
Chess coaches have been known to inflict a kind of torture on beginners by taking a chess board, placing pennies on some squares and requiring that a Knight's tour be constructed that avoids the squares with pennies.

This kind of knight's tour puzzle is similar to   Hidato.

The present task is to produce a solution to such problems. At least demonstrate your program by solving the following:



Example

  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

Note that the zeros represent the available squares, not the pennies.

Extra credit is available for other interesting examples.



Related tasks

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


import java.util.*;
 
public class HolyKnightsTour {
 
    final static String[] board = {
        " xxx    ",
        " x xx   ",
        " xxxxxxx",
        "xxx  x x",
        "x x  xxx",
        "1xxxxxx ",
        "  xx x  ",
        "   xxx  "};
 
    private final static int base = 12;
    private final static int[][] moves = {{1, -2}, {2, -1}, {2, 1}, {1, 2},
    {-1, 2}, {-2, 1}, {-2, -1}, {-1, -2}};
    private static int[][] grid;
    private static int total = 2;
 
    public static void main(String[] args) {
        int row = 0, col = 0;
 
        grid = new int[base][base];
 
        for (int r = 0; r < base; r++) {
            Arrays.fill(grid[r], -1);
            for (int c = 2; c < base - 2; c++) {
                if (r >= 2 && r < base - 2) {
                    if (board[r - 2].charAt(c - 2) == 'x') {
                        grid[r][c] = 0;
                        total++;
                    }
                    if (board[r - 2].charAt(c - 2) == '1') {
                        row = r;
                        col = c;
                    }
                }
            }
        }
 
        grid[row][col] = 1;
 
        if (solve(row, col, 2))
            printResult();
    }
 
    private static boolean solve(int r, int c, int count) {
        if (count == total)
            return true;
 
        List<int[]> nbrs = neighbors(r, c);
 
        if (nbrs.isEmpty() && count != total)
            return false;
 
        Collections.sort(nbrs, (a, b) -> a[2] - b[2]);
 
        for (int[] nb : nbrs) {
            r = nb[0];
            c = nb[1];
            grid[r][c] = count;
            if (solve(r, c, count + 1))
                return true;
            grid[r][c] = 0;
        }
 
        return false;
    }
 
    private static List<int[]> neighbors(int r, int c) {
        List<int[]> nbrs = new ArrayList<>();
 
        for (int[] m : moves) {
            int x = m[0];
            int y = m[1];
            if (grid[r + y][c + x] == 0) {
                int num = countNeighbors(r + y, c + x) - 1;
                nbrs.add(new int[]{r + y, c + x, num});
            }
        }
        return nbrs;
    }
 
    private static int countNeighbors(int r, int c) {
        int num = 0;
        for (int[] m : moves)
            if (grid[r + m[1]][c + m[0]] == 0)
                num++;
        return num;
    }
 
    private static void printResult() {
        for (int[] row : grid) {
            for (int i : row) {
                if (i == -1)
                    System.out.printf("%2s ", ' ');
                else
                    System.out.printf("%2d ", i);
            }
            System.out.println();
        }
    }
}