Max Heap in JavaScript

A max-heap is a complete binary tree in which the value in each internal node is greater than or equal to the values in the children of that node. Mapping the elements of a heap into an array is trivial: if a node is stored at index k, then its left child is stored at index 2k + 1 and its right child at index 2k + 2.

Max Heap in JavaScript

How is Max Heap represented?

A-Max Heap is a Complete Binary Tree. A-Max heap is typically represented as an array. The root element will be at Arr[0]. Below table shows indexes of other nodes for the ith node, i.e., Arr[i]: 

Arr[(i-1)/2] Returns the parent node. 
Arr[(2*i)+1] Returns the left child node. 
Arr[(2*i)+2] Returns the right child node.

Operations of Heap Data Structure:

• Heapify: a process of creating a heap from an array.
• Insertion: process to insert an element in existing heap time complexity O(log N).
• Deletion: deleting the top element of the heap or the highest priority element, and then organizing the heap and returning the element with time complexity O(log N).
• Peek: to check or find the most prior element in the heap, (max or min element for max and min heap).

Explanation: Now let us understand how the various helper methods maintain the order of the heap

• The helper methods like rightChild, leftChild, parent help us to get the element and its children at the specified index.
• The add() and remove() methods handle the insertion and deletion process
• The heapifyDown() method maintains the heap structure when an element is deleted.
• The heapifyUp() method maintains the heap structure when an element is added to the heap. 
• The peek() method returns the root element of the heap and swap() method interchanges value at two nodes.

Example: In this example, we will implement the Max Heap data structure.

Javascript

class MaxHeap {
 constructor() {
     this.heap = [];
 }

 // Helper Methods
 getLeftChildIndex(parentIndex) { return 2 * parentIndex + 1; }
 getRightChildIndex(parentIndex) { return 2 * parentIndex + 2; }

 getParentIndex(childIndex) {
     return Math.floor((childIndex - 1) / 2);
 }

 hasLeftChild(index) {
     return this.getLeftChildIndex(index) < this.heap.length;
 }

 hasRightChild(index) {
     return this.getRightChildIndex(index) < this.heap.length;
 }

 hasParent(index) {
     return this.getParentIndex(index) >= 0;
 }

 leftChild(index) {
     return this.heap[this.getLeftChildIndex(index)];
 }

 rightChild(index) {
     return this.heap[this.getRightChildIndex(index)];
 }

 parent(index) {
     return this.heap[this.getParentIndex(index)];
 }

 swap(indexOne, indexTwo) {
     const temp = this.heap[indexOne];
     this.heap[indexOne] = this.heap[indexTwo];
     this.heap[indexTwo] = temp;
 }

 peek() {
     if (this.heap.length === 0) {
         return null;
     }
     return this.heap[0];
 }

 // Removing an element will remove the
 // top element with highest priority then
 // heapifyDown will be called
 remove() {
     if (this.heap.length === 0) {
         return null;
     }
     const item = this.heap[0];
     this.heap[0] = this.heap[this.heap.length - 1];
     this.heap.pop();
     this.heapifyDown();
     return item;
 }

 add(item) {
     this.heap.push(item);
     this.heapifyUp();
 }

 heapifyUp() {
     let index = this.heap.length - 1;
     while (this.hasParent(index) && this.parent(index) < this.heap[index]) {
         this.swap(this.getParentIndex(index), index);
         index = this.getParentIndex(index);
     }
 }

 heapifyDown() {
     let index = 0;
     while (this.hasLeftChild(index)) {
         let largerChildIndex = this.getLeftChildIndex(index);
         if (this.hasRightChild(index) && this.rightChild(index) > this.leftChild(index)) {
             largerChildIndex = this.getRightChildIndex(index);
         }
         if (this.heap[index] > this.heap[largerChildIndex]) {
             break;
         } else {
             this.swap(index, largerChildIndex);
         }
         index = largerChildIndex;
     }
 }

 printHeap() {
     var heap =` ${this.heap[0]} `
     for(var i = 1; i<this.heap.length;i++) {
         heap += ` ${this.heap[i]} `;
     }
     console.log(heap);
 }
}

// Creating the Heap
var heap = new MaxHeap();

// Adding The Elements
heap.add(10);
heap.add(15);
heap.add(30);
heap.add(40);
heap.add(50);
heap.add(100);
heap.add(40);

// Printing the Heap
heap.printHeap();

// Peeking And Removing Top Element
console.log(heap.peek());
console.log(heap.remove());

// Printing the Heap
// After Deletion.
heap.printHeap();

Output

 100  40  50  10  30  15  40 
100
100
 50  40  40  10  30  15