Welcome to this in-depth tutorial on the concept of heap in data structure. In this article, we will explore what a heap is and provide examples to help you understand its functionality. So, let’s dive right in!
What is a Heap?
A heap is a specialized tree-based data structure that satisfies the heap property. The heap property states that for every node in the tree, the key of that node is either greater than or equal to (in a max heap) or less than or equal to (in a min heap) the keys of its children.
Heaps are commonly used to implement priority queues, as they allow efficient insertion, deletion, and retrieval of the element with the highest (or lowest) priority.
Types of Heaps
There are two main types of heaps:
- Max Heap: In a max heap, the key of each node is greater than or equal to the keys of its children. The maximum element is always stored at the root.
- Min Heap: In contrast, in a min heap, the key of each node is less than or equal to the keys of its children. The minimum element is always stored at the root.
To better understand how heaps work, let’s consider an example using a max heap:
100 / \ 50 70 / \ / \ 30 20 10 5
In this example, we have a max heap where each parent node has a key greater than or equal to its children’s keys. The maximum element (100) is located at the root of the heap.
Heaps support several operations, including:
- Insertion: To insert an element into a heap, we add it as a new leaf node and then perform a heapify operation to maintain the heap property.
- Deletion: To delete an element from a heap, we typically remove the root node (which contains the maximum or minimum element) and replace it with the last leaf node. We then perform a heapify operation to restore the heap property.
- Retrieval (Max/Min): We can easily retrieve the maximum or minimum element from a max or min heap, respectively, by accessing the root node.
In summary, a heap is a tree-based data structure that satisfies the heap property. Heaps are commonly used to implement priority queues and support efficient insertion, deletion, and retrieval operations. Understanding heaps is essential for building efficient algorithms and solving various computational problems.
I hope this article has provided you with a clear understanding of what a heap is and how it works. Happy coding!