集合 属于

关于 集合

set是一种_可变_且_无序_的可哈希对象集合。 集合的成员必须互不相同，不允许出现重复项。 集合可以容纳多种不同的数据类型，甚至可以容纳嵌套结构，比如由tuple组成的tuples，只要所有元素都能被_哈希_即可。 集合还有一种不可变的frozenset版本。

集合最常用于快速去除其他数据结构或项目分组中的重复项。 当不需要关注顺序和重复项跟踪时，集合也能用于高效比较。

与其他集合类型（字典、数组、元组）一样，sets支持：

• 通过for item in <set>进行迭代，
• 通过in和not in检查成员，
• 通过len()计算长度，
• 通过copy()进行浅拷贝。

sets不支持：

• 任何形式的索引
• 通过排序或插入来确定顺序
• 切片
• 通过+进行拼接

在set中检查成员具有常数时间复杂度（平均而言），相比之下，在list或string中检查成员时，时间复杂度会随着数据长度的增长而增加。 <set>.union()、<set>.intersection()、<set>.difference()等方法同样具有常数时间复杂度（平均而言）。

集合的构建

虽然创建集合的方式有很多，但最直接的构建方法有三种：声明_集合字面量_、使用set类的构造函数（set()），以及使用_集合推导式_。

集合字面量

set可以直接写成_集合字面量_：用花括号{}括起元素，元素之间用逗号分隔。 重复项会被静默省略：

>>> one_element = {'➕'}
{'➕'}

>>> multiple_elements = {'➕', '🔻', '🔹', '🔆'}
{'➕', '🔻', '🔹', '🔆'}

>>> multiple_duplicates =  {'Hello!', 'Hello!', 'Hello!', 
                            '¡Hola!','Привіт!', 'こんにちは！', 
                            '¡Hola!','Привіт!', 'こんにちは！'}
{'こんにちは！', '¡Hola!', 'Hello!', 'Привіт!'}

集合字面量使用的花括号和dict字面量相同，这意味着创建空set必须使用set()。

集合的构造函数

set()（set类的构造函数）可以接受任何作为参数传入的iterable。 它会逐个遍历iterable中的元素，并逐一添加到set中。 元素的顺序不会被保留，重复项会被静默省略：

# To create an empty set, the constructor must be used.
>>> no_elements = set()
set()

# The tuple is unpacked & each element is added.  
# Duplicates are removed.
>>> elements_from_tuple = set(("Parrot", "Bird", 
                               334782, "Bird", "Parrot"))
{334782, 'Bird', 'Parrot'}

# The list is unpacked & each element is added.
# Duplicates are removed.
>>> elements_from_list = set([2, 3, 2, 3, 3, 3, 5, 
                              7, 11, 7, 11, 13, 13])
{2, 3, 5, 7, 11, 13}

集合推导式

和lists、dicts一样，集合也可以通过_推导式_创建：

# First, a list with duplicates
>>> numbers = [1,2,3,4,5,6,6,5,4,8,9,9,9,2,3,12,18]

# This set comprehension squares the numbers divisible by 3
# Duplicates are removed.
>>> calculated = {item**2 for item in numbers if item % 3 == 0}
{9, 36, 81, 144, 324}

创建集合时的坑

由于set构造函数具有“解包”行为，用它处理字符串时的结果可能会让你意外：

# String elements (Unicode code points) are 
# iterated through and added *individually*.
>>> elements_string = set("Timbuktu")
{'T', 'b', 'i', 'k', 'm', 't', 'u'}

# Unicode separators and positioning code points 
# are also added *individually*.
>>> multiple_code_points_string = set('अभ्यास')
{'अ', 'भ', 'य', 'स', 'ा', '्'}

记住：集合可以容纳不同的数据类型，也可以容纳_嵌套_的数据类型，但所有set元素都必须是_可哈希_的：

# Attempting to use a list for a set member throws a TypeError
>>> lists_as_elements = {['🌈','💦'], 
                        ['☁️','⭐️','🌍'], 
                        ['⛵️', '🚲', '🚀']}

Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: unhashable type: 'list'


