题目描述

题目链接：36. Valid Sudoku

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.

例子

例子 1

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

例子 2

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.

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.

Constraints

• board.length == 9
• board[i].length == 9
• board[i][j] is a digit or '.'

解题思路

这道题思路比较直观，按照题目要求对数独中每一行、每一列以及每一个方块进行逐个判断是否有重复数字即可，判断重复可以用维度为 9 的数组作为哈希表。代码如下：

#include <vector>

class Solution {
public:
    bool isValidSudoku(std::vector<std::vector<char>>& board) {
        std::vector<bool> is_used(10, false);

        // iterate each block
        for (int r = 0; r < 3; ++r) {
            for (int c = 0; c < 3; ++c) {
                is_used = std::vector<bool>(10, false);
                for (int i = 0; i < 3; ++i) {
                    for (int j = 0; j < 3; ++j) {
                        int val = board[r * 3 + i][c * 3 + j] - '0';
                        if (val > 9 || val < 1) continue;
                        if (is_used[val]) {
                            return false;
                        }
                        is_used[val] = true;
                    }
                }
            }
        }

        // iterate each row
        for (int r = 0; r < 9; r++) {
            is_used = std::vector<bool>(10, false);
            for (int c = 0; c < 9; ++c) {
                int val = board[r][c] - '0';
                if (val > 9 || val < 1) continue;
                if (is_used[val]) {
                    return false;
                }
                is_used[val] = true;
            }
        }

        // iterate each coloumn
        for (int c = 0; c < 9; c++) {
            is_used = std::vector<bool>(10, false);
            for (int r = 0; r < 9; ++r) {
                int val = board[r][c] - '0';
                if (val > 9 || val < 1) continue;
                if (is_used[val]) {
                    return false;
                }
                is_used[val] = true;
            }
        }

        return true;
    }
};

• 时间复杂度: O(1) –> 数独尺寸为常数
• 空间复杂度: O(1)

GitHub 代码同步地址： 36.ValidSudoku.cpp

其他题目： GitHub: Leetcode-C++-Solution 博客： Leetcode-Solutions