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'''Original version by Andrew Dalke''' '''Original version by Andrew Dalke with a major update by Raymond Hettinger'''
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Python lists have a built-in {{{sort()}}} method that modifies the list in-place
and a {{{sorted()}}} built-in function that builds a new sorted list from an iterable.

There are many ways to use them to sort data and there doesn't appear
to be a single, central place in the various manuals describing them,
so I'll do so here.

== Backward compatibility note ==

Man
y constructs given in the HOWTO assume Python 2.4.
Before that, there was no
{{{sorted()}}} builtin and
{{{list
.sort()}}} took no keyword arguments.

== Sorting basic data types ==

A simple ascending sort is very easy: just call the
{{{sorted()}}} function.
It returns a new sorted list:

{{{
>>> print sorted([5, 2, 3, 1, 4])
[1, 2, 3, 4, 5]
}}}

You can also use the {{{sort()}}} method of a list.   It modifies the list in-place (and returns None to avoid confusion).
Usually it's less convenient than {{{sorted()}}} - but if you don't
need the original list, it's slightly more efficient.
Python lists have a built-in {{{sort()}}} method that modifies the list in-place and a {{{sorted()}}} built-in function that builds a new sorted list from an iterable.

There are many ways to use them to sort data and there doesn't appear to be a single, central place in the various manuals describing them, so I'll do so here.

== Sorting Basics ==
A simple ascending sort is very easy -- just call the {{{sorted()}}} function. It returns a new sorted list:

{{{
>>> sorted([5, 2, 3, 1, 4])
[1, 2, 3, 4, 5]
}}}
You can also use the {{{list.sort()}}} method of a list. It modifies the list in-place (and returns None to avoid confusion). Usually it's less convenient than {{{sorted()}}} - but if you don't need the original list, it's slightly more efficient.
Line 37: Line 22:
>>> 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 using {{{cmp}}}:

{{{
>>> print sorted([5, 2, 3, 1, 4], cmp)
[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 we can do:
>>> a
[1, 2, 3, 4, 5]
}}}
Another difference is that the {{{list.sort()}}} method is only defined for lists. In contrast, the {{{sorted()}}} function accepts any iterable.

{{{
>>> sorted({1: 'D', 2: 'B', 3: 'B', 4: 'E', 5: 'A'})
[1, 2, 3, 4, 5]
}}}
== Key Functions ==
Starting with Python 2.4, both {{{list.sort()}}} and {{{sorted()}}} added a {{{key}}} parameter to specify a function to be called on each list element prior to making comparisons.

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

{{{
>>> sorted("This is a test string from Andrew".split(), key=str.lower)
['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. This technique is fast because the key function is called exactly once for each input record.

A common pattern is to sort complex objects using some of the object's indices as a key. For example:

{{{
>>> student_tuples = [
        ('john', 'A', 15),
        ('jane', 'B', 12),
        ('dave', 'B', 10),
]
>>> sorted(student_tuples, key=lambda student: student[2]) # sort by age
[('dave', 'B', 10), ('jane', 'B', 12), ('john', 'A', 15)]
}}}
The same technique works for objects with named attributes. For example:

{{{
>>> class Student:
        def __init__(self, name, grade, age):
                self.name = name
                self.grade = grade
                self.age = age
        def __repr__(self):
                return repr((self.name, self.grade, self.age))
        def weighted_grade(self):
                return 'CBA'.index(self.grade) / float(self.age)

>>> student_objects = [
        Student('john', 'A', 15),
        Student('jane', 'B', 12),
        Student('dave', 'B', 10),
]
>>> sorted(student_objects, key=lambda student: student.age) # sort by age
[('dave', 'B', 10), ('jane', 'B', 12), ('john', 'A', 15)]
}}}
== Operator Module Functions ==
The key-function patterns shown above are very common, so Python provides convenience functions to make accessor functions easier and faster. The [[http://docs.python.org/library/operator.html#module-operator|operator module]] has {{{itemgetter}}}, {{{attrgetter}}}, and starting in Python 2.6 a {{{methodcaller}}} function.

