Leetcode–数组–有效的数独
题目 有效的数独
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。
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。
思路
1.判断一行中是否有重复元素
2.判断一列中是否有重复元素
3.判断一个3*3的块中是否有重复元素
以上思路太蠢,用3个矩阵分别记录 每一行,每一列,每一块的出现过的数字。对整个9*9的区域只循环一次。
细节
1.使用enumerate循环,同时返回下标和数组元素
2.对于第i行,第j个元素,属于第k个块 k=(i/3)*3+j/3
3.向 row[i]中添加i行元素 column[j]中添加j列元素 block[k]中添加k块元素
代码块
class Solution:
def isValidSudoku(self, board):
rows = [[] for i in range(9)]
column = [[] for j in range(9)]
block = [[] for k in range(9)]
for i,row in enumerate(board):
for j,num in enumerate(row):
if num != '.':
k = (i//3)*3+j//3
if num in rows[i] or num in column[j] or num in block[k]:
print(i)
print(j)
print(k)
return False
else:
rows[i].append(num)
column[j].append(num)
block[k].append(num)
return True