LeetCode: 有效的數獨 python實現

1. 題目描述

36.有效的數獨
判斷一個 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 在每一個以粗實線分隔的 3x3 宮內只能出現一次。

上圖是一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:
  [
  [“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
• 示例 2:
  輸入:
  [
  [“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”]
  ]
  輸出: false
  解釋: 除了第一行的第一個數字從 5 改爲 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。

說明:

一個有效的數獨（部分已被填充）不一定是可解的。 只需要根據以上規則，驗證已經填入的數字是否有效即可。 給定數獨序列只包含數字 1-9 和字符 ‘.’ 。 給定數獨永遠是 9x9 形式的。

2. 代碼實現

一個簡單的解決方案是遍歷該 9 x 9 數獨 三 次，以確保：
        行中沒有重複的數字。
        列中沒有重複的數字。
        3 x 3 子數獨內沒有重複的數字。

1. 先創建字典：

rows = [{} for i in range(9)]
columns = [{} for i in range(9)]
boxes = [{} for i in range(9)]

2. 依次獲得每行，每列，每個3x3小格的鍵值（數值：數目）

    for i in range(9):
        for j in range(9):
            num = board[i][j]
            if num != '.':
                num = int(num)
                # 這個設計很巧妙獲得了每個[i][j]對應的3x3九宮小格
                box_index = (i // 3) * 3 + j // 3

                # keep the current cell value
                rows[i][num] = rows[i].get(num, 0) + 1
                columns[j][num] = columns[j].get(num, 0) + 1
                boxes[box_index][num] = boxes[box_index].get(num, 0) + 1

比如輸入：

isValidSudoku([
  ["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：
rows:

[{5: 1, 3: 1, 7: 1},
  {6: 1, 1: 1, 9: 1, 5: 1},
  {9: 1, 8: 1, 6: 1},
  {8: 1, 6: 1, 3: 1},
  {4: 1, 8: 1, 3: 1, 1: 1},
  {7: 1, 2: 1, 6: 1},
  {6: 1, 2: 1, 8: 1},
  {4: 1, 1: 1, 9: 1, 5: 1},
  {8: 1, 7: 1, 9: 1}]

columns:

 [{5: 1, 6: 1, 8: 1, 4: 1, 7: 1},
  {3: 1, 9: 1, 6: 1}, {8: 1},
  {1: 1, 8: 1, 4: 1},
  {7: 1, 9: 1, 6: 1, 2: 1, 1: 1, 8: 1},
  {5: 1, 3: 1, 9: 1},
  {2: 1},
  {6: 1, 8: 1, 7: 1},
  {3: 1, 1: 1, 6: 1, 5: 1, 9: 1}]

boxes:

 [{5: 1, 3: 1, 6: 1, 9: 1, 8: 1},
  {7: 1, 1: 1, 9: 1, 5: 1},
  {6: 1},
  {8: 1, 4: 1, 7: 1},
  {6: 1, 8: 1, 3: 1, 2: 1},
  {3: 1, 1: 1, 6: 1},
  {6: 1},
  {4: 1, 1: 1, 9: 1, 8: 1},
  {2: 1, 8: 1, 5: 1, 7: 1, 9: 1}]

3. 判斷字典中是否有數目大於1的鍵，是則數獨有誤

if rows[i][num] > 1 or columns[j][num] > 1 or boxes[box_index][num] > 1:
     return False

4. 下面是完整代碼

class Solution(object):
    def isValidSudoku(self, board):
        """
        :type board: List[List[str]]
        :rtype: bool
        """
        # init data
        # 創建[{}, {}, {}, {}, {}, {}, {}, {}, {}]
        rows = [{} for i in range(9)]
        columns = [{} for i in range(9)]
        boxes = [{} for i in range(9)]

        # validate a board
        for i in range(9):
            for j in range(9):
                num = board[i][j]
                if num != '.':
                    num = int(num)
                    box_index = (i // 3) * 3 + j // 3

                    # keep the current cell value
                    rows[i][num] = rows[i].get(num, 0) + 1
                    columns[j][num] = columns[j].get(num, 0) + 1
                    boxes[box_index][num] = boxes[box_index].get(num, 0) + 1

                    # check if this value has been already seen before
                    if rows[i][num] > 1 or columns[j][num] > 1 or boxes[box_index][num] > 1:
                        return False
        return True