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请你判断一个 9 x 9 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。(请参考示例图)
注意:
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。
空白格用 '.' 表示。
示例 1:
[["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:
[["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。
提示:
board.length == 9
board[i].length == 9
board[i][j] 是一位数字(1-9)或者 '.'
解题思路
1.遍历给出的数独,将每个不为“.”的元素所在的行、列、3*3小格对应的数字分别存放在rows、cols、boxs三个数组中;
2.利用set将步骤1得到的数组去重,分别保存在newRowArr、newColArr、newBoxsArr中,与没有去重的数组进行长度比较;
3.长度全部相等,为有效数独,返回true;存在一组长度比较值不相等,则为无效数独,返回false;
重点:
如何将9 * 9 共81个数字,按照数独的规则分成 3 * 3 为一个小格,即1个数组包含3 * 3小格里面有值的数字。
代码
def isValidSudoku(self, board):
"""
:type board: List[List[str]]
:rtype: bool
"""
count_row = [collections.Counter() for _ in range(9)]
count_col = [collections.Counter() for _ in range(9)]
count_9 = [collections.Counter() for _ in range(9)]
for i in range(9):
for j in range(9):
ele = board[i][j]
count_row[i][ele] += 1
count_col[j][ele] += 1
idx_9 = i // 3 * 3 + j // 3 # 给九宫格的下标进行编码,方式如最下方
count_9[idx_9][ele] += 1
for count in count_row:
for key in count:
if count[key] > 1 and key != '.':
return False
for count in count_col:
for key in count:
if count[key] > 1 and key != '.':
return False
for count in count_9:
for key in count:
if count[key] > 1 and key != '.':
return False
return True
if 0 <= i <= 2:
if 0 <= j <= 2:
count_9[0][ele] += 1
if 3 <= j <= 5:
count_9[1][ele] += 1
if 6 <= j <= 8:
count_9[2][ele] += 1
if 3 <= i <= 5:
if 0 <= j <= 2:
count_9[3][ele] += 1
if 3 <= j <= 5:
count_9[4][ele] += 1
if 6 <= j <= 8:
count_9[5][ele] += 1
if 6 <= i <= 8:
if 0 <= j <= 2:
count_9[6][ele] += 1
if 3 <= j <= 5:
count_9[7][ele] += 1
if 6 <= j <= 8:
count_9[8][ele] += 1