Differences between revisions 1 and 12 (spanning 11 versions)
 ⇤ ← Revision 1 as of 2005-11-30 01:18:35 → Size: 7460 Editor: AndrewKuchling Comment: Make wiki version of Sorting HOWTO ← Revision 12 as of 2006-01-05 15:19:47 → ⇥ Size: 9346 Editor: ten-cache1-vif-3 Comment: Changed explanation of cmp() based on cmp.__doc__. Deletions are marked like this. Additions are marked like this. Line 4: Line 4: This document is a little tutorialshowing a half dozen ways to sort a list with the built-in{{{sort()}}} method. Line 25: Line 21: Line 35: Line 32: where {{{cmp}}} is the built-in function which compares two objects,{{{x}}} and {{{y}}}, and returns -1, 0 or 1 depending on whetherxy. During the course of the sort therelationships must stay the same for the final list to make sense.If you want, you can define your own function for the comparison. For where {{{cmp()}}} is the built-in function that compares two objects,{{{x}}} and {{{y}}}, and returns a negative number, 0 or a positivenumber depending on whether xy. During the course ofthe sort the relationships must stay the same for the final list tomake sense.If you want, you can define your own function for the comparison. For Line 46: Line 44: >>> >>> Line 53: Line 51: By the way, this function won't work if result of the subtraction By the way, this function won't work if the result of the subtraction Line 66: Line 64: If you want the numbers sorted in reverse you can do Python 2.4 adds three keyword arguments to {{{sort()}}} thatsimplify many common usages: {{{cmp}}}, {{{key}}}, and {{{reverse}}}. The {{{cmp}}} keyword is for providing a sorting function; the previous examples could be written as:{{{>>> a.sort(cmp=numeric_compare)>>> a.sort(cmp=lambda x,y: x-y)}}}The {{{reverse}}} parameter is a Boolean value; if it's true, the list is sorted into reverse order.{{{>>> a = [5, 2, 3, 1, 4]>>> a.sort(reverse=True)>>> a[5, 4, 3, 2, 1]}}}For Python versions before 2.4, you can reverse the senseof the comparison function: Line 72: Line 85: >>> >>> Line 74: Line 87: >>> print a >>> a Line 81: Line 94: every comparison, so if you want a reverse-sorted list of basic datatypes, do the forward sort first, then use the {{{reverse()}}} method. every comparison, so the most efficient solution is to do the forward sort first, then use the {{{reverse()}}} method. Line 88: Line 100: >>> print a >>> a Line 92: Line 104: Here's a case-insensitive string comparison using a {{{lambda}}} function: == Sorting by keys ==Python 2.4's {{{key}}} parameter lets you derive a sorting key for each element of the list, and then sort using the key.For example, here's a case-insensitive string comparison:{{{>>> a = "This is a test string from Andrew".split()>>> a.sort(key=str.lower)>>> a['a', 'Andrew', 'from', 'is', 'string', 'test', 'This']}}}The value of the {{{key}}} parameter should be a functionthat takes a single argument and returns a key to use for sorting purposes.Often there's a built-in that will match your needs, such as {{{string.lower()}}}. The {{{operator}}} module contains a number of functions useful for this purpose.For example, you can sort tuplesbased on their second elementusing {{{operator.itemgetter()}}}:{{{>>> import operator>>> L = [('c', 2), ('d', 1), ('a', 4), ('b', 3)]>>> map(operator.itemgetter(0), L)['c', 'd', 'a', 'b']>>> map(operator.itemgetter(1), L)[2, 1, 4, 3]>>> sorted(L, key=operator.itemgetter(1))[('d', 1), ('c', 2), ('b', 3), ('a', 4)]}}}Versions of Python before 2.4 don't have the convenient{{{key}}} parameter of {{{sort()}}}, so you have to write acomparison function that embodies the key-generating logic: Line 102: Line 146: every time it must be compared. At times it may be faster to computethese 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])>>> every