Python编程之黑板上排列组合,你舍得解开吗


Posted in Python onOctober 30, 2017

考虑这样一个问题,给定一个矩阵(多维数组,numpy.ndarray()),如何shuffle这个矩阵(也就是对其行进行全排列),如何随机地选择其中的k行,这叫组合,实现一种某一维度空间的切片。例如五列中选三列(全部三列的排列数),便从原有的五维空间中降维到三维空间,因为是全部的排列数,故不会漏掉任何一种可能性。

涉及的函数主要有:

np.random.permutation()
itertools.combinations()
itertools.permutations()

# 1. 对0-5之间的数进行一次全排列
>>>np.random.permutation(6)
array([3, 1, 5, 4, 0, 2])

# 2. 创建待排矩阵
>>>A = np.array([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]])

# 3. shuffle矩阵A
>>>p = np.random.permutation(A.shape[0])
>>>p
array([1, 2, 0])
>>>A[p, :]     
array([[ 5, 6, 7, 8],
  [ 9, 10, 11, 12],
  [ 1, 2, 3, 4]])

C52的实现

>>>from itertools import combinations
>>>combins = [c for c in combinations(range(5), 2)]
>>>len(combins)
10
>>>combins    # 而且是按序排列
[(0, 1), (0, 2), (0, 3), (0, 4), (1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)]

A52的实现

>>>from itertools import permutations
>>>pertumations(range(5), 2)
<itertools.permutations object at 0x0233E360>

>>>perms = permutations(range(5), 2)
>>>perms
[(0, 1), (0, 2), (0, 3), (0, 4), (1, 0), (1, 2), (1, 3), (1, 4), (2, 0), (2, 1),
 (2, 3), (2, 4), (3, 0), (3, 1), (3, 2), (3, 4), (4, 0), (4, 1), (4, 2), (4, 3)]
>>>len(perms)
20
# 5. 任取其中的k(k=2)行
>>>c = [c for c in combinations(range(A.shape[0]), 2)]
>>>A[c[0], :]   # 一种排列
array([[1, 2, 3, 4],
  [5, 6, 7, 8]])

下面再介绍一个列表数据任意组合,主要是利用自带的库

#_*_ coding:utf-8 _*_
#__author__='dragon'
import itertools
list1 = [1,2,3,4,5]
list2 = []
for i in range(1,len(list1)+1):
 iter = itertools.combinations(list1,i)
 list2.append(list(iter))
print(list2)
[[(1,), (2,), (3,), (4,), (5,)], [(1, 2), (1, 3), (1, 4), (1, 5), (2, 3), (2, 4), (2, 5), (3, 4), (3, 5), (4, 5)], [(1, 2, 3), (1, 2, 4), (1, 2, 5), (1, 3, 4), (1, 3, 5), (1, 4, 5), (2, 3, 4), (2, 3, 5), (2, 4, 5), (3, 4, 5)], [(1, 2, 3, 4), (1, 2, 3, 5), (1, 2, 4, 5), (1, 3, 4, 5), (2, 3, 4, 5)], [(1, 2, 3, 4, 5)]]

排列的实现

#_*_ coding:utf-8 _*_
#__author__='dragon'
import itertools
list1 = [1,2,3,4,5]
list2 = []
for i in range(1,len(list1)+1):
 iter = itertools.permutations(list1,i)
 list2.append(list(iter))
print(list2)

运行结果:

