Sets
Unique collections with fast membership testing
What Makes Sets Special
Sets store unique elements with O(1) membership testing. Unlike arrays, adding a duplicate has no effect. Sets shine for deduplication, quick lookups, and mathematical set operations.
Use Sets For:
- • Removing duplicates from a list
- • Fast membership checking (is X in the set?)
- • Finding common elements between groups
- • Tracking unique visitors/items
Set Operations:
- • Union: All elements from both sets
- • Intersection: Elements in both sets
- • Difference: Elements in A but not B
- • Symmetric: Elements in one but not both
Venn Diagram Visualization
Set A
1
2
3
4
5
Set B
4
5
6
7
8
Complexity Analysis
| Operation | Average | Notes |
|---|---|---|
| Add | O(1) | Duplicates ignored |
| Has (membership) | O(1) | Much faster than array includes |
| Delete | O(1) | No shifting needed |
| Union/Intersection | O(n) | Must iterate through sets |