Using those functions, the above examples become simpler and faster.

{{{
>>> from operator import itemgetter, attrgetter, methodcaller

>>> sorted(student_tuples, key=itemgetter(2))
[('dave', 'B', 10), ('jane', 'B', 12), ('john', 'A', 15)]

>>> sorted(student_objects, key=attrgetter('age'))
[('dave', 'B', 10), ('jane', 'B', 12), ('john', 'A', 15)]
}}}

The operator module functions allow multiple levels of sorting. For example, to sort by grade then by age:

{{{
>>> sorted(student_tuples, key=itemgetter(1,2))
[('john', 'A', 15), ('dave', 'B', 10), ('jane', 'B', 12)]

>>> sorted(student_objects, key=attrgetter('grade', 'age'))
[('john', 'A', 15), ('dave', 'B', 10), ('jane', 'B', 12)]
}}}

The third function from the operator module, {{{methodcaller}}} is used in the following example in which the weighted grade of each student is shown before sorting on it:
{{{
>>> [(student.name, student.weighted_grade()) for student in student_objects]
[('john', 0.13333333333333333), ('jane', 0.08333333333333333), ('dave', 0.1)]
>>> sorted(student_objects, key=methodcaller('weighted_grade'))
[('jane', 'B', 12), ('dave', 'B', 10), ('john', 'A', 15)]
}}}
== Ascending and Descending ==
Both {{{list.sort()}}} and {{{sorted()}}} accept a {{{reverse}}} parameter with a boolean value. This is using to flag descending sorts. For example, to get the student data in reverse age order:

{{{
>>> sorted(student_tuples, key=itemgetter(2), reverse=True)
[('john', 'A', 15), ('jane', 'B', 12), ('dave', 'B', 10)]

>>> sorted(student_objects, key=attrgetter('age'), reverse=True)
[('john', 'A', 15), ('jane', 'B', 12), ('dave', 'B', 10)]
}}}
== Sort Stability and Complex Sorts ==
Starting with Python 2.2, sorts are guaranteed to be [[http://en.wikipedia.org/wiki/Sorting_algorithm#Stability|stable]]. That means that when multiple records have the same key, their original order is preserved.

{{{
>>> data = [('red', 1), ('blue', 1), ('red', 2), ('blue', 2)]
>>> sorted(data, key=itemgetter(0))
[('blue', 1), ('blue', 2), ('red', 1), ('red', 2)]
}}}
Notice how the two records for {{{'blue'}}} retain their original order so that {{{('blue', 1)}}} is guaranteed to precede {{{('blue', 2)}}}.

This wonderful property lets you build complex sorts in a series of sorting steps. For example, to sort the student data by descending grade and then ascending age, do the age sort first and then sort again using grade:

{{{
>>> s = sorted(student_objects, key=attrgetter('age')) # sort on secondary key
>>> sorted(s, key=attrgetter('grade'), reverse=True) # now sort on primary key, descending
[('dave', 'B', 10), ('jane', 'B', 12), ('john', 'A', 15)]
}}}
The [[http://en.wikipedia.org/wiki/Timsort|Timsort]] algorithm used in Python does multiple sorts efficiently because it can take advantage of any ordering already present in a dataset.

== The Old Way Using Decorate-Sort-Undecorate ==
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.

For example, to sort the student data by grade using the DSU approach:

{{{
>>> decorated = [(student.grade, i, student) for i, student in enumerate(student_objects)]
>>> decorated.sort()
>>> [student for grade, i, student in decorated] # undecorate
[('john', 'A', 15), ('jane', 'B', 12), ('dave', 'B', 10)]
}}}
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 before 2.4, DSU is likely to be the fastest way to sort the list. For 2.4 and later, key functions provide the same functionality.

== The Old Way Using the cmp Parameter ==
Many constructs given in this HOWTO assume Python 2.4 or later. Before that, there was no {{{sorted()}}} builtin and {{{list.sort()}}} took no keyword arguments. Instead, all of the Py2.x versions supported a {{{cmp}}} parameter to handle user specified comparison functions.

