【leetcode】36 有效的数独（哈希表）

最新推荐文章于 2022-03-16 22:16:57 发布

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最新推荐文章于 2022-03-16 22:16:57 发布

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分类专栏： LeetCode 文章标签：哈希表

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本文介绍了一种使用C++实现的数独有效性验证算法。通过遍历数独的每一行、每一列以及每个3x3的子网格，利用哈希集合来确保每个数字在相应范围内仅出现一次，从而判断数独是否有效。

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题目链接：https://leetcode-cn.com/problems/valid-sudoku/

题目描述

判断一个 9x9 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。

在这里插入图片描述
上图是一个部分填充的有效的数独。

数独部分空格内已填入了数字，空白格用 ‘.’ 表示。

示例 1:

输入:
[
  ["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:
[
  ["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。

说明:

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。
给定数独序列只包含数字 1-9 和字符 ‘.’ 。
给定数独永远是 9x9 形式的。

思路

class Solution {
public:
    bool isValidSudoku(vector<vector<char>>& board) {
        unordered_set<char> s;
        // 检查每一行
        for (int i = 0; i < board.size(); ++i) {
            s.clear();
            for (int j = 0; j < board[0].size(); ++j) {
                if(board[i][j] != '.'){
                    if(s.count(board[i][j]) == 0)
                        s.insert(board[i][j]);
                    else
                        return false;
                }
            }
        }
        // 检查每一列
        for (int j = 0; j < board[0].size(); ++j) {
            s.clear();
            for (int i = 0; i < board.size(); ++i) {
                if(board[i][j] != '.'){
                    if(s.count(board[i][j]) == 0)
                        s.insert(board[i][j]);
                    else
                        return false;
                }
            }
        }

        // 检查每个九宫格
        for (int k = 0; k < 9; ++k) {
            int x = k /3 * 3, y = (k %3) * 3;
            s.clear();
            for (int i = x; i < x+3; ++i) {
                for (int j = y; j < y+3; ++j) {
                    if(board[i][j] != '.'){
                        if(s.count(board[i][j]) == 0)
                            s.insert(board[i][j]);
                        else
                            return false;
                    }
                }
            }
        }
        return true;
    }
};

在这里插入图片描述