【leetcode】36. Valid Sudoku

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本文详细解析了如何通过两次遍历验证9x9数独板的有效性，包括按行、按列和按3x3子网格检查数字1-9是否重复出现。提供了两种方法：暴力法和空间换时间法，并附带了C++代码实现。

36. Valid Sudoku

Determine if a 9x9 Sudoku board is valid. Only the filled cells need to be validated according to the following rules:

Each row must contain the digits 1-9 without repetition.
Each column must contain the digits 1-9 without repetition.
Each of the 9 3x3 sub-boxes of the grid must contain the digits 1-9 without repetition.

A partially filled sudoku which is valid.

The Sudoku board could be partially filled, where empty cells are filled with the character '.'.

Example 1:

Input:
[
  ["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:

Input:
[
  ["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.
The given board contain only digits 1-9 and the character '.'.
The given board size is always 9x9.

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

法一：暴力法

暴力法很容易就能想到，先按行判断，再按列判断，再按方阵判断，一共3次遍历。

时间复杂度O(n)，空间复杂度O(1)。

法二：空间换时间

只需要一次遍历，开辟空间来储存元素，比较简单的就是数组，查找方便。

时间复杂度O(n)，空间复杂度O(n)。

网友用的哈希表存储：https://leetcode.wang/leetCode-36-Valid-Sudoku.html

class Solution {
public:
    bool isValidSudoku(vector<vector<char>>& board) {
        int len = board.size();
        int box[len * 3][10];
        for (int i=0;i<len*3;++i){
            memset(box,0,sizeof(box));
        }
        for(int i = 0; i<len;++i){
            for(int j = 0; j<len;++j){
                int tmp = board[i][j] - '0';
                int dot = '.' - '0';
                if(tmp==dot) continue;
                if(tmp>=1 && tmp<=9 
                   && box[i][tmp]!=1 && box[j+9][tmp]!=1
                  && box[int(i/3)*3+int(j/3)+18][tmp]!=1){
                    box[i][tmp]=1;
                    box[j+9][tmp]=1;
                    box[int(i/3)*3+int(j/3)+18][tmp]=1;
                }else return false;
            }
        }
        return true;
    }
};

代码很简单，但花了很多时间在数组初始化的调试上：

数组声明后，元素值是随机的，没有统一初始化就会导致后续的!=1判断出错。

void *memset(void *s,int c,size_t n)
总的作用：将已开辟内存空间 s 的首 n 个字节的值设为值 c。

ps.看来要找本书仔细复习下c++啦