In Py3.0, the {{{cmp}}} parameter was removed entirely (as part of a larger effort to simplify and unify the language, eliminating the conflict between rich comparisons and the {{{__cmp__}}} methods).

In Py2.x, sort allowed an optional function which can be called for doing the comparisons. That function should take two arguments to be compared and then return a negative value for less-than, return zero if they are equal, or return a positive value for greater-than. For example, we can do:
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>>> return x - y
>>>
}}}

Note that this does not work for numbers in general, as the comparison
function must return integers.

For numbers in general, but a little more understandably:

{{{
>>> def numeric_compare(x, y):
>>> if x > y:
>>> return 1
>>> elif x == y:
>>> return 0
>>> else: #x < y
>>> return -1
>>>
>>> a = [5, 2, 3, 1, 4]
>>> a.sort(numeric_compare)
>>> print a
[1, 2, 3, 4, 5]
}}}

By the way, the {{{sort()}}} 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
        return x - y
>>> sorted([5, 2, 4, 1, 3], cmp=numeric_compare)
[1, 2, 3, 4, 5]
}}}
Or you can reverse the order of comparison with:

{{{
>>> def reverse_numeric(x, y):
        return y - x
>>> sorted([5, 2, 4, 1, 3], cmp=reverse_numeric)
Line 110: Line 182:

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
When porting code from Python 2.x to 3.x, the situation can arise when you have the user supplying a comparison function and you need to convert that to a key function. The following wrapper makes that easy to do:

{{{
def cmp_to_key(mycmp):
    'Convert a cmp= function into a key= function'
    class K(object):
        def __init__(self, obj, *args):
            self.obj = obj
        def __lt__(self, other):
            return mycmp(self.obj, other.obj) < 0
        def __gt__(self, other):
            return mycmp(self.obj, other.obj) > 0
        def __eq__(self, other):
            return mycmp(self.obj, other.obj) == 0
        def __le__(self, other):
            return mycmp(self.obj, other.obj) <= 0
        def __ge__(self, other):
            return mycmp(self.obj, other.obj) >= 0
        def __ne__(self, other):
            return mycmp(self.obj, other.obj) != 0
    return K
}}}
To convert to a key function, just wrap the old comparison function:

{{{
>>> sorted([5, 2, 4, 1, 3], key=cmp_to_key(reverse_numeric))
Line 122: Line 210:

(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 {{{str.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)]
}}}

If the invocation of {{{key}}} returns a tuple, second and subsequent items in the tuple will be treated as sub-keys in the same way that Python generally sorts tuples:

{{{
>>> L = [('d', 2), ('a', 4), ('b', 3), ('c', 2)]
>>> sorted(L, key=lambda x:(x[1], x[0]))
[('c', 2), ('d', 2), ('b', 3), ('a', 4)]
}}}

To reverse sort based on the second item in each tuple, but forward sort based on the first item when a tie is met, then forward sort first and then reverse sort based on 2nd item:
{{{
>>> L = [('a', 2), ('d', 4), ('b', 3), ('c', 2)]
>>> L.sort(); L
[('a', 2), ('b', 3), ('c', 2), ('d', 4)]
>>> sorted(L, key=operator.itemgetter(1), reverse=True)
[('d', 4), ('b', 3), ('a', 2), ('c', 2)]
}}}

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 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, 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, 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, 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
a 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(), 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(), 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
 1. sort using a comparison function
 1. reverse sort not using a comparison function
 1. sort on an intermediate list (two forms)
 1. sort using class defined __cmp__ method
 1. sort using a sort function object