# Standard sets are mutable, so they cannot be hashed.
>>> sets_as_elements = {{'🌈','💦'}, 
                        {'☁️','⭐️','🌍'}, 
                        {'⛵️', '🚲', '🚀'}}

Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: unhashable type: 'set'

不过，可以用frozenset()类型来创建由set组成的set：

# Frozensets don't have a literal form.
>>> set_1 = frozenset({'🌈','💦'})
>>> set_2 = frozenset({'☁️','⭐️','🌍'})
>>> set_3 = frozenset({'⛵️', '🚲', '🚀'})

>>> frozen_sets_as_elements = {set_1, set_2, set_3}
>>> frozen_sets_as_elements
{frozenset({'⛵️', '🚀', '🚲'}),
 frozenset({'🌈', '💦'}),
 frozenset({'☁️', '⭐️', '🌍'})}

添加和删除集合成员

可以使用<set>.add(<item>)和<set>.remove(<item>)方法向set中添加或删除元素。 如果要删除的项不在set中，.remove(<item>)方法会抛出KeyError：

>>> creatures = {'crow', 'duck', 'fish', 'monkey', 'elephant'}
>>> creatures.add('beaver')
>>> creatures.remove('duck')
>>> creatures
{'beaver', 'crow', 'elephant', 'fish', 'monkey'}

# Trying to remove an item that is not present raises a KeyError
>>> creatures.remove('bear')
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  KeyError: 'bear'

移除集合成员的其他方法

• <set>.discard(<item>)会从set中移除一项，但如果该项不存在，不会抛出KeyError。
• <set>.clear()会移除集合中的所有项。
• <set>.pop()会移除并_返回_一个任意的项，如果set为空则抛出KeyError。

集合运算

集合的方法大体上模仿了数学中的集合运算。 这些方法中的大多数（并非全部）都有对应的运算符。 方法通常接受任何iterable作为参数，而运算符要求运算两边都是set或frozenset。

集合之间的成员测试

<set>.isdisjoint(<other_collection>)方法用于测试一个set的元素是否与另一个集合的元素有重叠。 该方法接受任何iterable或set作为参数。 如果两个集合没有共同元素，它返回True；如果有元素共享，则返回False。

# Both mammals and additional_animals are lists.
>>> mammals = ['squirrel','dog','cat','cow', 'tiger', 'elephant']
>>> additional_animals = ['pangolin', 'panda', 'parrot', 
                          'lemur', 'tiger', 'pangolin']

# Animals is a dict.
>>> animals = {'chicken': 'white',
               'sparrow': 'grey',
               'eagle': 'brown and white',
               'albatross': 'grey and white',
               'crow': 'black',
               'elephant': 'grey', 
               'dog': 'rust',
               'cow': 'black and white',
               'tiger': 'orange and black',
               'cat': 'grey',
               'squirrel': 'black'}
               
# Birds is a set.
>>> birds = {'crow','sparrow','eagle','chicken', 'albatross'}

# Mammals and birds don't share any elements.
>>> birds.isdisjoint(mammals)
True

# There are also no shared elements between 
# additional_animals and birds.
>>> birds.isdisjoint(additional_animals)
True

# Animals and mammals have shared elements.
# **Note** The first object needs to be a set or converted to a set
# since .isdisjoint() is a set method.
>>> set(animals).isdisjoint(mammals)
False

检查子集和超集

<set>.issubset(<other_collection>)用于检查<set>中的每个元素是否也都在<other_collection>中。 对应的运算符形式是<set> <= <other_set>：

# Set methods will take any iterable as an argument.
# All members of birds are also members of animals.
>>> birds.issubset(animals)
True

# All members of mammals also appear in animals.
# **Note** The first object needs to be a set or converted to a set
# since .issubset() is a set method.
>>> set(mammals).issubset(animals)
True

# Both objects need to be sets to use a set operator
>>> birds <= set(mammals)
False

# A set is always a loose subset of itself.
>>> set(additional_animals) <= set(additional_animals)
True

<set>.issuperset(<other_collection>)与.issubset()的作用相反。 它用于检查<other_collection>中的每个元素是否也都在<set>中。 对应的运算符形式是<set> >= <other_set>：

