25 54 55 56 69
36 37 30  1 26 53 74 73 70
39 38 29 28 27 52 75 72 71
40 43 44 47 48 51 76 77 78
41 42 45 46 49 50 81 80 79
solution found in 334 tries (0.00s)

```

## Python

```
from sys import stdout
neighbours = [[-1, 0], [0, -1], [1, 0], [0, 1]]
exists = []
lastNumber = 0
wid = 0
hei = 0

def find_next(pa, x, y, z):
for i in range(4):
a = x + neighbours[i][0]
b = y + neighbours[i][1]
if wid > a > -1 and hei > b > -1:
if pa[a][b] == z:
return a, b

return -1, -1

def find_solution(pa, x, y, z):
if z > lastNumber:
return 1
if exists[z] == 1:
s = find_next(pa, x, y, z)
if s[0] < 0:
return 0
return find_solution(pa, s[0], s[1], z + 1)

for i in range(4):
a = x + neighbours[i][0]
b = y + neighbours[i][1]
if wid > a > -1 and hei > b > -1:
if pa[a][b] == 0:
pa[a][b] = z
r = find_solution(pa, a, b, z + 1)
if r == 1:
return 1
pa[a][b] = 0

return 0

def solve(pz, w, h):
global lastNumber, wid, hei, exists

lastNumber = w * h
wid = w
hei = h
exists = [0 for j in range(lastNumber + 1)]

pa = [[0 for j in range(h)] for i in range(w)]
st = pz.split()
idx = 0
for j in range(h):
for i in range(w):
if st[idx] == ".":
idx += 1
else:
pa[i][j] = int(st[idx])
exists[pa[i][j]] = 1
idx += 1

x = 0
y = 0
t = w * h + 1
for j in range(h):
for i in range(w):
if pa[i][j] != 0 and pa[i][j] < t:
t = pa[i][j]
x = i
y = j

return find_solution(pa, x, y, t + 1), pa

def show_result(r):
if r[0] == 1:
for j in range(hei):
for i in range(wid):
stdout.write(" {:0{}d}".format(r[1][i][j], 2))
print()
else:
stdout.write("No Solution!\n")

print()

r = solve(". . . . . . . . . . . 46 45 . 55 74 . . . 38 . . 43 . . 78 . . 35 . . . . . 71 . . . 33 . . . 59 . . . 17"
" . . . . . 67 . . 18 . . 11 . . 64 . . . 24 21 . 1  2 . . . . . . . . . . .", 9, 9)
show_result(r)

r = solve(". . . . . . . . . . 11 12 15 18 21 62 61 . .  6 . . . . . 60 . . 33 . . . . . 57 . . 32 . . . . . 56 . . 37"
" .  1 . . . 73 . . 38 . . . . . 72 . . 43 44 47 48 51 76 77 . . . . . . . . . .", 9, 9)
show_result(r)

r = solve("17 . . . 11 . . . 59 . 15 . . 6 . . 61 . . . 3 . . .  63 . . . . . . 66 . . . . 23 24 . 68 67 78 . 54 55"
" . . . . 72 . . . . . . 35 . . . 49 . . . 29 . . 40 . . 47 . 31 . . . 39 . . . 45", 9, 9)
show_result(r)

```

{{out}}

```
49 50 51 52 53 54 75 76 81
48 47 46 45 44 55 74 77 80
37 38 39 40 43 56 73 78 79
36 35 34 41 42 57 72 71 70
31 32 33 14 13 58 59 68 69
30 17 16 15 12 61 60 67 66
29 18 19 20 11 62 63 64 65
28 25 24 21 10 01 02 03 04
27 26 23 22 09 08 07 06 05

09 10 13 14 19 20 63 64 65
08 11 12 15 18 21 62 61 66
07 06 05 16 17 22 59 60 67
34 33 04 03 24 23 58 57 68
35 32 31 02 25 54 55 56 69
36 37 30 01 26 53 74 73 70
39 38 29 28 27 52 75 72 71
40 43 44 47 48 51 76 77 78
41 42 45 46 49 50 81 80 79

