Sorting HOW TO
**************

Author:
   Andrew Dalke and Raymond Hettinger

Release:
   0.1

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.


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.lower)
   ['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)]


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
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 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.


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, 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 "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__()" 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:
           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 standard library.


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 (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)]
     >>> standard_way = sorted(data, key=itemgetter(0), reverse=True)
     >>> double_reversed = list(reversed(sorted(reversed(data), key=itemgetter(0))))
     >>> assert standard_way == double_reversed
     >>> standard_way
     [('red', 1), ('red', 2), ('blue', 1), ('blue', 2)]

* 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']
