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= Sorting Mini-HOWTO =

'''Original version by Andrew Dalke'''

This document is a little tutorial
showing a half dozen ways to sort a list with the built-in
{{{sort()}}} method.

Python lists have a built-in {{{sort()}}} method. There are many
ways to use it to sort a list and there doesn't appear to be a single,
central place in the various manuals describing them, so I'll do so
here.

== Sorting basic data types ==

A simple ascending sort is easy; just call the {{{sort()}}} method of a list.
= Sorting Mini-HOW TO =
'''Original version by Andrew Dalke with a major update by Raymond Hettinger'''

<<TableOfContents>>

Python lists have a built-in {{{sort()}}} method that modifies the list in-place
and a {{{sorted()}}} built-in function that builds a new sorted list from an iterable.

There are many ways to use them to sort data and there doesn't appear
to be a single, central place in the various manuals describing them,
so I'll do so here.


== 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 of a list.
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.
Line 21: Line 32:
>>> print a >>> a
Line 25: Line 36:
Sort takes an optional function which can be called for doing the
comparisons. The default sort routine is equivalent to:

{{{
>>> a = [5, 2, 3, 1, 4]
>>> a.sort(cmp)
>>> print a
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'})
Line 35: Line 44:
where {{{cmp}}} is the built-in function which compares two objects,
{{{x}}} and {{{y}}}, and returns -1, 0 or 1 depending on whether
x<y, x==y, or x>y. During the course of the sort the
relationships must stay the same for the final list to make sense.

If you want, you can define your own function for the comparison. For
integers (and numbers in general) we can do:
== Key Functions ==

Starting with Python 2.4, both {{{list.sort()}}} and {{{sorted()}}} added a {{{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 a key. 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 [[http://docs.python.org/library/operator.html#module-operator|operator module]]
has {{{itemgetter}}}, {{{attrgetter}}},
and starting in Python 2.6 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)]
}}}

== Ascending and Descending ==

Both {{{list.sort()}}} and {{{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 ==

Starting with Python 2.2, sorts are guaranteed to be
[[http://en.wikipedia.org/wiki/Sorting_algorithm#Stability|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)]
}}}

The [[http://en.wikipedia.org/wiki/Timsort|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. 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 [[http://en.wikipedia.org/wiki/Schwartzian_transform|Schwartzian transform]], after Randal L. Schwartz, who popularized it among Perl programmers.

For large lists and lists where the comparison information
is expensive to calculate, and Python versions before 2.4, DSU is likely to be the
fastest way to sort the list. For 2.4 and later, key functions provide the same
functionality.

== The Old Way Using the cmp Parameter ==

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 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
{{{__cmp__}}} methods).

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:
Line 45: Line 217:
>>> return x-y
>>>
>>> a =
[5, 2, 3, 1, 4]
>>>
a.sort(numeric_compare)
>>> print a
     return x - y
>>> sorted([5, 2, 4, 1, 3], cmp=numeric_compare)
Line 53: Line 222:
By the way, this function won't work if result of the subtraction
is out of range, as in {{{sys.maxint - (-1)}}}.

Or, if you don't want to define a new named function you can create an
anonymous one using {{{lambda}}}, as in:

{{{
>>> a = [5, 2, 3, 1, 4]
>>> a.sort(lambda x, y: x-y)
>>> print a
[1, 2, 3, 4, 5]
}}}

If you want the numbers sorted in reverse you can do

{{{
>>> a = [5, 2, 3, 1, 4]
Or you can reverse the order of comparison with:

{{{
Line 71: Line 226:
>>> return y-x
>>>
>>> a.
sort(reverse_numeric)
>>> print a
    return y - x
>>> sorted([5, 2, 4, 1, 3], cmp=reverse_numeric)
Line 78: Line 231:
(a more general implementation could return {{{cmp(y,x)}}} or {{{-cmp(x,y)}}}).

However, it's faster if Python doesn't have to call a function for
every comparison, so if you want a reverse-sorted list of basic data
types, do the forward sort first, then use the {{{reverse()}}} method.

{{{
>>> a = [5, 2, 3, 1, 4]
>>> a.sort()
>>> a.reverse()
>>> print a
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))
Line 92: Line 264:
Here's a case-insensitive string comparison using a {{{lambda}}} function:

{{{
>>> a = "This is a test string from Andrew".split()
>>> a.sort(lambda x, y: cmp(x.lower(), y.lower()))
>>> print a
['a', 'Andrew', 'from', 'is', 'string', 'test', 'This']
}}}

This goes through the overhead of converting a word to lower case
every time it must be compared. At times it may be faster to compute
these once and use those values, and the following example shows how.

