Valid Sudoku

Problem

Determine if a 9 x 9 Sudoku board is valid. Only the filled cells need to be validated according to the following rules:

  1. Each row must contain the digits 1-9 without repetition.
  2. Each column must contain the digits 1-9 without repetition.
  3. Each of the nine 3 x 3 sub-boxes of the grid must contain the digits 1-9 without repetition.

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.

Example 1:

Sudoku Image

Input: board =
[["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: board =
[["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.

Constraints:

  • board.length == 9
  • board[i].length == 9
  • board[i][j] is a digit 1-9 or '.'.

Solution

  • HashMap
  • Time: O(9^2) ~ O(1)
  • Space: O(9^2) ~ O(1)
class Solution(object):
    def isValidSudoku(self, board):
        """
        :type board: List[List[str]]
        :rtype: bool
        """
        colMap = collections.defaultdict(set)
        rowMap = collections.defaultdict(set)
        boxMap = collections.defaultdict(set)

        for r in range(9):
            for c in range(9):
                if board[r][c] == ".":
                    continue

                if (board[r][c] in rowMap[r] or
                    board[r][c] in colMap[c] or
                    board[r][c] in boxMap[(r // 3, c // 3)]):
                    return False

                colMap[c].add(board[r][c])
                rowMap[r].add(board[r][c])
                boxMap[(r // 3, c // 3)].add(board[r][c])

        return True

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