Min Heap in Java - GeeksforGeeks

19 Dec, 2021
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 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 MinHeap(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) && pos <= size) {            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 the node is a non-leaf node and greater        // than any of its child        if (!isLeaf(pos)) {            if (Heap[pos] > Heap[leftChild(pos)]                || Heap[pos] > Heap[rightChild(pos)]) {                 // Swap with the left child and heapify                // the left child                if (Heap[leftChild(pos)]                    < Heap[rightChild(pos)]) {                    swap(pos, leftChild(pos));                    minHeapify(leftChild(pos));                }                 // Swap with the right child and heapify                // the right child                else {                    swap(pos, rightChild(pos));                    minHeapify(rightChild(pos));                }            }        }    }     // 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());    }}
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 program to Demonstrate working of PriorityQueue// Using Library Functions // Importing utility classesimport java.util.*; // Main classclass 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());    }}
  
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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