# Heap Data Structure

#### In this tutorial, you will learn what heap data structure is. Also, you will find working examples of heap operations in C.

Heap data structure is a complete binary tree that satisfies **the heap property**. It is also called as **a binary heap**.

A complete binary tree is a special binary tree in which

- every level, except possibly the last, is filled
- all the nodes are as far left as possible

Heap Property is the property of a node in which

- (for max heap) key of each node is always greater than its child node/s and the key of the root node is the largest among all other nodes;

- (for min heap) key of each node is always smaller than the child node/s and the key of the root node is the smallest among all other nodes.

## Heap Operations

Some of the important operations performed on a heap are described below along with their algorithms.

### Heapify

Heapify is the process of creating a heap data structure from a binary tree. It is used to create a Min-Heap or a Max-Heap.

- Let the input array be

- Create a complete binary tree from the array

- Start from the first index of non-leaf node whose index is given by
`n/2 - 1`

.

- Set current element
`i`

as`largest`

. - The index of left child is given by
`2i + 1`

and the right child is given by`2i + 2`

.

If`leftChild`

is greater than`currentElement`

(i.e. element at`ith`

index), set`leftChildIndex`

as largest.

If`rightChild`

is greater than element in`largest`

, set`rightChildIndex`

as`largest`

. - Swap
`largest`

with`currentElement`

- Repeat steps 3-7 until the subtrees are also heapified.

**Algorithm**

```
Heapify(array, size, i)
set i as largest
leftChild = 2i + 1
rightChild = 2i + 2
if leftChild > array[largest]
set leftChildIndex as largest
if rightChild > array[largest]
set rightChildIndex as largest
swap array[i] and array[largest]
```

To create a Max-Heap:

```
MaxHeap(array, size)
loop from the first index of non-leaf node down to zero
call heapify
```

For Min-Heap, both `leftChild`

and `rightChild`

must be smaller than the parent for all nodes.

### Insert Element into Heap

Algorithm for insertion in Max Heap

```
If there is no node,
create a newNode.
else (a node is already present)
insert the newNode at the end (last node from left to right.)
heapify the array
```

- Insert the new element at the end of the tree.

- Heapify the tree.

For Min Heap, the above algorithm is modified so that `parentNode`

is always smaller than `newNode`

.

### Delete Element from Heap

Algorithm for deletion in Max Heap

```
If nodeToBeDeleted is the leafNode
remove the node
Else swap nodeToBeDeleted with the lastLeafNode
remove noteToBeDeleted
heapify the array
```

- Select the element to be deleted.

- Swap it with the last element.

- Remove the last element.

- Heapify the tree.

For Min Heap, above algorithm is modified so that both `childNodes`

are greater smaller than `currentNode`

.

### Peek (Find max/min)

Peek operation returns the maximum element from Max Heap or minimum element from Min Heap without deleting the node.

For both Max heap and Min Heap

return rootNode

### Extract-Max/Min

Extract-Max returns the node with maximum value after removing it from a Max Heap whereas Extract-Min returns the node with minimum after removing it from Min Heap.

## C Examples

```
// Max-Heap data structure in C
#include <stdio.h>
int size = 0;
void swap(int *a, int *b){
int temp = *b;
*b = *a;
*a = temp;
}
void heapify(int array[], int size, int i){
if (size == 1)
{
printf("Single element in the heap");
}
else
{
int largest = i;
int l = 2 * i + 1;
int r = 2 * i + 2;
if (l < size && array[l] > array[largest])
largest = l;
if (r < size && array[r] > array[largest])
largest = r;
if (largest != i)
{
swap(&array[i], &array[largest]);
heapify(array, size, largest);
}
}
}
void insert(int array[], int newNum){
if (size == 0)
{
array[0] = newNum;
size += 1;
}
else
{
array[size] = newNum;
size += 1;
for (int i = size / 2 - 1; i >= 0; i--)
{
heapify(array, size, i);
}
}
}
void deleteRoot(int array[], int num){
int i;
for (i = 0; i < size; i++)
{
if (num == array[i])
break;
}
swap(&array[i], &array[size - 1]);
size -= 1;
for (int i = size / 2 - 1; i >= 0; i--)
{
heapify(array, size, i);
}
}
void printArray(int array[], int size){
for (int i = 0; i < size; ++i)
printf("%d ", array[i]);
printf("n");
}
int main(){
int array[10];
insert(array, 3);
insert(array, 4);
insert(array, 9);
insert(array, 5);
insert(array, 2);
printf("Max-Heap array: ");
printArray(array, size);
deleteRoot(array, 4);
printf("After deleting an element: ");
printArray(array, size);
}
```

## Heap Data Structure Applications

- Heap is used while implementing a priority queue.
- Dijkstra’s Algorithm
- Heap Sort

# Python Example for Beginners

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