3.4 Sets

In Python, sets are a collection of unordered, unique elements. A set is similar to a list or a dictionary but does not allow duplicate values. Sets are commonly used when you need to store multiple items and want to ensure there are no duplicates.

1. What is a Set?

A set is an unordered collection of unique elements. The elements in a set are not indexed and cannot be accessed via an index or key, unlike lists or dictionaries. A set is useful when you need to store distinct values and perform set operations like union, intersection, and difference.

2. Creating a Set

You can create a set in Python using curly braces {} or the built-in set() function.

Examples:

# Creating a set using curly braces
my_set = {1, 2, 3, 4, 5}
print(my_set)  # Output: {1, 2, 3, 4, 5}

# Creating a set using the set() function
another_set = set([1, 2, 3, 4, 5])
print(another_set)  # Output: {1, 2, 3, 4, 5}

• A set does not allow duplicate elements. If you try to add duplicates, they will be ignored.

duplicate_set = {1, 2, 2, 3, 4}
print(duplicate_set)  # Output: {1, 2, 3, 4} (duplicates removed)

3. Accessing Elements in a Set

Since sets are unordered, they do not support indexing, slicing, or other sequence-like behavior. However, you can iterate over a set using loops (e.g., for loop).

Example:

# Iterating through a set
for element in my_set:
    print(element)

This will print each element in the set, but the order is not guaranteed.

4. Modifying a Set

Sets are mutable, meaning you can add or remove elements after they have been created.

Adding Elements:

You can add individual elements to a set using the add() method.

# Adding an element to a set
my_set.add(6)
print(my_set)  # Output: {1, 2, 3, 4, 5, 6}

To add multiple elements at once, use the update() method.

# Adding multiple elements
my_set.update([7, 8, 9])
print(my_set)  # Output: {1, 2, 3, 4, 5, 6, 7, 8, 9}

Removing Elements:

You can remove elements from a set using remove() or discard(). The remove() method raises an error if the element is not found, while discard() will not raise an error.

# Removing an element
my_set.remove(5)  # Removes 5
print(my_set)  # Output: {1, 2, 3, 4, 6, 7, 8, 9}

# Discarding an element (no error if not found)
my_set.discard(10)  # 10 is not in the set, so no error
print(my_set)  # Output: {1, 2, 3, 4, 6, 7, 8, 9}

If you want to remove and return an arbitrary element, use pop(). This is particularly useful when you don't care about which element is removed.

# Removing and returning an arbitrary element
element = my_set.pop()
print(element)  # Outputs the popped element
print(my_set)  # Output: remaining elements in the set

To clear all elements in a set, use the clear() method.

# Clearing all elements
my_set.clear()
print(my_set)  # Output: set() (empty set)

5. Set Operations

Python sets support several powerful operations, allowing you to perform various mathematical set operations such as union, intersection, difference, and symmetric difference.

Union (|)

The union of two sets is a set containing all elements from both sets, without duplicates.

set1 = {1, 2, 3}
set2 = {3, 4, 5}
union_set = set1 | set2
print(union_set)  # Output: {1, 2, 3, 4, 5}

Intersection (&)

The intersection of two sets is a set containing only the elements that are present in both sets.

set1 = {1, 2, 3}
set2 = {3, 4, 5}
intersection_set = set1 & set2
print(intersection_set)  # Output: {3}

Difference (-)

The difference of two sets is a set containing elements that are in the first set but not in the second.

set1 = {1, 2, 3}
set2 = {3, 4, 5}
difference_set = set1 - set2
print(difference_set)  # Output: {1, 2}

Symmetric Difference (^)

The symmetric difference of two sets is a set containing elements that are in either of the sets, but not in both.

set1 = {1, 2, 3}
set2 = {3, 4, 5}
symmetric_difference_set = set1 ^ set2
print(symmetric_difference_set)  # Output: {1, 2, 4, 5}

6. Set Membership

You can check if an element is a member of a set using the in keyword.

# Checking membership
print(3 in my_set)  # Output: True
print(10 in my_set)  # Output: False

7. Set Comprehension

Just like list comprehension, you can create sets using set comprehension. This provides a concise way to create sets based on existing iterables or conditions.

Example of set comprehension:

# Creating a set of squares of numbers
squares = {x**2 for x in range(5)}
print(squares)  # Output: {0, 1, 4, 9, 16}

8. Use Cases of Sets

Sets are useful in scenarios where:

• Unique elements are required (e.g., eliminating duplicates from a collection of data).
• Mathematical set operations (such as union, intersection, etc.) need to be performed efficiently.
• Fast membership testing is needed (i.e., checking if an item exists in a collection).
• Removing duplicates from a list or another iterable.

Summary of Sets in Python

• Unordered collection of unique elements.
• Supports set operations like union, intersection, difference, and symmetric difference.
• Provides methods for adding, removing, and updating elements.
• Allows efficient membership testing and is useful for mathematical and logical set operations.

Sets are a versatile data structure in Python, useful for handling collections of unique items and performing set-based operations.