题目
-
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：
输入：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"]]
输出：true
示例 2：
输入：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"]]
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。
法一、暴力法
class Solution:
def isValidSudoku(self, board: List[List[str]]) -> bool:
for i in range(9): #对每一行进行判断
storage = [] #每一行单独进行加载时，storage都置空
for j in range(9):
if board[i][j] == '.': #如果该元素是空，继续下一个元素的判断
continue
if board[i][j] in storage: #如果该元素在列表中，返回False
return False
else:
storage.append(board[i][j]) #如果该元素不是空且不在列表中，加入列表
for i in range(9): #对每一列进行判断
storage = [] #每一列单独进行加载时，storage都置空
for j in range(9):
if board[j][i] == '.':
continue
if board[j][i] in storage:
return False
else:
storage.append(board[j][i])
for i in range(0, 9, 3): #对九宫格是否重复进行判断
for j in range(0, 9, 3): #从0到9每隔3步取一次
storage = [] #每一块单独进行加载时，storage都置空
for x in range(0, 3):
for y in range(0, 3):
if board[i + x][j + y] == '.':
continue
if board[i + x][j + y] in storage:
return False
else:
storage.append(board[i + x][j + y])
return True
法二、哈希表
class Solution:
def isValidSudoku(self, board):
row = {}
col = {}
small = {}
# 初始化字典
for i in range(9):
row[i] = set()
col[i] = set()
small[i] = set()
for i in range(9):
for j in range(9):
val = board[i][j] #拷贝一份
if val == '.':
continue
point = i // 3 * 3 + j // 3#计算当前方格属于9宫格哪个，从0开始
if val in row[i] or val in col[j] or val in small[point]:
return False
row[i].add(val)#如果该元素不在，加入对应的行集合
col[j].add(val)#如果该元素不在，加入对应的列集合
small[point].add(val)#如果该元素不在，加入对应的方块集合
return True