17 16 13 12 11 10 09 60 59
18 15 14 05 06 07 08 61 58
19 20 03 04 65 64 63 62 57
22 21 00 00 66 79 80 81 56
23 24 69 68 67 78 77 54 55
26 25 70 71 72 75 76 53 52
27 28 35 36 73 74 49 50 51
30 29 34 37 40 41 48 47 46
31 32 33 38 39 42 43 44 45

```

## Racket

This is a general "Hidato" style solver (which is why there is a search for a 0 start point (which supports [[Solve a Hopido puzzle|Hopido]]). There is already a Racket implementation of [[Solve a Hidato puzzle|Hidato]], so to allow a variety of approaches to be demonstrated, the main library for this set of problems is here.

`hidato-family-solver.rkt`

```#lang racket
;;; Used in my solutions of:
;;; "Solve a Hidato Puzzle"
;;; "Solve a Holy Knights Tour"
;;; "Solve a Numbrix Puzzle"
;;; "Solve a Hopido Puzzle"

;;; As well as the solver being common, the solution renderer and input formats are common
(provide
;; Input:  list of neighbour offsets
;; Output: a solver function:
;;         Input:  a puzzle
;;         Output: either the solved puzzle or #f if impossible
solve-hidato-family
;; Input:  puzzle
;;         optional minimum cell width
;; Output: a pretty string that can be printed
puzzle->string)

;; Cell values are:
;; zero?     - unvisited
;; positive? - nth visitied
;; else      - unvisitable. In the puzzle layout, it's a _. In the hash it's a -1, so we can care less
;; A puzzle is a sequence of sequences of cell values
;; We work with a puzzle as a hash keyed on (cons row-num col-num)

;; Take a puzzle and get a working hash of it
(define (puzzle->hash p)
(for*/hash
(((r row-num) (in-parallel p (in-naturals)))
((v col-num) (in-parallel r (in-naturals)))
#:when (integer? v))
(values (cons row-num col-num) v)))

;; Takes a hash and recreates a vector of vectors puzzle
(define (hash->puzzle h# (blank '_))
(define keys (hash-keys h#))
(define n-rows (add1 (car (argmax car keys))))
(define n-cols (add1 (cdr (argmax cdr keys))))
(for/vector #:length n-rows ((r n-rows))
(for/vector #:length n-cols ((c n-cols))
(hash-ref h# (cons r c) blank))))

;; See "provide" section for description
(define (puzzle->string p (w #f))
(match p
[#f "unsolved"]
[(? sequence? s)
(define (max-n-digits p)
(and p (add1 (order-of-magnitude (* (vector-length p) (vector-length (vector-ref p 0)))))))
(define min-width (or w (max-n-digits p)))
(string-join
(for/list ((r s))
(string-join
(for/list ((c r)) (~a c #:align 'right #:min-width min-width))
" "))
"\n")]))

(define ((solve-hidato-family neighbour-offsets) board)
(define board# (puzzle->hash board))
;; reverse mapping, will only take note of positive values
(define targets# (for/hash ([(k v) (in-hash board#)] #:when (positive? v)) (values v k)))

(define (neighbours r.c)
(for/list ((r+.c+ neighbour-offsets))
(match-define (list r+ c+) r+.c+)
(match-define (cons r  c ) r.c)
(cons (+ r r+) (+ c c+))))

;; Count the moves, rather than check for "no more zeros" in puzzle
(define last-move (length (filter number? (hash-values board#))))

;; Depth first solution of the puzzle (we have to go deep, it's where the solutions are!
(define (inr-solve-pzl b# move r.c)
(cond
[(= move last-move) b#] ; no moves needed, so solved
[else
(for*/or ; check each neighbour as an option
((r.c+ (in-list (neighbours r.c)))
#:when (equal? (hash-ref targets# move r.c) r.c) ; we're where we should be!
#:when (match (hash-ref b# r.c+ -1) (0 #t) ((== m++) #t) (_ #f)))
(inr-solve-pzl (hash-set b# r.c+ m++) m++ r.c+))]))

(define (solution-starting-at n)
(define start-r.c (for/first (((k v) (in-hash board#)) #:when (= n v)) k))
(and start-r.c (inr-solve-pzl board# n start-r.c)))

(define sltn
(cond [(solution-starting-at 1) => values]
;; next clause starts from 0 for hopido
[(solution-starting-at 0) => values]))

(and sltn (hash->puzzle sltn)))
```
```#lang racket
(require "hidato-family-solver.rkt")

(define von-neumann-neighbour-offsets
'((+1 0) (-1 0) (0 +1) (0 -1)))

