# Min Heap in Java

• 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. 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[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 pQueue` `            ``= ``new` `PriorityQueue();`   `        ``// 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 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 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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