LeetCode-37 解数独

来源：力扣（LeetCode）
链接：https://leetcode-cn.com/problems/sudoku-solver

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。

示例：

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：

提示：

board.length == 9
board[i].length == 9
board[i][j] 是一位数字或者 '.'
题目数据保证输入数独仅有一个解

解题思路

数独问题是个np问题，只能采用回溯算法来求解。

将行列和块分别使用一个九位的二进制数作为标志，分别表示他们区域内1-9数字的使用情况，将需要填充的格子坐标写入一个栈中，然后利用深度优先的算法尝试为格子填入合法的数字。

代码展示

class Solution {
public:
    vector<int> viRow, viCol;
    vector<vector<int>> vviBlock;
    stack<pair<int, int>> vpairiiNeed;

    void dfs(vector<vector<char>>& board, bool &Flag)
    {
        if(vpairiiNeed.empty()) 
            Flag = true;
        if(Flag)
            return;
        auto Temp = vpairiiNeed.top();
        vpairiiNeed.pop();
        for(int i = 0; i < 9; i++)
        {
            if(viRow[Temp.first] & (1 << i))
                continue;
            if(viCol[Temp.second] & (1 << i))
                continue;
            if(vviBlock[Temp.first / 3][Temp.second / 3] & (1 << i))
                continue;
            board[Temp.first][Temp.second] = i + '1';

            viRow[Temp.first] += 1 << (board[Temp.first][Temp.second] - '1');
            viCol[Temp.second] += 1 << (board[Temp.first][Temp.second] - '1');
            vviBlock[Temp.first / 3][Temp.second / 3] += 1 << (board[Temp.first][Temp.second] - '1');
            dfs(board, Flag);
            if(Flag)
                break;
            viRow[Temp.first] -= 1 << (board[Temp.first][Temp.second] - '1');
            viCol[Temp.second] -= 1 << (board[Temp.first][Temp.second] - '1');
            vviBlock[Temp.first / 3][Temp.second / 3] -= 1 << (board[Temp.first][Temp.second] - '1');
        }
        if(!Flag)
        {
            vpairiiNeed.push(Temp);
        }
            
    }


    void solveSudoku(vector<vector<char>>& board) {
        viRow.resize(9, 0);
        viCol.resize(9, 0);
        vviBlock.resize(3, vector<int>(3, 0));
        bool Flag = false;
        for(int i = 0; i < 9; i++)
            for(int j = 0; j < 9; j++)
            {
                if(board[i][j] == '.')
                    vpairiiNeed.push({i, j});
                else
                {
                    viRow[i] += 1 << (board[i][j] - '1');
                    viCol[j] += 1 << (board[i][j] - '1');
                    vviBlock[i / 3][j / 3] += 1 << (board[i][j] - '1');
                }
            }

        dfs(board, Flag);
    }
};