用最少的元素比较对5个元素进行排序 [英] Sorting 5 elements with minimum element comparison

问题描述

我必须使用最少的元素间比较数，在python中对5个元素的列表进行排序的执行计划建模.除此之外，复杂性无关紧要.

I have to model the execution plan of sorting a list of 5 elements, in python, using the minimum number of comparisons between elements. Other than that, the complexity is irrelevant.

结果是成对的列表，表示在另一时间对列表进行排序所需的比较.

The result is a list of pairs representing the comparisons needed to sort the list at another time.

我知道有一种算法可以在7个比较中做到这一点(在元素之间，总是，而不是在复杂度方面)，但是我找不到可读的(对我来说)版本.

I know there's an algorithm that does this in 7 comparisons (between elements, always, not complexity-wise), but I can't find a readable (for me) version.

如何对7个比较中的5个元素进行排序，并为排序建立一个执行计划"?

How can I sort the 5 elements in 7 comparisons, and build an "execution plan" for the sort?

PD:不是作业.

推荐答案

这符合您对5 elements in 7 comparisons排序的描述:

This fits your description of sorting 5 elements in 7 comparisons:

import random

n=5
ran=[int(n*random.random()) for i in xrange(n)]
print ran

def selection_sort(li):  
    l=li[:]                  
    sl=[]        
    i=1         
    while len(l):              
        lowest=l[0]            
        for x in l:            
            if x<lowest:      
                lowest=x  
        sl.append(lowest)  
        l.remove(lowest)     
        print i  
        i+=1
    return sl

print selection_sort(ran)  

这使用了选择排序，它不是最有效的方法，但使用的比较很少.

This uses a Selection Sort which is NOT the most efficient, but does use very few comparisons.

这可以简化为:

def ss(li):  
    l=li[:]                  
    sl=[]                 
    while len(l):              
        sl.append(l.pop(l.index(min(l))))       
    return sl    

在任何一种情况下，都将打印以下内容:

In either case, prints something like this:

[0, 2, 1, 1, 4]
1
2
3
4
5
[0, 1, 1, 2, 4]

Perl有一个名为 Algorithm :: Networksort 的可爱模块，可让您玩用这些. Knuth引用了Bose-Nelson算法的几个比较器，您可以在此处看到它.

Perl has a lovely module called Algorithm::Networksort that allows you to play with these. The Bose-Nelson algorithm is cited by Knuth for few comparators and you can see it here.

修改

插入排序也可以很好地工作:

def InsertionSort(l):
    """ sorts l in place using an insertion sort """
    for j in range(1, len(l)):
        key = l[j]
        i = j - 1
        while (i >=0) and (l[i] > key):
            l[i+1] = l[i]
            i = i - 1

        l[i+1] = key

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