(define solve-numbrix (solve-hidato-family von-neumann-neighbour-offsets))

(displayln
(puzzle->string
(solve-numbrix
#(#(0  0  0  0  0  0  0  0  0)
#(0  0 46 45  0 55 74  0  0)
#(0 38  0  0 43  0  0 78  0)
#(0 35  0  0  0  0  0 71  0)
#(0  0 33  0  0  0 59  0  0)
#(0 17  0  0  0  0  0 67  0)
#(0 18  0  0 11  0  0 64  0)
#(0  0 24 21  0  1  2  0  0)
#(0  0  0  0  0  0  0  0  0)))))

(newline)

(displayln
(puzzle->string
(solve-numbrix
#(#(0  0  0  0  0  0  0  0  0)
#(0 11 12 15 18 21 62 61  0)
#(0  6  0  0  0  0  0 60  0)
#(0 33  0  0  0  0  0 57  0)
#(0 32  0  0  0  0  0 56  0)
#(0 37  0  1  0  0  0 73  0)
#(0 38  0  0  0  0  0 72  0)
#(0 43 44 47 48 51 76 77  0)
#(0  0  0  0  0  0  0  0  0)))))
```

{{out}}

```49 50 51 52 53 54 75 76 81
48 47 46 45 44 55 74 77 80
37 38 39 40 43 56 73 78 79
36 35 34 41 42 57 72 71 70
31 32 33 14 13 58 59 68 69
30 17 16 15 12 61 60 67 66
29 18 19 20 11 62 63 64 65
28 25 24 21 10  1  2  3  4
27 26 23 22  9  8  7  6  5

9 10 13 14 19 20 63 64 65
8 11 12 15 18 21 62 61 66
7  6  5 16 17 22 59 60 67
34 33  4  3 24 23 58 57 68
35 32 31  2 25 54 55 56 69
36 37 30  1 26 53 74 73 70
39 38 29 28 27 52 75 72 71
40 43 44 47 48 51 76 77 78
41 42 45 46 49 50 81 80 79
```

## REXX

This solution is essentially same as the REXX Hidato puzzle solver.

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).

''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='Numbrix 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\='';          _=@.r.c
parse var marks  x  marks
if datatype(x,'N')   then x=abs(x)/1               /*normalize  │x│  */
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"."
say;  say 'A solution for the'   PZ   "exists.";    say;                call show
exit                                             /*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 return 1 /*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 input of:

1 1 . . . . . . . . ./2 1 . . 24 21 . 1 2 . ./3 1 . 18 . . 11 . . 64 ./4 1 . 17 . . . . . 67 ./5 1 . . 33 . . . 59 . ./6 1 . 35 . . . . . 71 ./7 1 . 38 . . 43 . . 78 ./8 1 . . 46 45 . 55 74 . ./9 1 . . . . . . . . .

```
.  .  .  .  .  .  .  .  .
.  . 46 45  . 55 74  .  .
. 38  .  . 43  .  . 78  .
. 35  .  .  .  .  . 71  .
.  . 33  .  .  . 59  .  .
. 17  .  .  .  .  . 67  .
. 18  .  . 11  .  . 64  .
.  . 24 21  .  1  2  .  .
.  .  .  .  .  .  .  .  .

A solution for the Numbrix puzzle exists.

49 50 51 52 53 54 75 76 81
48 47 46 45 44 55 74 77 80
37 38 39 40 43 56 73 78 79
36 35 34 41 42 57 72 71 70
31 32 33 14 13 58 59 68 69
30 17 16 15 12 61 60 67 66
29 18 19 20 11 62 63 64 65
28 25 24 21 10  1  2  3  4
27 26 23 22  9  8  7  6  5

```

'''output''' when using the input of:

1 1 . . . . . . . . .\2 1 . 43 44 47 48 51 76 77 .\3 1 . 38 . . . . . 72 .\4 1 . 37 . 1 . . . 73 .\5 1 . 32 . . . . . 56 .\6 1 . 33 . . . . . 57 .\7 1 . 6 . . . . . 60 .\8 1 . 11 12 15 18 21 62 61 .\9 1 . . . . . . . . .

```
.  .  .  .  .  .  .  .  .
. 11 12 15 18 21 62 61  .
.  6  .  .  .  .  . 60  .
. 33  .  .  .  .  . 57  .
. 32  .  .  .  .  . 56  .
. 37  .  1  .  .  . 73  .
. 38  .  .  .  .  . 72  .
. 43 44 47 48 51 76 77  .
.  .  .  .  .  .  .  .  .

