Python Sets

1. What is a Set?

A set is an unordered collection data type that is iterable, mutable, and contains no duplicate elements. Python sets are based on the mathematical concept of sets.

Key characteristics of a Python set:

• Unordered
• Mutable (except frozen sets)
• Does not allow duplicates
• Supports mathematical operations

2. Creating Sets

Sets are created using curly braces {} or the built-in set() function.

Example:

# Creating a set using curly braces
my_set = {1, 2, 3, 4}
print(my_set)  # Output: {1, 2, 3, 4}

# Creating a set from a list
my_list = [1, 2, 2, 3, 4, 4]
unique_set = set(my_list)
print(unique_set)  # Output: {1, 2, 3, 4}

# Creating an empty set
empty_set = set()
print(type(empty_set))  # Output: <class 'set'>

Note: {} creates an empty dictionary, not an empty set. Always use set() to create an empty set.

3. Set Operations

Python supports several useful set operations that mimic mathematical sets:

Union (| or .union())

Combines all elements from two sets, removing duplicates.

A = {1, 2, 3}
B = {3, 4, 5}

# Using operator |
print(A | B)  # {1, 2, 3, 4, 5}

# Using .union()
print(A.union(B))  # {1, 2, 3, 4, 5}

Intersection (& or .intersection())

Returns elements common to both sets.

# Using operator &
print(A & B)  # {3}

# Using .intersection()
print(A.intersection(B))  # {3}

Difference (- or .difference())

Returns elements present in the first set but not in the second.

# Using operator -
print(A - B)  # {1, 2}

# Using .difference()
print(A.difference(B))  # {1, 2}

Symmetric Difference (^ or .symmetric_difference())

Returns elements in either set but not in both.

# Using operator ^
print(A ^ B)  # {1, 2, 4, 5}

# Using .symmetric_difference()
print(A.symmetric_difference(B))  # {1, 2, 4, 5}

4. Modifying Sets

Sets are mutable, allowing you to add or remove elements.

Adding Elements (.add())

my_set = {1, 2, 3}
my_set.add(4)
print(my_set)  # {1, 2, 3, 4}

Removing Elements (.remove() and .discard())

• .remove(element) removes the element if it exists, raises an error otherwise.
• .discard(element) removes the element if it exists, does nothing otherwise.

my_set.remove(2)
print(my_set)  # {1, 3, 4}

my_set.discard(5)  # No error even if element doesn't exist

Pop Elements (.pop())

Removes and returns an arbitrary element from the set.

element = my_set.pop()
print(element)
print(my_set)

Clearing Sets (.clear())

Empties the set entirely.

my_set.clear()
print(my_set)  # set()

5. Set Methods Summary

6. Frozen Sets

A frozenset is an immutable version of a set. Once created, its elements cannot be changed. Frozen sets are useful for using sets as keys in dictionaries or elements of other sets.

Example:

my_frozen_set = frozenset([1, 2, 3])
print(my_frozen_set)  # frozenset({1, 2, 3})

# my_frozen_set.add(4)  # Raises AttributeError: 'frozenset' object has no attribute 'add'

7. Set Comprehensions

Python supports set comprehensions for concise set creation.

squares = {x * x for x in range(1, 6)}
print(squares)  # {1, 4, 9, 16, 25}

8. Practical Examples with Sets

Eliminate duplicates from a list:

duplicates = [1, 2, 3, 2, 1, 5, 5]
unique_items = list(set(duplicates))
print(unique_items)  # [1, 2, 3, 5]

Check membership quickly:

my_set = {1, 2, 3, 4}
print(2 in my_set)  # True
print(5 in my_set)  # False