by Brandon Rhodes • Home

Counting, without counting, in Python

Date: 30 March 2012
Tags:python, computing

It often irks me that the normal Python pattern for running the body of a loop n times results in the allocation and destruction of n integer objects, even if the body of the loop does not need them.

# Creates one million integers

for i in range(1000000):

# Creates them one at a time

for i in xrange(1000000):

Yes, I know, you will rightly complain that I am too easily irked. The range() pattern is standard. The pattern is simple. The pattern is easy to read. The implementation is really quite fast compared to any real work that I might do in the loop. And, in the bright future when we all use PyPy, the extra million integer objects will be optimized away anyway.

But the thought always remained with me that, whatever the convenience of using a range() in a for loop, it still meant something a little heavyhanded: “create these million integers” for me to loop across. So while in real life, of course, I will keep writing my for loops with range(), I wondered if there were an alternative with — shall we say — less semantic overhead.

A first alternative, that still creates a list of length n but without creating a million actual objects to loop across, uses list multiplication to create a million-item list that is simply a million references to the same item (in this example, the innocuous value None):

# Creates only the list object

for i in [None] * 1000000:

Not only does this have the conceptual clarity of creating only a single extra object for the sake of the iteration, but some quick experiments with timeit suggests that this is noticeably faster than using range() though not quite as fast as using xrange(). But it still allocates a useless region of memory whose size must be proportional to the number of iterations we need.

What if we want a solution that is better than O(n) in the memory it allocates across its lifespan? Well, had I written this blog post ten years ago, I could have had a field day building a series of increasingly complex options that each used even fewer objects than the last. One such possibility, just to give you a taste of what might have been, is to start creating concentric loops:

thousand_things = [None] * 1000
for i in thousand_things:
    for j in thousand_things:

Here the memory footprint drops to O(√n) since we have only two lists of a thousand pointers. Yes, I know, a thousand extra iterator objects will also be created — one to keep up with each journey across the thousand_things list in the inner loop — but that is still a vast improvement over a million-item list sitting in memory.

Think of all the fun I would have had bringing the problem down to O(log n) by using a list of binary digits that I decremented using simple list operations.

But it was not to be — because, when I finally sat down this evening to play, I discovered within a few minutes that the modern itertools module contains a solution that involves not even O(log n) but actual O(1) memory usage! Behold, the repeat() iterator:

# Gives us `None` a million times
# without creating Python integers!

from itertools import repeat
for x in repeat(None, 1000000):

For C Python, this method is the fastest of the alternatives we have discussed, as you can quickly verify if you do some timeit experiments. For those of you who are new to timeit, here is a simple command line to get you started:

$ python -m timeit \
>  -s 'from itertools import repeat' \
>  'for x in repeat(None, 1000000): pass'

100 loops, best of 3: 16.8 msec per loop

So while pursuing an impractical goal, I did get to learn a useful new itertools trick that will probably come in handy someday. And I can always use repeat() for iteration, too, in case I wind up on an embedded device where every byte is precious!

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