In this tutorial, you will learn what heap data structure is. Likewise, you will discover working instances of the heap operations in C, C++, Java, and Python.
Heap is a very useful data structure that every programmer should know well.
In this article, you will learn-
What is Heap?
A heap is a complete binary tree, and the binary tree is a tree wherein the node can have most extreme two children. Before knowing more about the heap data structure, we should know about the complete binary tree.
Heap data structure is a complete binary tree that fulfills the heap property. It is additionally called 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 wherein
- (for max heap) key of each node is consistently more prominent than its kid node/s and the key of the root node is the largest among any remaining nods;
(for min-heap) key of each node is consistently smaller than the child node/s and the key of the root node is the littlest among any remaining nods.
Heap Operations
A portion of the significant activities performed on a heap is portrayed beneath alongside their algorithms.
Heapify
Heapify is the way toward making a heap data structure from a binary tree. It is used to make a Min-Heap or a Max-Heap.
- Let the input array be
2. Create a complete binary tree from the array
3. Start from the first index of non-leaf node whose index is given by n/2 – 1.
4. Set current element i as largest.
5. 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.
6. Swap largest with currentElement
7. 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.
2. 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
2. Swap it with the last element.
3. Remove the last element.
4. Heapify the tree.
For Min Heap, the above algorithm is altered so both childNodes are greater smaller than currentNode.
Peek (Find max/min)
Peek operation returns the maximum element from Max Heap or least element from Min Heap without erasing the node.
For both Max heap and Min Heap
return rootNode
Extract-Max/Min
Extract Max returns the node with maximum value subsequent to eliminating it from a Max Heap though Extract-Min returns the node with least in the wake of eliminating it from Min Heap.
Python, Java, C/C++ Examples
Python
# 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(num)
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))
Java
// Max-Heap data structure in Java
import java.util.ArrayList;
class Heap {
void heapify(ArrayList<Integer> hT, int i) {
int size = hT.size();
int largest = i;
int l = 2 * i + 1;
int r = 2 * i + 2;
if (l < size && hT.get(l) > hT.get(largest))
largest = l;
if (r < size && hT.get(r) > hT.get(largest))
largest = r;
if (largest != i) {
int temp = hT.get(largest);
hT.set(largest, hT.get(i));
hT.set(i, temp);
heapify(hT, largest);
}
}
void insert(ArrayList<Integer> hT, int newNum) {
int size = hT.size();
if (size == 0) {
hT.add(newNum);
} else {
hT.add(newNum);
for (int i = size / 2 - 1; i >= 0; i--) {
heapify(hT, i);
}
}
}
void deleteNode(ArrayList<Integer> hT, int num)
{
int size = hT.size();
int i;
for (i = 0; i < size; i++)
{
if (num == hT.get(i))
break;
}
int temp = hT.get(i);
hT.set(i, hT.get(size-1));
hT.set(size-1, temp);
hT.remove(size-1);
for (int j = size / 2 - 1; j >= 0; j--)
{
heapify(hT, j);
}
}
void printArray(ArrayList<Integer> array, int size) {
for (Integer i : array) {
System.out.print(i + " ");
}
System.out.println();
}
public static void main(String args[]) {
ArrayList<Integer> array = new ArrayList<Integer>();
int size = array.size();
Heap h = new Heap();
h.insert(array, 3);
h.insert(array, 4);
h.insert(array, 9);
h.insert(array, 5);
h.insert(array, 2);
System.out.println("Max-Heap array: ");
h.printArray(array, size);
h.deleteNode(array, 4);
System.out.println("After deleting an element: ");
h.printArray(array, size);
}
}
C
// 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);
}
C++
// Max-Heap data structure in C++
#include <iostream>
#include <vector>
using namespace std;
void swap(int *a, int *b)
{
int temp = *b;
*b = *a;
*a = temp;
}
void heapify(vector<int> &hT, int i)
{
int size = hT.size();
int largest = i;
int l = 2 * i + 1;
int r = 2 * i + 2;
if (l < size && hT[l] > hT[largest])
largest = l;
if (r < size && hT[r] > hT[largest])
largest = r;
if (largest != i)
{
swap(&hT[i], &hT[largest]);
heapify(hT, largest);
}
}
void insert(vector<int> &hT, int newNum)
{
int size = hT.size();
if (size == 0)
{
hT.push_back(newNum);
}
else
{
hT.push_back(newNum);
for (int i = size / 2 - 1; i >= 0; i--)
{
heapify(hT, i);
}
}
}
void deleteNode(vector<int> &hT, int num)
{
int size = hT.size();
int i;
for (i = 0; i < size; i++)
{
if (num == hT[i])
break;
}
swap(&hT[i], &hT[size - 1]);
hT.pop_back();
for (int i = size / 2 - 1; i >= 0; i--)
{
heapify(hT, i);
}
}
void printArray(vector<int> &hT)
{
for (int i = 0; i < hT.size(); ++i)
cout << hT[i] << " ";
cout << "\n";
}
int main()
{
vector<int> heapTree;
insert(heapTree, 3);
insert(heapTree, 4);
insert(heapTree, 9);
insert(heapTree, 5);
insert(heapTree, 2);
cout << "Max-Heap array: ";
printArray(heapTree);
deleteNode(heapTree, 4);
cout << "After deleting an element: ";
printArray(heapTree);
}
Heap Data Structure Applications
- Heap is used while implementing a priority queue.
- Dijkstra’s Algorithm
- Heap Sort
Thanks for reading! We hope you found this tutorial helpful and we would love to hear your feedback in the Comments section below. And show us what you’ve learned by sharing your photos and creative projects with us.
