36. Valid Sudoku.py

"""
https://leetcode.com/problems/valid-sudoku/

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

Each row must contain the digits 1-9 without repetition.
Each column must contain the digits 1-9 without repetition.
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.

"""
from collections import defaultdict


class Solution(object):
    def isValidSudoku(self, board):
        """
        :type board: List[List[str]]
        :rtype: bool
        """
        rows, cols, squares = defaultdict(set), defaultdict(set), defaultdict(set)

        for row_idx in range(9):
            for col_idx in range(9):
                symbol = board[row_idx][col_idx]
                if symbol == '.':
                    continue
                square = row_idx // 3, col_idx // 3
                if symbol in rows[row_idx] or symbol in cols[col_idx] or symbol in squares[square]:
                    return False
                rows[row_idx].add(symbol)
                cols[col_idx].add(symbol)
                squares[square].add(symbol)

        return True


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"]
]


s = Solution()
assert s.isValidSudoku(board) is True