A solution for the Numbrix puzzle exists.

9 10 13 14 19 20 63 64 65
8 11 12 15 18 21 62 61 66
7  6  5 16 17 22 59 60 67
34 33  4  3 24 23 58 57 68
35 32 31  2 25 54 55 56 69
36 37 30  1 26 53 74 73 70
39 38 29 28 27 52 75 72 71
40 43 44 47 48 51 76 77 78

```

## Ruby

This solution uses HLPsolver from [[Solve_a_Hidato_puzzle#With_Warnsdorff | here]]

```require 'HLPsolver'

ADJACENT = [[-1, 0], [0, -1], [0, 1], [1, 0]]

board1 = <<EOS
0  0  0  0  0  0  0  0  0
0  0 46 45  0 55 74  0  0
0 38  0  0 43  0  0 78  0
0 35  0  0  0  0  0 71  0
0  0 33  0  0  0 59  0  0
0 17  0  0  0  0  0 67  0
0 18  0  0 11  0  0 64  0
0  0 24 21  0  1  2  0  0
0  0  0  0  0  0  0  0  0
EOS
HLPsolver.new(board1).solve

board2 = <<EOS
0  0  0  0  0  0  0  0  0
0 11 12 15 18 21 62 61  0
0  6  0  0  0  0  0 60  0
0 33  0  0  0  0  0 57  0
0 32  0  0  0  0  0 56  0
0 37  0  1  0  0  0 73  0
0 38  0  0  0  0  0 72  0
0 43 44 47 48 51 76 77  0
0  0  0  0  0  0  0  0  0
EOS
HLPsolver.new(board2).solve
```

Which produces:

```
Problem:
0  0  0  0  0  0  0  0  0
0  0 46 45  0 55 74  0  0
0 38  0  0 43  0  0 78  0
0 35  0  0  0  0  0 71  0
0  0 33  0  0  0 59  0  0
0 17  0  0  0  0  0 67  0
0 18  0  0 11  0  0 64  0
0  0 24 21  0  1  2  0  0
0  0  0  0  0  0  0  0  0

Solution:
49 50 51 52 53 54 75 76 81
48 47 46 45 44 55 74 77 80
37 38 39 40 43 56 73 78 79
36 35 34 41 42 57 72 71 70
31 32 33 14 13 58 59 68 69
30 17 16 15 12 61 60 67 66
29 18 19 20 11 62 63 64 65
28 25 24 21 10  1  2  3  4
27 26 23 22  9  8  7  6  5

Problem:
0  0  0  0  0  0  0  0  0
0 11 12 15 18 21 62 61  0
0  6  0  0  0  0  0 60  0
0 33  0  0  0  0  0 57  0
0 32  0  0  0  0  0 56  0
0 37  0  1  0  0  0 73  0
0 38  0  0  0  0  0 72  0
0 43 44 47 48 51 76 77  0
0  0  0  0  0  0  0  0  0

Solution:
9 10 13 14 19 20 63 64 65
8 11 12 15 18 21 62 61 66
7  6  5 16 17 22 59 60 67
34 33  4  3 24 23 58 57 68
35 32 31  2 25 54 55 56 69
36 37 30  1 26 53 74 73 70
39 38 29 28 27 52 75 72 71
40 43 44 47 48 51 76 77 78
41 42 45 46 49 50 81 80 79

```

## SystemVerilog

```

//////////////////////////////////////////////////////////////////////////////
///  NumbrixSolver                                                         ///
///     Solve the puzzle, by using system verilog randomization engine     ///
//////////////////////////////////////////////////////////////////////////////
class NumbrixSolver;
rand int solvedBoard[][];
int fixedBoard[][];
int numCells;
////////////////////////////////////////////////////////////////////////////
/// Dynamically resize the board accordingly to the size of the reference///
/// board                                                                ///
////////////////////////////////////////////////////////////////////////////
constraint height {
solvedBoard.size == fixedBoard.size;
}
constraint width {
foreach(solvedBoard[i]) solvedBoard[i].size == fixedBoard[i].size;
}

