Module Review: Heaps
You’ve mastered priority. From sorting in O(N log N) to finding shortest paths.
1. Key Takeaways
- Structure: Complete Binary Tree stored as an Array.
- Property: Parent is always smaller (Min Heap) or larger (Max Heap) than children.
- Efficiency: Insert and Remove Min/Max are O(log N).
- Applications:
- Priority Queue: Task scheduling.
- Dijkstra: Shortest Path in Graphs.
- Median: Two Heaps pattern.
2. Cheat Sheet
| Operation | Time Complexity | Note |
|---|---|---|
| Insert | O(log N) | Sift Up. |
| Remove Min/Max | O(log N) | Swap with last, Sift Down. |
| Peek | O(1) | Root is always at index 0. |
| Heapify | O(N) | Build heap from array. |
| Heap Sort | O(N log N) | In-place, not stable. |
3. Interactive Flashcards
What is the index of the Left Child of node `i` in an array-based heap?
`2 * i + 1`.
What is the Time Complexity of Heapify (building a heap from scratch)?
O(N). Not O(N log N).
Which data structure does Dijkstra's Algorithm use to select the next node?
Min Priority Queue (Min Heap).
In the Two Heaps pattern for Median, what does the Max Heap store?
The smaller half of the numbers.
4. Next Steps
Next Module: Hashing - O(1) lookups and the magic of Hash Maps.
DSA Glossary
Module Review: Heaps
[!NOTE] This module explores the core principles of Module Review: Heaps, deriving solutions from first principles and hardware constraints to build world-class, production-ready expertise.
1. Practice in the Vault
Looking to solidify your understanding? Head over to the Problem Vault to solve curated problems related to this module with detailed walkthroughs and optimal solutions.