# All members of mammals also appear in animals.
# **Note** The first object needs to be a set or converted to a set
# since .issuperset() is a set method.
>>> set(animals).issuperset(mammals)
True

# All members of animals do not show up as members of birds.
>>> birds.issuperset(animals)
False

# Both objects need to be sets to use a set operator
>>> birds >= set(mammals)
False

# A set is always a loose superset of itself.
>>> set(animals) >= set(animals)
True

“真”子集和超集

<set> < <other_set>和<set> > <other_set>用于测试_真子集_。 对于<运算符，如果（<set> <= <other_set>）并且（<set> != <other_set>），那么这个set就是真子集。

对于>运算符，如果（<set> >= <other_set>）并且（<set> != <other_set>），那么这个set就是真超集。 这两个运算符没有对应的方法：

>>> animal_names = {'albatross','cat','chicken','cow','crow','dog',
                   'eagle','elephant','sparrow','squirrel','tiger'}

>>> animals_also = {'albatross','cat','chicken','cow','crow','dog',
                   'eagle','elephant','sparrow','squirrel','tiger'}

>>> mammals = {'squirrel','dog','cat','cow', 'tiger', 'elephant'}
>>> birds   = {'crow','sparrow','eagle','chicken', 'albatross'}

>>> mammals < animal_names
True

>>> animal_names > birds
True

# A set is not a *proper subset* if set == other set.
>>> animals_also < animal_names
False

# A set is never a *proper subset* of itself
>>> animals_also < animals_also
False

集合的并集

<set>.union(*<other iterables>)返回一个新的set，其中包含来自<set>以及所有<other iterables>的元素。 该方法的运算符形式是<set> | <other set 1> | <other set 2> | ... | <other set n>。

>>> perennials = {'Asparagus', 'Broccoli', 'Sweet Potato', 'Kale'}
>>> annuals = {'Corn', 'Zucchini', 'Sweet Peas', 'Summer Squash'}
>>> more_perennials = ['Radicchio', 'Rhubarb', 
                      'Spinach', 'Watercress']

# Methods will take any iterable as an argument.
>>> perennials.union(more_perennials)
{'Asparagus','Broccoli','Kale','Radicchio','Rhubarb',
'Spinach','Sweet Potato','Watercress'}

# Operators require sets.
>>> set(more_perennials) | perennials
{'Asparagus',
 'Broccoli',
 'Kale',
 'Radicchio',
 'Rhubarb',
 'Spinach',
 'Sweet Potato',
 'Watercress'}

集合的差集

<set>.difference(*<other iterables>)返回一个新的set，其中包含在原来的<set>中、但不在<others>中的元素。 该方法的运算符版本是<set> - <other set 1> - <other set 2> - ... - <other set n>。

>>> berries_and_veggies = {'Asparagus', 
                          'Broccoli', 
                          'Watercress', 
                          'Goji Berries', 
                          'Goose Berries', 
                          'Ramps', 
                          'Walking Onions', 
                          'Blackberries', 
                          'Strawberries', 
                          'Rhubarb', 
                          'Kale', 
                          'Artichokes', 
                          'Currants'}

>>> veggies = ('Asparagus', 'Broccoli', 'Watercress', 'Ramps',
               'Walking Onions', 'Rhubarb', 'Kale', 'Artichokes')

# Methods will take any iterable as an argument.
>>> berries = berries_and_veggies.difference(veggies)
{'Blackberries','Currants','Goji Berries',
 'Goose Berries', 'Strawberries'}

# Operators require sets.
>>> berries_and_veggies - berries
{'Artichokes','Asparagus','Broccoli','Kale',
'Ramps','Rhubarb','Walking Onions','Watercress'}

集合的交集

<set>.intersection(*<other iterables>)返回一个新的set，其中包含原来的set与所有<others>共有的元素（换句话说，就是所有元素都相交的那个set）。 该方法的运算符版本是<set> & <other set> & <other set 2> & ... & <other set n>

>>> perennials = {'Annatto','Asafetida','Asparagus','Azalea',
                 'Winter Savory', 'Broccoli','Curry Leaf','Fennel', 
                 'Kaffir Lime','Kale','Lavender','Mint','Oranges',
                 'Oregano', 'Tarragon', 'Wild Bergamot'}

