howto-sorting.pdf

SortingHOWTO

Release3.4.0

GuidovanRossum

FredL.Drake,Jr.,editor

April 17, 2014

PythonSoftwareFoundation

Email:docs@python.org

Contents

1SortingBasics

2KeyFunctions

3OperatorModuleFunctions

4AscendingandDescending

5SortStabilityandComplexSorts

6TheOldWayUsingDecorate-Sort-Undecorate

7TheOldWayUsingthecmpParameter

8OddandEnds

AuthorAndrew Dalke and Raymond Hettinger

Release0.1

Python lists have a built-in list.sort() method that modiﬁes the list in-place. There is also a 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.

1SortingBasics

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. It modiﬁes the list in-place (and returnsNoneto 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]

2KeyFunctions

Both list.sort() and sorted() have akeyparameter 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 ( "ThisisateststringfromAndrew" . split(),key = str . lower)

[’a’,’Andrew’,’from’,’is’,’string’,’test’,’This’]

The value of thekeyparameter 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 ]) #sortbyage

[(’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):

returnrepr((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) #sortbyage

[(’dave’,’B’,10),(’jane’,’B’,12),(’john’,’A’,15)]

3OperatorModuleFunctions

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 a

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 bygradethen byage:

>>> 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)]

4AscendingandDescending

Both list.sort() and sorted() accept areverseparameter with a boolean value.

This is used to ﬂag

descending sorts. For example, to get the student data in reverseageorder:

>>> 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)]

5SortStabilityandComplexSorts

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 forblueretain 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 descendinggradeand then ascendingage, do theagesort ﬁrst and then sort again usinggrade:

>>> s = sorted (student_objects,key = attrgetter( ’age’ )) #sortonsecondarykey

>>> sorted (s,key = attrgetter( ’grade’ ),reverse = True ) #nowsortonprimarykey,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.

6TheOldWayUsingDecorate-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 bygradeusing 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 indexiin 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 deter-

mined 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.

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

7TheOldWayUsingthecmpParameter

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 acmpparameter to

handle user speciﬁed comparison functions.

In Py3.0, thecmpparameter was removed entirely (as part of a larger effort to simplify and unify the language,

eliminating the conﬂict between rich comparisons and the __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):

returnx-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):

returny-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):

’Convertacmp=functionintoakey=function’

class K :

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 functools.cmp_to_key() function was added to the functools module in the stan-

dard library.

8OddandEnds

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

comparison function.

• Thereverseparameter 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 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 __lt__() when making comparisons between two objects. So, it

is easy to add a standard sort order to a class by deﬁning an __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’]

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