[LeetCode] Problem 37 - Sudoku Solver

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Write a program to solve a Sudoku puzzle by filling the empty cells.

A sudoku solution must satisfy all of the following rules:

  1. Each of the digits 1-9 must occur exactly once in each row.
  2. Each of the digits 1-9 must occur exactly once in each column.
  3. Each of the the digits 1-9 must occur exactly once in each of the 9 3x3 sub-boxes of the grid.

Empty cells are indicated by the character ‘.’.

Zv4Ey4.png

A sudoku puzzle…

ZvLcB8.png

…and its solution numbers marked in red.

Note

  • The given board contain only digits 1-9 and the character ‘.’.
  • You may assume that the given Sudoku puzzle will have a single unique solution.
  • The given board size is always 9x9.

Code

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private boolean[][] row = new boolean[9][9];
private boolean[][] col = new boolean[9][9];
private boolean[][] cell = new boolean[9][9];

public void solveSudoku(char[][] board) {
    for (int i = 0; i < 9; i++) {
        for (int j = 0; j < 9; j++) {
            if (board[i][j] == '.')
                continue;

            int num = board[i][j] - '1';
            row[i][num] = true;
            col[j][num] = true;
            cell[(i / 3) * 3 + (j / 3)][num] = true;
        }
    }

    helper(board, 0);
}

private boolean helper(char[][] board, int pos) {
    if (pos == 81)
        return true;

    int x = pos / 9;
    int y = pos % 9;

    if (board[x][y] != '.')
        return helper(board, pos + 1);

    for (int k = 0; k < 9; k++) {
        int p = (x / 3) * 3 + (y / 3);

        if (!row[x][k] && !col[y][k] && !cell[p][k]) {
            board[x][y] = (char) (k + 1 + '0');
            row[x][k] = true;
            col[y][k] = true;
            cell[p][k] = true;

            if (helper(board, pos + 1))
                return true;

            board[x][y] = '.';
            row[x][k] = false;
            col[y][k] = false;
            cell[p][k] = false;
        }
    }

    return false;
}