Max Heap in Java

• Difficulty Level : Medium
• Last Updated : 18 Dec, 2021

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 an index k, then its left child is stored at index 2k+1 and its right child at index 2k+2.

Illustration: Max Heap 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. 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 on Max Heap are as follows:

• getMax(): It returns the root element of Max Heap. The Time Complexity of this operation is O(1).
• extractMax(): Removes the maximum element from MaxHeap. The Time Complexity of this Operation is O(Log n) as this operation needs to maintain the heap property by calling the heapify() method after removing the root.
•  insert(): Inserting a new key takes O(Log n) time. We add a new key at the end of the tree. If the new key is smaller than its parent, then we don’t need to do anything. Otherwise, we need to traverse up to fix the violated heap property.

Note: In the below implementation, we do indexing from index 1 to simplify the implementation.

Methods:

There are 2 methods by which we can achieve the goal as listed:

1. Basic approach by creating maxHeapify() method
2. Using Collections.reverseOrder() method via library Functions

Method 1: Basic approach by creating maxHeapify() method

We will be creating a method assuming that the left and right subtrees are already heapified, we only need to fix the root.

Example

Java

 // Java program to implement Max Heap   // Main class public class MaxHeap {     private int[] Heap;     private int size;     private int maxsize;       // Constructor to initialize an     // empty max heap with given maximum     // capacity     public MaxHeap(int maxsize)     {         // This keyword refers to current instance itself         this.maxsize = maxsize;         this.size = 0;         Heap = new int[this.maxsize];     }       // Method 1     // Returning position of parent     private int parent(int pos) { return (pos - 1) / 2; }       // Method 2     // Returning left children     private int leftChild(int pos) { return (2 * pos); }       // Method 3     // Returning left children     private int rightChild(int pos)     {         return (2 * pos) + 1;     }       // Method 4     // Returning true of given node is leaf     private boolean isLeaf(int pos)     {         if (pos > (size / 2) && pos <= size) {             return true;         }         return false;     }       // Method 5     // Swapping nodes     private void swap(int fpos, int spos)     {         int tmp;         tmp = Heap[fpos];         Heap[fpos] = Heap[spos];         Heap[spos] = tmp;     }       // Method 6     // Recursive function to max heapify given subtree     private void maxHeapify(int pos)     {         if (isLeaf(pos))             return;           if (Heap[pos] < Heap[leftChild(pos)]             || Heap[pos] < Heap[rightChild(pos)]) {               if (Heap[leftChild(pos)]                 > Heap[rightChild(pos)]) {                 swap(pos, leftChild(pos));                 maxHeapify(leftChild(pos));             }             else {                 swap(pos, rightChild(pos));                 maxHeapify(rightChild(pos));             }         }     }       // Method 7     // Inserts a new element to max heap     public void insert(int element)     {         Heap[size] = element;           // Traverse up and fix violated property         int current = size;         while (Heap[current] > Heap[parent(current)]) {             swap(current, parent(current));             current = parent(current);         }         size++;     }       // Method 8     // To display heap     public void print()     {               for(int i=0;i

Output

The Max Heap is
Parent Node : 84 Left Child Node: 84 Right Child Node: 22
Parent Node : 22 Left Child Node: 19 Right Child Node: 17
Parent Node : 19 Left Child Node: 10 Right Child Node: 5
Parent Node : 17 Left Child Node: 6 Right Child Node: 3
The max val is 22

Method 2: Using Collections.reverseOrder() method via library Functions

We use PriorityQueue class to implement Heaps in Java. By default Min Heap is implemented by this class. To implement Max Heap, we use Collections.reverseOrder() method.

Example

Java

 // Java program to demonstrate working // of PriorityQueue as a Max Heap // Using Collections.reverseOrder() method   // Importing all utility classes import java.util.*;   // Main class class GFG {       // Main driver method     public static void main(String args[])     {           // Creating empty priority queue         PriorityQueue pQueue             = new PriorityQueue(                 Collections.reverseOrder());           // Adding items to our priority queue         // using add() method         pQueue.add(10);         pQueue.add(30);         pQueue.add(20);         pQueue.add(400);           // Printing the most priority element         System.out.println("Head value using peek function:"                            + pQueue.peek());           // Printing all elements         System.out.println("The queue elements:");         Iterator itr = pQueue.iterator();         while (itr.hasNext())             System.out.println(itr.next());           // Removing the top priority element (or head) and         // printing the modified pQueue using poll()         pQueue.poll();         System.out.println("After removing an element "                            + "with poll function:");         Iterator itr2 = pQueue.iterator();         while (itr2.hasNext())             System.out.println(itr2.next());           // Removing 30 using remove() method         pQueue.remove(30);         System.out.println("after removing 30 with"                            + " remove function:");           Iterator itr3 = pQueue.iterator();         while (itr3.hasNext())             System.out.println(itr3.next());           // Check if an element is present using contains()         boolean b = pQueue.contains(20);         System.out.println("Priority queue contains 20 "                            + "or not?: " + b);           // Getting objects from the queue using toArray()         // in an array and print the array         Object[] arr = pQueue.toArray();         System.out.println("Value in array: ");           for (int i = 0; i < arr.length; i++)             System.out.println("Value: "                                + arr[i].toString());     } }

Output

The queue elements:
400
30
20
10
After removing an element with poll function:
30
10
20
after removing 30 with remove function:
20
10
Priority queue contains 20 or not?: true
Value in array:
Value: 20
Value: 10

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