medium!
題目描述:
判斷乙個 9x9 的數獨是否有效。只需要根據以下規則,驗證已經填入的數字是否有效即可。
數字1-9
在每一行只能出現一次。
數字1-9
在每一列只能出現一次。
數字1-9
在每乙個以粗實線分隔的3x3
宮內只能出現一次。
上圖是乙個部分填充的有效的數獨。
數獨部分空格內已填入了數字,空白格用'.'
表示。
示例 1:
輸入:示例 2:[ ["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"]
]輸出: true
輸入:說明:[ ["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"]
]輸出: false
解釋: 除了第一行的第乙個數字從 5 改為 8 以外,空格內其他數字均與 示例1 相同。
但由於位於左上角的 3x3 宮內有兩個 8 存在, 因此這個數獨是無效的。
解題思路:
這道題讓我們驗證乙個方陣是否為數獨矩陣。判斷標準是看各行各列是否有重複數字,以及每個小的3x3的小方陣裡面是否有重複數字,如果都無重複,則當前矩陣是數獨矩陣,但不代表該數獨矩陣有解,只是單純的判斷當前未填完的矩陣是否是數獨矩陣。
根據數獨矩陣的定義,在遍歷每個數字的時候,就看看包含當前位置的行和列以及3x3小方陣中是否已經出現該數字,那麼我們需要三個標誌矩陣,分別記錄各行,各列,各小方陣是否出現某個數字,其中行和列標誌下標很好對應,就是小方陣的下標需要稍稍轉換一下。
c++解法一:
class solution }}return true;}};
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