Determine if a 9×9 Sudoku board is valid. Only the filled cells need to be validated according to the following rules:
- Each row must contain the digits
1-9without repetition. - Each column must contain the digits
1-9without repetition. - Each of the 9
3x3sub-boxes of the grid must contain the digits1-9without 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
1-9and the character'.'. - The given board size is always
9x9.
Solution: HashTable
Use hashtable to store the numbers of each row, column and each 3×3 box. If there number appears more than once then it’s an invalid Sudoku.
Time complexity: O(1)
Space complexity: O(1)
C++
|
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// Author: Huahua class Solution { public: bool isValidSudoku(vector<vector<char> > &board) { for (int i = 0; i < 9;i++) { set<char> r, c; for (int j = 0; j < 9; j++) { if (board[i][j] != '.' && !r.insert(board[i][j]).second) return false; if (board[j][i] != '.' && !c.insert(board[j][i]).second) return false; } } for (int p = 0; p < 3; p++) for (int q = 0; q < 3; q++) { set<char> b; for (int i = 0; i < 3; i++) for (int j = 0; j < 3; j++) { int x = p * 3 + i; int y = q * 3 + j; if (board[y][x] != '.' && !b.insert(board[y][x]).second) return false; } } return true; } }; |
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