datastructure@ implementation of minimal heap

A binary heap is a heap data structure created using a binary tree.

Binary tree has a rules-

1. Binary Heap have to is complete binary tree at all levels except. This is called the shapeproperty.
2. All nodes is either greater than equal to (max-heap) or less than equal to (min-heap) to each of its CH ILD nodes. This is called the heapproperty.

Implementation:

• Use array to store the data.
• Start storing from index 1, not 0.
• For any given node at position I:
• Its left-child is at [2*i] if available.
• It right child is at [2*i+1] if available.
• Its Parent Node was at [I/2]if available.

Heap Majorly has 3 operations-

1. Insert operation
2. Delete operation
3. Extract-min (OR Extract-max)

Insert Operation:

• Add the element at the bottom leaf of the Heap.
• Perform the bubble-up operation.
• All inserts Operations must perform the bubble-up operation (It is also called as Up-heap, percolate-up, S Ift-up, trickle-up, heapify-up, or cascade-up)

bubble-up Operation:

• If inserted element is smaller than it parent node in case of Min-heap OR greater than it parent node in case of Max-heap, swap the element with its parent.
• Keep repeating the above step, if node reaches its correct position, STOP.

Insert ()-bubble-up min-heap

Extract-min OR Extract-max operation:

• Take the-out of the element from the root. (It'll be minimum in case of min-heap and maximum in case of max-heap).
• The last element is the last, from the same as the heap and replace the root with the element.
• Perform Sink-down
• All delete operation must perform Sink-down operation (also known as Bubble-down, percolate-down, Sift-down, trickledown, heapify-down, cascade-down).

Sink-down Operation:

• If replaced element is greater than any of it child node in case of Min-heap OR smaller than any if it child node In case of Max-heap, the swap the element has a smallest child (min-heap) or a with its greatest child (MAX-HEAP).
• Keep repeating the above step, if node reaches its correct position, STOP.

Delete OR Extract Min from Heap

Delete Operation:

• Find the index for the element to be deleted.
• The last element is the last, from the same as the heap and replace the index with this element.
• Perform Sink-down

Time and Space complexity:

Space	O (N)
Search	O (N)
Insert	O (log n)
Delete	O (log n)

 Packagedata_structure_testing;Importjava.util.ArrayList;ImportJava.util.HashSet; Public classMinheap { PublicArraylist<integer> minheap =NULL;  Publicminheap () { This. Minheap =NewArraylist<integer> ();  This. Minheap.add (Integer.min_value); /***-------------------------------------------------------------------------* integer.min_value |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |         | * -------------------------------------------------------------------------         */    }         Public voidSwapintIintj) {if(i = = j)return; intTMP =Minheap.get (i);        Minheap.set (I, Minheap.get (j));    Minheap.set (J, TMP); }         Public intGetSize () {returnminheap.size (); }         Public intParentinti) {returnI/2; }         Public intLeftchild (inti) {returnI*2; }         Public intRightchild (inti) {returnI*2 + 1; }         Public voidOfferintx) {minheap.add (x); intPosition = Minheap.size ()-1;    BubbleUp (position); }         Public voidBubbleUp (intposition) {                intPA =parent (position); if(PA! = 0 && minheap.get (position) <Minheap.get (PA))            {Swap (position, PA);        BubbleUp (PA); }    }         Public intPeek () {if(GetSize () = = 1) {System.out.println ("The Min Heap is empty!"); returnMinheap.get (0); } Else{            returnMinheap.get (1); }    }         Public voidPushdown (inti) {intMin_position = i, Min_value =Minheap.get (i); intLC = Leftchild (i), rc = LC + 1; if(LC >=GetSize ()) {            return; }                if(LC <GetSize ()) {            if(Minheap.get (LC) <min_value) {min_position=LC; Min_value=Minheap.get (LC); }            if(RC < GetSize () && minheap.get (RC) <min_value) {min_position=RC;        }} swap (min_position, i); if(Min_position! =i) {pushdown (min_position); }    }         Public intpoll () {if(GetSize () = = 1) {System.out.println ("Since the min heap is empty, so we cannot poll any element from it!"); returnMinheap.get (0); }                inttop = Minheap.get (1); Swap (1, GetSize ()-1); Minheap.remove (GetSize ()-1); if(GetSize () > 1) {pushdown (1); }                returntop; }         Public Static voidMain (string[] args) {minheap minheap=Newminheap (); Minheap.offer (5); Minheap.offer (4); Minheap.offer (2); Minheap.offer (4); Minheap.offer (3);        System.out.println (Minheap.poll ());        System.out.println (Minheap.poll ());        System.out.println (Minheap.poll ());        System.out.println (Minheap.poll ());        System.out.println (Minheap.poll ());    System.out.println (Minheap.poll ()); }}

min Heap

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