《LeetCode之每日一题》:279.有效的数独

Posted 2022-02-12 是七喜呀！

有效的数独

• 有关题目
• • 题解

题目链接： 有效的数独

有关题目

请你判断一个 9 x 9 的数独是否有效。只需要 根据以下规则 ，验证已经填入的数字是否有效即可。

	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）

注意：

一个有效的数独（部分已被填充）不一定是可解的。
只需要根据以上规则，验证已经填入的数字是否有效即可。
空白格用 '.' 表示。

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：true

示例 2：

输入：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"]]
输出：false
解释：除了第一行的第一个数字从 5 改为 8 以外，空格内其他数字均与 示例1 相同。 
但由于位于左上角的 3x3 宫内有两个 8 存在, 因此这个数独是无效的。

提示：

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

题解

法一：一次遍历
代码一：数组

class Solution 
public:
    bool isValidSudoku(vector<vector<char>>& board) 
        int i, j;
        vector<vector<bool>> row(9, vector<bool>(9, 0));
        vector<vector<bool>> col(9, vector<bool>(9, 0));
        vector<vector<bool>> bigGrid(9, vector<bool>(9, 0));

        for (i = 0; i < 9; i++)
        
            for (j = 0; j < 9; j++)
            
                if (board[i][j] != '.')
                
                    int num = board[i][j] - '1';
                    int gridIndex = i / 3 * 3 + j / 3;//以粗实线分割的3 * 3宫内的下标
                    if (row[i][num] || col[j][num] || bigGrid[gridIndex][num])
                        return false;
                    else 
                    
                        row[i][num] = true;
                        col[j][num] = true;
                        bigGrid[gridIndex][num] = true;
                    
                
            
        
        return true;
    
;

时间复杂度：O(1)
空间复杂度：O(1)

代码二：位运算
参考官方题解

class Solution 
public:
    bool isValidSudoku(vector<vector<char>>& board) 
        int i, j;
        int i1, i2, i3;
        int x[9] =  0 ;

        for (i = 0; i < 9; i++)
        
            for (j = 0; j < 9; j++)
            
                if (board[i][j] != '.')
                
                    int num = board[i][j] - '1';
                    i1 = 0x01 << num;
                    i2 = 0x01 << 9 << num;
                    i3 = 0x01 << 9 << 9 << num;
                    int gridIndex = i / 3 * 3 + j / 3;//以粗实线分割的3 * 3宫内的下标
                    if (((x[i] & i1) !=  i1) && ((x[j] & i2) !=  i2) && ((x[gridIndex] & i3) !=  i3))
                    
                        x[i] |= i1;
                        x[j] |= i2;
                        x[gridIndex] |= i3;
                        
                    else 
                        return false;
                
            
        
        return true;
    
;

时间复杂度：O(1)
空间复杂度：O(1)