== Topics to be covered ==

 * Rich comparisons
   * With custom comparisons, it is possible to create
   insane combinations, such as {{{((x < y) and (x == y))}}}
   or {{{((x < y) and not (x <= y))}}}.
   * The most important comparisons are __eq__ (but be
   sure to update __hash__ as well), and __lt__ (which
   is used by the sorting algorithms in practice).
 * Sorting stability
   * Python sorts are stable. Guido has indicated that
   this is a promise of the language. Therefore, if
   x == y, sorted ([x, y]) returns [x, y] but
   sorted([y, x]) returns [y, x].
 * The sorted() function
   * It takes any iterable, and returns a sorted version.
   If the items in the iterable are not sensibly compared,
   it will still return a canonical ordering, unless
   someone went out of their way to prevent one.
 * Small info about locale aware sorting, eg:
   {{{
>>> l = [u'\xc4\x85', u'a', u'z']
>>> sorted(l, reverse=False)
['a', 'z', '\xc4\x85']
>>> import locale
>>> locale.setlocale(locale.LC_ALL, "pl_PL.UTF-8")
>>> sorted(l, cmp=locale.strcoll, reverse=False)
['a', '\xc4\x85', 'z']
   }}}
 * Alternate datastructure for performance with ordered data
   * If you're needing a sorted list every step of the way as you process each item to be added to the sorted list, then lst.sort(), sorted() and bisect.insort() are all very slow and tend to yield quadratic behavior or worse. In such a scenario, it's better to use something like a heap, red-black tree or treap (like the included heapq module, or this [[http://stromberg.dnsalias.org/~dstromberg/treap/|treap module]] - shameless plug added by python treap module author).

== See Also ==

 * SortingListsOfDictionaries
In Python 2.7, the ''cmp_to_key()'' tool was added to the ''functools'' module.

== Maintaining Sort Order ==
Python does not provide modules like C++'s set and map data types as part of its standard library. This is a concious decision on the part of Guido, et al to preserve "one obvious way to do it." Instead Python delegates this task to third-party libraries that are available on the [[https://pypi.python.org/pypi|Python Package Index]]. These libraries use various techniques to maintain list, dict, and set types in sorted order. Maintaining order using a specialized data structure can avoid very slow behavior (quadratic run-time) in the naive approach of editing and constantly re-sorting. Several implementations are described here.

 * [[http://www.grantjenks.com/docs/sortedcontainers/|Python SortedContainers Module]] - Pure-Python implementation that is fast-as-C implementations. Implements sorted list, dict, and set data types. Testing includes 100% code coverage and hours of stress. Documentation includes full API reference, [[http://www.grantjenks.com/docs/sortedcontainers/performance.html|performance comparison]], and contributing/development guidelines.
 * [[https://pypi.python.org/pypi/rbtree|Python rbtree Module]] - Provides a fast, C-implementation for dict and set data types. Based on a red-black tree implementation.
 * [[https://pypi.python.org/pypi/treap|Python treap Module]] - Provides a sorted dict data type. Uses a treap for implementation and improves performance using Cython.
 * [[https://pypi.python.org/pypi/bintrees|Python bintrees Module]] - Provides several tree-based implementations for dict and set data types. Fastest implementations are based on AVL and Red-Black trees. Implemented in C. Extends the conventional API to provide set operations for dict data types.
 * [[https://pypi.python.org/pypi/Banyan|Python banyan Module]] - Provides a fast, C-implementation for dict and set data types.
 * [[https://pypi.python.org/pypi/skiplistcollections|Python skiplistcollections Module]] - Pure-Python implementation based on skip-lists providing a limited API for dict and set data types.
 * [[https://pypi.python.org/pypi/blist|Python blist Module]] - Provides sorted list, dict and set data types based on the "blist" data type, a B-tree implementation. Implemented in Python and C.

== Odd and Ends ==
 * For locale aware sorting, use {{{locale.strxfrm()}}} for a key function or {{{locale.strcoll()}}} for a comparison function.

 * The {{{reverse}}} parameter still maintains sort stability (i.e. records with equal keys retain the original order). Interestingly, that effect can be simulated without the parameter by using the builtin {{{reversed}}} function twice:
  . {{{
>>> data = [('red', 1), ('blue', 1), ('red', 2), ('blue', 2)]
>>> assert sorted(data, reverse=True) == list(reversed(sorted(reversed(data))))
}}}

 * To create a standard sort order for a class, just add the appropriate rich comparison methods:
  . {{{
>>> Student.__eq__ = lambda self, other: self.age == other.age
>>> Student.__ne__ = lambda self, other: self.age != other.age
>>> Student.__lt__ = lambda self, other: self.age < other.age
>>> Student.__le__ = lambda self, other: self.age <= other.age
>>> Student.__gt__ = lambda self, other: self.age > other.age
>>> Student.__ge__ = lambda self, other: self.age >= other.age
>>> sorted(student_objects)
[('dave', 'B', 10), ('jane', 'B', 12), ('john', 'A', 15)]
}}}
  For general purpose comparisons, the recommended approach is to define all six rich comparison operators. The {{{functools.total_ordering}}} class decorator makes this easy to implement.