[[(1,), (2,), (3,), (4,), (5,)], [(1, 2), (1, 3), (1, 4), (1, 5), (2, 1), (2, 3), (2, 4), (2, 5), (3, 1), (3, 2), (3, 4), (3, 5), (4, 1), (4, 2), (4, 3), (4, 5), (5, 1), (5, 2), (5, 3), (5, 4)], [(1, 2, 3), (1, 2, 4), (1, 2, 5), (1, 3, 2), (1, 3, 4), (1, 3, 5), (1, 4, 2), (1, 4, 3), (1, 4, 5), (1, 5, 2), (1, 5, 3), (1, 5, 4), (2, 1, 3), (2, 1, 4), (2, 1, 5), (2, 3, 1), (2, 3, 4), (2, 3, 5), (2, 4, 1), (2, 4, 3), (2, 4, 5), (2, 5, 1), (2, 5, 3), (2, 5, 4), (3, 1, 2), (3, 1, 4), (3, 1, 5), (3, 2, 1), (3, 2, 4), (3, 2, 5), (3, 4, 1), (3, 4, 2), (3, 4, 5), (3, 5, 1), (3, 5, 2), (3, 5, 4), (4, 1, 2), (4, 1, 3), (4, 1, 5), (4, 2, 1), (4, 2, 3), (4, 2, 5), (4, 3, 1), (4, 3, 2), (4, 3, 5), (4, 5, 1), (4, 5, 2), (4, 5, 3), (5, 1, 2), (5, 1, 3), (5, 1, 4), (5, 2, 1), (5, 2, 3), (5, 2, 4), (5, 3, 1), (5, 3, 2), (5, 3, 4), (5, 4, 1), (5, 4, 2), (5, 4, 3)], [(1, 2, 3, 4), (1, 2, 3, 5), (1, 2, 4, 3), (1, 2, 4, 5), (1, 2, 5, 3), (1, 2, 5, 4), (1, 3, 2, 4), (1, 3, 2, 5), (1, 3, 4, 2), (1, 3, 4, 5), (1, 3, 5, 2), (1, 3, 5, 4), (1, 4, 2, 3), (1, 4, 2, 5), (1, 4, 3, 2), (1, 4, 3, 5), (1, 4, 5, 2), (1, 4, 5, 3), (1, 5, 2, 3), (1, 5, 2, 4), (1, 5, 3, 2), (1, 5, 3, 4), (1, 5, 4, 2), (1, 5, 4, 3), (2, 1, 3, 4), (2, 1, 3, 5), (2, 1, 4, 3), (2, 1, 4, 5), (2, 1, 5, 3), (2, 1, 5, 4), (2, 3, 1, 4), (2, 3, 1, 5), (2, 3, 4, 1), (2, 3, 4, 5), (2, 3, 5, 1), (2, 3, 5, 4), (2, 4, 1, 3), (2, 4, 1, 5), (2, 4, 3, 1), (2, 4, 3, 5), (2, 4, 5, 1), (2, 4, 5, 3), (2, 5, 1, 3), (2, 5, 1, 4), (2, 5, 3, 1), (2, 5, 3, 4), (2, 5, 4, 1), (2, 5, 4, 3), (3, 1, 2, 4), (3, 1, 2, 5), (3, 1, 4, 2), (3, 1, 4, 5), (3, 1, 5, 2), (3, 1, 5, 4), (3, 2, 1, 4), (3, 2, 1, 5), (3, 2, 4, 1), (3, 2, 4, 5), (3, 2, 5, 1), (3, 2, 5, 4), (3, 4, 1, 2), (3, 4, 1, 5), (3, 4, 2, 1), (3, 4, 2, 5), (3, 4, 5, 1), (3, 4, 5, 2), (3, 5, 1, 2), (3, 5, 1, 4), (3, 5, 2, 1), (3, 5, 2, 4), (3, 5, 4, 1), (3, 5, 4, 2), (4, 1, 2, 3), (4, 1, 2, 5), (4, 1, 3, 2), (4, 1, 3, 5), (4, 1, 5, 2), (4, 1, 5, 3), (4, 2, 1, 3), (4, 2, 1, 5), (4, 2, 3, 1), (4, 2, 3, 5), (4, 2, 5, 1), (4, 2, 5, 3), (4, 3, 1, 2), (4, 3, 1, 5), (4, 3, 2, 1), (4, 3, 2, 5), (4, 3, 5, 1), (4, 3, 5, 2), (4, 5, 1, 2), (4, 5, 1, 3), (4, 5, 2, 1), (4, 5, 2, 3), (4, 5, 3, 1), (4, 5, 3, 2), (5, 1, 2, 3), (5, 1, 2, 4), (5, 1, 3, 2), (5, 1, 3, 4), (5, 1, 4, 2), (5, 1, 4, 3), (5, 