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 digits1-9and the character'.'.
The given board size is always9x9
.
Solution 1:
Idea:
Loop over each row, column and sub grid to check if duplicates exist
Time Complexity: O(n2)
Space Complexity: O(n)
defisValidSudoku(self,board):""" :type board: List[List[str]] :rtype: bool """# define a function to check if a list is validdefisValidList(l) : nums = [l[i]for i inrange(len(l))if l[i]!='.']returnlen(nums)==len(set(nums))# check rowsfor i inrange(9):ifnotisValidList(board[i]):returnFalse# check columnsfor j inrange(9): l = [board[i][j] for i inrange(9)]ifnotisValidList(l):returnFalse# check small grids for m inrange(3):for n inrange(3): l = [board[i][j] for i inrange(3*m, 3*m+3)for j inrange(3*n, 3*n+3)]ifnotisValidList(l):returnFalsereturnTrue
Solution 2:
Loop once instead of 3 times as in solution 1 sacrificing space complexity as O(n2)
defisValidSudoku(self,board):""" :type board: List[List[str]] :rtype: bool """ seen =sum(([(c, i), (j, c), (i/3, j/3, c)] for i, row inenumerate(board)for j, c inenumerate(row)if c !='.'), [])returnlen(seen)==len(set(seen))