37. Sudoku Solver

Problem Statement

Hard

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

A sudoku solution must satisfy all of the following rules:

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

The '.' character indicates empty cells.

Example 1:

Input: board = [["5","3",".",".","7",".",".",".","."],["6",".",".","1","9","5",".",".","."],[".","9","8",".",".",".",".","6","."],["8",".",".",".","6",".",".",".","3"],["4",".",".","8",".","3",".",".","1"],["7",".",".",".","2",".",".",".","6"],[".","6",".",".",".",".","2","8","."],[".",".",".","4","1","9",".",".","5"],[".",".",".",".","8",".",".","7","9"]]
Output: [["5","3","4","6","7","8","9","1","2"],["6","7","2","1","9","5","3","4","8"],["1","9","8","3","4","2","5","6","7"],["8","5","9","7","6","1","4","2","3"],["4","2","6","8","5","3","7","9","1"],["7","1","3","9","2","4","8","5","6"],["9","6","1","5","3","7","2","8","4"],["2","8","7","4","1","9","6","3","5"],["3","4","5","2","8","6","1","7","9"]]
Explanation: The input board is shown above and the only valid solution is shown below:

Constraints:

board.length == 9
board[i].length == 9
board[i][j] is a digit or '.'.
It is guaranteed that the input board has only one solution.

Java

Source file

class Solution {
    public void solveSudoku(char[][] board) {
        solve(board, 0, 0);
    }

    boolean solve(char[][] board, int i, int j) {
        if (i == 9) // crossed last row, EOF
            return true;
        if (j == 9) // cross last col, CRLF
            return solve(board, i + 1, 0);
        if (board[i][j] != '.') // skip fixed digits (non-wild card)
            return solve(board, i, j + 1);
        for (char d = '1'; d <= '9'; d++) { // try each char
            if (isSafe(board, i, j, d)) {
                board[i][j] = d;
                if (solve(board, i, j + 1))
                    return true;
                board[i][j] = '.';
            }
        }
        return false;
    }

    boolean isSafe(char[][] board, int i, int j, char d) {
        for (int k = 0; k < 9; k++)
            if (board[k][j] == d || board[i][k] == d || board[3 * (i / 3) + k / 3][3 * (j / 3) + k % 3] == d)
                return false;
        return true;
    }
}