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:要檢驗,幾個特定區域中是否有重複的值,最容易想到的方法當然是將這幾個區域中的複製出來,放入新建立的陣列(或其他資料結構中),再判斷,其中是否有重複的值,當然,為避免不必要的計算,可以選擇邊複製,邊檢驗,一旦發現重複,直接停止複製操作,返回false。["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。
此題中:
行和列兩個區域的複製比較簡單,此處不贅述。
9*9的座標格劃分成9個格仔是此題難點,我的解決方案是:輸入橫縱座標i、j,計算:top_id = i//3*3 + j//3相同top_id 的點屬於同一區域。(「//」表示取整數的除法操作)
class solution:
def isvalidsudoku(self, board):
""":type board: list[list[str]]
:rtype: bool
"""row = [ for _ in range(9)] # 行
col = [ for _ in range(9)] # 列
area = [ for _ in range(9)] # 子區域
for i in range(9):
for j in range(9):
element = board[i][j]
if element != '.': # 檢驗是否為數字
top_id = i//3*3 + j//3 # 子區域的計算
if element in row[i] or element in col[j] or element in area[top_id]: # 如果在這一行列子區域重讀出現過了
return false
else: # 沒有出現過就加進去
return true
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