Using Frozen Sets in Python

A frozen set in Python is an unordered and immutable collection of unique elements. It behaves similarly to a set (set), but cannot be modified once created.

That is, once created, we cannot add or remove elements, nor modify the existing ones. Attempting to add, remove, or modify elements will raise an error.

Just like set, frozenset can only contain unique elements. Duplicate elements are automatically removed.

Also, like set, the elements within a frozenset do not have a specific order. Elements cannot be accessed by index, unlike lists.

Frozen sets are useful when a collection of unique elements is needed that will not be modified during the program’s execution. For example, as keys in a dictionary or to be included in other sets, as both require hashable and immutable values.

Creating Frozen Sets

Frozen sets are created using the frozenset() function and can contain elements of any hashable type.

# Create a frozenset from a list
immutable_set = frozenset([1, 2, 3, 4, 5])
print(immutable_set)  # Output: frozenset({1, 2, 3, 4, 5})

# Create a frozenset from a list of strings
fruits = frozenset(["apple", "banana", "orange"])

print(fruits)  # Output: frozenset({'apple', 'banana', 'orange'})

# Create a frozenset from a set
mutable_set = {1, 2, 3, 4, 5}
immutable_set = frozenset(mutable_set)
print(immutable_set)  # Output: frozenset({1, 2, 3, 4, 5})

# Create a frozenset from a string
immutable_set = frozenset('python')
print(immutable_set)  # Output: frozenset({'p', 'y', 't', 'h', 'o', 'n'})

Operations with FrozenSet

Despite their immutability, frozenset allows several set operations such as union, intersection, and difference.

# Create two frozensets
set_a = frozenset([1, 2, 3])
set_b = frozenset([3, 4, 5])

# Union of frozensets
union_set = set_a | set_b
print(union_set)  # Output: frozenset({1, 2, 3, 4, 5})

# Intersection of frozensets
intersection_set = set_a & set_b
print(intersection_set)  # Output: frozenset({3})

# Difference of frozensets
difference_set = set_a - set_b
print(difference_set)  # Output: frozenset({1, 2})

# Symmetric difference of frozensets
symmetric_difference_set = set_a ^ set_b
print(symmetric_difference_set)  # Output: frozenset({1, 2, 4, 5})

# Check if frozenset is a subset
isSubset = frozenset([3, 4]) < set_b
print(isSubset)  # True

Although frozenset allows basic set operations, it does not support methods that modify the set, such as add(), remove(), or discard().

Common Uses of frozenset

As Keys in Dictionaries

Since frozenset are hashable and immutable, they can be used as keys in dictionaries.

# Use a frozenset as a key in a dictionary
dictionary = {frozenset([1, 2, 3]): "value1", frozenset([4, 5, 6]): "value2"}

print(dictionary[frozenset([1, 2, 3])])  # Output: value1

Elements of Other Sets

frozenset can be elements of other sets, which is not possible with mutable sets.

# Use frozensets as elements of a set
set_of_frozensets = {frozenset([1, 2]), frozenset([3, 4])}

print(set_of_frozensets)  # Output: {frozenset({1, 2}), frozenset({3, 4})}