有效的数独
题目描述：
判断一个 9x9 的数独是否有效。只需要根据以下规则，验证已经填入的数字是否有效即可。
数字
1-9在每一行只能出现一次。数字
1-9在每一列只能出现一次。数字
1-9在每一个以粗实线分隔的3x3宫内只能出现一次。
image
上图是一个部分填充的有效的数独。
数独部分空格内已填入了数字，空白格用 '.' 表示。
示例1
输入:
[
["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"]
]
输出: true
示例2
输入:
[
["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"]
]
输出: false
解释: 除了第一行的第一个数字从 5 改为 8 以外，空格内其他数字均与 示例1 相同。
但由于位于左上角的 3x3 宫内有两个 8 存在, 因此这个数独是无效的。
说明:
- 一个有效的数独（部分已被填充）不一定是可解的。
- 只需要根据以上规则，验证已经填入的数字是否有效即可。
- 给定数独序列只包含数字
1-9和字符'.'。 - 给定数独永远是
9x9形式的。
解题思路：
主要是利用多层循环判断，判断矩阵是否一一满足题目条件
首先先将
9x9矩阵中的.转换为数字0,然后利用多层循环来判断是否满足条件第一层是判断每一行和每一列是否满足条件，判断在同一行是否出现两个相同的值，（
if column != j and board[i][j] == board[i][column]）；同理，判断在同一列是否出现两个相同的值，（if row != i and board[i][j] == board[row][j]）第二层是判断在每一个
3x3小格内是否能满足要求，首先，每3x3小格的范围可以通过range((i // 3) * 3, (i // 3) * 3 + 3)来获得，然后判断在3x3小格内是否出现在不同位置却相同的值（if row != i and col != j and board[i][j] == board[row][col]）如果上述条件都满足，返回
True，只要有一个不满足，就返回False
Python源码：
class Solution:
def isValidSudoku(self, board: 'List[List[str]]') -> 'bool':
for i in range(9):
for j in range(9):
if board[i][j] == '.':
board[i][j] = 0
for i in range(9):
for j in range(9):
if board[i][j] != 0:
for column in range(9):
if column != j and board[i][j] == board[i][column]:
return False
for row in range(9):
if row != i and board[i][j] == board[row][j]:
return False
for row in range((i // 3) * 3, (i // 3) * 3 + 3):
for col in range((j // 3) * 3, (j // 3) * 3 + 3):
if row != i and col != j and board[i][j] == board[row][col]:
return False
return True
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