LeetCode 36. 有效的数独(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。
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。
解题思路
对于一个9x9的数独,遍历表格时分成三部分分别判断:第i行、第i列以及第i个方框,每个部分分别判断第j个元素是否满足条件。所以分别构造三个map,遍历到不为‘.’的数字时首先判断当前部分map中是否存在此字符,若存在就返回true,否则置当前字符为true。注意对于每个部分遍历数独时要进行正确的行列转换。
代码
class Solution {
public:
bool isValidSudoku(vector<vector<char>>& board) {
for(int i = ; i < ; i++){
map<char, bool> row, col, grid;
for(int j = ; j < ; j++){
if(board[i][j] != '.'){
if(row[board[i][j]] == true)
return false;
row[board[i][j]] = true;
}
if(board[j][i] != '.'){
if(col[board[j][i]] == true)
return false;
col[board[j][i]] = true;
}
int r = i / * + j / ;
int c = i % * + j % ;
if(board[r][c] != '.'){
if(grid[board[r][c]] == true)
return false;
grid[board[r][c]] = true;
}
}
}
return true;
}
};
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