بايثون ونظرية المجموعات

لدى Python نوع بيانات مفيد جدًا للعمل مع المجموعات - set . هذا النوع من البيانات ، وأمثلة للاستخدام ، ومقتطف قصير من نظرية المجموعات ستتم مناقشته لاحقًا.

يجب أن يتم التحفظ على الفور بأن هذه المقالة لا تدعي بأي شكل من الأشكال أنها دقة رياضية واكتمال ؛ بدلاً من ذلك ، هذه محاولة لإثبات بطريقة يسهل الوصول إليها أمثلة لاستخدام المجموعات في لغة برمجة بايثون.

– , , , - , . :

– .

? , , .

, . , , .

, , , – . , , . Python, .

Python

Python . – :

fruits = {"banana", "apple", "orange"}

, . :

wrong_empty_set = {}
print(type(wrong_empty_set))

# 
<class "dict">

set():

correct_empty_set = set()
print(type(correct_empty_set))

# 
<class "set">

set() - , (Iterable):

color_list = ["red", "green", "green", "blue", "purple", "purple"]
color_set = set(color_list)
print(color_set)

#  (   ):
{"red", "purple", "blue", "green"}

– set comprehension. , list comprehension ( ).

numbers = [1, 2, 2, 2, 3, 3, 4, 4, 5, 6]

#      - 
#     
even_numbers = {
    number for number in numbers
    if number % 2 == 0
}
print(even_numbers)

#  (   ):
{2, 4, 6}

, ( ) Python (Hashable) . , set -. , – , . Python (int, float, str, bool, ..) – . , tuple, , .

#   (tuple)
records = {
    ("", 17_200_000), 
    ("-", 5_400_000), 
    ("", 1_600_000),
    ("", 17_200_000),
}

for city, population in records:
    print(city)

#  (   ):


-

. - , , .. "" .

class City:
    def __init__(self, name: str):
        self.name = name

    def __repr__(self) -> str:
        """   __repr__    
        """
        return f'City("{self.name}")'

print(City("Moscow") == City("Moscow"))

# :
False

cities = {City("Moscow"), City("Moscow")}
print(cities)

# 
{City("Moscow"), City("Moscow")}

, City("Moscow") , cities .

, City:

class City:
    def __init__(self, name: str):
        #  name   ,   
        #       
        self._name = name

    def __hash__(self) -> int:
        """   
        """
        return hash((self._name, self.__class__))

    def __eq__(self, other) -> bool:
        """    ( ==)
        """
        if not isinstance(other, self.__class__):
            return False
        return self._name == other._name

    def __repr__(self) -> str:
        """   __repr__    
        """
        return f'City("{self._name}")'

, :

moscow = City("Moscow")
moscow_again = City("Moscow")

print(moscow == moscow_again and hash(moscow) == hash(moscow_again))
# :
True

#        
cities = {City("Moscow"), City("Kazan"), City("Moscow")}
print(cities)

#  (   ):
{City("Kazan"), City("Moscow")}

set Python Collection ( ), :

iterable-

- in. . O(1) , -.

tremendously_huge_set = {"red", "green", "blue"}

if "green" in tremendously_huge_set:
    print("Green is there!")
else:
    print("Unfortunately, there is no green...")

# :
Green is there!

if "purple" in tremendously_huge_set:
    print("Purple is there!")
else:
    print("Unfortunately, there is no purple...")

# :
Unfortunately, there is no purple...

– , . .

even_numbers = {i for i in range(100) if i % 2 == 0}

#  
cardinality = len(even_numbers)
print(cardinality)

# :
50

, , , iterable-.

colors = {"red", "green", "blue"}

#        for
for color in colors:
    print(color)

#  (   ):
red
green
blue

#    ,   iterable-
color_counter = dict.fromkeys(colors, 1)
print(color_counter)

#  (   ):
{"green": 1, "red": 1, "blue": 1}

, . .

– , . , .

my_fruits = {"banana", "apple", "orange", "orange"}
your_fruits = {"apple", "apple", "banana", "orange", "orange"}
print(my_fruits == your_fruits)

# :
True

, , . , .

even_numbers = {i for i in range(10) if i % 2 == 0}
odd_numbers = {i for i in range(10) if i % 2 == 1}

# ,        
if even_numbers.isdisjoint(odd_numbers):
    print("  !")

# :
  !

S – , S. S .

#     100
fibonacci_numbers = {0, 1, 2, 3, 34, 5, 8, 13, 21, 55, 89}

#     100
natural_numbers = set(range(100))

#       
#  
if fibonacci_numbers.issubset(natural_numbers):
    print("!")

# :
!

#       
#    
if natural_numbers.issuperset(fibonacci_numbers):
    print("!")

# :
!

empty = set()

#  issubset  issuperset    iterable-
print(
    empty.issubset(range(100))
    and empty.issubset(["red", "green", "blue"])
    and empty.issubset(set())
)

# :
True

natural_numbers = set(range(100))

if natural_numbers.issubset(natural_numbers):
    print("!")

