Sorting Mini-HOWTO

Sorting Mini-HOWTO

Andrew Dalke

Abstract:

This document is a little tutorial showing a half dozen ways to sort a list with the built-in sort() method.

This document is available from the Python HOWTO page at http://www.python.org/doc/howto.



Contents

Python lists have a built-in sort() method. There are many ways to use it to sort a list and there doesn't appear to be a single, central place in the various manuals describing them, so I'll do so here.

1 Sorting basic data types

A simple ascending sort is easy; just call the sort() method of a list. 

>>> a = [5, 2, 3, 1, 4]
>>> a.sort()
>>> print a
[1, 2, 3, 4, 5]

Sort takes an optional function which can be called for doing the comparisons. The default sort routine is equivalent to 

>>> a = [5, 2, 3, 1, 4]
>>> a.sort(cmp)
>>> print a
[1, 2, 3, 4, 5]

where cmp is the built-in function which compares two objects, x and y, and returns -1, 0 or 1 depending on whether $x<y$, $x==y$, or $x>y$. During the course of the sort the relationships must stay the same for the final list to make sense.

If you want, you can define your own function for the comparison. For integers (and numbers in general) we can do: 

>>> def numeric_compare(x, y):
>>>    return x-y
>>> 
>>> a = [5, 2, 3, 1, 4]
>>> a.sort(numeric_compare)
>>> print a
[1, 2, 3, 4, 5]

By the way, this function won't work if result of the subtraction is out of range, as in sys.maxint - (-1).

Or, if you don't want to define a new named function you can create an anonymous one using lambda, as in: 

>>> a = [5, 2, 3, 1, 4]
>>> a.sort(lambda x, y: x-y)
>>> print a
[1, 2, 3, 4, 5]

If you want the numbers sorted in reverse you can do 

>>> a = [5, 2, 3, 1, 4]
>>> def reverse_numeric(x, y):
>>>     return y-x
>>> 
>>> a.sort(reverse_numeric)
>>> print a
[5, 4, 3, 2, 1]

(a more general implementation could return cmp(y,x) or -cmp(x,y)).

However, it's faster if Python doesn't have to call a function for every comparison, so if you want a reverse-sorted list of basic data types, do the forward sort first, then use the reverse() method. 

>>> a = [5, 2, 3, 1, 4]
>>> a.sort()
>>> a.reverse()
>>> print a
[1, 2, 3, 4, 5]

Here's a case-insensitive string comparison using a lambda function: 

>>> import string
>>> a = string.split("This is a test string from Andrew.")
>>> a.sort(lambda x, y: cmp(string.lower(x), string.lower(y)))
>>> print a
['a', 'Andrew.', 'from', 'is', 'string', 'test', 'This']

This goes through the overhead of converting a word to lower case every time it must be compared. At times it may be faster to compute these once and use those values, and the following example shows how. 

>>> words = string.split("This is a test string from Andrew.")
>>> offsets = []
>>> for i in range(len(words)):
>>>     offsets.append( (string.lower(words[i]), i) )
>>> 
>>> offsets.sort()
>>> new_words = []
>>> for dontcare, i in offsets:
>>>      new_words.append(words[i])
>>> 
>>> print new_words

The offsets list is initialized to a tuple of the lower-case string and its position in the words list. It is then sorted. Python's sort method sorts tuples by comparing terms; given x and y, compare x[0] to y[0], then x[1] to y[1], etc. until there is a difference.

The result is that the offsets list is ordered by its first term, and the second term can be used to figure out where the original data was stored. (The for loop assigns dontcare and i to the two fields of each term in the list, but we only need the index value.)

Another way to implement this is to store the original data as the second term in the offsets list, as in: 

>>> words = string.split("This is a test string from Andrew.")
>>> offsets = []
>>> for word in words:
>>>     offsets.append( (string.lower(word), word) )
>>> 
>>> offsets.sort()
>>> new_words = []
>>> for word in offsets:
>>>     new_words.append(word[1])
>>> 
>>> print new_words

This isn't always appropriate because the second terms in the list (the word, in this example) will be compared when the first terms are the same. If this happens many times, then there will be the unneeded performance hit of comparing the two objects. This can be a large cost if most terms are the same and the objects define their own __cmp__ method, but there will still be some overhead to determine if __cmp__ is defined.

Still, for large lists, or for lists where the comparison information is expensive to calculate, the last two examples are likely to be the fastest way to sort a list. It will not work on weakly sorted data, like complex numbers, but if you don't know what that means, you probably don't need to worry about it.

2 Comparing classes

The comparison for two basic data types, like ints to ints or string to string, is built into Python and makes sense. There is a default way to compare class instances, but the default manner isn't usually very useful. You can define your own comparison with the __cmp__ method, as in: 

>>> class Spam:
>>>     def __init__(self, spam, eggs):
>>>         self.spam = spam
>>>         self.eggs = eggs
>>>     def __cmp__(self, other):
>>>         return cmp(self.spam+self.eggs, other.spam+other.eggs)
>>>     def __str__(self):
>>>         return str(self.spam + self.eggs)
>>> 
>>> a = [Spam(1, 4), Spam(9, 3), Spam(4,6)]
>>> a.sort()
>>> for spam in a:
>>>   print str(spam)
5
10
12

Sometimes you may want to sort by a specific attribute of a class. If appropriate you should just define the __cmp__ method to compare those values, but you cannot do this if you want to compare between different attributes at different times. Instead, you'll need to go back to passing a comparison function to sort, as in: 

>>> a = [Spam(1, 4), Spam(9, 3), Spam(4,6)]
>>> a.sort(lambda x, y: cmp(x.eggs, y.eggs))
>>> for spam in a:
>>>   print spam.eggs, str(spam)
3 12
4 5
6 10

If you want to compare two arbitrary attributes (and aren't overly concerned about performance) you can even define your own comparison function object. This uses the ability of a class instance to emulate an function by defining the __call__ method, as in: 

>>> class CmpAttr:
>>>     def __init__(self, attr):
>>>         self.attr = attr
>>>     def __call__(self, x, y):
>>>         return cmp(getattr(x, self.attr), getattr(y, self.attr))
>>> 
>>> a = [Spam(1, 4), Spam(9, 3), Spam(4,6)]
>>> a.sort(CmpAttr("spam"))  # sort by the "spam" attribute
>>> for spam in a:
>>>    print spam.spam, spam.eggs, str(spam)
1 4 5
4 6 10
9 3 12

>>> a.sort(CmpAttr("eggs"))   # re-sort by the "eggs" attribute
>>> for spam in a:
>>>    print spam.spam, spam.eggs, str(spam)
9 3 12
1 4 5
4 6 10

Of course, if you want a faster sort you can extract the attributes into an intermediate list and sort that list.

So, there you have it; about a half-dozen different ways to define how to sort a list:

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