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#: ../../howto/sorting.rst:4
msgid "Sorting Techniques"
#: ../../howto/sorting.rst
msgid "Author"
#: ../../howto/sorting.rst:6
msgid "Andrew Dalke and Raymond Hettinger"
#: ../../howto/sorting.rst:9
"Python lists have a built-in :meth:`list.sort` method that modifies the "
"list in-place.  There is also a :func:`sorted` built-in function that "
"builds a new sorted list from an iterable."
#: ../../howto/sorting.rst:13
"In this document, we explore the various techniques for sorting data "
"using Python."
#: ../../howto/sorting.rst:17
msgid "Sorting Basics"
#: ../../howto/sorting.rst:19
"A simple ascending sort is very easy: just call the :func:`sorted` "
"function. It returns a new sorted list:"
#: ../../howto/sorting.rst:22
">>> sorted([5, 2, 3, 1, 4])\n"
"[1, 2, 3, 4, 5]"
#: ../../howto/sorting.rst:27
"You can also use the :meth:`list.sort` method. It modifies the list in-"
"place (and returns ``None`` to avoid confusion). Usually it's less "
"convenient than :func:`sorted` - but if you don't need the original list,"
" it's slightly more efficient."
#: ../../howto/sorting.rst:32
">>> a = [5, 2, 3, 1, 4]\n"
">>> a.sort()\n"
"[1, 2, 3, 4, 5]"
#: ../../howto/sorting.rst:39
"Another difference is that the :meth:`list.sort` method is only defined "
"for lists. In contrast, the :func:`sorted` function accepts any iterable."
#: ../../howto/sorting.rst:42
#, python-brace-format
">>> sorted({1: 'D', 2: 'B', 3: 'B', 4: 'E', 5: 'A'})\n"
"[1, 2, 3, 4, 5]"
#: ../../howto/sorting.rst:48
msgid "Key Functions"
#: ../../howto/sorting.rst:50
"Both :meth:`list.sort` and :func:`sorted` have a *key* parameter to "
"specify a function (or other callable) to be called on each list element "
"prior to making comparisons."
#: ../../howto/sorting.rst:54
msgid "For example, here's a case-insensitive string comparison:"
#: ../../howto/sorting.rst:56
">>> sorted(\"This is a test string from Andrew\".split(), "
"key=str.casefold)\n"
"['a', 'Andrew', 'from', 'is', 'string', 'test', 'This']"
#: ../../howto/sorting.rst:61
"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."
#: ../../howto/sorting.rst:66
"A common pattern is to sort complex objects using some of the object's "
"indices as keys. For example:"
#: ../../howto/sorting.rst:69
">>> student_tuples = [\n"
"...     ('john', 'A', 15),\n"
"...     ('jane', 'B', 12),\n"
"...     ('dave', 'B', 10),\n"
">>> sorted(student_tuples, key=lambda student: student[2])   # sort by "
"[('dave', 'B', 10), ('jane', 'B', 12), ('john', 'A', 15)]"
#: ../../howto/sorting.rst:79
msgid "The same technique works for objects with named attributes. For example:"
#: ../../howto/sorting.rst:81
">>> class Student:\n"
"...     def __init__(self, name, grade, age):\n"
"...         self.name = name\n"
"...         self.grade = grade\n"
"...         self.age = age\n"
"...     def __repr__(self):\n"
"...         return repr((self.name, self.grade, self.age))\n"
">>> student_objects = [\n"
"...     Student('john', 'A', 15),\n"
"...     Student('jane', 'B', 12),\n"
"...     Student('dave', 'B', 10),\n"
">>> sorted(student_objects, key=lambda student: student.age)   # sort by "
"[('dave', 'B', 10), ('jane', 'B', 12), ('john', 'A', 15)]"
#: ../../howto/sorting.rst:99
"Objects with named attributes can be made by a regular class as shown "
"above, or they can be instances of :class:`~dataclasses.dataclass` or a "
":term:`named tuple`."
#: ../../howto/sorting.rst:104
msgid "Operator Module Functions and Partial Function Evaluation"
#: ../../howto/sorting.rst:106
"The :term:`key function` patterns shown above are very common, so Python "
"provides convenience functions to make accessor functions easier and "
"faster. The :mod:`operator` module has :func:`~operator.itemgetter`, "
":func:`~operator.attrgetter`, and a :func:`~operator.methodcaller` "
"function."
