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 41Let 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)){
int swapPos= pos;
// swap with the minimum of the two children
// to check if right child exists. Otherwise default value will be '0'
// and that will be swapped with parent node.
if(rightChild(pos)<=size)
swapPos = Heap[leftChild(pos)]<Heap[rightChild(pos)]?leftChild(pos):rightChild(pos);
else
swapPos= leftChild(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 of class in main() method
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 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());
}
} |
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