////////////////////////////////////////////////////////////////////////////
///  Fix the positions defined in the input board                        ///
////////////////////////////////////////////////////////////////////////////
constraint fixed {
foreach(solvedBoard[i]) foreach(solvedBoard[i][j])
if(fixedBoard[i][j] != 0)solvedBoard[i][j] == fixedBoard[i][j];
}
////////////////////////////////////////////////////////////////////////////
///  Ensures that the whole board is filled from the number with numbers ///
///   1,2,3,...,numCells                                                 ///
////////////////////////////////////////////////////////////////////////////
constraint range {
foreach(solvedBoard[i])foreach(solvedBoard[i][j])
solvedBoard[i][j] inside {[1:numCells]};
}
////////////////////////////////////////////////////////////////////////////
///  Ensures that there is no repeated number, consequently every number ///
///  is present on the board                                             ///
////////////////////////////////////////////////////////////////////////////
constraint uniqueness {
foreach(solvedBoard[i1]) foreach(solvedBoard[i1][j1])
foreach(solvedBoard[i2]) foreach(solvedBoard[i2][j2])
if((i1 != i2) || (j1 != j2)) solvedBoard[i1][j1] != solvedBoard[i2][j2];
}

////////////////////////////////////////////////////////////////////////////
/// Ensures that exists one direction connecting the numbers in          ///
/// increasing order                                                     ///
////////////////////////////////////////////////////////////////////////////
constraint f_seq {
foreach(solvedBoard[i])foreach(solvedBoard[i][j])
(solvedBoard[i][j] == (numCells)) ||
(solvedBoard[(i < solvedBoard.size-1) ? (i+1): i][j]    ==
solvedBoard[i][j]+1) ||
(solvedBoard[i][(j < solvedBoard[i].size - 1) ? j+1: j] ==
solvedBoard[i][j]+1) ||
(solvedBoard[(i > 0) ? i-1: i][j]                       ==
solvedBoard[i][j]+1) ||
(solvedBoard[i][(j > 0)? j-1:j]                         ==
solvedBoard[i][j]+1);
}

function void pre_randomize();
// the multiplication is not supported in the constraints
numCells = fixedBoard.size * fixedBoard[0].size;
endfunction
function void printSolvedBoard();
foreach(solvedBoard[i]) begin
foreach(solvedBoard[j]) begin
\$write("%4d", solvedBoard[i][j]);
end
\$display("");
end
endfunction
endclass

//////////////////////////////////////////////////////////////////////////////
/// SolveNumBrix: A program demonstrating how to use NumbrixSolver class   ///
//////////////////////////////////////////////////////////////////////////////

program SolveNumbrix;
NumbrixSolver board;
initial begin
board = new;
board.fixedBoard = '{
'{0,  0,  0,  0,  0,  0,  0,  0,  0},
'{0,  0, 46, 45,  0, 55, 74,  0,  0},
'{0, 38,  0,  0, 43,  0,  0, 78,  0},
'{0, 35,  0,  0,  0,  0,  0, 71,  0},
'{0,  0, 33,  0,  0,  0, 59,  0,  0},
'{0, 17,  0,  0,  0,  0,  0, 67,  0},
'{0, 18,  0,  0, 11,  0,  0, 64,  0},
'{0,  0, 24, 21,  0,  1,  2,  0,  0},
'{0,  0,  0,  0,  0,  0,  0,  0,  0}};
if(board.randomize()) begin
\$display("Solution for the Example 1");
board.printSolvedBoard();
end
else begin
\$display("Failed to solve Example 1");
end

board.fixedBoard = '{
{0,  0,  0,  0,  0,  0,  0,  0,  0},
{0, 11, 12, 15, 18, 21, 62, 61,  0},
{0,  6,  0,  0,  0,  0,  0, 60,  0},
{0, 33,  0,  0,  0,  0,  0, 57,  0},
{0, 32,  0,  0,  0,  0,  0, 56,  0},
{0, 37,  0,  1,  0,  0,  0, 73,  0},
{0, 38,  0,  0,  0,  0,  0, 72,  0},
{0, 43, 44, 47, 48, 51, 76, 77,  0},
'{0,  0,  0,  0,  0,  0,  0,  0,  0}};

if(board.randomize()) begin
\$display("Solution for the Example 2");
board.printSolvedBoard();
end
else begin
\$display("Failed to solve Example 2");
end
\$finish;
end
endprogram

```

Running the above program in ncverilog

