📚 Heap Tree in Data Structures

 Follow Me

A Heap Tree is a complete binary tree that satisfies the heap property:

• Complete Binary Tree: All levels are filled except possibly the last, and the last level has all keys as left as possible.

• Heap Property:

  • In a Max Heap, the parent node ≥ child nodes.

  • In a Min Heap, the parent node ≤ child nodes.

🔧 Types of Heap Tree:

Type	Property	Root Node	Usage
Max Heap	Parent ≥ Children	Maximum	Priority Queues, Sorting (Heap Sort)
Min Heap	Parent ≤ Children	Minimum	Dijkstra’s Algorithm, Huffman Coding

🔢 Example (Min Heap):

10 / \ 20 15 / \ / 30 40 50

⚙️ Basic Operations:

Operation	Description	Time Complexity
Insertion()	Add element and heapify up	O(log n)
Deletion()	Remove root and heapify down	O(log n)
Peek()	Get root element (max/min)	O(1)
Heapify()	Convert array into heap	O(n)

✅ Applications of Heap Tree

• Priority Queue implementation

• Heap Sort algorithm

• Graph Algorithms (Dijkstra, Prim)

• Scheduling Systems (CPU Scheduling)

✅ Advantages and Diadvantages of Heap Tree