Max Heap in Java

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 

👁 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[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 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

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