# :
!

, .

– , . Python , .

my_fruits = {"apple", "orange"}
your_fruits = {"orange", "banana", "pear"}

#       `|`,
#       set
our_fruits = my_fruits | your_fruits
print(our_fruits)

#  (   ):
{"apple", "banana", "orange", "pear"}

#     union.
#    ,   union   
#   set,   iterable-
you_fruit_list: list = list(your_fruits)
our_fruits: set = my_fruits.union(you_fruit_list)
print(our_fruits)

#  (   ):
{"apple", "banana", "orange", "pear"}

, , . O(1).

colors = {"red", "green", "blue"}

#  add     
colors.add("purple")
#  ,     ,  
#  
colors.add("red")
print(colors)

#  (   ):
{"red", "green", "blue", "purple"}

#  update  iterable- (, ,   ..)
#      
numbers = {1, 2, 3}
numbers.update(i**2 for i in [1, 2, 3])
print(numbers)

#  (   ):
{1, 2, 3, 4, 9}

– , , .

def is_prime(number: int) -> bool:
    """  True,  number -   
    """
    assert number > 1
    return all(number % i for i in range(2, int(number**0.5) + 1))

def is_fibonacci(number: int) -> bool:
    """  True,  number -   
    """
    assert number > 1
    a, b = 0, 1
    while a + b < number:
        a, b = b, a + b
    return a + b == number

#     100
primes = set(filter(is_prime, range(2, 101)))

#     100
fibonacci = set(filter(is_fibonacci, range(2, 101)))

#     100,   
#  
prime_fibonacci = primes.intersection(fibonacci)

#    `&`,    
prime_fibonacci = fibonacci & primes

print(prime_fibonacci)

#  (   ):
{2, 3, 5, 13, 89}

& , set. intersection, , iterable-. , , intersection_update, intersection, -.

– , , .

i_know: set = {"Python", "Go", "Java"}
you_know: dict = {
    "Go": 0.4, 
    "C++": 0.6, 
    "Rust": 0.2, 
    "Java": 0.9
}

#  ,   `-`  
#    set
you_know_but_i_dont = set(you_know) - i_know
print(you_know_but_i_dont)

#  (   ):
{"Rust", "C++"}

#  difference     iterable-,
#   dict, 
i_know_but_you_dont = i_know.difference(you_know)
print(i_know_but_you_dont)

# :
{"Python"}

, – . , , , . O(1).

fruits = {"apple", "orange", "banana"}

#    .   
#   ,    
fruits.discard("orange")
fruits.discard("pineapple")
print(fruits)

#  (   ):
{"apple", "banana"}

#  remove   discard,   ,
#      
fruits.remove("pineapple")  # KeyError: "pineapple"

differene_update, iterable- iterable-. difference, , .

numbers = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
even_numbers_under_100 = (i for i in range(1, 101) if i % 2 == 0)
numbers.difference_update(even_numbers_under_100)
print(numbers)

#  (   ):
{1, 3, 5, 7, 9}

– , , . .

non_positive = {-3, -2, -1, 0}
non_negative = {0, 1, 2, 3}

#  ,   `^`  
#     set
non_zero = non_positive ^ non_negative
print(non_zero)

#  (   ):
{-1, -2, -3, 1, 2, 3}

, 0 , . , ^, – symmetric_difference symmetric_difference_update. iterable- , , symmetric_difference -, symmetric_difference_update .

non_positive = {-3, -2, -1, 0}
non_negative = range(4)

non_zero = non_positive.symmetric_difference(non_negative)
print(non_zero)

#  (   ):
{-1, -2, -3, 1, 2, 3}

#  symmetric_difference_update   
colors = {"red", "green", "blue"}
colors.symmetric_difference_update(["green", "blue", "yellow"])
print(colors)

#  (   ):
{"red", "yellow"}

خاتمة

آمل أن أكون قادرًا على إظهار أن لغة Python لديها أدوات مضمنة لطيفة جدًا للعمل مع المجموعات. من الناحية العملية ، يسمح لك هذا غالبًا بتقليل مقدار الكود ، وجعله أكثر تعبيرًا وأسهل في الفهم ، وبالتالي أكثر قابلية للصيانة. سأكون سعيدًا إذا كان لديك أي تعليقات وإضافات بناءة.

روابط مفيدة

مجموعات (مقالة ويكيبيديا)

اكتب التوثيق لمجموعة

Iterables (Python Glossary)

كائنات قابلة للتجزئة (Python Glossary)

مجموعات في Python

Set Theory: the Method To Database Madness

بايثون ونظرية المجموعات

بايثون ونظرية المجموعات

Python

خاتمة

روابط مفيدة

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