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Min Heap in Java

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  • Difficulty Level : Medium
  • Last Updated : 04 Jul, 2022

A Min-Heap is a complete binary tree in which the value in each internal node is smaller 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:  

            5                      13
         /      \               /       \  
       10        15           16         31 
      /                      /  \        /  \
    30                     41    51    100   41

Let us go through the representation of Min heap. So basically Min Heap is a complete binary tree. A Min heap is typically represented as an array. The root element will be at Arr[0]. For any ith node, i.e., Arr[i] 

  • Arr[(i -1) / 2] returns its parent node.
  • Arr[(2 * i) + 1] returns its left child node.
  • Arr[(2 * i) + 2] returns its right child node.

Now let us discuss the operations on Min Heap which is as follows:

  • getMin(): It returns the root element of Min Heap. The Time Complexity of this operation is O(1).
  • extractMin(): Removes the minimum element from MinHeap. The 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.
  • insert(): Inserting a new key takes O(Log n) time. We add a new key at the end of the tree. If a new key is larger than its parent, then we don’t need to do anything. Otherwise, we need to traverse up to fix the violated heap property.

Example 1:

Java




// Java Program to Implement Heaps
// by Illustrating Min Heap
 
// Main class (MinHeap)
class GFG {
 
    // Member variables of this class
    private int[] Heap;
    private int size;
    private int maxsize;
 
    // Initializing front as static with unity
    private static final int FRONT = 1;
 
    // Constructor of this class
    public GFG(int maxsize)
    {
 
        // This keyword refers to current object itself
        this.maxsize = maxsize;
        this.size = 0;
 
        Heap = new int[this.maxsize + 1];
        Heap[0] = Integer.MIN_VALUE;
    }
 
    // Method 1
    // Returning the position of
    // the parent for the node currently
    // at pos
    private int parent(int pos) { return pos / 2; }
 
    // Method 2
    // Returning the position of the
    // left child for the node currently at pos
    private int leftChild(int pos) { return (2 * pos); }
 
    // Method 3
    // Returning the position of
    // the right child for the node currently
    // at pos
    private int rightChild(int pos)
    {
        return (2 * pos) + 1;
    }
 
    // Method 4
    // Returning true if the passed
    // node is a leaf node
    private boolean isLeaf(int pos)
    {
 
        if (pos > (size / 2)) {
            return true;
        }
 
        return false;
    }
 
    // Method 5
    // To swap two nodes of the heap
    private void swap(int fpos, int spos)
    {
 
        int tmp;
        tmp = Heap[fpos];
 
        Heap[fpos] = Heap[spos];
        Heap[spos] = tmp;
    }
 
    // Method 6
    // To heapify the node at pos
   private void minHeapify(int pos)
   {     
     if(!isLeaf(pos)){
        
       //swap with the minimum of the two children
       int swapPos = Heap[leftChild(pos)]<Heap[rightChild(pos)]?leftChild(pos):rightChild(pos);
        
       if(Heap[pos]>Heap[leftChild(pos)] || Heap[pos]> Heap[rightChild(pos)]){
         swap(pos,swapPos);
         minHeapify(swapPos);
       }
        
     }      
   }
 
    // Method 7
    // To insert a node into the heap
    public void insert(int element)
    {
 
        if (size >= maxsize) {
            return;
        }
 
        Heap[++size] = element;
        int current = size;
 
        while (Heap[current] < Heap[parent(current)]) {
            swap(current, parent(current));
            current = parent(current);
        }
    }
 
    // Method 8
    // To print the contents of the heap
    public void print()
    {
        for (int i = 1; i <= size / 2; i++) {
 
            // Printing the parent and both childrens
            System.out.print(
                " PARENT : " + Heap[i]
                + " LEFT CHILD : " + Heap[2 * i]
                + " RIGHT CHILD :" + Heap[2 * i + 1]);
 
            // By here new line is required
            System.out.println();
        }
    }
 
    // Method 9
    // To remove and return the minimum
    // element from the heap
    public int remove()
    {
 
        int popped = Heap[FRONT];
        Heap[FRONT] = Heap[size--];
        minHeapify(FRONT);
 
        return popped;
    }
 
    // Method 10
    // Main driver method
    public static void main(String[] arg)
    {
 
        // Display message
        System.out.println("The Min Heap is ");
 
        // Creating object opf class in main() methodn
        GFG minHeap = new GFG(15);
 
        // Inserting element to minHeap
        // using insert() method
 
        // Custom input entries
        minHeap.insert(5);
        minHeap.insert(3);
        minHeap.insert(17);
        minHeap.insert(10);
        minHeap.insert(84);
        minHeap.insert(19);
        minHeap.insert(6);
        minHeap.insert(22);
        minHeap.insert(9);
 
        // Print all elements of the heap
        minHeap.print();
 
        // Removing minimum value from above heap
        // and printing it
        System.out.println("The Min val is "
                           + minHeap.remove());
    }
}


Output

The Min Heap is 
 PARENT : 3 LEFT CHILD : 5 RIGHT CHILD :6
 PARENT : 5 LEFT CHILD : 9 RIGHT CHILD :84
 PARENT : 6 LEFT CHILD : 19 RIGHT CHILD :17
 PARENT : 9 LEFT CHILD : 22 RIGHT CHILD :10
The Min val is 3

We use PriorityQueue class to implement Heaps in Java. By default Min Heap is implemented by this class which is as shown in below example as follows: 

Example 2:

Java




// Java program to Demonstrate working of PriorityQueue
// Using Library Functions
 
// Importing utility classes
import java.util.*;
 
// Main class
class GFG {
 
    // Main driver method
    public static void main(String args[])
    {
 
        // Creating empty priority queue
        PriorityQueue<Integer> pQueue
            = new PriorityQueue<Integer>();
 
        // Adding items to the 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:");
 
        // Iterating over objects using Iterator
        // so do creating an Iterator class
        Iterator itr = pQueue.iterator();
 
        // Iterating toill there is single element left in
        // object using next() method
        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:");
 
        // Again creating iterator object
        Iterator<Integer> 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:");
 
        // Again creating iterator object
        Iterator<Integer> 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:10
The queue elements:
10
30
20
400
After removing an element with poll function:
20
30
400
after removing 30 with remove function:
20
400
Priority queue contains 20 or not?: true
Value in array: 
Value: 20
Value: 400

 


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