#: ../../howto/sorting.rst:111
msgid "Using those functions, the above examples become simpler and faster:"
#: ../../howto/sorting.rst:113
">>> from operator import itemgetter, attrgetter\n"
">>> sorted(student_tuples, key=itemgetter(2))\n"
"[('dave', 'B', 10), ('jane', 'B', 12), ('john', 'A', 15)]\n"
">>> sorted(student_objects, key=attrgetter('age'))\n"
"[('dave', 'B', 10), ('jane', 'B', 12), ('john', 'A', 15)]"
#: ../../howto/sorting.rst:123
"The operator module functions allow multiple levels of sorting. For "
"example, to sort by *grade* then by *age*:"
#: ../../howto/sorting.rst:126
">>> sorted(student_tuples, key=itemgetter(1,2))\n"
"[('john', 'A', 15), ('dave', 'B', 10), ('jane', 'B', 12)]\n"
">>> sorted(student_objects, key=attrgetter('grade', 'age'))\n"
"[('john', 'A', 15), ('dave', 'B', 10), ('jane', 'B', 12)]"
#: ../../howto/sorting.rst:134
"The :mod:`functools` module provides another helpful tool for making key-"
"functions.  The :func:`~functools.partial` function can reduce the `arity"
" <https://en.wikipedia.org/wiki/Arity>`_ of a multi-argument function "
"making it suitable for use as a key-function."
#: ../../howto/sorting.rst:139
">>> from functools import partial\n"
">>> from unicodedata import normalize\n"
">>> names = 'Zoë Åbjørn Núñez Élana Zeke Abe Nubia Eloise'.split()\n"
">>> sorted(names, key=partial(normalize, 'NFD'))\n"
"['Abe', 'Åbjørn', 'Eloise', 'Élana', 'Nubia', 'Núñez', 'Zeke', 'Zoë']\n"
">>> sorted(names, key=partial(normalize, 'NFC'))\n"
"['Abe', 'Eloise', 'Nubia', 'Núñez', 'Zeke', 'Zoë', 'Åbjørn', 'Élana']"
#: ../../howto/sorting.rst:153
msgid "Ascending and Descending"
#: ../../howto/sorting.rst:155
"Both :meth:`list.sort` and :func:`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:"
#: ../../howto/sorting.rst:159
">>> sorted(student_tuples, key=itemgetter(2), reverse=True)\n"
"[('john', 'A', 15), ('jane', 'B', 12), ('dave', 'B', 10)]\n"
">>> sorted(student_objects, key=attrgetter('age'), reverse=True)\n"
"[('john', 'A', 15), ('jane', 'B', 12), ('dave', 'B', 10)]"
#: ../../howto/sorting.rst:168
msgid "Sort Stability and Complex Sorts"
#: ../../howto/sorting.rst:170
"Sorts are guaranteed to be `stable "
"<https://en.wikipedia.org/wiki/Sorting_algorithm#Stability>`_\\. That "
"means that when multiple records have the same key, their original order "
"is preserved."
#: ../../howto/sorting.rst:174
">>> data = [('red', 1), ('blue', 1), ('red', 2), ('blue', 2)]\n"
">>> sorted(data, key=itemgetter(0))\n"
"[('blue', 1), ('blue', 2), ('red', 1), ('red', 2)]"
#: ../../howto/sorting.rst:180
"Notice how the two records for *blue* retain their original order so that"
" ``('blue', 1)`` is guaranteed to precede ``('blue', 2)``."
#: ../../howto/sorting.rst:183
"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*:"
#: ../../howto/sorting.rst:187
">>> s = sorted(student_objects, key=attrgetter('age'))     # sort on "
"secondary key\n"
">>> sorted(s, key=attrgetter('grade'), reverse=True)       # now sort on "
"primary key, descending\n"
"[('dave', 'B', 10), ('jane', 'B', 12), ('john', 'A', 15)]"
#: ../../howto/sorting.rst:193
"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."
#: ../../howto/sorting.rst:196
">>> def multisort(xs, specs):\n"
"...     for key, reverse in reversed(specs):\n"
"...         xs.sort(key=attrgetter(key), reverse=reverse)\n"
"...     return xs\n"
">>> multisort(list(student_objects), (('grade', True), ('age', False)))\n"
"[('dave', 'B', 10), ('jane', 'B', 12), ('john', 'A', 15)]"
#: ../../howto/sorting.rst:206
"The `Timsort <https://en.wikipedia.org/wiki/Timsort>`_ algorithm used in "
"Python does multiple sorts efficiently because it can take advantage of "
"any ordering already present in a dataset."
#: ../../howto/sorting.rst:211
msgid "Decorate-Sort-Undecorate"
#: ../../howto/sorting.rst:213
msgid "This idiom is called Decorate-Sort-Undecorate after its three steps:"
#: ../../howto/sorting.rst:215
"First, the initial list is decorated with new values that control the "
"sort order."
#: ../../howto/sorting.rst:217
msgid "Second, the decorated list is sorted."
#: ../../howto/sorting.rst:219
"Finally, the decorations are removed, creating a list that contains only "
"the initial values in the new order."
