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Nozibul Islam
Nozibul Islam

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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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Top comments (2)

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navneet_verma profile image
Navneet Verma

Nice collection! Appreciate it.

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nozibul_islam_113b1d5334f profile image
Nozibul Islam

Thank you.
There are more various DSA-related interview questions posted on this profile. Feel free to check them out if you'd like. I hope you find them helpful.