{{{
>>> words = string.split("This is a test string from Andrew.")
>>> offsets = []
>>> for i in range(len(words)):
>>> offsets.append( (string.lower(words[i]), i) )
>>>
>>> offsets.sort()
>>> new_words = []
>>> for dontcare, i in offsets:
>>> new_words.append(words[i])
>>>
>>> print new_words
}}}

The {{{offsets}}} list is initialized to a tuple of the lower-case
string and its position in the {{{words}}} list. It is then sorted.
Python's sort method sorts tuples by comparing terms; given {{{x}}}
and {{{y}}}, compare {{{x[0]}}} to {{{y[0]}}}, then {{{x[1]}}} to
{{{y[1]}}}, etc. until there is a difference.

The result is that the {{{offsets}}} list is ordered by its first
term, and the second term can be used to figure out where the original
data was stored. (The {{{for}}} loop assigns {{{dontcare}}} and
{{{i}}} to the two fields of each term in the list, but we only need
the index value.)

Another way to implement this is to store the original data as the
second term in the {{{offsets}}} list, as in:

{{{
>>> words = string.split("This is a test string from Andrew.")
>>> offsets = []
>>> for word in words:
>>> offsets.append( (string.lower(word), word) )
>>>
>>> offsets.sort()
>>> new_words = []
>>> for word in offsets:
>>> new_words.append(word[1])
>>>
>>> print new_words
}}}

This isn't always appropriate because the second terms in the list
(the word, in this example) will be compared when the first terms are
the same. If this happens many times, then there will be the unneeded
performance hit of comparing the two objects. This can be a large
cost if most terms are the same and the objects define their own
{{{__cmp__}}} method, but there will still be some overhead to determine if
{{{__cmp__}}} is defined.

Still, for large lists, or for lists where the comparison information
is expensive to calculate, the last two examples are likely to be the
fastest way to sort a list. It will not work on weakly sorted data,
like complex numbers, but if you don't know what that means, you
probably don't need to worry about it.

== Comparing classes ==

The comparison for two basic data types, like ints to ints or string to
string, is built into Python and makes sense. There is a default way
to compare class instances, but the default manner isn't usually very
useful. You can define your own comparison with the {{{__cmp__}}} method,
as in:

{{{
>>> class Spam:
>>> def __init__(self, spam, eggs):
>>> self.spam = spam
>>> self.eggs = eggs
>>> def __cmp__(self, other):
>>> return cmp(self.spam+self.eggs, other.spam+other.eggs)
>>> def __str__(self):
>>> return str(self.spam + self.eggs)
>>>
>>> a = [Spam(1, 4), Spam(9, 3), Spam(4,6)]
>>> a.sort()
>>> for spam in a:
>>> print str(spam)
5
10
12
}}}

Sometimes you may want to sort by a specific attribute of a class. If
appropriate you should just define the {{{__cmp__}}} method to compare
those values, but you cannot do this if you want to compare between
different attributes at different times. Instead, you'll need to go
back to passing a comparison function to sort, as in:

{{{
>>> a = [Spam(1, 4), Spam(9, 3), Spam(4,6)]
>>> a.sort(lambda x, y: cmp(x.eggs, y.eggs))
>>> for spam in a:
>>> print spam.eggs, str(spam)
3 12
4 5
6 10
}}}

If you want to compare two arbitrary attributes (and aren't overly
concerned about performance) you can even define your own comparison
function object. This uses the ability of a class instance to emulate
an function by defining the {{{__call__}}} method, as in:

{{{
>>> class CmpAttr:
>>> def __init__(self, attr):
>>> self.attr = attr
>>> def __call__(self, x, y):
>>> return cmp(getattr(x, self.attr), getattr(y, self.attr))
>>>
>>> a = [Spam(1, 4), Spam(9, 3), Spam(4,6)]
>>> a.sort(CmpAttr("spam")) # sort by the "spam" attribute
>>> for spam in a:
>>> print spam.spam, spam.eggs, str(spam)
1 4 5
4 6 10
9 3 12

>>> a.sort(CmpAttr("eggs")) # re-sort by the "eggs" attribute
>>> for spam in a:
>>> print spam.spam, spam.eggs, str(spam)
9 3 12
1 4 5
4 6 10
}}}

Of course, if you want a faster sort you can extract the attributes
into an intermediate list and sort that list.


