# Heap Data Structure

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

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.

## Python Examples

```
/* Max-Heap data structure in Python */
def heapify(arr, n, i):
largest = i
l = 2 * i + 1
r = 2 * i + 2
if l < n and arr[i] < arr[l]:
largest = l
if r < n and arr[largest] < arr[r]:
largest = r
if largest != i:
arr[i],arr[largest] = arr[largest],arr[i]
heapify(arr, n, largest)
def insert(array, newNum):
size = len(array)
if size == 0:
array.append(newNum)
else:
array.append(newNum);
for i in range((size//2)-1, -1, -1):
heapify(array, size, i)
def deleteNode(array, num):
size = len(array)
i = 0
for i in range(0, size):
if num == array[i]:
break
array[i], array[size-1] = array[size-1], array[i]
array.remove(size-1)
for i in range((len(array)//2)-1, -1, -1):
heapify(array, len(array), i)
arr = []
insert(arr, 3)
insert(arr, 4)
insert(arr, 9)
insert(arr, 5)
insert(arr, 2)
print ("Max-Heap array: " + str(arr))
deleteNode(arr, 4)
print("After deleting an element: " + str(arr))
```

## 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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There are two sides to machine learning:

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