Advanced Sets

Set operations, frozenset, set comprehensions, and mathematical operations.

Overview

Master advanced set operations.

Set Operations

A = {1, 2, 3, 4, 5}
B = {4, 5, 6, 7, 8}

# Union (all elements)
print(A | B)  # {1, 2, 3, 4, 5, 6, 7, 8}
print(A.union(B))

# Intersection (common elements)
print(A & B)  # {4, 5}
print(A.intersection(B))

# Difference (elements in A not in B)
print(A - B)  # {1, 2, 3}
print(A.difference(B))

# Symmetric difference (elements in either but not both)
print(A ^ B)  # {1, 2, 3, 6, 7, 8}
print(A.symmetric_difference(B))

# Subset and superset
print({1, 2} <= {1, 2, 3})  # True (subset)
print({1, 2, 3} >= {1, 2})  # True (superset)

Frozenset

# Immutable set
fs = frozenset([1, 2, 3, 4, 5])

# Can be used as dictionary key
d = {frozenset([1, 2]): "pair", frozenset([3, 4]): "another pair"}

# Can be element of another set
nested = {frozenset([1, 2]), frozenset([3, 4])}

Set Comprehensions

# Create set from comprehension
squares = {x**2 for x in range(10)}
print(squares)  # {0, 1, 4, 9, 16, 25, 36, 49, 64, 81}

# Filter with condition
evens = {x for x in range(20) if x % 2 == 0}
print(evens)  # {0, 2, 4, 6, 8, 10, 12, 14, 16, 18}

# Transform
words = ["hello", "world", "python"]
unique_chars = {char for word in words for char in word}
print(unique_chars)  # {'h', 'e', 'l', 'o', 'w', 'r', 'd', 'p', 'y', 't', 'n'}

Practice

Find common elements between multiple lists using sets.