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:

https://upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Sudoku-by-L2G-20050714.svg/250px-Sudoku-by-L2G-20050714.svg.png

!https://upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Sudoku-by-L2G-20050714.svg/250px-Sudoku-by-L2G-20050714.svg.png

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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:

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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 the5 in the top left corner being modified to8. 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 '.'.

Solve

sol1暴力解

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class Solution:
    def isValidSudoku(self, board: List[List[str]]) -> bool:
        for i in range(9):
            for j in range(9):
                if board[i][j] == ".":
                    continue

                for k in range(i, 9):
                    if i != k and board[i][j] == board[k][j]:
                        return False
                for l in range(j,9):
                    if l != j and board[i][j] == board[i][l]:
                        return False

        box = {}
        for i in range(9):
            for j in range(9):
                if board[i][j] == ".":
                    continue
                pos = (i//3,j//3)
                if pos not in box:
                    box[pos] = []
                if board[i][j] in box[pos]:
                    return False
                else:
                    box[pos].append(board[i][j])
                
        return True

sol2

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class Solution:
    def isValidSudoku(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 i in range(9):
            for j in range(9):
                num = board[i][j]
                if num == '.':
                    continue

                if num in rows[i]:
                    return False
                rows[i].add(num)

                if num in cols[j]:
                    return False
                cols[j].add(num)

                box_index = (i // 3) * 3 + (j // 3)
                if num in boxes[box_index]:
                    return False
                boxes[box_index].add(num)

        return True

特殊解

直接計算個數方法

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class Solution(object):
    def isValidSudoku(self, board):
        res = []
        for i in range(9):
            for j in range(9):
                element = board[i][j]
                if element != '.':
                    res += [(i, element), (element, j), (i // 3, j // 3, element)]
        return len(res) == len(set(res))