Applications of Heaps

• Heap Sort: Heap Sort uses Binary Heap to sort an array in O(nLogn) time.
• Priority Queue: Priority queues can be efficiently implemented using Binary Heap because it supports insert(), delete() and extractmax(), decreaseKey() operations in O(log N) time. Binomial Heap and Fibonacci Heap are variations of Binary Heap. These variations perform union also efficiently.
• Graph Algorithms: The priority queues are especially used in Graph Algorithms like Dijkstra’s Shortest Path and Prim’s Minimum Spanning Tree.
• Many problems can be efficiently solved using Heaps. See following for example. a) K’th Largest Element in an array. b) Sort an almost sorted array/ c) Merge K Sorted Arrays.

Related Links:

• Coding Practice on Heap 
• All Articles on Heap 
• Quiz on Heap 
• PriorityQueue : Binary Heap Implementation in Java Library 

A Binary Heap is a complete Binary Tree which is used to store data efficiently to get the max or min element based on its structure.

A Binary Heap is either Min Heap or Max Heap. In a Min Binary Heap, the key at the root must be minimum among all keys present in Binary Heap. The same property must be recursively true for all nodes in Binary Tree. Max Binary Heap is similar to MinHeap. 

Examples of Min Heap:

            10                       10
         /      \                 /         \  
     20     100        15           30  
   /                        /    \         /    \
30                     40   50   100   40