36. Valid Sudoku

题目

Determine if a 9 x 9 Sudoku board is valid. Only the filled cells need to be validated according to the following rules:

  1. Each row must contain the digits 1-9 without repetition.
  2. Each column must contain the digits 1-9 without repetition.
  3. Each of the nine 3 x 3 sub-boxes of the grid must contain the digits 1-9 without repetition.

Note:

  • A Sudoku board (partially filled) could be valid but is not necessarily solvable.
  • Only the filled cells need to be validated according to the mentioned rules.

Example 1:

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Input: 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"]]
Output: true

Example 2:

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Input: 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"]]
Output: false
Explanation: Same as Example 1, except with the 5 in the top left corner being modified to 8. Since there are two 8's in the top left 3x3 sub-box, it is invalid.

题目大意

判断一个 9x9 的数独是否有效。只需要根据规则验证已填入的数字：每行、每列、每个 3x3 宫内数字 1-9 不能重复。

解题思路

方法：哈希表记录

思路

使用哈希表（或数组）记录每一行、每一列、每一个 3x3 宫格中已经出现过的数字。遍历整个数独，对于每个已填入的数字：

  1. 检查是否在当前行出现过
  2. 检查是否在当前列出现过
  3. 检查是否在当前 3x3 宫格出现过

如果任一检查发现重复，返回 false。

对于 3x3 宫格的索引计算：box_index = (row / 3) * 3 + (col / 3)

复杂度分析

  • 时间复杂度：O(1)，因为数独固定为 9x9，遍历次数恒定。
  • 空间复杂度：O(1)，记录空间固定为 9x9 = 81 个元素。

代码实现

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#include <vector>
#include <string>
using namespace std;

class Solution {
public:
    bool isValidSudoku(vector<vector<char>>& board) {
        bool rows[9][9] = {false};
        bool cols[9][9] = {false};
        bool boxes[9][9] = {false};
        
        for (int i = 0; i < 9; i++) {
            for (int j = 0; j < 9; j++) {
                if (board[i][j] == '.') continue;
                
                int num = board[i][j] - '1';
                int box_index = (i / 3) * 3 + (j / 3);
                
                if (rows[i][num] || cols[j][num] || boxes[box_index][num]) {
                    return false;
                }
                
                rows[i][num] = true;
                cols[j][num] = true;
                boxes[box_index][num] = true;
            }
        }
        
        return true;
    }
};