集合 是一種 可變 且 無序 的群組，用來存放 可雜湊 的物件。
集合的成員必須互不相同，不允許有重複的項目。
它們可以存放多種不同的資料型態，甚至可以存放像由 tuples 組成的 tuple 這類巢狀結構，只要其中所有元素都能被_雜湊_即可。
集合還有不可變的 frozensets 版本。
集合最常被用來快速移除其他資料結構或項目分組中的重複項。
當不需要排序與追蹤重複項時，集合也很適合用來進行高效率的比較。
和其他集合型別（字典、陣列、元組）一樣，set 支援：
- 透過
for item in <set> 進行疊代
- 透過
in 和 not in 檢查成員資格，
- 透過
len() 計算長度，以及
- 透過
copy() 建立淺拷貝
sets 不支援：
- 任何形式的索引
- 透過排序或插入來決定順序
- 切片
- 透過
+ 串接
檢查 set 中是否包含某個元素，平均而言具有常數時間複雜度；相對地，檢查 list 或 string 中的成員時，時間複雜度會隨著資料長度增加而成長。
像 <set>.union()、<set>.intersection() 或 <set>.difference() 這些方法，平均而言也具有常數時間複雜度。
集合字面值
set 可以直接以 集合字面值 的形式建立，使用大括號{}，並以逗號分隔各元素。
重複的項目會被默默省略：
>>> 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!'}
集合字面值使用與 dict 字面值相同的大括號，因此你必須使用 set() 才能建立空的 set。
集合建構子
set()（set 類別的建構子）可以接受任何 iterable 作為引數。
iterable 的元素會被逐一走訪，並個別加入 set 中。
元素的順序不會被保留，重複的項目則會被默默省略：
# 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}
建立集合時的陷阱
因為它具有「展開」的行為，把字串傳給 set() 可能會出乎意料：
# 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', 'ा', '्'}
集合可以存放不同的資料型態與_巢狀_資料型態，但所有 set 元素都必須是_可雜湊_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'
操作集合
集合有一些方法，大致上模仿了數學集合運算。
這些方法大多（但並非全部）都有對應的運算子。
方法通常可以接受任何 iterable 作為引數，而運算子則要求運算的兩邊都是 sets 或 frozensets。
不相交集合
<set>.isdisjoint(<other_collection>) 方法用來測試某個集合的元素是否與另一個集合的元素有任何重疊。
這個方法可以接受任何 iterable 或 set 作為引數。
如果兩個集合沒有共同元素，它會回傳 True；如果元素有共用，則回傳 False。
它沒有對應的運算子：
# 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
子集合與超集合
<set>.issubset(<other_collection>) 用來檢查 <set> 中的每個元素是否也都在 <other_collection> 中。
運算子的形式是 <set> <= <other_set>：
# 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'}
# 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>) 是 .issubset() 的反操作。
它用來檢查 <other_collection> 中的每個元素是否也都在 <set> 中。
運算子的形式是 <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
集合交集
<set>.intersection(*<other iterables>) 會回傳一個新的 set，其中包含原始 set 與所有 <others> 共有的元素（換句話說，就是所有元素都相交的那個 set）。
這個方法的運算子版本是 <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'}
集合聯集
<set>.union(*<other iterables>) 會回傳一個新的 set，其中包含來自 <set> 以及所有 <other iterables> 的元素。
這個方法的運算子形式是 <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'}
集合差集
<set>.difference(*<other iterables>) 會回傳一個新的 set，其中包含原始 <set> 中不在 <others> 裡的元素。
這個方法的運算子版本是 <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'}
<set>.symmetric_difference(<other iterable>) 會回傳一個新的 set，其中包含在 <set> 或 <other> 中、但不同時存在於兩者的元素。
這個方法的運算子版本是 <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)
{'🥭', '🌴', '🌵', '🍈', '🌲', '🥑'}
超過兩個集合的對稱差集，會產生一個 set，其中同時包含每個 set 各自獨有的元素，以及序列中超過兩個集合之間共用的元素（詳情請見維基百科上關於對稱差集的文章）。
若只想取得序列中每個 set 獨有的項目，則需要在另一個步驟中彙整所有兩兩集合組合之間的交集，並將其移除：
>>> 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'}
學習練習