```
> ncverilog +sv numbrix.sv
Solution for the Example 1
49  50  51  52  53  54  75  76  81
48  47  46  45  44  55  74  77  80
37  38  39  40  43  56  73  78  79
36  35  34  41  42  57  72  71  70
31  32  33  14  13  58  59  68  69
30  17  16  15  12  61  60  67  66
29  18  19  20  11  62  63  64  65
28  25  24  21  10   1   2   3   4
27  26  23  22   9   8   7   6   5
Solution for the Example 2
9  10  13  14  19  20  63  64  65
8  11  12  15  18  21  62  61  66
7   6   5  16  17  22  59  60  67
34  33   4   3  24  23  58  57  68
35  32  31   2  25  54  55  56  69
36  37  30   1  26  53  74  73  70
39  38  29  28  27  52  75  72  71
40  43  44  47  48  51  76  77  78
41  42  45  46  49  50  81  80  79

```

## Tcl

Following loosely the structure of [[Solve_a_Hidato_puzzle#Tcl]].

```# Loop over adjacent pairs in a list.
# Example:
#  % eachpair {a b} {1 2 3} {puts \$a \$b}
#  1 2
#  2 3
proc eachpair {varNames ls script} {
if {[lassign \$varNames _i _j] ne ""} {
return -code error "Must supply exactly two arguments"
}
tailcall foreach \$_i [lrange \$ls 0 end-1] \$_j [lrange \$ls 1 end] \$script
}

namespace eval numbrix {

namespace path {::tcl::mathop ::tcl::mathfunc}

proc parse {txt} {
set map [split [string trim \$txt] \n]
}

proc print {map} {
join [lmap row \$map {
join [lmap val \$row {
format %2d \$val
}] " "
}] \n
}

proc mark {map x y i} {
lset map \$x \$y \$i
}

proc moves {x y} {
foreach {dx dy} {
0  1
-1 0      1 0
0 -1
} {
lappend r [+ \$dx \$x] [+ \$dy \$y]
}
return \$r
}

proc rmap {map} {   ;# generate a reverse map in a dict {val {x y} ..}
set rmap {}
set h [llength \$map]
set w [llength [lindex \$map 0]]
set x \$w
while {[incr x -1]>=0} {
set y \$h
while {[incr y -1]>=0} {
set i [lindex \$map \$x \$y]
if {\$i} {
dict set rmap [lindex \$map \$x \$y] [list \$x \$y]
}
}
}
return \$rmap
}

proc gaps {rmap} {  ;# list all the gaps to be filled
set known [lsort -integer [dict keys \$rmap]]
set gaps {}
eachpair {i j} \$known {
if {\$j > \$i+1} {
lappend gaps \$i \$j
}
}
return \$gaps
}

proc fixgaps {map rmap gaps} {  ;# add a "tail" gap if needed
set w [llength \$map]
set h [llength [lindex \$map 0]]
set size [* \$h \$w]
set max [max {*}[dict keys \$rmap]]
if {\$max ne \$size} {
lappend gaps \$max Inf
}
return \$gaps
}

proc paths {map x0 y0 n} {  ;# generate all the maps with a single path filled legally
if {\$n == 0} {return [list \$map]}
set i [lindex \$map \$x0 \$y0]
set paths {}
foreach {x y} [moves \$x0 \$y0] {
set j [lindex \$map \$x \$y]
if {\$j eq ""} {
continue
} elseif {\$j == 0 && \$n == \$n+1} {
return [list [mark \$map \$x \$y [+ \$i 1]]]
} elseif {\$j == \$i+1} {
lappend paths \$map
continue
} elseif {\$j || (\$n == 1)} {
continue
} else {
lappend paths {*}[
paths [
mark \$map \$x \$y [+ \$i 1]
] \$x \$y [- \$n 1]
]
}
}
return \$paths
}

