Python dan teori himpunan

Python memiliki tipe data yang sangat berguna untuk bekerja dengan set - set . Jenis data ini, contoh penggunaan, dan kutipan singkat dari teori himpunan akan dibahas nanti.

Reservasi harus dibuat segera bahwa artikel ini sama sekali tidak berpura-pura menjadi ketelitian dan kelengkapan matematis, melainkan, ini adalah upaya untuk menunjukkan dengan cara yang dapat diakses contoh penggunaan set dalam bahasa pemrograman Python.

– , , , - , . :

– .

? , , .

, . , , .

, , , – . , , . 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"}

Kesimpulan

Saya harap saya bisa menunjukkan bahwa Python memiliki alat bawaan yang sangat bagus untuk bekerja dengan set. Dalam praktiknya, hal ini sering kali memungkinkan Anda untuk mengurangi jumlah kode, membuatnya lebih ekspresif dan lebih mudah dipahami, dan karenanya lebih mudah dipelihara. Saya akan senang jika Anda memiliki komentar dan tambahan yang membangun.

link yang berguna

Set (Artikel Wikipedia)

Jenis dokumentasi untuk himpunan

Iterabel (Daftar Istilah Python)

Objek hashable (Daftar Istilah Python)

Set dalam Teori Himpunan Python

: Metode Ke Madness Database

Python dan teori himpunan

Python dan teori himpunan

Python

Kesimpulan

link yang berguna

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