 * Key functions need not access data internal to objects being sorted. A key function can also access external resources. For instance, if the student grades are stored in a dictionary, they can be used to sort a separate list of student names:
  . {{{
>>> students = ['dave', 'john', 'jane']
>>> newgrades = {'john': 'F', 'jane':'A', 'dave': 'C'}
>>> sorted(students, key=newgrades.__getitem__)
['jane', 'dave', 'john']
}}}

Sorting Mini-HOW TO

Original version by Andrew Dalke with a major update by Raymond Hettinger

Python lists have a built-in sort() method that modifies the list in-place and a sorted() built-in function that builds a new sorted list from an iterable.

There are many ways to use them to sort data and there doesn't appear to be a single, central place in the various manuals describing them, so I'll do so here.

Sorting Basics

A simple ascending sort is very easy -- just call the sorted() function. It returns a new sorted list:

>>> sorted([5, 2, 3, 1, 4])
[1, 2, 3, 4, 5]

You can also use the list.sort() method of a list. It modifies the list in-place (and returns None to avoid confusion). Usually it's less convenient than sorted() - but if you don't need the original list, it's slightly more efficient.

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

Another difference is that the list.sort() method is only defined for lists. In contrast, the sorted() function accepts any iterable.

>>> sorted({1: 'D', 2: 'B', 3: 'B', 4: 'E', 5: 'A'})
[1, 2, 3, 4, 5]

Key Functions

Starting with Python 2.4, both list.sort() and sorted() added a key parameter to specify a function to be called on each list element prior to making comparisons.

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

>>> sorted("This is a test string from Andrew".split(), key=str.lower)
['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. This technique is fast because the key function is called exactly once for each input record.

A common pattern is to sort complex objects using some of the object's indices as a key. For example:

>>> student_tuples = [
        ('john', 'A', 15),
        ('jane', 'B', 12),
        ('dave', 'B', 10),
]
>>> sorted(student_tuples, key=lambda student: student[2])   # sort by age
[('dave', 'B', 10), ('jane', 'B', 12), ('john', 'A', 15)]

The same technique works for objects with named attributes. For example:

>>> class Student:
        def __init__(self, name, grade, age):
                self.name = name
                self.grade = grade
                self.age = age
        def __repr__(self):
                return repr((self.name, self.grade, self.age))
        def weighted_grade(self):
                return 'CBA'.index(self.grade) / float(self.age)

>>> student_objects = [
        Student('john', 'A', 15),
        Student('jane', 'B', 12),
        Student('dave', 'B', 10),
]
>>> sorted(student_objects, key=lambda student: student.age)   # sort by age
[('dave', 'B', 10), ('jane', 'B', 12), ('john', 'A', 15)]

Operator Module Functions

The key-function patterns shown above are very common, so Python provides convenience functions to make accessor functions easier and faster. The operator module has itemgetter, attrgetter, and starting in Python 2.6 a methodcaller function.

Using those functions, the above examples become simpler and faster.

