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

binary tree has two rules –

Binary Heap has to be complete binary tree at all levels except the last level. This is called shape property.

All nodes are either greater than equal to (Max-Heap) or less than equal to (Min-Heap) to each of its child nodes. This is called heap property.

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.

Its Right Child is at [2*i+1] if available.

Its Parent Node is at [i/2]if available.

Heap Majorly has 3 operations –

Insert Operation

Delete Operation

Extract-Min (OR Extract-Max)

Insert Operation:

Add the element at the bottom leaf of the Heap.

Perform the Bubble-Up operation.

All Insert Operations must perform the bubble-up operation(it is also called as up-heap, percolate-up, sift-up, trickle-up, heapify-up, or cascade-up)

Bubble-up Operation:

If inserted element is smaller than its parent node in case of Min-Heap OR greater than its 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 out the element from the root.( it will be minimum in case of Min-Heap and maximum in case of Max-Heap).

Take out the last element from the last level from 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, trickle down, heapify-down, cascade-down).

Sink-Down Operation:

If replaced element is greater than any of its child node in case of Min-Heap OR smaller than any if its child node in case of Max-Heap, swap the element with its smallest child(Min-Heap) or 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.

Take out the last element from the last level from the heap and replace the index with this element .

If you find anything incorrect or you feel that there is any better approach to solve the above problem, please write comment.
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