2, 1, 3), (5, 2, 1, 4), (5, 2, 3, 1), (5, 2, 3, 4), (5, 2, 4, 1), (5, 2, 4, 3), (5, 3, 1, 2), (5, 3, 1, 4), (5, 3, 2, 1), (5, 3, 2, 4), (5, 3, 4, 1), (5, 3, 4, 2), (5, 4, 1, 2), (5, 4, 1, 3), (5, 4, 2, 1), (5, 4, 2, 3), (5, 4, 3, 1), (5, 4, 3, 2)], [(1, 2, 3, 4, 5), (1, 2, 3, 5, 4), (1, 2, 4, 3, 5), (1, 2, 4, 5, 3), (1, 2, 5, 3, 4), (1, 2, 5, 4, 3), (1, 3, 2, 4, 5), (1, 3, 2, 5, 4), (1, 3, 4, 2, 5), (1, 3, 4, 5, 2), (1, 3, 5, 2, 4), (1, 3, 5, 4, 2), (1, 4, 2, 3, 5), (1, 4, 2, 5, 3), (1, 4, 3, 2, 5), (1, 4, 3, 5, 2), (1, 4, 5, 2, 3), (1, 4, 5, 3, 2), (1, 5, 2, 3, 4), (1, 5, 2, 4, 3), (1, 5, 3, 2, 4), (1, 5, 3, 4, 2), (1, 5, 4, 2, 3), (1, 5, 4, 3, 2), (2, 1, 3, 4, 5), (2, 1, 3, 5, 4), (2, 1, 4, 3, 5), (2, 1, 4, 5, 3), (2, 1, 5, 3, 4), (2, 1, 5, 4, 3), (2, 3, 1, 4, 5), (2, 3, 1, 5, 4), (2, 3, 4, 1, 5), (2, 3, 4, 5, 1), (2, 3, 5, 1, 4), (2, 3, 5, 4, 1), (2, 4, 1, 3, 5), (2, 4, 1, 5, 3), (2, 4, 3, 1, 5), (2, 4, 3, 5, 1), (2, 4, 5, 1, 3), (2, 4, 5, 3, 1), (2, 5, 1, 3, 4), (2, 5, 1, 4, 3), (2, 5, 3, 1, 4), (2, 5, 3, 4, 1), (2, 5, 4, 1, 3), (2, 5, 4, 3, 1), (3, 1, 2, 4, 5), (3, 1, 2, 5, 4), (3, 1, 4, 2, 5), (3, 1, 4, 5, 2), (3, 1, 5, 2, 4), (3, 1, 5, 4, 2), (3, 2, 1, 4, 5), (3, 2, 1, 5, 4), (3, 2, 4, 1, 5), (3, 2, 4, 5, 1), (3, 2, 5, 1, 4), (3, 2, 5, 4, 1), (3, 4, 1, 2, 5), (3, 4, 1, 5, 2), (3, 4, 2, 1, 5), (3, 4, 2, 5, 1), (3, 4, 5, 1, 2), (3, 4, 5, 2, 1), (3, 5, 1, 2, 4), (3, 5, 1, 4, 2), (3, 5, 2, 1, 4), (3, 5, 2, 4, 1), (3, 5, 4, 1, 2), (3, 5, 4, 2, 1), (4, 1, 2, 3, 5), (4, 1, 2, 5, 3), (4, 1, 3, 2, 5), (4, 1, 3, 5, 2), (4, 1, 5, 2, 3), (4, 1, 5, 3, 2), (4, 2, 1, 3, 5), (4, 2, 1, 5, 3), (4, 2, 3, 1, 5), (4, 2, 3, 5, 1), (4, 2, 5, 1, 3), (4, 2, 5, 3, 1), (4, 3, 1, 2, 5), (4, 3, 1, 5, 2), (4, 3, 2, 1, 5), (4, 3, 2, 5, 1), (4, 3, 5, 1, 2), (4, 3, 5, 2, 1), (4, 5, 1, 2, 3), (4, 5, 1, 3, 2), (4, 5, 2, 1, 3), (4, 5, 2, 3, 1), (4, 5, 3, 1, 2), (4, 5, 3, 2, 1), (5, 1, 2, 3, 4), (5, 1, 2, 4, 3), (5, 1, 3, 2, 4), (5, 1, 3, 4, 2), (5, 1, 4, 2, 3), (5, 1, 4, 3, 2), (5, 2, 1, 3, 4), (5, 2, 1, 4, 3), (5, 2, 3, 1, 4), (5, 2, 3, 4, 1), (5, 2, 4, 1, 3), (5, 2, 4, 3, 1), (5, 3, 1, 2, 4), (5, 3, 1, 4, 2), (5, 3, 2, 1, 4), (5, 3, 2, 4, 1), (5, 3, 4, 1, 2), (5, 3, 4, 2, 1), (5, 4, 1, 2, 3), (5, 4, 1, 3, 2), (5, 4, 2, 1, 3), (5, 4, 2, 3, 1), (5, 4, 3, 1, 2), (5, 4, 3, 2, 1)]]

