Sorting Techniques (original) (raw)

Author:

Andrew Dalke and Raymond Hettinger

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.

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. 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

Both list.sort() and sorted() 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:

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=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)]

Objects with named attributes can be made by a regular class as shown above, or they can be instances of dataclass or a named tuple.

Operator Module Functions and Partial Function Evaluation

The key function patterns shown above are very common, so Python provides convenience functions to make accessor functions easier and faster. Theoperator 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 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 functools module provides another helpful tool for making key-functions. The partial() function can reduce thearity of a multi-argument function making it suitable for use as a key-function.

from functools import partial from unicodedata import normalize

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 list.sort() and sorted() 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 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)]

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.

def multisort(xs, specs): ... for key, reverse in reversed(specs): ... xs.sort(key=attrgetter(key), reverse=reverse) ... return xs

multisort(list(student_objects), (('grade', True), ('age', False))) [('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.

Decorate-Sort-Undecorate

This idiom is called Decorate-Sort-Undecorate after its three steps:

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:

Another name for this idiom isSchwartzian transform, 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 balance scalecompares 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, locale.strcoll() is a comparison function.

To accommodate those situations, Python providesfunctools.cmp_to_key to wrap the comparison function to make it usable as a key function:

sorted(words, key=cmp_to_key(strcoll)) # locale-aware sort order

Odds and Ends

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: