Task: Solve a Hidato puzzle
C#: 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)[]
        
        hidatoMoves = {(1,0),(1,1),(0,1),(-1,1),(-1,0),(-1,-1),(0,-1),(1,-1)};

    private (int dx, int dy)[] moves;
        
    public static void Main()
    {
        Print(new Solver(hidatoMoves).Solve(false, new [,] {
            {  0, 33, 35,  0,  0, -1, -1, -1 },
            {  0,  0, 24, 22,  0, -1, -1, -1 },
            {  0,  0,  0, 21,  0,  0, -1, -1 },
            {  0, 26,  0, 13, 40, 11, -1, -1 },
            { 27,  0,  0,  0,  9,  0,  1, -1 },
            { -1, -1,  0,  0, 18,  0,  0, -1 },
            { -1, -1, -1, -1,  0,  7,  0,  0 },
            { -1, -1, -1, -1, -1, -1,  5,  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();
    }

}

Java: 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) {
        

        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();
        }
    }
}