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.

class Solution {
public:
   bool isValid(vector<vector<char> > &board, int x, int y)  
    {  
        int i, j;  
        for (i = 0; i < 9; i++)  
            if (i != x && board[i][y] == board[x][y])  
                return false;  
        for (j = 0; j < 9; j++)  
            if (j != y && board[x][j] == board[x][y])  
                return false;  
        for (i = 3 * (x / 3); i < 3 * (x / 3 + 1); i++)  
            for (j = 3 * (y / 3); j < 3 * (y / 3 + 1); j++)  
                if (i != x && j != y && board[i][j] == board[x][y])  
                    return false;  
        return true;  
    }  
    bool solveSudoku(vector<vector<char> > &board)  
    {  
        for (int i = 0; i < 9; ++i)  
            for (int j = 0; j < 9; ++j)  
            {  
                if ('.' == board[i][j])  
                {  
                    for (int k = 1; k <= 9; ++k)  
                    {  
                        board[i][j] = '0' + k;  
                        if (isValid(board, i, j) && solveSudoku(board))  
                            return true;  
                        board[i][j] = '.';  
                    }  
                    return false;  
                }  
            }  
        return true;  
    }
};