# 排序指南

作者: | Andrew Dalke 和 Raymond Hettinger
发布版本: | 0.1

Python 列表有一个内置的 `list.sort()` 方法可以直接修改列表。还有一个 `sorted()` 内置函数，它会从一个可迭代对象构建一个新的排序列表。

在本文档中，我们将探索使用Python对数据进行排序的各种技术。

## 基本排序

简单的升序排序非常简单：只需调用 `sorted()` 函数即可。它会返回一个新的已排序列表。

    >>> sorted([5, 2, 3, 1, 4])
    [1, 2, 3, 4, 5]

你也可以使用 `list.sort()` 方法，它会直接修改原列表（并返回 `None` 以避免混淆），通常来说它不如 `sorted()` 方便 ——— 但如果你不需要原列表，它会更有效率。

    >>> a = [5, 2, 3, 1, 4]
    >>> a.sort()
    >>> a
    [1, 2, 3, 4, 5]

另外一个区别是， `list.sort()` 方法只是为列表定义的，而 `sorted()` 函数可以接受任何可迭代对象。

    >>> sorted({1: 'D', 2: 'B', 3: 'B', 4: 'E', 5: 'A'})
    [1, 2, 3, 4, 5]

## 关键函数

`list.sort()` 和 `sorted()` 都有一个 key 形参来指定在进行比较之前要在每个列表元素上进行调用的函数。

例如，下面是一个不区分大小写的字符串比较：

    >>> sorted("This is a test string from Andrew".split(), key=str.lower)
    ['a', 'Andrew', 'from', 'is', 'string', 'test', 'This']

key 形参的值应该是一个函数，它接受一个参数并并返回一个用于排序的键。这种技巧速度很快，因为对于每个输入记录只会调用一次 key 函数。

一种常见的模式是使用对象的一些索引作为键对复杂对象进行排序。例如：

    >>> 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)]

同样的技术也适用于具有命名属性的对象。例如：

    >>> 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 模块函数

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) # doctest: +SKIP
    [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) # doctest: +SKIP
    [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']