Sorting HOW TO

:Author: Andrew Dalke and Raymond Hettinger

:Release: 0.1

Python lists have a built-in :meth:`list.sort` method that modifies the list

in-place and a :func:`sorted` built-in function that builds a new sorted list

from an iterable.

In this document, we explore the various techniques for sorting data using Python.

Sorting Basics

A simple ascending sort is very easy: just call the :func:`sorted` function. It

returns a new sorted list::

You can also use the :meth:`list.sort` method of a list. It modifies the list

in-place (and returns *None* to avoid confusion). Usually it's less convenient

than :func:`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 :meth:`list.sort` method is only defined for

lists. In contrast, the :func:`sorted` function accepts any iterable.

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

[1, 2, 3, 4, 5]

Key Functions

Both :meth:`list.sort` and :func:`sorted` have *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 keys. 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))

>>> 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 :func:`operator.itemgetter`, :func:`operator.attrgetter`, and

an :func:`operator.methodcaller` function.

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

>>> from operator import itemgetter, attrgetter

>>> 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)]

Ascending and Descending

Both :meth:`list.sort` and :func:`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

Sorts are guaranteed to be `stable

<http://en.wikipedia.org/wiki/Sorting_algorithm#Stability>`_\. 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 <http://en.wikipedia.org/wiki/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, but 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 <http://en.wikipedia.org/wiki/Schwartzian_transform>`_\,

after Randal L. Schwartz, who popularized it among Perl programmers.

Now that Python sorting provides key-functions, this technique is not often needed.

The Old Way Using the *cmp* Parameter

Many constructs given in this HOWTO assume Python 2.4 or later. Before that,

there was no :func:`sorted` builtin and :meth:`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 :meth:`__cmp__` magic method).

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::

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 3.2, the :func:`functools.cmp_to_key` function was added to the

functools module in the standard library.

Odd and Ends

* For locale aware sorting, use :func:`locale.strxfrm` for a key function or

:func:`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 :func:`reversed` function

twice:

>>> data = [('red', 1), ('blue', 1), ('red', 2), ('blue', 2)]

>>> assert sorted(data, reverse=True) == list(reversed(sorted(reversed(data))))

* The sort routines are guaranteed to use :meth:`__lt__` when making comparisons

between two objects. So, it is easy to add a standard sort order to a class by

defining an :meth:`__lt__` method::

* Key functions need not depend directly on the 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']