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
django 自定义用户user模型的三种方法
Nov 18 Python
Python实现把xml或xsl转换为html格式
Apr 08 Python
浅谈终端直接执行py文件,不需要python命令
Jan 23 Python
PyQt5每天必学之关闭窗口
Apr 19 Python
python实现图片文件批量重命名
Mar 23 Python
python 使用socket传输图片视频等文件的实现方式
Aug 07 Python
使用Python实现牛顿法求极值
Feb 10 Python
python模拟实现分发扑克牌
Apr 22 Python
PyCharm中配置PySide2的图文教程
Jun 18 Python
keras实现VGG16方式(预测一张图片)
Jul 07 Python
python opencv图像处理(素描、怀旧、光照、流年、滤镜 原理及实现)
Dec 10 Python
python实现学生信息管理系统(面向对象)
Jun 05 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
基于php冒泡排序算法的深入理解
2013/06/09 PHP
php生成curl命令行的方法
2015/12/14 PHP
php实现和c#一致的DES加密解密实例
2017/07/24 PHP
PHP tp5中使用原生sql查询代码实例
2020/10/28 PHP
JavaScript触发器详解
2007/03/10 Javascript
ajax请求get与post的区别总结
2013/11/04 Javascript
Checbox的操作含已选、未选及判断代码
2013/11/07 Javascript
JQueryiframe页面操作父页面中的元素与方法(实例讲解)
2013/11/19 Javascript
跨域传值即主页面与iframe之间互相传值
2013/12/09 Javascript
七个很有意思的PHP函数
2014/05/12 Javascript
简洁实用的BootStrap jQuery手风琴插件
2016/08/31 Javascript
浅谈vue中.vue文件解析流程
2018/04/24 Javascript
通过jquery的ajax请求本地的json文件方法
2018/08/08 jQuery
vuejs使用axios异步访问时用get和post的实例讲解
2018/08/09 Javascript
解决vue 单文件组件中样式加载问题
2019/04/24 Javascript
Python中的startswith和endswith函数使用实例
2014/08/25 Python
简单介绍Python中的RSS处理
2015/04/13 Python
介绍Python中的文档测试模块
2015/04/28 Python
python实现bucket排序算法实例分析
2015/05/04 Python
python爬取NUS-WIDE数据库图片
2016/10/05 Python
python中os模块详解
2016/10/14 Python
详解python string类型 bytes类型 bytearray类型
2017/12/16 Python
python实现微信远程控制电脑
2018/02/22 Python
Python实现两个list求交集,并集,差集的方法示例
2018/08/02 Python
python生成lmdb格式的文件实例
2018/11/08 Python
Django保护敏感信息的方法示例
2019/05/09 Python
Python 3 实现定义跨模块的全局变量和使用教程
2019/07/07 Python
Canvas制作旋转的太极的示例
2018/03/09 HTML / CSS
迷你分体式空调:SoGoodToBuy
2018/08/07 全球购物
Edwaybuy西班牙:小米在线商店
2019/12/04 全球购物
金融管理专业毕业生求职信
2014/03/12 职场文书
作文评语怎么写
2014/12/25 职场文书
给老婆道歉的话
2015/01/20 职场文书
小学教师见习总结
2015/06/23 职场文书
护士岗位竞聘书
2015/09/15 职场文书
Python-typing: 类型标注与支持 Any类型详解
2021/05/10 Python