So, there you have it; about a half-dozen different ways to define how
to sort a list:

 1. sort using the default method
 1. sort using a comparison function
 1. reverse sort not using a comparison function
 1. sort on an intermediate list (two forms)
 1. sort using class defined __cmp__ method
 1. sort using a sort function object
In Python 2.7, the ''cmp_to_key()'' tool was added to the ''functools'' module.

== Odd and Ends ==

 * For locale aware sorting, use {{{locale.strxfrm()}}} for a key function or {{{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 {{{reversed}}} function twice:
   {{{
>>> data = [('red', 1), ('blue', 1), ('red', 2), ('blue', 2)]
>>> assert sorted(data, reverse=True) == list(reversed(sorted(reversed(data))))
   }}}

 * To create a standard sort order for a class, just add the appropriate rich comparison methods:

   {{{
>>> Student.__eq__ = lambda self, other: self.age == other.age
>>> Student.__ne__ = lambda self, other: self.age != other.age
>>> Student.__lt__ = lambda self, other: self.age < other.age
>>> Student.__le__ = lambda self, other: self.age <= other.age
>>> Student.__gt__ = lambda self, other: self.age > other.age
>>> Student.__ge__ = lambda self, other: self.age >= other.age
>>> sorted(student_objects)
[('dave', 'B', 10), ('jane', 'B', 12), ('john', 'A', 15)]
   }}}

   For general purpose comparisons, the recommended approach is to define all six rich comparison operators. The {{{functools.total_ordering}}} class decorator makes this easy to implement.

 * Key functions need not access data internal to 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']
}}}

 * Alternate datastructure for performance with ordered data

   If you're needing a sorted list every step of the way as you process each item to be added to the sorted list, then list.sort(), sorted() and bisect.insort() are all very slow and tend to yield quadratic behavior or worse. In such a scenario, it's better to use something like a heap, red-black tree or treap (like the included heapq module, or this [[http://stromberg.dnsalias.org/~dstromberg/treap/|treap module]] - shameless plug added by python treap module author).

Sorting Mini-HOW TO

Original version by Andrew Dalke with a major update by Raymond Hettinger

Python lists have a built-in sort() method that modifies the list in-place and a sorted() built-in function that builds a new sorted list from an iterable.

There are many ways to use them to sort data and there doesn't appear to be a single, central place in the various manuals describing them, so I'll do so here.

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 of a list. 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

Starting with Python 2.4, both list.sort() and sorted() added a 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 a key. 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 itemgetter, attrgetter, and starting in Python 2.6 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)]

Ascending and Descending

Both list.sort() and 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

Starting with Python 2.2, 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)]

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

For large lists and lists where the comparison information is expensive to calculate, and Python versions before 2.4, DSU is likely to be the fastest way to sort the list. For 2.4 and later, key functions provide the same functionality.

The Old Way Using the cmp Parameter

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 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 __cmp__ methods).

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 2.7, the cmp_to_key() tool was added to the functools module.

Odd and Ends

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

    • >>> data = [('red', 1), ('blue', 1), ('red', 2), ('blue', 2)]
      >>> assert sorted(data, reverse=True) == list(reversed(sorted(reversed(data))))
  • To create a standard sort order for a class, just add the appropriate rich comparison methods:
    • >>> Student.__eq__ = lambda self, other: self.age == other.age
      >>> Student.__ne__ = lambda self, other: self.age != other.age
      >>> Student.__lt__ = lambda self, other: self.age < other.age
      >>> Student.__le__ = lambda self, other: self.age <= other.age
      >>> Student.__gt__ = lambda self, other: self.age > other.age
      >>> Student.__ge__ = lambda self, other: self.age >= other.age
      >>> sorted(student_objects)
      [('dave', 'B', 10), ('jane', 'B', 12), ('john', 'A', 15)]

      For general purpose comparisons, the recommended approach is to define all six rich comparison operators. The functools.total_ordering class decorator makes this easy to implement.

  • Key functions need not access data internal to 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']
  • Alternate datastructure for performance with ordered data
    • If you're needing a sorted list every step of the way as you process each item to be added to the sorted list, then list.sort(), sorted() and bisect.insort() are all very slow and tend to yield quadratic behavior or worse. In such a scenario, it's better to use something like a heap, red-black tree or treap (like the included heapq module, or this treap module - shameless plug added by python treap module author).

HowTo/Sorting (last edited 2014-10-12 06:26:39 by Paddy3118)

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