37. Sudoku Solver

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

Empty cells are indicated by the character '.'.

You may assume that there will be only one unique solution.

A sudoku puzzle...

...and its solution numbers marked in red.

public class Solution {
    public void solveSudoku(char[][] board) {
        if (board == null || board.length == 0) return;
        solve(board);
    }

    public boolean solve(char[][] board) {
        for (int i = 0; i < board.length; i++) {
            for (int j = 0; j < board[0].length; j++) {
                if (board[i][j] == '.') {
                    for (char c = '1'; c <= '9'; c++) {// trial. Try 1 through 9
                        if (isValid(board, i, j, c)) {
                            board[i][j] = c; // Put c for this cell
                            if (solve(board)) {
                                return true; // If it's the solution return true
                            } else {
                                board[i][j] = '.'; // Otherwise go back
                            }
                        }
                    }
                    return false;
                }
            }
        }
        return true;
    }

    private boolean isValid(char[][] board, int row, int col, char c) {
        for (int i = 0; i < 9; i++) {
            // check row
            if (board[i][col] != '.' && board[i][col] == c) return false;
            // check column
            if (board[row][i] != '.' && board[row][i] == c) return false;
            // check 3*3 block
            int cubeRow = 3 * (row / 3) + i / 3;
            int cubeColumn = 3 * (col / 3) + i % 3;
            if (board[cubeRow][cubeColumn] != '.' && board[cubeRow][cubeColumn] == c) return false;
        }
        return true;
    }
}