Forward port sorting howto

Doc/howto/index.rst

@@ -20,6 +20,7 @@ Currently, the HOWTOs are:
    functional.rst
    regex.rst
    sockets.rst
+   sorting.rst
    unicode.rst
    urllib2.rst
    webservers.rst

Doc/howto/sorting.rst

+Sorting HOW TO
+**************
+
+:Author: Andrew Dalke and Raymond Hettinger
+:Release: 0.1
+
+
+Python lists have a built-in :meth:`list.sort` method that modifies the list
+in-place and a :func:`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 :func:`sorted` function. It
+returns a new sorted list::
+
+    >>> sorted([5, 2, 3, 1, 4])
+    [1, 2, 3, 4, 5]
+
+You can also use the :meth:`list.sort` method of a list. 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.
+
+    >>> a = [5, 2, 3, 1, 4]
+    >>> a.sort()
+    >>> a
+    [1, 2, 3, 4, 5]
+
+Another difference is that the :meth:`list.sort` method is only defined for
+lists. In contrast, the :func:`sorted` function accepts any iterable.
+
+    >>> sorted({1: 'D', 2: 'B', 3: 'B', 4: 'E', 5: 'A'})
+    [1, 2, 3, 4, 5]
+
+Key Functions
+=============
+
+Both :meth:`list.sort` and :func:`sorted` have *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 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 :func:`operator.itemgetter`, :func:`operator.attrgetter`, and
+an :func:`operator.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 :meth:`list.sort` and :func:`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
+================================
+
+Sorts are guaranteed to be `stable
+<http://en.wikipedia.org/wiki/Sorting_algorithm#Stability>`_\. 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 <http://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.
+
+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 <http://en.wikipedia.org/wiki/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 :func:`sorted` builtin and :meth:`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 :meth:`__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(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]
+
+
+Odd and Ends
+============
+
+* For locale aware sorting, use :func:`locale.strxfrm` for a key function or
+  :func:`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 :func:`reversed` function
+  twice:
+
+    >>> data = [('red', 1), ('blue', 1), ('red', 2), ('blue', 2)]
+    >>> assert sorted(data, reverse=True) == list(reversed(sorted(reversed(data))))
+
+* The sort routines are guaranteed to use :meth:`__lt__` when making comparisons
+  between two objects. So, it is easy to add a standard sort order to a class by
+  defining an :meth:`__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']