Welcome to CodingZap’s new blog * “How to build max heap from an array using C”. *You might have come across this topic and must be wondering:

**What is Heap?**

A heap is a special tree data structure that satisfies heap property. In this implementation, I am using a binary tree for simplicity.

How to represent binary tree as an array

- Root is at index 0 in the array.
- Left child of i-th node is at (2*i + 1)th index.
- Right child of i-th node is at (2*i + 2)th index.
- The parent of the i-th node is at (i-1)/2 index.

**What are the Properties of Heap? **

A heap can be of two types based on either of two heap properties –

**Max Heap **

A max-heap is a heap in which the value of each node is greater than or equal to the values of its children.

**Min-Heap**

A min-heap is a heap in which the value of each node is less than or equal to the values of its children

**What is Heapify?**

Heapify is the basic building block of the algorithm of creating a heap data structure from a binary tree.

Heapify goes through a top-down approach and makes every subtree satisfy the max heap starting from the given node.

**PseudoCode of Heap :**

**indexOfNode** is the root of a subtree

Heapify(array , sizeOfArray , indexOfNode)

Largest = findMaximum of ( indexOfNode , leftChild , rightChild )

If Largest != indexOfNode i.e the root

Swap ( Largest with indexOfNode )

Heapify( array , sizeOfArray , Largest )

**Build Max Heap**

If we start making subtree heaps from down to the bottom, eventually the whole tree will become a heap.

The Build Heap function will loop starting from the last non-leaf node to the root node, and call the Heapify function on each. So that each node satisfies the max heap property.

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We are starting from the last non-leaf node because leaves are already heaps.

To find an index of the Last Non-leaf Node,

** index of Last Non Leaf Node = (n/2) – 1 **

where,

n is the number of nodes in a tree

**Supporting Functions**

These functions will help in basic utilities for

- Printing an array
- Swapping two variables

**Driver Code**

This will run our code.

**Final Code of “How to Build Max Heap from an array using C”**

// Build a Heap from an Array with C

#include <stdio.h>

// swap function

void swap(int *a, int *b)

{

int temp = *b;

*b = *a;

*a = temp;

}

// Function to print the Heap as array

// will print as - 'message array[]\n'

void printArray(char message[], int arr[], int n)

{

printf("%s ",message);

for (int i = 0; i < n; ++i)

{

printf("%d ", arr[i]);

}

printf("\n");

}

// To heapify a subtree with node i as root

// Size of heap is n

void heapify(int arr[], int n, int i)

{

int largest = i; // Initialize largest as root

int leftChild = 2 * i + 1; // left child = 2*i + 1

int rightChild = 2 * i + 2; // right child = 2*i + 2

// If left child is greater than root

if (leftChild < n && arr[leftChild] > arr[largest])

largest = leftChild;

// If right child is greater than new largest

if (rightChild < n && arr[rightChild] > arr[largest])

largest = rightChild;

// If largest is not the root

if (largest != i)

{

// swap root with the new largest

swap(&arr[i], &arr[largest]);

// Recursively heapify the affected sub-tree i.e, subtree with root as largest

heapify(arr, n, largest);

}

}

// Function to build a Max-Heap from a given array

void buildHeap(int arr[], int n)

{

// Index of last non-leaf node

int lastNonLeafNode = (n / 2) - 1;

// Perform level order traversal in reverse from last non-leaf node to the root node and heapify each node

for (int i = lastNonLeafNode; i >= 0; i--)

{

heapify(arr, n, i);

}

}

// Driver Code

void main()

{

// Array

int arr[] = {4, 18, 17, 10, 19, 20, 14, 8, 3, 12};

// Size of array

int n = sizeof(arr) / sizeof(arr[0]);

printArray("Array is : ", arr, n);

buildHeap(arr, n);

printArray("Array representation of Heap is : ", arr, n);

}Output

**Input Array :**

4

/ \

18 17

/ \ / \

10 19 20 14

/\. /

8 3 12

**Output Max Heap :**

20

/ \

19 17

/ \ / \

10 18 4 14

/\ /

8 3 12

As we can see every node is greater than its child nodes ( max heap property )

**Heap Data Structure Applications:**

- Priority queue.
- Dijkstra’s Algorithm
- Heap Sort

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