Python编程之黑板上排列组合，你舍得解开吗

2023-09-21 19:42:05 252

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

>>>fromitertoolsimportcombinations
>>>combins=[cforcincombinations(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

>>>fromitertoolsimportpermutations
>>>pertumations(range(5),2)


>>>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=[cforcincombinations(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'
importitertools
list1=[1,2,3,4,5]
list2=[]
foriinrange(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'
importitertools
list1=[1,2,3,4,5]
list2=[]
foriinrange(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)!
defget_value(n):
ifn==1:
returnn
else:
returnn*get_value(n-1)
defgen_last_value(n,m):
first=get_value(n)
print"n:%svalue:%s"%(n,first)
second=get_value(m)
print"n:%svalue:%s"%(m,second)
third=get_value((n-m))
print"n:%svalue:%s"%((n-m),third)
returnfirst/(second*third)

if__name__=="__main__":
#C(12,5)
rest=gen_last_value(5,3)
print"value:",rest

运行结果：

n:5value:120
n:3value:6
n:2value: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，linkedlist）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编程之黑板上排列组合，你舍得解开吗

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