Python实现有效数独验证算法详解

本文分享了使用Python验证有效数独的算法实现，供读者参考学习。

一、题目要求

需要判断一个9x9的数独棋盘是否有效。验证时仅需检查已填入的数字是否符合以下规则即可。

1. 数字1-9在每一行中只能出现一次。 2. 数字1-9在每一列中只能出现一次。 3. 数字1-9在每一个由粗实线分隔的3x3宫格内只能出现一次。

数独棋盘中的部分空格已填入数字，空白格使用字符 '.' 表示。

示例1：

输入: [ ["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"] ] 输出: true

示例2：

输入: [ ["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"] ] 输出: false

解释：与示例1相比，仅第一行第一个数字由5变为8，其余空格数字保持一致。

然而，由于左上角的3x3宫格内出现了两个数字8，违反了规则，因此该数独无效。

二、解题思路

• 首先创建三个空数组：row、col和cell。其中cell数组中的每个字典代表一个3x3宫格，后续需将数据逐一填入这些结构中。
• 遍历整个二维数组，在遍历过程中将数字分别存入行row、列col以及3x3宫格cell对应的字典中。这里将数字作为字典的key，而非value。
• 随后进行判断：检查行、列、3x3宫格对应的字典中是否已存在当前棋盘值board[x][y]作为键名。若已存在，说明该数字重复，直接返回False。
• 注意：字典中的值在此处均设为1，具体数值无实际意义，可根据需要随意更改。
• 将数据存入3x3宫格是难点所在，关键公式为：num = 3*(x//3)+y//3。建议结合具体数独实例代入该公式深入理解其逻辑。
• 当然，也可以不使用上述公式，改用if/else语句进行判断，虽然逻辑更直观，但不如该公式简洁高效。
• 例如使用类似结构：if y<3 : ... elif 3<=y<6 : ... elif 6<=y : ...，通过列索引范围判断所属宫格。

具体代码如下：

#row，col，cell分别代表行，列，3x3单元格
row, col, cell =
[{}, {}, {}, {}, {}, {}, {}, {}, {}],
[{}, {}, {}, {}, {}, {}, {}, {}, {}],
[{}, {}, {}, {}, {}, {}, {}, {}, {}]
for x in range(9):
  for y in range(9):
    #取得单元格
    num = 3*(x//3)+y//3
    temp = board[x][y]
    #不需要存入 '.'
    if temp != '.':
      if (temp not in row[x]
      and temp not in col[y]
      and temp not in cell[num]):
        row[x][temp] = '1'
        col[y][temp] = '1'
        cell[num][temp] = '1'
      else:
        return False
return True

运行时间64ms，击败了99.3%的提交记录。

更多关于Python相关内容感兴趣的读者可查看本站专题：《Python数组操作技巧总结》、《Python数据结构与算法教程》、《Python列表(list)操作技巧总结》、《Python函数使用技巧总结》、《Python字符串操作技巧汇总》及《Python入门与进阶经典教程》。

希望本文所述的算法思路与代码实现能对读者的Python程序设计有所帮助。