题目描述

编写一个程序，通过填充空格来解决数独问题。

数独的解法需 遵循如下规则：

数字 1-9 在每一行只能出现一次。
数字 1-9 在每一列只能出现一次。
数字 1-9 在每一个以粗实线分隔的 3x3 宫内只能出现一次。（请参考示例图）
数独部分空格内已填入了数字，空白格用 ‘.’ 表示。

样例

示例1

输入：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"]]
输出：[["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"]]
解释：输入的数独如上图所示，唯一有效的解决方案如下所示：

DFS（每个空从1~9枚举）

C++ 代码

class Solution {
public:
    bool row[9][9] = {0}, col[9][9] = {0}, cell[3][3][9] = {0};

    void solveSudoku(vector<vector<char>>& board) {
        for (int i = 0; i < 9; i ++)
            for (int j = 0; j < 9; j ++)
            {
                char c = board[i][j];
                if (c != '.')
                {
                    int t = c - '1';
                    row[i][t] = col[j][t] = cell[i / 3][j / 3][t] = true;
                }
            }
        dfs(board, 0, 0);
    }

    bool dfs(vector<vector<char>>& board, int x, int y)
    {
        if (y == 9) x ++, y = 0;
        if (x == 9) return true;
        if (board[x][y] != '.') return dfs(board, x, y + 1);

        for (int i = 0; i < 9; i ++)
        {
            if (!row[x][i] && !col[y][i] && !cell[x / 3][y / 3][i])
            {
                board[x][y] = '1' + i;
                row[x][i] = col[y][i] = cell[x / 3][y / 3][i] = true;
                if (dfs(board, x, y + 1)) return true;
                row[x][i] = col[y][i] = cell[x / 3][y / 3][i] = false;
                board[x][y] = '.';
            }
        }
        return false;
    }
};