來源：力扣（LeetCode）
連結：https://leetcode-cn.com/problems/valid-sudoku

題目描述

請你判斷一個 9 x 9 的數獨是否有效。只需要 根據以下規則 ，驗證已經填入的數字是否有效即可。

數字 1-9 在每一行只能出現一次。
數字 1-9 在每一列只能出現一次。
數字 1-9 在每一個以粗實線分隔的 3x3 宮內只能出現一次。（請參考示例圖）
 

注意：

一個有效的數獨（部分已被填充）不一定是可解的。
只需要根據以上規則，驗證已經填入的數字是否有效即可。
空白格用 '.' 表示。
 

示例 1：

輸入：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"]]
輸出：true

示例 2：

輸入：board =
[["8","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"]]
輸出：false
解釋：除了第一行的第一個數字從 5 改為 8 以外，空格內其他數字均與 示例1 相同。 但由於位於左上角的 3x3 宮內有兩個 8 存在, 因此這個數獨是無效的。
 

提示：

board.length == 9
board[i].length == 9
board[i][j] 是一位數字（1-9）或者 '.'

解題思路

本題僅需要確定已經填入的數字是否符合規則，不需要判斷數獨是否有解，很大的降低了解題難度。

利用狀態壓縮的策略，每行的情況可以使用一個int來記錄，其中0-8位分別代表該行1-9是否出現過，如果出現則直接可以判定這個數獨不符合規則，同樣每列和每個格子都可以使用這種思路。

程式碼展示

class Solution {
public:
    bool isValidSudoku(vector<vector<char>>& board) {
        vector
 
<int> Row(9, 0), Col(9, 0);
        vector<vector<int>> Block(3, vector<int>(3, 0));
        for(int i = 0; i < 9; i++)
            for(int j = 0; j < 9; j++)
            {
                if(board[i][j] != '.')
                {
                    int c = board[i][j] - '1';
                    if(Row[i] & 1 << c)
                        return false;
                    if(Col[j] & 1 << c)
                        return false;
                    if(Block[i / 3][j / 3] & 1 << c)
                        return false;
                    Row[i] |= 1 << c;
                    Col[j] |= 1 << c;
                    Block[i / 3][j / 3] |= 1 << c;
                }
            }
        return true;
    }
};

執行結果