Operations of Heap Data Structure:

Heap Data Structure is a complete binary tree that satisfies the heap property. It is also called as a binary heap. This property of a data structure makes it useful in priority queues, graph algorithms like Dijkstra’s algorithm and Prim’s Algorithm.

Here are the basic operations of a Heap Data Structure:

1. Insertion: This operation involves adding a new key to the end of the heap. After adding the key, the properties of the heap may be disrupted. Therefore, the heap property is restored by comparing the added key with its parent and moving the added key up the heap until it is in the correct position. This process is also known as up-heap, heapify-up, bubble-up, sift-up, trickle-up, heapify-up, or cascade-up.

2. Deletion: This operation involves removing the root node of the heap. After removing the root node, the last node of the heap is moved to the root. The heap property is then restored by comparing the new root node with its children and moving it down the heap until it is in the correct position. This process is also known as down-heap, heapify-down, bubble-down, sift-down, sink-down, trickle down, heapify-down, or cascade-down.

3. Peek: This operation involves returning the maximum item of max heap or the minimum item of min heap without deleting the node.

4. Heapify: This operation involves creating a heap from an array. Heapify operation can be performed in linear time, unlike linear search operations for array or linked list, which take a lot more time to perform.

5. Update: This operation involves updating the key of a node. To update a key in a heap, the value of the key is first decreased, then the procedure to delete a node is followed.

6. Display: This operation involves displaying all the nodes of the heap.

These are the basic operations that can be performed on a heap data structure. Each of these operations play a crucial role in maintaining the properties of the heap and ensuring that it functions correctly.