[LeetCode] 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.

题目的输入保证是有效的。用回溯法我们只要检查新加入的值能否在行、列以及小方块里有效即可，没有必要检查整个矩阵。

其实就是对于每一个'.' 尝试1~9 9个值，如果合法，就继续查下一个'.' ，如果非法，尝试下一个值。

若对于某一个'.' 1~9都尝试过且都失败了，就是无解，可以提前返回。

此题是边检查边求解。。

class Solution {
public:
    bool isValidSudoku(vector<vector<char> > &board, int x, int y) {
        int row, col;
        
        // Same value in the same column?
        for (row = 0; row < 9; ++row) {
            if ((x != row) && (board[row][y] == board[x][y])) {
                return false;
            }
        }
        
        // Same value in the same row?
        for (col = 0; col < 9; ++col) {
            if ((y != col) && (board[x][col] == board[x][y])) {
                return false;
            }
        }
        
        // Same value in the 3 * 3 block it belong to?
        for (row = (x / 3) * 3; row < (x / 3 + 1) * 3; ++row) {
            for (col = (y / 3) * 3; col < (y / 3 + 1) * 3; ++col) {
                if ((x != row) && (y != col) && (board[row][col] == board[x][y])) {
                    return false;
                }
            }
        }
        
        return true;
    }
    
    // 内部check，能否找到结果用bool返回值标示
    bool internalSolveSudokuCheck(vector<vector<char> > &board) {
        for (int row = 0; row < 9; ++row) {
            for (int col = 0; col < 9; ++col) {
                if ('.' == board[row][col]) {
            // 对每一个'.' 尝试 1~9,如果不合法，立刻返回
                    for (int i = 1; i <= 9; ++i) {
                        board[row][col] = '0' + i;
                        
                        if (isValidSudoku(board, row, col)) {
                            if (internalSolveSudokuCheck(board)) {
                                return true;
                            }
                        }
                        //如果不合法，回复'.',进入下次尝试
                        board[row][col] = '.';
                    }
                    //对于某一个'.',尝试1~9都不行，就返回false
                    return false;
                }
            }
        }
        
        return true;
    }
    
    void solveSudoku(vector<vector<char> > &board) {
        internalSolveSudokuCheck(board);
    }
};