36 Valid Sudoku (David)

Here we solve the Valid Sudoku Problem from LeetCode.

Determine if a 9x9 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 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.

This solution holds all data in a set called big instead of using separate data structures for the rows, columns and boxes. Rows that already have a given number are placed in big as (row, cell) tuples, where cell is the number the row already contains. Columns reverse the tuple order with (cell, col) tuples. And the boxes use integer division to find the value of the nearest upper-left-hand corner with row//3 and col//3 . This means that the 3-tuple (row//3, col//3, cell) associates each number in cell with the closest upper-left-hand corner.

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class Solution:
    def isValidSudoku(self, board: List[List[str]]) -> bool:

        big = set()
        for row in range(0,9):
            for col in range(0,9):

                if board[row][col]!='.':

                    cell = board[row][col]

                    if (row, cell) in big or (cell,col) in big or (row//3,col//3,cell) in big:
                        return False

                    big.add((row, cell))
                    big.add((cell,col))
                    big.add((row//3,col//3,cell))
        return True

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