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''' | ||
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. | ||
''' | ||
|
||
class Solution(object): | ||
def isValidSudoku(self, board): | ||
""" | ||
:type board: List[List[str]] | ||
:rtype: bool | ||
""" | ||
import collections | ||
dict_row, dict_col, dict_cell = collections.defaultdict(set), collections.defaultdict(set), collections.defaultdict(set) | ||
|
||
for row_index in range(1, 4): | ||
for col_index in range(1, 4): | ||
for row in range(3*(row_index-1), 3*row_index): | ||
for col in range(3*(col_index-1), 3*col_index): | ||
cell_data = board[row][col] | ||
if cell_data == '.': | ||
continue | ||
if cell_data in dict_row[row] or cell_data in dict_col[col] or cell_data in dict_cell[(row_index, col_index)]: | ||
return False | ||
|
||
dict_row[row].add(cell_data) | ||
dict_col[col].add(cell_data) | ||
dict_cell[(row_index, col_index)].add(cell_data) | ||
|
||
return True |
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