36_Valid Sudoku
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 digits1-9
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
.
Solution 1:
Idea:
Loop over each row, column and sub grid to check if duplicates exist
Time Complexity:
Space Complexity:
def isValidSudoku(self, board):
"""
:type board: List[List[str]]
:rtype: bool
"""
# define a function to check if a list is valid
def isValidList(l) :
nums = [l[i] for i in range(len(l)) if l[i] != '.']
return len(nums) == len(set(nums))
# check rows
for i in range(9) :
if not isValidList(board[i]):
return False
# check columns
for j in range(9) :
l = [board[i][j] for i in range(9)]
if not isValidList(l) :
return False
# check small grids
for m in range(3) :
for n in range(3) :
l = [board[i][j] for i in range(3*m, 3*m+3) for j in range(3*n, 3*n+3)]
if not isValidList(l) :
return False
return True
Solution 2:
Loop once instead of 3 times as in solution 1 sacrificing space complexity as
def isValidSudoku(self, board):
"""
:type board: List[List[str]]
:rtype: bool
"""
seen = sum(([(c, i), (j, c), (i/3, j/3, c)]
for i, row in enumerate(board)
for j, c in enumerate(row)
if c != '.'), [])
return len(seen) == len(set(seen))
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