Sets

Key Characteristics of Sets

1. Unordered: The elements of a set have no index and do not preserve insertion order.

s = {22, 25, 14, 21}
print(s)  
# Output order may vary

2. Unique Elements: Duplicates are removed automatically.

s = {25, 14, 98, 63, 75, 98}
print(s)
# {98, 25, 75, 14, 63}

3. No Indexing or Slicing: Sets are unordered, direct indexing is not allowed.

s[1]
# TypeError: 'set' object is not subscriptable

4. Hash-Based Storage: All elements must be immutable, enabling Python to assign a unique hash value for fast lookup.

Creating Sets

Standard Set

• A set is created using the {} braces in Python.

set1 = {23, 56, 78, 21}

Empty Set

Empty {} creates a dictionary, so use set():

set2 = set()
print(type(set2))   # <class 'set'>

Basic Operations with Sets

1. Membership Test

Extremely fast due to hashing.

21 in set1    # True
50 in set1    # False

2. Size of Set

len(set1)     # 4

Adding & Removing Elements

Sets support limited but efficient modification operations:

add() — Add a single element

s = {10, 20}
s.add(30)
print(s)   # {10, 20, 30}

update() — Add multiple elements

s.update([40, 50])
print(s)   # {10, 20, 30, 40, 50}

remove() — Removes a specific element (error if not found)

s.remove(20)
print(s)   # {10, 30, 40, 50}

discard() — Same as remove but no error if element missing

s.discard(100)   # No error

pop() — Removes an arbitrary element

s.pop()   # Removes a random element (since no indexing)

clear() — Remove all elements

s.clear()
# Result: set()

Mathematical Set Operations

Given:

A = set("abcdmnop")
B = set("aeioupd")

1. Difference (A – B)

Elements in A not in B:

A - B
# {'m', 'n', 'c', 'b'}

2. Union (A | B)

All unique elements from both sets:

A | B
# {'a','b','c','d','e','i','m','n','o','p','u'}

3. Intersection (A & B)

Elements common to both sets:

A & B
# {'a', 'o', 'p', 'd'}

4. Symmetric Difference (A ^ B)

Elements not common (unique to each set):

A ^ B
# {'u', 'e', 'm', 'i', 'c', 'n'}

Why Sets Are Fast?

Because of hashing, which allows:

• O(1) membership testing (in)
• Efficient union/intersection operations
• Automatic uniqueness handling

This makes sets ideal for large datasets where performance matters.

Usage of Sets

Use a set when:

• You need unique elements with no duplicates
• The order of elements is not important
• You require fast membership testing
• You need to perform mathematical operations like union/intersection
• You want to remove duplicates from a list quickly
• You want efficient comparisons between collections

Summary

• A set is an unordered, mutable, hash-based collection of unique items.
• No indexing or slicing is possible due to lack of order.
• Ideal for fast membership testing, duplicate removal, and mathematical set operations.
• Supports operations like add(), update(), remove(), discard(), and mathematical operators (-, |, &, ^).