#: ../../howto/sorting.rst:222
msgid "For example, to sort the student data by *grade* using the DSU approach:"
#: ../../howto/sorting.rst:224
">>> decorated = [(student.grade, i, student) for i, student in "
"enumerate(student_objects)]\n"
">>> decorated.sort()\n"
">>> [student for grade, i, student in decorated]               # "
"undecorate\n"
"[('john', 'A', 15), ('jane', 'B', 12), ('dave', 'B', 10)]"
#: ../../howto/sorting.rst:231
"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."
#: ../../howto/sorting.rst:235
"It is not strictly necessary in all cases to include the index *i* in the"
" decorated list, but including it gives two benefits:"
#: ../../howto/sorting.rst:238
"The sort is stable -- if two items have the same key, their order will be"
" preserved in the sorted list."
#: ../../howto/sorting.rst:241
"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."
#: ../../howto/sorting.rst:246
"Another name for this idiom is `Schwartzian transform "
"<https://en.wikipedia.org/wiki/Schwartzian_transform>`_\\, after Randal "
"L. Schwartz, who popularized it among Perl programmers."
#: ../../howto/sorting.rst:250
"Now that Python sorting provides key-functions, this technique is not "
"often needed."
#: ../../howto/sorting.rst:253
msgid "Comparison Functions"
#: ../../howto/sorting.rst:255
"Unlike key functions that return an absolute value for sorting, a "
"comparison function computes the relative ordering for two inputs."
#: ../../howto/sorting.rst:258
"For example, a `balance scale "
"<https://upload.wikimedia.org/wikipedia/commons/1/17/Balance_à_tabac_1850.JPG>`_"
" 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."
#: ../../howto/sorting.rst:265
"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, :func:`locale.strcoll` is "
"a comparison function."
#: ../../howto/sorting.rst:269
"To accommodate those situations, Python provides "
":class:`functools.cmp_to_key` to wrap the comparison function to make it "
"usable as a key function::"
#: ../../howto/sorting.rst:273
msgid "sorted(words, key=cmp_to_key(strcoll))  # locale-aware sort order"
#: ../../howto/sorting.rst:276
msgid "Odds and Ends"
#: ../../howto/sorting.rst:278
"For locale aware sorting, use :func:`locale.strxfrm` for a key function "
"or :func:`locale.strcoll` for a comparison function.  This is necessary "
"because \"alphabetical\" sort orderings can vary across cultures even if "
"the underlying alphabet is the same."
#: ../../howto/sorting.rst:283
"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 "
":func:`reversed` function twice:"
#: ../../howto/sorting.rst:288
">>> data = [('red', 1), ('blue', 1), ('red', 2), ('blue', 2)]\n"
">>> standard_way = sorted(data, key=itemgetter(0), reverse=True)\n"
">>> double_reversed = list(reversed(sorted(reversed(data), "
"key=itemgetter(0))))\n"
">>> assert standard_way == double_reversed\n"
">>> standard_way\n"
"[('red', 1), ('red', 2), ('blue', 1), ('blue', 2)]"
#: ../../howto/sorting.rst:297
"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 "
":meth:`~object.__lt__` method:"
#: ../../howto/sorting.rst:301
">>> Student.__lt__ = lambda self, other: self.age < other.age\n"
">>> sorted(student_objects)\n"
"[('dave', 'B', 10), ('jane', 'B', 12), ('john', 'A', 15)]"
#: ../../howto/sorting.rst:307
"However, note that ``<`` can fall back to using :meth:`~object.__gt__` if"
" :meth:`~object.__lt__` is not implemented (see :func:`object.__lt__` for"
" details on the mechanics).  To avoid surprises, :pep:`8` recommends that"
" all six comparison methods be implemented. The "
":func:`~functools.total_ordering` decorator is provided to make that task"
#: ../../howto/sorting.rst:314
"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:"
#: ../../howto/sorting.rst:319
#, python-brace-format
">>> students = ['dave', 'john', 'jane']\n"
">>> newgrades = {'john': 'F', 'jane':'A', 'dave': 'C'}\n"
">>> sorted(students, key=newgrades.__getitem__)\n"
"['jane', 'dave', 'john']"
#: ../../howto/sorting.rst:327
msgid "Partial Sorts"
#: ../../howto/sorting.rst:329
"Some applications require only some of the data to be ordered.  The "
"standard library provides several tools that do less work than a full "
#: ../../howto/sorting.rst:332
":func:`min` and :func:`max` return the smallest and largest values, "
"respectively.  These functions make a single pass over the input data and"
" require almost no auxiliary memory."
#: ../../howto/sorting.rst:336
":func:`heapq.nsmallest` and :func:`heapq.nlargest` 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."
#: ../../howto/sorting.rst:342
":func:`heapq.heappush` and :func:`heapq.heappop` 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."
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