284 lines
11 KiB
ReStructuredText
284 lines
11 KiB
ReStructuredText
.. _sortinghowto:
|
|
|
|
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. There is also 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::
|
|
|
|
>>> sorted([5, 2, 3, 1, 4])
|
|
[1, 2, 3, 4, 5]
|
|
|
|
You can also use the :meth:`list.sort` method. 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
|
|
:mod:`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::
|
|
|
|
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 3.2, the :func:`functools.cmp_to_key` function was added to the
|
|
:mod:`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 (so that 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::
|
|
|
|
>>> Student.__lt__ = lambda self, other: self.age < other.age
|
|
>>> sorted(student_objects)
|
|
[('dave', 'B', 10), ('jane', 'B', 12), ('john', 'A', 15)]
|
|
|
|
* 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']
|