>>> annuals = {'Corn', 'Zucchini', 'Sweet Peas', 'Marjoram', 
              'Summer Squash', 'Okra','Shallots', 'Basil', 
              'Cilantro', 'Cumin', 'Sunflower', 'Chervil', 
              'Summer Savory'}

>>> herbs = ['Annatto','Asafetida','Basil','Chervil','Cilantro',
            'Curry Leaf','Fennel','Kaffir Lime','Lavender',
            'Marjoram','Mint','Oregano','Summer Savory', 
            'Tarragon','Wild Bergamot','Wild Celery',
            'Winter Savory']


# Methods will take any iterable as an argument.
>>> perennial_herbs = perennials.intersection(herbs)
{'Annatto', 'Asafetida', 'Curry Leaf', 'Fennel', 'Kaffir Lime',
 'Lavender', 'Mint', 'Oregano', 'Wild Bergamot','Winter Savory'}

# Operators require both groups be sets.
>>> annuals & set(herbs)
 {'Basil', 'Chervil', 'Marjoram', 'Cilantro'}

集合的对称差

<set>.symmetric_difference(<other iterable>)返回一个新的set，其中包含在<set>或<other>中，但不同时在两者中的元素。 该方法的运算符版本是<set> ^ <other set>。

>>> plants_1 = {'🌲','🍈','🌵', '🥑','🌴', '🥭'}
>>> plants_2 = ('🌸','🌴', '🌺', '🌲', '🌻', '🌵')


# Methods will take any iterable as an argument.
>>> fruit_and_flowers = plants_1.symmetric_difference(plants_2)
>>> fruit_and_flowers
{'🌸', '🌺', '🍈', '🥑', '🥭','🌻' }


# Operators require both groups be sets.
>>> fruit_and_flowers ^ plants_1
{'🌲',  '🌸', '🌴', '🌵','🌺', '🌻'}

>>> fruit_and_flowers ^ set(plants_2)
{'🥭', '🌴', '🌵', '🍈', '🌲', '🥑'}

>>> one = {'black pepper','breadcrumbs','celeriac','chickpea flour',
           'flour','lemon','parsley','salt','soy sauce',
           'sunflower oil','water'}

>>> two = {'black pepper','cornstarch','garlic','ginger',
           'lemon juice','lemon zest','salt','soy sauce','sugar',
           'tofu','vegetable oil','vegetable stock','water'}

>>> three = {'black pepper','garlic','lemon juice','mixed herbs',
             'nutritional yeast', 'olive oil','salt','silken tofu',
             'smoked tofu','soy sauce','spaghetti','turmeric'}

>>> four = {'barley malt','bell pepper','cashews','flour',
            'fresh basil','garlic','garlic powder', 'honey',
            'mushrooms','nutritional yeast','olive oil','oregano',
            'red onion', 'red pepper flakes','rosemary','salt',
            'sugar','tomatoes','water','yeast'}

>>> intersections = (one & two | one & three | one & four | 
                     two & three | two & four | three & four)
...
{'black pepper','flour','garlic','lemon juice','nutritional yeast', 
'olive oil','salt','soy sauce', 'sugar','water'}

# The ^ operation will include some of the items in intersections, 
# which means it is not a "clean" symmetric difference - there
# are overlapping members.
>>> (one ^ two ^ three ^ four) & intersections
{'black pepper', 'garlic', 'soy sauce', 'water'}

# Overlapping members need to be removed in a separate step
# when there are more than two sets that need symmetric difference.
>>> (one ^ two ^ three ^ four) - intersections
...
{'barley malt','bell pepper','breadcrumbs', 'cashews','celeriac',
  'chickpea flour','cornstarch','fresh basil', 'garlic powder',
  'ginger','honey','lemon','lemon zest','mixed herbs','mushrooms',
  'oregano','parsley','red onion','red pepper flakes','rosemary',
  'silken tofu','smoked tofu','spaghetti','sunflower oil', 'tofu', 
  'tomatoes','turmeric','vegetable oil','vegetable stock','yeast'}