可以根据你需要随意组合

python实现排列组合公式C(m,n)求值

# -*- coding:utf-8 -*- 
# 用python实现排列组合C(n,m) = n!/m!*(n-m)! 
def get_value(n): 
 if n==1: 
  return n 
 else: 
  return n * get_value(n-1) 
def gen_last_value(n,m): 
  first = get_value(n) 
  print "n:%s  value:%s"%(n, first) 
  second = get_value(m) 
  print "n:%s  value:%s"%(m, second) 
  third = get_value((n-m)) 
  print "n:%s  value:%s"%((n-m), third) 
  return first/(second * third) 
   
if __name__ == "__main__": 
 # C(12,5) 
 rest = gen_last_value(5,3) 
 print "value:", rest

运行结果:

n:5  value:120
n:3  value:6
n:2  value:2
value: 10

总结

以上就是本文关于Python排列组合算法的全部内容,希望对大家有所帮助。感兴趣的朋友可以继续参阅本站:Python数据结构与算法之列表(链表,linked list)简单实现、Python算法之求n个节点不同二叉树个数等,有什么问题可以随时留言,小编会及时回复大家的。

Python 相关文章推荐
easy_install python包安装管理工具介绍
Feb 10 Python
python实现网页链接提取的方法分享
Feb 25 Python
用Python编写一个每天都在系统下新建一个文件夹的脚本
May 04 Python
python简单分割文件的方法
Jul 30 Python
基于Python数据可视化利器Matplotlib,绘图入门篇,Pyplot详解
Oct 13 Python
关于Python正则表达式 findall函数问题详解
Mar 22 Python
python中多个装饰器的执行顺序详解
Oct 08 Python
Django框架模板介绍
Jan 15 Python
用 Python 制作地球仪的方法
Apr 24 Python
python爬虫线程池案例详解(梨视频短视频爬取)
Feb 20 Python
一行代码python实现文件共享服务器
Apr 22 Python
Python中Matplotlib的点、线形状、颜色以及绘制散点图
Apr 07 Python
Python数据结构与算法之列表(链表,linked list)简单实现
Oct 30 #Python
Python进程间通信之共享内存详解
Oct 30 #Python
import的本质解析
Oct 30 #Python
python中hashlib模块用法示例
Oct 30 #Python
浅谈Python由__dict__和dir()引发的一些思考
Oct 30 #Python
Android分包MultiDex策略详解
Oct 30 #Python
Python 判断是否为质数或素数的实例
Oct 30 #Python
You might like
DC四月将推出百页特刊漫画 纪念小丑诞生80周年
2020/04/09 欧美动漫
用PHP和ACCESS写聊天室(三)
2006/10/09 PHP
PHP读MYSQL中文乱码的解决方法
2006/12/17 PHP
escape unescape的php下的实现方法
2007/04/27 PHP
PHP网站开发中常用的8个小技巧
2015/02/13 PHP
PHP单例模式详细介绍
2015/07/01 PHP
PHP利用imagick生成组合缩略图
2016/02/19 PHP
yii框架搜索分页modle写法
2016/12/19 PHP
php常用字符串长度函数strlen()与mb_strlen()用法实例分析
2019/06/25 PHP
贴一个在Mozilla中常用的Javascript代码
2007/01/09 Javascript
javascript编程起步(第二课)
2007/01/10 Javascript
Web前端设计模式  制作漂亮的弹出层
2010/10/29 Javascript
基于jQuery的左右滚动实现代码
2010/12/03 Javascript
Javascript计算两个marker之间的距离(Google Map V3)
2013/04/26 Javascript
js控制淡入淡出示例代码
2013/11/12 Javascript
jQuery中选择器小问题(新人难免遇到)
2014/03/31 Javascript
js面向对象之公有、私有、静态属性和方法详解
2015/04/17 Javascript
基于jQuery 实现bootstrapValidator下的全局验证
2015/12/07 Javascript
JavaScript仿商城实现图片广告轮播实例代码
2016/02/06 Javascript
js关于getImageData跨域问题的解决方法
2016/10/14 Javascript
jQGrid动态填充select下拉框的选项值(动态填充)
2016/11/28 Javascript
js与jQuery实现获取table中的数据并拼成json字符串操作示例
2018/07/12 jQuery
详解easyui基于 layui.laydate日期扩展组件
2018/07/18 Javascript
python实现数据清洗(缺失值与异常值处理)
2019/12/02 Python
python3中的logging记录日志实现过程及封装成类的操作
2020/05/12 Python
Python通过zookeeper实现分布式服务代码解析
2020/07/22 Python
python实现企业微信定时发送文本消息的示例代码
2020/11/24 Python
五分钟学会怎么用python做一个简单的贪吃蛇
2021/01/12 Python
韩国家庭购物网上商店:Nsmall
2017/05/07 全球购物
家具厂厂长岗位职责
2014/01/01 职场文书
电子专业毕业生自我鉴定
2014/01/22 职场文书
客户接待方案
2014/02/26 职场文书
安卓程序员求职信
2014/02/28 职场文书
教育技术职业规划范文
2014/03/04 职场文书
2014年文明创建工作总结
2014/11/25 职场文书
pytorch交叉熵损失函数的weight参数的使用
2021/05/24 Python