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[Leetcode]36. Valid Sudoku(C++)

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:

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#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