time it must be compared, roughly O(n lg n) times.Python 2.4's {{{key}}} parameter is called once for each item in the list, which is O(n) and therefore more efficient.You can manually perform the same optimization bycomputing the keys onceand using those values to control the sort order:{{{>>> words = "This is a test string from Andrew.".split()>>> deco = [ (word.lower(), i, word) for i, word in enumerate(words) ]>>> deco.sort()>>> new_words = [ word for _, _, word in deco ] Line 117: Line 158: }}}The {{{offsets}}} list is initialized to a tuple of the lower-casestring 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 firstterm, and the second term can be used to figure out where the originaldata was stored. (The {{{for}}} loop assigns {{{dontcare}}} and{{{i}}} to the two fields of each term in the list, but we only needthe index value.)Another way to implement this is to store the original data as thesecond 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 arethe same. If this happens many times, then there will be the unneededperformance hit of comparing the two objects. This can be a largecost 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 informationis expensive to calculate, the last two examples are likely to be thefastest 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, youprobably don't need to worry about it. ['a', 'Andrew.', 'from', 'is', 'string', 'test', 'This']}}}This idiom is called Decorate-Sort-Undecorate after its three steps:  * First, the initial list is decorated with new values that control the sort order.  * Second, the decorated list is sorted.  * Finally, the decorations are removed, creating a list that contains only the initial values in the new order.This idiom works because tuples are compared lexicographically; the first items are compared; if they are the same then the second items are compared, and so on.It is not strictly necessary in all cases to include the index {{{i}}} in the decorated list. Including it gives two benefits:  * The sort is stable - if two items have the same key, their order will be preserved in the sorted list.  * The original items do not have to be comparable because the ordering of the decorated tuples will be determined by at most the first two items. So for example the original list could contain {{{complex}}} numbers which cannot be sorted directly.Another name for this idiom is [http://en.wikipedia.org/wiki/Schwartzian_transform Schwartzian transform], after Randal L. Schwartz, who popularized it among Perl programmers.For large lists and lists where the comparison informationis expensive to calculate, and Python versions < 2.4, DSU is likely to be thefastest way to sort the list. Line 179: Line 195: >>> >>> a = [Spam(1, 4), Spam(9, 3), Spam(4,6)] >>>>>> a = [Spam(1, 4), Spam(9, 3), Spam(4, 6)] Line 192: Line 208: different attributes at different times. Instead, you'll need to go different attributes at different times.Python 2.4 has an {{{operator.attrgetter()}}} functionthat makes this easy:{{{>>> import operator>>> a = [Spam(1, 4), Spam(9, 3), Spam(4, 6)]>>> a.sort(key=operator.attrgetter('eggs'))>>> for spam in a:>>> print spam.eggs, str(spam)3 124 56 10}}}In Python 2.4 if you don't want to import the operator module you can:{{{>>> a = [Spam(1, 4), Spam(9, 3), Spam(4, 6)]>>> a.sort(key=lambda obj:obj.eggs)>>> for spam in a:>>> print spam.eggs, str(spam)3 124 56 10}}}Again, earlier Python version require you to go Line 196: Line 238: >>> a = [Spam(1, 4), Spam(9, 3), Spam(4,6)] >>> a = [Spam(1, 4), Spam(9, 3), Spam(4, 6)] Line 216: Line 258: >>> >>> Line 246: Line 288: == Topics to be covered == * Rich comparisons * Sorting stability * The sorted() function== See Also == * SortingListsOfDictionaries

