leetCode 37.解数独 + 回溯算法 + 图解

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：

1. 数字?1-9?在每一行只能出现一次。
2. 数字?1-9?在每一列只能出现一次。
3. 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 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：

class Solution {
public:
    bool isValid(int row,int col,char val,vector<vector<char>>& board) {
        for(int j=0;j<9;j++) { // 判断这一行里是否重复
            if(board[row][j] == val) return false;
        }
        for(int i=0;i<9;i++) { // 判断这一列里是否重复
            if(board[i][col] == val) return false;
        }
        int startRow = (row / 3) * 3;
        int startCol = (col / 3) * 3;
        for (int i = startRow; i < startRow + 3; i++) { // 判断9方格里是否重复
            for (int j = startCol; j < startCol + 3; j++) {
                if (board[i][j] == val ) {
                    return false;
                }
            }
        }
        return true;
    }
    bool backtracking(vector<vector<char>>& board) {
        for (int i = 0; i < board.size(); i++) {        // 遍历行
            for (int j = 0; j < board[0].size(); j++) { // 遍历列
                if (board[i][j] == '.') {
                    for (char k = '1'; k <= '9'; k++) {     // (i, j) 这个位置放k是否合适
                        if (isValid(i, j, k, board)) {
                            board[i][j] = k;                // 放置k
                            if (backtracking(board)) return true; // 如果找到合适一组立刻返回
                            board[i][j] = '.';              // 回溯，撤销k
                        }
                    }
                    return false;  // 9个数都试完了，都不行，那么就返回false
                }
            }
        }
        return true; // 遍历完没有返回false，说明找到了合适棋盘位置了
    }
    void solveSudoku(vector<vector<char>>& board) {
        backtracking(board);
    }
};

参考和推荐文章、视频：

回溯算法二维递归？解数独不过如此！| LeetCode：37. 解数独-代码随想录-代码随想录-哔哩哔哩视频 (bilibili.com)https://www.bilibili.com/list/525438321?tid=0&sort_field=pubtime&spm_id_from=333.999.0.0&oid=944861498&bvid=BV1TW4y1471V代码随想录 (programmercarl.com)https://www.programmercarl.com/0037.%E8%A7%A3%E6%95%B0%E7%8B%AC.html#%E6%80%9D%E8%B7%AF