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# Max Heap in Java

• Difficulty Level : Medium
• Last Updated : 01 Feb, 2023

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) + ``1``; }` `    ``// Method 3``    ``// Returning right children``    ``private` `int` `rightChild(``int` `pos)``    ``{``        ``return` `(``2` `* pos) + ``2``;``    ``}` `    ``// 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 < size / ``2``; i++) {` `            ``System.out.print(``"Parent Node : "` `+ Heap[i]);` `            ``if` `(leftChild(i)``                ``< size) ``// if the child is out of the bound``                        ``// of the array``                ``System.out.print(``" Left Child Node: "``                                 ``+ Heap[leftChild(i)]);` `            ``if` `(rightChild(i)``                ``< size) ``// if the right child index must not``                        ``// be out of the index of the array``                ``System.out.print(``" Right Child Node: "``                                 ``+ Heap[rightChild(i)]);` `            ``System.out.println(); ``// for new line``        ``}``    ``}` `    ``// Method 9``    ``// Remove an element from max heap``    ``public` `int` `extractMax()``    ``{``        ``int` `popped = Heap[``0``];``        ``Heap[``0``] = Heap[--size];``        ``maxHeapify(``0``);``        ``return` `popped;``    ``}` `    ``// Method 10``    ``// main driver method``    ``public` `static` `void` `main(String[] arg)``    ``{``        ``// Display message for better readability``        ``System.out.println(``"The Max Heap is "``);` `        ``MaxHeap maxHeap = ``new` `MaxHeap(``15``);` `        ``// Inserting nodes``        ``// Custom inputs``        ``maxHeap.insert(``5``);``        ``maxHeap.insert(``3``);``        ``maxHeap.insert(``17``);``        ``maxHeap.insert(``10``);``        ``maxHeap.insert(``84``);``        ``maxHeap.insert(``19``);``        ``maxHeap.insert(``6``);``        ``maxHeap.insert(``22``);``        ``maxHeap.insert(``9``);` `        ``// Calling maxHeap() as defined above``        ``maxHeap.print();` `        ``// Print and display the maximum value in heap``        ``System.out.println(``"The max val is "``                           ``+ maxHeap.extractMax());``    ``}``}`

Output

```The Max Heap is
Parent Node : 84 Left Child Node: 22 Right Child Node: 19
Parent Node : 22 Left Child Node: 17 Right Child Node: 10
Parent Node : 19 Left Child Node: 5 Right Child Node: 6
Parent Node : 17 Left Child Node: 3 Right Child Node: 9
The max val is 84```

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

```Head value using peek function:400
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```

My Personal Notes arrow_drop_up