DSA: Heap - Key Questions and Challenges

DSA: Heap - Key Questions and Challenges

1. Basic Heap Operations

• Implement a Min Heap
• Implement a Max Heap
• Insert an Element into a Min Heap
• Insert an Element into a Max Heap
• Delete the Minimum Element from a Min Heap
• Delete the Maximum Element from a Max Heap
• Peek the Minimum Element in a Min Heap
• Peek the Maximum Element in a Max Heap
• Heapify an Array (Build a Heap)
• Convert an Array into a Min Heap or Max Heap

2. Heap Construction and Maintenance

• Convert a Min Heap to a Max Heap
• Convert a Max Heap to a Min Heap
• Implement Heap Sort (Ascending and Descending Order)
• Decrease Key in a Min Heap
• Increase Key in a Max Heap
• Find the Kth Largest Element in an Array (Using a Max Heap)
• Find the Kth Smallest Element in an Array (Using a Min Heap)
• Merge K Sorted Lists (Using a Min Heap)
• Merge K Sorted Arrays (Using a Min Heap)
• K Closest Points to the Origin (Using a Min Heap)

3. Heap-Based Problem Solving

• Top K Frequent Elements (Using a Min Heap)
• Find Median of a Stream of Integers (Using Two Heaps)
• Sliding Window Maximum (Using a Double-Ended Queue or Heap)
• Kth Largest Element in a Stream (Using a Min Heap)
• Kth Smallest Element in a Stream (Using a Max Heap)
• Shortest Path in a Weighted Graph (Dijkstra’s Algorithm with a Min Heap)
• Find the Range of a Given Subarray with Minimum Sum (Using a Min Heap)
• Find the Median of a Set of Numbers (Using Two Heaps)
• Longest Subarray with Sum Less Than K (Using a Min Heap)
• Reconstruct a Heap from a Given Set of Values

4. Advanced Heap Problems

• Find All Valid Combinations with Sum Equal to Target (Using a Min Heap)
• Implement a Priority Queue Using Heaps
• Find the Maximum Sum of a Subarray of Size K (Using a Max Heap)
• Find the Maximum Sum of k Non-Overlapping Subarrays (Using a Max Heap)
• Heap-Based Approach to Solve Job Scheduling Problems
• Implement a Median Maintenance Algorithm (Using Two Heaps)
• Find Top K Elements in a Matrix (Using a Min Heap)
• Sort K-Sorted Array (Using a Min Heap)
• Rearrange Characters in a String so No Two Adjacent Characters are the Same (Using a Max Heap)
• Implement a Heap-Based Algorithm to Solve the Traveling Salesman Problem (Approximate Solution)

5. Heap Applications in Graph Algorithms

• Implement Prim’s Algorithm for Minimum Spanning Tree (Using a Min Heap)
• Implement Kruskal’s Algorithm for Minimum Spanning Tree (Using Union-Find and Min Heap)
• Find the Shortest Path in a Graph with Non-Negative Weights (Using Dijkstra’s Algorithm with a Min Heap)
• Find the Longest Path in a Graph with Positive Weights (Using a Max Heap)
• Compute the Minimum Cost Path in a Weighted Grid (Using a Min Heap)
• Find All Pair Shortest Paths (Using Floyd-Warshall with Heap Optimization)
• Implement A* Search Algorithm (Using a Min Heap)
• Compute the Shortest Path Tree from a Source Node (Using Dijkstra’s Algorithm with a Min Heap)
• Find the Most Frequent Path in a Graph (Using a Max Heap)
• Compute the Minimum Cost to Connect All Nodes (Using Prim’s Algorithm with a Min Heap)

6. Additional Key Questions:

• How does a Fibonacci Heap improve certain operations?
• Implement a heap to solve real-time stream processing challenges.
• Use heaps for efficient skyline problems.
• Solve interval scheduling and meeting room allocation with heaps.
• Apply heap-based techniques for topological sorting.

This expanded list provides a detailed roadmap for understanding, implementing, and solving complex problems using heaps, making it a vital resource for mastering this data structure.

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