Python判断有效的数独算法示例

yipeiwu_com6年前Python基础

本文实例讲述了Python判断有效的数独算法。分享给大家供大家参考,具体如下:

一、题目

判断一个 9x9 的数独是否有效。只需要根据以下规则,验证已经填入的数字是否有效即可。

1. 数字 1-9 在每一行只能出现一次。
2. 数字 1-9 在每一列只能出现一次。
3. 数字 1-9 在每一个以粗实线分隔的 3x3 宫内只能出现一次。

数独部分空格内已填入了数字,空白格用 ‘.' 表示。

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

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: 除了第一行的第一个数字从 5 改为 8 以外,空格内其他数字均与 示例1 相同。

但由于位于左上角的 3x3 宫内有两个 8 存在, 因此这个数独是无效的。

二、解法

  • 先创建三个空数组 row、col、cell,以 cell 为例,里面的每个空字典都代表一个 3×3单元格,然后我们需要把数据一个个填进去
  • 遍历整个二维数组,然后边遍历边把数组分别存入到 行 row , 列 col , 3×3单元格 cell 内的字典,存为key ,而不是 value 。
  • 然后我们就可以判断,行、列、3×3单元格 对应的字典内是否已经存在board[x][y]这个键名,如果存在,那么说明重复了,返回 False
  • 注意,字典中的值这里都为1,但是没有任何意义,你可以随意更改
  • 把数组存入 3×3的单元格是一个难点,num = 3*(x//3)+y//3,这个式子是关键,可以找个数独,然后代入进去好好理解下
  • 当然你也可以不用这个式子,用if/else语句来判断也行,那样比较好理解,但是不如这个式子简洁
  • 类似于: if y<3 : ... elif 3<=y<6 : ... elif 6<=y : ...,

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

时间 64ms,击败了 99.3%

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

希望本文所述对大家Python程序设计有所帮助。

相关文章

Python编程学习之如何判断3个数的大小

前言 大部分初学编程的人来说刚开始都会练习判断两个数或者三个数的大小,来熟悉某种语言的特性和最基本的if,else循环,当我们学习了更高级的语法知识后,又会有不同的实现方式,比如这道练习...

Python使用reportlab模块生成PDF格式的文档

(1)使用python生成pdf文档需要的最基本的包是pdfgen。它属于reportlab模块,而reportlab模块并没有默认集成到python的安装包中,所以需要安装该模块。 (...

深入理解Python3 内置函数大全

深入理解Python3 内置函数大全

本文主要介绍了Python3 内置函数,分享给大家,具体如下: 内置函数 以下代码以Python3.6.1为例 #coding=utf-8 # builtin_function....

使用Python OpenCV为CNN增加图像样本的实现

使用Python OpenCV为CNN增加图像样本的实现

我们在做深度学习的过程中,经常面临图片样本不足、不平衡的情况,在本文中,作者结合实际工作经验,通过图像的移动、缩放、旋转、增加噪声等图像变换技术,能快速、简便的增加样本数量。 本文所有案...

pyqt5的QWebEngineView 使用模板的方法

说明1:关于QWebEngineView pyqt5 已经抛弃 QtWebKit和QtWebKitWidgets,而使用最新的QtWebEngineWidgets。 QtWebEng...