# Sorting Mini-HOWTO

Original version by Andrew Dalke

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.

## 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 that compares two objects, x and y, and returns a negative number, 0 or a positive number 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 the 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]```

Python 2.4 adds three keyword arguments to sort() that simplify many common usages: cmp, key, and reverse. The cmp keyword is for providing a sorting function; the previous examples could be written as:

```>>> a.sort(cmp=numeric_compare)
>>> a.sort(cmp=lambda x,y: x-y)```

The reverse parameter is a Boolean value; if it's true, the list is sorted into reverse order.

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

For Python versions before 2.4, you can reverse the sense of the comparison function:

```>>> a = [5, 2, 3, 1, 4]
>>> def reverse_numeric(x, y):
>>>     return y-x
>>>
>>> a.sort(reverse_numeric)
>>> 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 the most efficient solution is to do the forward sort first, then use the reverse() method.

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

## Sorting by keys

Python 2.4's key parameter lets you derive a sorting key for each element of the list, and then sort using the key.

For example, here's a case-insensitive string comparison:

```>>> a = "This is a test string from Andrew".split()
>>> a.sort(key=str.lower)
>>> a
['a', 'Andrew', 'from', 'is', 'string', 'test', 'This']```

The value of the key parameter should be a function that takes a single argument and returns a key to use for sorting purposes.

Often there's a built-in that will match your needs, such as string.lower(). The operator module contains a number of functions useful for this purpose. For example, you can sort tuples based on their second element using operator.itemgetter():

{{{>>> import operator >>> L = [('c', 2), ('d', 1), ('a', 4), ('b', 3)] >>> map(operator.itemgetter(0), L) ['c', 'd', 'a', 'b'] >>> map(operator.itemgetter(1), L) [2, 1, 4, 3] >>> sorted(L, key=operator.itemgetter(1)) [('d', 1), ('c', 2), ('b', 3), ('a', 4)] }}}

Versions of Python before 2.4 don't have the convenient key parameter of sort(), so you have to write a comparison function that embodies the key-generating logic:

```>>> a = "This is a test string from Andrew".split()
>>> a.sort(lambda x, y: cmp(x.lower(), y.lower()))
>>> 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, roughly O(n lg n) times. Python 2.4's key parameter is called once for each item in the list, which is O(n) and therefore more efficient. You can manually perform the same optimization by computing the keys once and using those values to control the sort order:

```>>> words = "This is a test string from Andrew.".split()
>>> deco = [ (word.lower(), i, word) for i, word in enumerate(words) ]
>>> deco.sort()
>>> new_words = [ word for _, _, word in deco ]
>>> print new_words
['a', 'Andrew.', 'from', 'is', 'string', 'test', 'This']```

This idiom is called Decorate-Sort-Undecorate after its three steps:

• First, the initial list is decorated with new values that control the sort order.
• Second, the decorated list is sorted.
• Finally, the decorations are removed, creating a list that contains only the initial values in the new order.

This idiom works because tuples are compared lexicographically; the first items are compared; if they are the same then the second items are compared, and so on.

It is not strictly necessary in all cases to include the index i in the decorated list. Including it gives two benefits:

• The sort is stable - if two items have the same key, their order will be preserved in the sorted list.
• The original items do not have to be comparable because the ordering of the decorated tuples will be determined by at most the first two items. So for example the original list could contain complex numbers which cannot be sorted directly.

Another name for this idiom is [http://en.wikipedia.org/wiki/Schwartzian_transform Schwartzian transform], after Randal L. Schwartz, who popularized it among Perl programmers.

For large lists and lists where the comparison information is expensive to calculate, and Python versions < 2.4, DSU is likely to be the fastest way to sort the list.

## 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.

Python 2.4 has an operator.attrgetter() function that makes this easy:

```>>> import operator
>>> a = [Spam(1, 4), Spam(9, 3), Spam(4, 6)]
>>> a.sort(key=operator.attrgetter('eggs'))
>>> for spam in a:
>>>   print spam.eggs, str(spam)
3 12
4 5
6 10```

In Python 2.4 if you don't want to import the operator module you can:

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

Again, earlier Python version require you 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:

1. sort using the default method
2. sort using a comparison function
3. reverse sort not using a comparison function
4. sort on an intermediate list (two forms)
5. sort using class defined cmp method

6. sort using a sort function object

## Topics to be covered

• Rich comparisons
• Sorting stability
• The sorted() function