>>> from operator import itemgetter, attrgetter, methodcaller

>>> sorted(student_tuples, key=itemgetter(2))
[('dave', 'B', 10), ('jane', 'B', 12), ('john', 'A', 15)]

>>> sorted(student_objects, key=attrgetter('age'))
[('dave', 'B', 10), ('jane', 'B', 12), ('john', 'A', 15)]

The operator module functions allow multiple levels of sorting. For example, to sort by grade then by age:

>>> sorted(student_tuples, key=itemgetter(1,2))
[('john', 'A', 15), ('dave', 'B', 10), ('jane', 'B', 12)]

>>> sorted(student_objects, key=attrgetter('grade', 'age'))
[('john', 'A', 15), ('dave', 'B', 10), ('jane', 'B', 12)]

The third function from the operator module, methodcaller is used in the following example in which the weighted grade of each student is shown before sorting on it:

>>> [(student.name, student.weighted_grade()) for student in student_objects]
[('john', 0.13333333333333333), ('jane', 0.08333333333333333), ('dave', 0.1)]
>>> sorted(student_objects, key=methodcaller('weighted_grade'))
[('jane', 'B', 12), ('dave', 'B', 10), ('john', 'A', 15)]

Ascending and Descending

Both list.sort() and sorted() accept a reverse parameter with a boolean value. This is using to flag descending sorts. For example, to get the student data in reverse age order:

>>> sorted(student_tuples, key=itemgetter(2), reverse=True)
[('john', 'A', 15), ('jane', 'B', 12), ('dave', 'B', 10)]

>>> sorted(student_objects, key=attrgetter('age'), reverse=True)
[('john', 'A', 15), ('jane', 'B', 12), ('dave', 'B', 10)]

Sort Stability and Complex Sorts

Starting with Python 2.2, sorts are guaranteed to be stable. That means that when multiple records have the same key, their original order is preserved.

>>> data = [('red', 1), ('blue', 1), ('red', 2), ('blue', 2)]
>>> sorted(data, key=itemgetter(0))
[('blue', 1), ('blue', 2), ('red', 1), ('red', 2)]

Notice how the two records for 'blue' retain their original order so that ('blue', 1) is guaranteed to precede ('blue', 2).

This wonderful property lets you build complex sorts in a series of sorting steps. For example, to sort the student data by descending grade and then ascending age, do the age sort first and then sort again using grade:

>>> s = sorted(student_objects, key=attrgetter('age'))     # sort on secondary key
>>> sorted(s, key=attrgetter('grade'), reverse=True)       # now sort on primary key, descending
[('dave', 'B', 10), ('jane', 'B', 12), ('john', 'A', 15)]

The Timsort algorithm used in Python does multiple sorts efficiently because it can take advantage of any ordering already present in a dataset.

The Old Way Using Decorate-Sort-Undecorate

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.

For example, to sort the student data by grade using the DSU approach:

>>> decorated = [(student.grade, i, student) for i, student in enumerate(student_objects)]
>>> decorated.sort()
>>> [student for grade, i, student in decorated]               # undecorate
[('john', 'A', 15), ('jane', 'B', 12), ('dave', 'B', 10)]

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 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 before 2.4, DSU is likely to be the fastest way to sort the list. For 2.4 and later, key functions provide the same functionality.

The Old Way Using the cmp Parameter

Many constructs given in this HOWTO assume Python 2.4 or later. Before that, there was no sorted() builtin and list.sort() took no keyword arguments. Instead, all of the Py2.x versions supported a cmp parameter to handle user specified comparison functions.

In Py3.0, the cmp parameter was removed entirely (as part of a larger effort to simplify and unify the language, eliminating the conflict between rich comparisons and the __cmp__ methods).

In Py2.x, sort allowed an optional function which can be called for doing the comparisons. That function should take two arguments to be compared and then return a negative value for less-than, return zero if they are equal, or return a positive value for greater-than. For example, we can do:

>>> def numeric_compare(x, y):
        return x - y
>>> sorted([5, 2, 4, 1, 3], cmp=numeric_compare)
[1, 2, 3, 4, 5]

Or you can reverse the order of comparison with:

>>> def reverse_numeric(x, y):
        return y - x
>>> sorted([5, 2, 4, 1, 3], cmp=reverse_numeric)
[5, 4, 3, 2, 1]

