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。
<small style="box-sizing: border-box; font-size: 12px;">上图是一个部分填充的有效的数独。</small>
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。</pre>
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。
class Solution:
def isValidSudoku(self, board):
"""
:type board: List[List[str]]
:rtype: bool
"""
row = [[] for _ in range(9)] # 行记录器
col = [[] for _ in range(9)] # 列记录器
area = [[] for _ in range(9)] # 子区域记录器
for i in range(9):
for j in range(9):
element = board[i][j] # 遍历所有元素
if element != '.': # 有数字才记录下来
top_id = i//3*3 + j//3 # 每个元素子区域的计算方法
if element in row[i] or element in col[j] or element in area[top_id]: # 如果在这一行列子区域重读出现过了
return False
else: # 没有出现过就加进去
row[i].append(element)
col[j].append(element)
area[top_id].append(element)
return True
class Solution:
def isValidSudoku(self, board):
"""
:type board: List[List[str]]
:rtype: bool
"""
row = [[0 for _ in range(9)] for _ in range(9)]
col = [[0 for _ in range(9)] for _ in range(9)]
mat = [[0 for _ in range(9)] for _ in range(9)]
for i in range(9):
for j in range(9):
if board[i][j] != ".":
num = int(board[i][j]) - 1
k = i // 3 * 3 + j // 3
if row[i][num] or col[j][num] or mat[k][num]:
return False
row[i][num] = col[j][num] = mat[k][num] = 1
return True
