A set is a collection of unique, unordered elements that supports fast membership testing and set operations. This post introduces sets in Python, their properties, common operations, and provides practical examples and problems for understanding their use cases.

Set

Overview

A set is a collection of unique, unordered elements. In Python, it is implemented using a hash table.

No duplicate elements
Fast lookup, add, and remove (average O(1) time)

🧩 Visualizing Sets

Set Operations

Set A: {1, 2, 3, 4}
Set B: {3, 4, 5, 6}

Union (A ∪ B):        {1, 2, 3, 4, 5, 6}
Intersection (A ∩ B): {3, 4}
Difference (A - B):   {1, 2}
Symmetric Diff (A⊕B): {1, 2, 5, 6}

Sets automatically remove duplicates and maintain uniqueness.

🛠️ How to Use (Python)

# Basic set operations in Python
- Create a set, add/remove elements, check membership, set operations
s = set()
s.add(3)                # Add 3 to the set
s.add(5)                # Add 5 to the set
s.remove(3)             # Remove 3 from the set
print(5 in s)           # Check if 5 is in the set (prints True)
s2 = {1, 2, 5}
s.union(s2)             # Union: {1, 2, 5, 9, 3, 4}
s.intersection(s2)      # Intersection: {5}
# Most set operations are O(1) on average

# Example:
s = {1, 2, 3}
s.add(4)
print(3 in s)  # Output: True
print(s)       # Output: {1, 2, 3, 4}

🧩 Contains Duplicate Step-by-Step

Suppose nums = [1, 2, 3, 1]

Step	num	num in seen	seen set	Action
1	1	False	{}	Add 1
2	2	False	{1}	Add 2
3	3	False	{1, 2}	Add 3
4	1	True	{1, 2, 3}	Return True

Found duplicate 1, return True.

📘 Sample Problem 1: Contains Duplicate

Given a list of numbers, return True if any value appears at least twice.

# This function checks if there are any duplicate numbers in the list.
def contains_duplicate(nums):
    seen = set()  # Set to keep track of seen numbers
    for num in nums:
        if num in seen:
            return True  # Found a duplicate
        seen.add(num)
    return False  # No duplicates found
# Time complexity: O(n), Space complexity: O(n)

# Example:
nums = [1, 2, 3, 1]
print(contains_duplicate(nums))  # Output: True

🧩 Longest Consecutive Sequence Flow

Suppose nums = [100, 4, 200, 1, 3, 2]

Convert to set: {100, 4, 200, 1, 3, 2}
For each number, check if it’s the start of a sequence:

num	num-1 in set?	Sequence Start	Length	Longest
100	False	Yes	1	1
4	True	No	-	1
200	False	Yes	1	1
1	False	Yes	1,2,3,4	4
3	True	No	-	4
2	True	No	-	4

Longest consecutive sequence: [1, 2, 3, 4] with length 4.

📘 Sample Problem 2: Longest Consecutive Sequence

Given an unsorted array, find the length of the longest consecutive elements sequence.

# This function finds the length of the longest sequence of consecutive numbers in the list.
def longest_consecutive(nums):
    num_set = set(nums)  # Convert list to set for O(1) lookups
    longest = 0

    for num in num_set:
        if num - 1 not in num_set:  # Start of a sequence
            length = 1
            while num + length in num_set:
                length += 1
            longest = max(longest, length)

    return longest
# Time complexity: O(n), Space complexity: O(n)

# Example:
nums = [100, 4, 200, 1, 3, 2]
print(longest_consecutive(nums))  # Output: 4 (sequence: 1,2,3,4)

Set Overview

Set