When porting code from Python 2.x to 3.x, the situation can arise when you have the user supplying a comparison function and you need to convert that to a key function. The following wrapper makes that easy to do:

def cmp_to_key(mycmp):
    'Convert a cmp= function into a key= function'
    class K(object):
        def __init__(self, obj, *args):
            self.obj = obj
        def __lt__(self, other):
            return mycmp(self.obj, other.obj) < 0
        def __gt__(self, other):
            return mycmp(self.obj, other.obj) > 0
        def __eq__(self, other):
            return mycmp(self.obj, other.obj) == 0
        def __le__(self, other):
            return mycmp(self.obj, other.obj) <= 0
        def __ge__(self, other):
            return mycmp(self.obj, other.obj) >= 0
        def __ne__(self, other):
            return mycmp(self.obj, other.obj) != 0
    return K

To convert to a key function, just wrap the old comparison function:

>>> sorted([5, 2, 4, 1, 3], key=cmp_to_key(reverse_numeric))
[5, 4, 3, 2, 1]

In Python 2.7, the cmp_to_key() tool was added to the functools module.

Maintaining Sort Order

Python does not provide modules like C++'s set and map data types as part of its standard library. This is a concious decision on the part of Guido, et al to preserve "one obvious way to do it." Instead Python delegates this task to third-party libraries that are available on the Python Package Index. These libraries use various techniques to maintain list, dict, and set types in sorted order. Maintaining order using a specialized data structure can avoid very slow behavior (quadratic run-time) in the naive approach of editing and constantly re-sorting. Several implementations are described here.

  • Python SortedContainers Module - Pure-Python implementation that is fast-as-C implementations. Implements sorted list, dict, and set data types. Testing includes 100% code coverage and hours of stress. Documentation includes full API reference, performance comparison, and contributing/development guidelines.

  • Python rbtree Module - Provides a fast, C-implementation for dict and set data types. Based on a red-black tree implementation.

  • Python treap Module - Provides a sorted dict data type. Uses a treap for implementation and improves performance using Cython.

  • Python bintrees Module - Provides several tree-based implementations for dict and set data types. Fastest implementations are based on AVL and Red-Black trees. Implemented in C. Extends the conventional API to provide set operations for dict data types.

  • Python banyan Module - Provides a fast, C-implementation for dict and set data types.

  • Python skiplistcollections Module - Pure-Python implementation based on skip-lists providing a limited API for dict and set data types.

  • Python blist Module - Provides sorted list, dict and set data types based on the "blist" data type, a B-tree implementation. Implemented in Python and C.

Odd and Ends

  • For locale aware sorting, use locale.strxfrm() for a key function or locale.strcoll() for a comparison function.

  • The reverse parameter still maintains sort stability (i.e. records with equal keys retain the original order). Interestingly, that effect can be simulated without the parameter by using the builtin reversed function twice:

    • >>> data = [('red', 1), ('blue', 1), ('red', 2), ('blue', 2)]
      >>> assert sorted(data, reverse=True) == list(reversed(sorted(reversed(data))))
  • To create a standard sort order for a class, just add the appropriate rich comparison methods:
    • >>> Student.__eq__ = lambda self, other: self.age == other.age
      >>> Student.__ne__ = lambda self, other: self.age != other.age
      >>> Student.__lt__ = lambda self, other: self.age < other.age
      >>> Student.__le__ = lambda self, other: self.age <= other.age
      >>> Student.__gt__ = lambda self, other: self.age > other.age
      >>> Student.__ge__ = lambda self, other: self.age >= other.age
      >>> sorted(student_objects)
      [('dave', 'B', 10), ('jane', 'B', 12), ('john', 'A', 15)]

      For general purpose comparisons, the recommended approach is to define all six rich comparison operators. The functools.total_ordering class decorator makes this easy to implement.

  • Key functions need not access data internal to objects being sorted. A key function can also access external resources. For instance, if the student grades are stored in a dictionary, they can be used to sort a separate list of student names:
    • >>> students = ['dave', 'john', 'jane']
      >>> newgrades = {'john': 'F', 'jane':'A', 'dave': 'C'}
      >>> sorted(students, key=newgrades.__getitem__)
      ['jane', 'dave', 'john']

HowTo/Sorting (last edited 2014-10-12 06:26:39 by Paddy3118)

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