Author:Andrew Dalke and Raymond Hettinger
Python lists have a built-in
method that modifies the list in-place. There is also a
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
function. It returns a new sorted list:
>>> sorted([5,2,3,1,4])[1, 2, 3, 4, 5]You can also use the
method. It modifies the list in-place (and returns None to avoid confusion). Usually it’s less convenient than
- 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
method is only defined for lists. In contrast, the
function accepts any iterable.
>>> sorted({1:'D',2:'B',3:'B',4:'E',5:'A'})[1, 2, 3, 4, 5]Key Functions
The
method and the functions
,
,
,
, and
have a key parameter to specify a function (or other callable) to be called on each list element prior to making comparisons.
For example, here’s a case-insensitive string comparison using
:
>>> sorted("This is a test string from Andrew".split(),key=str.casefold)['a', 'Andrew', 'from', 'is', 'string', 'test', 'This']The value of the key parameter should be a function (or other callable) 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=lambdastudent: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:
>>> classStudent:... 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=lambdastudent:student.age)# sort by age[('dave', 'B', 10), ('jane', 'B', 12), ('john', 'A', 15)]Objects with named attributes can be made by a regular class as shown above, or they can be instances of
or a
.
Operator Module Functions and Partial Function Evaluation
The
patterns shown above are very common, so Python provides convenience functions to make accessor functions easier and faster. The
module has
,
, and a
function.
Using those functions, the above examples become simpler and faster:
>>> fromoperatorimportitemgetter,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)]The
module provides another helpful tool for making key-functions. The
function can reduce the
of a multi-argument function making it suitable for use as a key-function.
>>> fromfunctoolsimportpartial>>> fromunicodedataimportnormalize>>> names='Zoë Åbjørn Núñez Élana Zeke Abe Nubia Eloise'.split()>>> sorted(names,key=partial(normalize,'NFD'))['Abe', 'Åbjørn', 'Eloise', 'Élana', 'Nubia', 'Núñez', 'Zeke', 'Zoë']>>> sorted(names,key=partial(normalize,'NFC'))['Abe', 'Eloise', 'Nubia', 'Núñez', 'Zeke', 'Zoë', 'Åbjørn', 'Élana']Ascending and Descending
Both
and
accept a reverse parameter with a boolean value. This is used 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
. 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)]This can be abstracted out into a wrapper function that can take a list and tuples of field and order to sort them on multiple passes.
>>> defmultisort(xs,specs):... forkey,reverseinreversed(specs):... xs.sort(key=attrgetter(key),reverse=reverse)... returnxs>>> multisort(list(student_objects),(('grade',True),('age',False)))[('dave', 'B', 10), ('jane', 'B', 12), ('john', 'A', 15)]The
algorithm used in Python does multiple sorts efficiently because it can take advantage of any ordering already present in a dataset.
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)fori,studentinenumerate(student_objects)]>>> decorated.sort()>>> [studentforgrade,i,studentindecorated]# 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
, after Randal L. Schwartz, who popularized it among Perl programmers.
Now that Python sorting provides key-functions, this technique is not often needed.
Comparison Functions
Unlike key functions that return an absolute value for sorting, a comparison function computes the relative ordering for two inputs.
For example, a
compares two samples giving a relative ordering: lighter, equal, or heavier. Likewise, a comparison function such as cmp(a,b) will return a negative value for less-than, zero if the inputs are equal, or a positive value for greater-than.
It is common to encounter comparison functions when translating algorithms from other languages. Also, some libraries provide comparison functions as part of their API. For example,
is a comparison function.
To accommodate those situations, Python provides
to wrap the comparison function to make it usable as a key function:
sorted(words,key=cmp_to_key(strcoll))# locale-aware sort orderStrategies For Unorderable Types and Values
A number of type and value issues can arise when sorting. Here are some strategies that can help:
Convert non-comparable input types to strings prior to sorting:
>>> data=['twelve','11',10]>>> sorted(map(str,data))['10', '11', 'twelve']This is needed because most cross-type comparisons raise a
.
Remove special values prior to sorting:
>>> frommathimportisnan>>> fromitertoolsimportfilterfalse>>> data=[3.3,float('nan'),1.1,2.2]>>> sorted(filterfalse(isnan,data))[1.1, 2.2, 3.3]This is needed because the
specifies that, “Every NaN shall compare unordered with everything, including itself.”
Likewise, None can be stripped from datasets as well:
>>> data=[3.3,None,1.1,2.2]>>> sorted(xforxindataifxisnotNone)[1.1, 2.2, 3.3]This is needed because None is not comparable to other types.
Convert mapping types into sorted item lists before sorting:
>>> data=[{'a':1},{'b':2}]>>> sorted(data,key=lambdad:sorted(d.items()))[{'a': 1}, {'b': 2}]This is needed because dict-to-dict comparisons raise a
.
Convert set types into sorted lists before sorting:
>>> data=[{'a','b','c'},{'b','c','d'}]>>> sorted(map(sorted,data))[['a', 'b', 'c'], ['b', 'c', 'd']]This is needed because the elements contained in set types do not have a deterministic order. For example, list({'a','b'}) may produce either ['a','b'] or ['b','a'].
Odds and Ends
For locale aware sorting, use
for a key function or
for a comparison function. This is necessary because “alphabetical” sort orderings can vary across cultures even if the underlying alphabet is the same.
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
function twice:
>>> data=[('red',1),('blue',1),('red',2),('blue',2)]>>> standard_way=sorted(data,key=itemgetter(0),reverse=True)>>> double_reversed=list(reversed(sorted(reversed(data),key=itemgetter(0))))>>> assertstandard_way==double_reversed>>> standard_way[('red', 1), ('red', 2), ('blue', 1), ('blue', 2)]
The sort routines use < when making comparisons between two objects. So, it is easy to add a standard sort order to a class by defining an
method:
>>> Student.__lt__=lambdaself,other:self.age<other.age>>> sorted(student_objects)[('dave', 'B', 10), ('jane', 'B', 12), ('john', 'A', 15)]However, note that < can fall back to using
if
is not implemented (see
for details on the mechanics). To avoid surprises,
recommends that all six comparison methods be implemented. The
decorator is provided to make that task easier.
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']
Partial Sorts
Some applications require only some of the data to be ordered. The standard library provides several tools that do less work than a full sort:
and
return the smallest and largest values, respectively. These functions make a single pass over the input data and require almost no auxiliary memory.
and
return the n smallest and largest values, respectively. These functions make a single pass over the data keeping only n elements in memory at a time. For values of n that are small relative to the number of inputs, these functions make far fewer comparisons than a full sort.
and
create and maintain a partially sorted arrangement of data that keeps the smallest element at position 0. These functions are suitable for implementing priority queues which are commonly used for task scheduling.