proc solve {map} {
# fixpoint map
while 1 {   ;# first we iteratively fill in paths with distinct solutions
set rmap [rmap \$map]
set gaps [gaps \$rmap]
set gaps [fixgaps \$map \$rmap \$gaps]
if {\$gaps eq ""} {
return \$map
}
set oldmap \$map
foreach {i j} \$gaps {
lassign [dict get \$rmap \$i] x0 y0
set n [- \$j \$i]
set paths [paths \$map \$x0 \$y0 \$n]
if {\$paths eq ""} {
return ""
} elseif {[llength \$paths] == 1} {
#puts "solved \$i..\$j"
#puts [print \$map]
set map [lindex \$paths 0]
}
;# we could intersect the paths to maybe get some tiles
}
if {\$map eq \$oldmap} {
break
}
}
#puts "unique paths exhausted - going DFS"
try {   ;# for any left over paths, go DFS
;# we might want to sort the gaps first
foreach {i j} \$gaps {
lassign [dict get \$rmap \$i] x0 y0
set n [- \$j \$i]
set paths [paths \$map \$x0 \$y0 \$n]
foreach path \$paths {
#puts "recursing on \$i..\$j"
set sol [solve \$path]
if {\$sol ne ""} {
return \$sol
}
}
}
}
}

namespace export {[a-z]*}
namespace ensemble create
}

set puzzles {
{
0  0  0  0  0  0  0  0  0
0  0 46 45  0 55 74  0  0
0 38  0  0 43  0  0 78  0
0 35  0  0  0  0  0 71  0
0  0 33  0  0  0 59  0  0
0 17  0  0  0  0  0 67  0
0 18  0  0 11  0  0 64  0
0  0 24 21  0  1  2  0  0
0  0  0  0  0  0  0  0  0
}

{
0  0  0  0  0  0  0  0  0
0 11 12 15 18 21 62 61  0
0  6  0  0  0  0  0 60  0
0 33  0  0  0  0  0 57  0
0 32  0  0  0  0  0 56  0
0 37  0  1  0  0  0 73  0
0 38  0  0  0  0  0 72  0
0 43 44 47 48 51 76 77  0
0  0  0  0  0  0  0  0  0
}
}

foreach puzzle \$puzzles {
set map [numbrix parse \$puzzle]
puts "\n== Puzzle [incr i] =="
puts [numbrix print \$map]
set sol [numbrix solve \$map]
if {\$sol ne ""} {
puts "\n== Solution \$i =="
puts [numbrix print \$sol]
} else {
puts "\n== No Solution for Puzzle \$i =="
}
}
```

{{Out}}

```
== Puzzle 1 ==
0  0  0  0  0  0  0  0  0
0  0 46 45  0 55 74  0  0
0 38  0  0 43  0  0 78  0
0 35  0  0  0  0  0 71  0
0  0 33  0  0  0 59  0  0
0 17  0  0  0  0  0 67  0
0 18  0  0 11  0  0 64  0
0  0 24 21  0  1  2  0  0
0  0  0  0  0  0  0  0  0

== Solution 1 ==
49 50 51 52 53 54 75 76 81
48 47 46 45 44 55 74 77 80
37 38 39 40 43 56 73 78 79
36 35 34 41 42 57 72 71 70
31 32 33 14 13 58 59 68 69
30 17 16 15 12 61 60 67 66
29 18 19 20 11 62 63 64 65
28 25 24 21 10  1  2  3  4
27 26 23 22  9  8  7  6  5

== Puzzle 2 ==
0  0  0  0  0  0  0  0  0
0 11 12 15 18 21 62 61  0
0  6  0  0  0  0  0 60  0
0 33  0  0  0  0  0 57  0
0 32  0  0  0  0  0 56  0
0 37  0  1  0  0  0 73  0
0 38  0  0  0  0  0 72  0
0 43 44 47 48 51 76 77  0
0  0  0  0  0  0  0  0  0

== Solution 2 ==
9 10 13 14 19 20 63 64 65
8 11 12 15 18 21 62 61 66
7  6  5 16 17 22 59 60 67
34 33  4  3 24 23 58 57 68
35 32 31  2 25 54 55 56 69
36 37 30  1 26 53 74 73 70
39 38 29 28 27 52 75 72 71
40 43 44 47 48 51 76 77 78
41 42 45 46 49 50 81 80 79

```

## zkl

{{trans|Python}} This code solves Hidato, Hopido and Numbrix puzzles.

