**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)

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