# C Programming Binary Heap (Tree-Based Structure) Exercises with Explanations and Solutions

## C Program to implement Heap [9 exercises with solution]

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From Wikipedia,

In computer science, a heap is a specialized tree-based data structure that satisfies the heap property: In a max heap, for any given node C, if P is a parent node of C, then the key (the value) of P is greater than or equal to the key of C. In a min heap, the key of P is less than or equal to the key of C. The node at the "top" of the heap (with no parents) is called the root node.

The heap is one maximally efficient implementation of an abstract data type called a priority queue, and in fact, priority queues are often referred to as "heaps", regardless of how they may be implemented. In a heap, the highest (or lowest) priority element is always stored at the root.

**Visual Presentation:**

**1.** Write a C program that implements the basic operations of a heap - insert, delete, and display.

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**2.** Write a C program function that constructs a max heap from an array of elements. Test it with both random and sorted input arrays.

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**3.** Write a C program function that constructs a min heap from an array of elements. Test it with both random and sorted input arrays.

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**4.** Write a C program that uses the max heap data structure to implement heap sort. Show the sorting process on an array of integers.

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**5.** Write a C program that implements a function to heapify a given node in a heap. Check the function with different positions in the heap.

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**6.** Write a C program that implements a priority queue using a max heap. Apply enqueue and dequeue operations on the priority queue.

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**7.** Write a C program that creates a function to merge two heaps into a single heap. Please make sure that the resulting heap satisfies the heap property.

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**8.** Write a C program that implements the decreaseKey operation in a maximum heap. Check the function by decreasing the key of a node and validating the heap property.

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**9.** Write a C program that uses a max heap to find the kth largest element in an array. Write a function that takes an array and an integer k as input and returns the kth largest element.

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