[Tutor] sorting algorithm

[C.T. Matsumoto]

Dave Angel wrote:
> C.T. Matsumoto wrote:
>> Hello,
>>
>> This is follow up on a question I had about algorithms. In the thread 
>> it was suggested I make my own sorting algorithm.
>>
>> Here are my results.
>>
>> #!/usr/bin/python
>>
>> def sort_(list_):
>>    for item1 in list_:
>>        pos1 = list_.index(item1)
>>        pos2 = pos1 + 1
>>        try:
>>            item2 = list_[pos2]
>>        except IndexError:
>>            pass
>>
>>        if item1 >= item2:
>>            try:
>>                list_.pop(pos2)
>>                list_.insert(pos1, item2)
>>                return True
>>            except IndexError:
>>                pass
>>
>> def mysorter(list_):
>>    while sort_(list_) is True:
>>        sort_(list_)
>>
>> I found this to be a great exercise. In doing the exercise, I got 
>> pretty stuck. I consulted another programmer (my dad) who described 
>> how to go about sorting. As it turned out the description he 
>> described was the Bubble sort algorithm. Since coding the solution I 
>> know the Bubble sort is inefficient because of repeated iterations 
>> over the entire list. This shed light on the quick sort algorithm 
>> which I'd like to have a go at.
>>
>> Something I haven't tried is sticking in really large lists. I was 
>> told that with really large list you break down the input list into 
>> smaller lists. Sort each list, then go back and use the same swapping 
>> procedure for each of the different lists. My question is, at what 
>> point to you start breaking things up? Is that based on list elements 
>> or is it based on memory(?) resources python is using?
>>
>> One thing I'm not pleased about is the while loop and I'd like to 
>> replace it with a for loop.
>>
>> Thanks,
>>
>> T
>>
>>
> There are lots of references on the web about Quicksort, including a 
> video at:
>     http://www.youtube.com/watch?v=y_G9BkAm6B8
>
> which I think illustrates it pretty well.  It would be a great 
> learning exercise to implement Python code directly from that 
> description, without using the sample C++ code available.
>
> (Incidentally, there are lots of variants of Quicksort, so I'm not 
> going to quibble about whether this is the "right" one to be called 
> that.)
>
> I don't know what your earlier thread was, since you don't mention the 
> subject line, but there are a number of possible reasons you might not 
> have wanted to use the built-in sort.  The best one is for educational 
> purposes.  I've done my own sort for various reasons in the past, even 
> though I had a library function, since the library function had some 
> limits.  One time I recall, the situation was that the library sort 
> was limited to 64k of total data, and I had to work with much larger 
> arrays (this was in 16bit C++, in "large" model).  I solved the size 
> problem by using the  C++ sort library on 16k subsets (because a 
> pointer was 2*2 bytes).  Then I merged the results of the sorts.  At 
> the time, and in the circumstances involved, there were seldom more 
> than a dozen or so sublists to merge, so this approach worked well 
> enough.
>
> Generally, it's better for both your development time and the 
> efficiency and reliabilty of the end code, to base a new sort 
> mechanism on the existing one.  In my case above, I was replacing what 
> amounted to an insertion sort, and achieved a 50* improvement for a 
> real customer.  It was fast enough that other factors completely 
> dominated his running time.
>
> But for learning purposes?  Great plan.  So now I'll respond to your 
> other questions, and comment on your present algorithm.
>
> It would be useful to understand about algorithmic complexity, the so 
> called Order Function.  In a bubble sort, if you double the size of 
> the array, you quadruple the number of comparisons and swaps.  It's 
> order N-squared or O(n*n).   So what works well for an array of size 
> 10 might take a very long time for an array of size 10000 (like a 
> million times as long).  You can do much better by sorting smaller 
> lists, and then combining them together.  Such an algorithm can  be 
> O(n*log(n)).
>
>
> You ask at what point you consider sublists?  In a language like C, 
> the answer is when the list is size 3 or more.  For anything larger 
> than 2, you divide into sublists, and work on them.
>
> Now, if I may comment on your code.  You're modifying a list while 
> you're iterating through it in a for loop.  In the most general case, 
> that's undefined.  I think it's safe in this case, but I would avoid 
> it anyway, by just using xrange(len(list_)-1) to iterate through it.  
> You use the index function to find something you would already know -- 
> the index function is slow.  And the first try/except isn't needed if 
> you use a -1 in the xrange argument, as I do above.
>
> You use pop() and push() to exchange two adjacent items in the list.  
> Both operations copy the remainder of the list, so they're rather 
> slow.  Since you're exchanging two items in the list, you can simply 
> do that:
>     list[pos1], list[pos2] = list[pos2], list[pos1]
>
> That also eliminates the need for the second try/except.
>
> You mention being bothered by the while loop.  You could replace it 
> with a simple for loop with xrange(len(list_)), since you know that N 
> passes will always be enough.  But if the list is partially sorted, 
> your present scheme will end sooner.  And if it's fully sorted, it'll 
> only take one pass over the data.
>
> There are many refinements you could do.  For example, you don't have 
> to stop the inner loop after the first swap.  You could finish the 
> buffer, swapping any other pairs that are out of order.  You'd then be 
> saving a flag indicating if you did any swaps.  You could keep a index 
> pointing to the last pair you swapped on the previous pass, and use 
> that for a limit next time.  Then you just terminate the outer loop 
> when that limit value is 1.  You could even keep two limit values, and 
> bubble back and forth between them, as they gradually close into the 
> median of the list.  You quit when they collide in the middle.
>
> The resultant function should be much faster for medium-sized lists, 
> but it still will slow down quadratically as the list size increases.  
> You still need to divide and conquer, and quicksort is just one way of 
> doing that.
>
> DaveA
>
Thanks a lot Dave,

Sorry the original thread is called 'Python and algorithms'.

Yes, I think it's best to use what python provides and build on top of 
that. I got to asking my original question based on trying to learn more 
about algorithms in general, through python. Of late many people have 
been asking me how well I can 'build' algorithms, and this prompted me 
to start the thread. This is for learning purposes (which the original 
thread will give you and indication where I'm coming from).

The refactored code looks like this. I have tackled a couple items. 
First the sub-listing (which I'll wait till I can get the full sort 
working), then the last couple of paragraphs about refinements. Starting 
with the first refinement, I'm not sure how *not* to stop the inner loop?

def s2(list_):
   for pos1 in xrange(len(list_)-1):
       item1 = list_[pos1]
       pos2 = pos1 + 1
       item2 = list_[pos2]
       if item1 >= item2:
           list_[pos1], list_[pos2] = list_[pos2], list_[pos1]
           return True

def mysorter(list_):
   # This is the outer loop?
   while s2(list_) is True:
       # Calling s2 kicks off the inner loop?
       s2(list_)

if __name__ == '__main__':
   from random import shuffle
   foo = range(10)
   shuffle(foo)
   mysorter(foo)

Thanks again.