```     // Solve Hidato/Hopido/Numbrix puzzles
class Puzzle{  // hold info concerning this puzzle
var board, nrows,ncols, cells,
start,      // (r,c) where 1 is located, Void if no 1
terminated, // if board holds highest numbered cell
given,	   // all the pre-loaded cells
adj,        // a list of (r,c) that are valid next cells
;

fcn print_board{
d:=Dictionary(-1,"  ", 0,"__");
foreach r in (board){
r.pump(String,'wrap(c){ "%2s ".fmt(d.find(c,c)) }).println();
}
}
lines:=s.split("\n");
ncols,nrows=lines[0].split().len(),lines.len();
board=nrows.pump(List(), ncols.pump(List(),-1).copy);
given,start=List(),Void;
cells,terminated=0,True;
foreach r,row in (lines.enumerate()){
foreach c,cell in (row.split().enumerate()){
if(cell=="X") continue;   // X == not in play, leave at -1
cells+=1;
val:=cell.toInt();
board[r][c]=val;
given.append(val);
if(val==1) start=T(r,c);
}
}
println("Number of cells = ",cells);
if(not given.holds(cells)){ given.append(cells); terminated=False; }
given=given.filter().sort();
}
fcn solve{   //-->Bool
if(start) return(_solve(start.xplode()));
foreach r,c in (nrows,ncols){
if(board[r][c]==0 and _solve(r,c)) return(True);
}
False
}
fcn [private] _solve(r,c,n=1, next=0){
if(n>given[-1])                       		   return(True);
if(not ( (0<=r<nrows) and (0<=c<ncols) ))		   return(False);
if(board[r][c] and board[r][c]!=n)                   return(False);
if(terminated and 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 (adj){ if(self.fcn(r+i,c+j,n+1, next)) return(True) }
board[r][c]=back;
False
}
} // Puzzle
```
```hi1:=  // 0==empty cell, X==not a cell
#<<<
"0  0  0  0  0  0  0  0  0
0  0 46 45  0 55 74  0  0
0 38  0  0 43  0  0 78  0
0 35  0  0  0  0  0 71  0
0  0 33  0  0  0 59  0  0
0 17  0  0  0  0  0 67  0
0 18  0  0 11  0  0 64  0
0  0 24 21  0  1  2  0  0
0  0  0  0  0  0  0  0  0";
#<<<

hi2:=  // 0==empty cell, X==not a cell
#<<<
"0  0  0  0  0  0  0  0  0
0 11 12 15 18 21 62 61  0
0  6  0  0  0  0  0 60  0
0 33  0  0  0  0  0 57  0
0 32  0  0  0  0  0 56  0
0 37  0  1  0  0  0 73  0
0 38  0  0  0  0  0 72  0
0 43 44 47 48 51 76 77  0
0  0  0  0  0  0  0  0  0";
#<<<
T( 0,-1),         T( 0,1),
T( 1,0) );

foreach hi in (T(hi1,hi2)){
puzzle.print_board();
puzzle.solve();
println();
puzzle.print_board();
println();
}
```

{{out}}

```
Number of cells = 81
__ __ __ __ __ __ __ __ __
__ __ 46 45 __ 55 74 __ __
__ 38 __ __ 43 __ __ 78 __
__ 35 __ __ __ __ __ 71 __
__ __ 33 __ __ __ 59 __ __
__ 17 __ __ __ __ __ 67 __
__ 18 __ __ 11 __ __ 64 __
__ __ 24 21 __  1  2 __ __
__ __ __ __ __ __ __ __ __

49 50 51 52 53 54 75 76 81
48 47 46 45 44 55 74 77 80
37 38 39 40 43 56 73 78 79
36 35 34 41 42 57 72 71 70
31 32 33 14 13 58 59 68 69
30 17 16 15 12 61 60 67 66
29 18 19 20 11 62 63 64 65
28 25 24 21 10  1  2  3  4
27 26 23 22  9  8  7  6  5

Number of cells = 81
__ __ __ __ __ __ __ __ __
__ 11 12 15 18 21 62 61 __
__  6 __ __ __ __ __ 60 __
__ 33 __ __ __ __ __ 57 __
__ 32 __ __ __ __ __ 56 __
__ 37 __  1 __ __ __ 73 __
__ 38 __ __ __ __ __ 72 __
__ 43 44 47 48 51 76 77 __
__ __ __ __ __ __ __ __ __

9 10 13 14 19 20 63 64 65
8 11 12 15 18 21 62 61 66
7  6  5 16 17 22 59 60 67
34 33  4  3 24 23 58 57 68
35 32 31  2 25 54 55 56 69
36 37 30  1 26 53 74 73 70
39 38 29 28 27 52 75 72 71
40 43 44 47 48 51 76 77 78
41 42 45 46 49 50 81 80 79

```

[[Category:Puzzles]]