判斷乙個 9*9 的數獨面板是否是有效的。
如果已經被填充的數字滿足以下條件，則說明是有效的：
備註：example 1:
input:
[[「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」]
]output: true
example 2:
input:
[[「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」]
]output: false
explanation: same as example 1, except with the 5 in the top left corner being
modified to 8. since there are two 8』s in the top left 3x3 sub-box, it is invalid.
按照數獨的有效性定義，需要從行、列、3*3子塊三個方面都滿足數字的唯一性。
因此，可以分三個步驟，分別檢驗三個條件，只要有乙個條件不滿足，則說明數獨無效。
1、檢驗每一行是否有重複數字。可以定義乙個set，存放掃瞄過的數字，一旦新數字已經被包含在set中，則說明重複。
2、檢驗每一列是否有重複數字。與行同理。
3、檢驗每乙個子塊是否有重複數字。需要檢查9個子塊。
上述方法是分別檢驗三個條件，每個條件都需要遍歷一遍所有的數字。
實際上，可以只通過一次遍歷，來同時判斷是否滿足三個條件。
維護乙個 set，這個set中存放三種格式的元素：
由於元組長度以及元素型別的不同，三種元素不會相互混合。
因此，每次掃瞄到乙個數字，便生成 3 個對應的元組，分別判斷是否存在於 set 中，如果存在，則說明數獨無效；否則，將 3 個元組都加入到 set 中，繼續掃瞄下乙個數字。
def
isvalidsudoku
(board)
:"""
:type board: list[list[str]]
:rtype: bool
依次判斷3個有效條件是否全部滿足。
"""defis_row_valid
(board)
:'''
判斷乙個數獨的每一行是否都包含無重複數字1-9
'''for row in board:
char_set =
set(
)for char in row:
if char !=
'.':
if char in char_set:
return
false
char_set.add(char)
return
true
# 1、每一行一定要包含無重複數字1-9
ifnot is_row_valid(board)
:return
false
# 2、每一列一定要包含無重複數字1-9
board_reverse =
[[board[i]
[j]for i in
range(9
)]for j in
range(9
)]ifnot is_row_valid(board_reverse)
:return
false
# 3、每乙個 3*3 的子面板一定要包含無重複數字1-9
for i in
range(3
):for j in
range(3
):char_set =
set(
)for ii in
range
(i*3
,(i+1)
*3):
for jj in
range
(j*3
,(j+1)
*3):
char = board[ii]
[jj]
if char !=
'.':
if char in char_set:
return
false
char_set.add(char)
return
true
defisvalidsudoku2
(board)
:"""
:type board: list[list[str]]
:rtype: bool
一次遍歷，同時判斷是否滿足3個有效條件。
"""char_set =
set(
)for i in
range(9
):for j in
range(9
):char = board[i]
[j]if char !=
'.':
if(i, char)
in char_set \
or(char, j)
in char_set \
or(i//
3, j//
3, char)
in char_set:
return
false
else
: char_set.add(
(i, char)
)# 第i行的char字元
char_set.add(
(char, j)
)# 第j列的char字元
# [i//3, j//3]位置的小面板的char字元
char_set.add(
(i//
3, j//
3, char)
)return
true
if'__main__'
== __name__:
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"]
]print
(isvalidsudoku2(board)
)
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