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Max Heap in Java
• Difficulty Level : Medium
• Last Updated : 19 Feb, 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.

Example of 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:

1) getMax(): It returns the root element of Max Heap. Time Complexity of this operation is O(1).

2) extractMax(): Removes the maximum element from MaxHeap. Time Complexity of this Operation is O(Log n) as this operation needs to maintain the heap property (by calling heapify()) after removing the root.

3) 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.

## Java

 `// Java program to implement Max Heap``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``.maxsize = maxsize;``        ``this``.size = ``0``;``        ``Heap = ``new` `int``[``this``.maxsize + ``1``];``        ``Heap[``0``] = Integer.MAX_VALUE;``    ``}`` ` `    ``// Returns position of parent``    ``private` `int` `parent(``int` `pos) { ``return` `pos / ``2``; }`` ` `    ``// Below two functions return left and``    ``// right children.``    ``private` `int` `leftChild(``int` `pos) { ``return` `(``2` `* pos); }``    ``private` `int` `rightChild(``int` `pos)``    ``{``        ``return` `(``2` `* pos) + ``1``;``    ``}`` ` `    ``// Returns true of given node is leaf``    ``private` `boolean` `isLeaf(``int` `pos)``    ``{``        ``if` `(pos > (size / ``2``) && pos <= size) {``            ``return` `true``;``        ``}``        ``return` `false``;``    ``}`` ` `    ``private` `void` `swap(``int` `fpos, ``int` `spos)``    ``{``        ``int` `tmp;``        ``tmp = Heap[fpos];``        ``Heap[fpos] = Heap[spos];``        ``Heap[spos] = tmp;``    ``}`` ` `    ``// A recursive function to max heapify the given``    ``// subtree. This function assumes that the left and``    ``// right subtrees are already heapified, we only need``    ``// to fix the root.``    ``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));``            ``}``        ``}``    ``}`` ` `    ``// 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);``        ``}``    ``}`` ` `    ``public` `void` `print()``    ``{``        ``for` `(``int` `i = ``1``; i <= size / ``2``; i++) {``            ``System.out.print(``                ``" PARENT : "` `+ Heap[i]``                ``+ ``" LEFT CHILD : "` `+ Heap[``2` `* i]``                ``+ ``" RIGHT CHILD :"` `+ Heap[``2` `* i + ``1``]);``            ``System.out.println();``        ``}``    ``}`` ` `    ``// Remove an element from max heap``    ``public` `int` `extractMax()``    ``{``        ``int` `popped = Heap[``1``];``        ``Heap[``1``] = Heap[size--];``        ``maxHeapify(``1``);``        ``return` `popped;``    ``}`` ` `    ``public` `static` `void` `main(String[] arg)``    ``{``        ``System.out.println(``"The Max Heap is "``);``        ``MaxHeap maxHeap = ``new` `MaxHeap(``15``);``        ``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``);`` ` `        ``maxHeap.print();``        ``System.out.println(``"The max val is "``                           ``+ maxHeap.extractMax());``    ``}``}`
Output
```The Max Heap is
PARENT : 84 LEFT CHILD : 22 RIGHT CHILD :19
PARENT : 22 LEFT CHILD : 17 RIGHT CHILD :10
PARENT : 19 LEFT CHILD : 5 RIGHT CHILD :6
PARENT : 17 LEFT CHILD : 3 RIGHT CHILD :9
The max val is 84```

Using 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()

## Java

 `// Java program to demonstrate working``// of PriorityQueue as a Max Heap``import` `java.util.*;`` ` `class` `Example {``    ``public` `static` `void` `main(String args[])``    ``{``        ``// Creating empty priority queue``        ``PriorityQueue pQueue``            ``= ``new` `PriorityQueue(``                ``Collections.reverseOrder());`` ` `        ``// Adding items to the pQueue using add()``        ``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()``        ``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```

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