What is the difference between set and frozenset?

set:

• A mutable unordered collection of unique elements.
• Supports adding and removing elements.
• Cannot be used as a dictionary key or element of another set.

colors = {"red", "green", "blue"}
colors.add("yellow")
colors.discard("red")

frozenset:

• An immutable version of a set.
• Does not support adding or removing elements.
• Is hashable — can be used as a dictionary key.

immutable_set = frozenset([1, 2, 3])
# immutable_set.add(4)  # AttributeError

# frozenset as a dictionary key
cache = {frozenset([1, 2]): "result"}

Common set operations:

a = {1, 2, 3, 4}
b = {3, 4, 5, 6}

a | b   # Union: {1, 2, 3, 4, 5, 6}
a & b   # Intersection: {3, 4}
a - b   # Difference: {1, 2}
a ^ b   # Symmetric difference: {1, 2, 5, 6}

In practice:

set is used for fast deduplication and membership checks (in runs in O(1)). frozenset is needed when a set must serve as a dictionary key or an element of another set.