0036-valid-sudoku

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Description

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:

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(Python)

class Solution:
    def isValidSudoku(self, board: List[List[str]]) -> bool:
        # 
        # 
        # validate row  takes row check for duplicate return false if duplicate;  row index
        # validate column ; colum index
        # validate grid ; sub matrix 
        # fail early
        return self.short(board)

    def obviousversion(self, board: List[List[str]]) -> bool:
        DIMENSION = 9

        def  validate_row(row):
             seen = set()

             for i in range(DIMENSION):
                cell = board[row][i]
                if cell == '.':
                    continue
                if cell in seen:
                    return False
                seen.add(cell)
             return True
        
        def  validate_column(col):
             seen = set()

             for i in range(DIMENSION):
                cell = board[i][col]
                if cell == '.':
                    continue
                if cell in seen:
                    return False
                seen.add(cell)
             return True

        def  validate_grid(split_x, split_y):
             seen = set()

             for i in range(split_x, split_x + 3):
                for j in range(split_y, split_y + 3):

                    cell = board[i][j]
                    if cell == '.':
                        continue
                    if cell in seen:
                        return False
                    seen.add(cell)
             return True

        for row in range(DIMENSION):
            if not validate_row(row):
                return False
        
        for col in range(DIMENSION):
            if not validate_column(col):
                return False
        
        #   
        for split_x in range(0, DIMENSION, 3):
                for split_y in range(0, DIMENSION, 3):
                    if not validate_grid(split_x, split_y):
                        return False
        return True

    def short(self, board: List[List[str]]) -> bool:
        rows = [set() for _ in range(9)]
        cols = [set() for _ in range(9)]
        boxes = [set() for _ in range(9)]

        for r in range(9):
            for c in range(9):
                val = board[r][c]
                if val == '.':
                    continue
                b = (r // 3) * 3 + c // 3
                if val in rows[r] or val in cols[c] or val in boxes[b]:
                    return False
                rows[r].add(val)
                cols[c].add(val)
                boxes[b].add(val)
        return True