## Introduction

In computer science, a heap is a specialized tree-based data structure that is used to store and retrieve items with a specific priority order. The heap data structure is commonly used in algorithms that require efficient access to the minimum or maximum element in a collection. This article will cover the basics of heap data structures, including what they are, how they work, and their common use cases.

## What is a Heap?

A heap is a binary tree-based data structure where each node has a priority value that is greater than or equal to the priority value of its parent node. The topmost node in the tree, also known as the root node, represents the element with the highest priority in the heap. A heap is said to be a max-heap if the highest priority value is stored in the root node, and a min-heap if the lowest priority value is stored in the root node.

**Types of Heap**

**1. Min Heap**

In a min heap, the parent node is smaller than its child nodes. This means that the root node is the minimum element in the heap. The left and right child nodes of a parent node are also min heaps.

**2. Max Heap**

In a max heap, the parent node is larger than its child nodes. This means that the root node is the maximum element in the heap. The left and right child nodes of a parent node are also max heaps.

**3. Binary Heap**

A binary heap is a type of heap that is represented as a binary tree. It is either a min heap or a max heap. The parent node is at index i, and its left and right child nodes are at indices 2i and 2i+1, respectively.

**4. Fibonacci Heap**

A Fibonacci heap is a type of heap that is optimized for operations such as insertion, deletion, and decrease key. It is a collection of min-heap-ordered trees. The root of each tree contains the minimum element in the heap.

**5. Pairing Heap**

A pairing heap is a type of heap that is optimized for operations such as insertion, deletion, and merging. It is a collection of trees, where each tree has the heap property.

**6. Binomial Heap**

A binomial heap is a type of heap that is optimized for operations such as insertion, deletion, and merging. It is a collection of binomial trees, where each binomial tree has the heap property.

## How Does a Heap Work?

A heap works by maintaining the heap property, which ensures that the priority value of each node is greater than or equal to the priority value of its parent node. When a new item is added to a heap, it is added as a new leaf node and then swapped with its parent node until the heap property is satisfied. When an item is removed from a heap, the root node is removed, and the last leaf node in the heap is swapped with the root node. The heap property is then restored by swapping the new root node with its child nodes until the heap property is satisfied.

**Heap Operations**

**1. Insertion**

To insert a new element into a heap, you add it to the end of the array and then perform a heapify operation to maintain the heap property.

**2. Deletion**

To delete an element from a heap, you remove the root node, which is either the minimum or maximum element in the heap. Then, you replace the root node with the last element in the array and perform a heapify operation to maintain the heap property.

**4. Extract Min/Max**

To extract the minimum or maximum element from a heap, you remove the root node, which is either the minimum or maximum element in the heap.

**5. Decrease/Increase Key**

To decrease or increase the key of an element in a heap, you first find the element and then modify its key. If the modified key violates the heap property, you perform a heapify operation to restore the heap property.

## Common Use Cases of Heaps

Heaps are commonly used in algorithms that require efficient access to the minimum or maximum element in a collection. Some examples of algorithms that use heaps include Dijkstra’s shortest path algorithm, the Huffman coding algorithm, and the heap sort algorithm. Heaps are also used in priority queues, which are data structures that store elements with a priority order and support operations such as insertion, deletion, and retrieval of the highest-priority element.

## Advantages of Using Heaps

The main advantage of using heaps is their efficiency in accessing the minimum or maximum element in a collection. The time complexity of accessing the minimum or maximum element in a heap is O(1), which means that it takes constant time regardless of the size of the heap. Heaps are also efficient in adding and removing elements, with a time complexity of O(log n).

## Disadvantages of Using Heaps

The main disadvantage of using heaps is their space complexity. Heaps require a lot of memory to store the tree structure, and the space requirements increase with the number of elements in the heap. Another disadvantage of using heaps is their lack of flexibility, as they only support a specific set of operations such as insertion, deletion, and retrieval of the highest-priority element.

**Applications of Heap**

The heap data structure has several applications in computer science. Some of these include:

- Priority queues
- Graph algorithms
- Sorting algorithms
- Dijkstra’s shortest path algorithm
- Huffman coding algorithm
- Heap sort algorithm
- Memory allocation in operating systems

**Pros and Cons of Heap**

**Pros**

- The heap data structure provides efficient access to the minimum or maximum element in a set of elements.
- Heap operations such as insertion, deletion, and extraction are efficient and have a time complexity of O(log n).
- Different types of heaps are optimized for different operations.

**Cons**

- Heaps are not suitable for searching for a specific element in a set of elements.
- The heap data structure uses more memory than an array or linked list.

## Conclusion

Heap data structures are a fundamental concept in computer science, used in a wide range of algorithms and applications. They are efficient in accessing the minimum or maximum element in a collection and are commonly used in priority queues. However, they also have disadvantages such as high space complexity and lack of flexibility. Understanding the fundamentals of heap data structures is essential for any computer science student or professional.

## FAQs

- What is the time complexity of accessing the minimum or maximum element in a heap?

- The time complexity of accessing the minimum or maximum element in a heap is O(1).

- What is the heap property?

- The heap property ensures that the priority value of each node is greater than or equal to the priority value of its parent node.

- What are some common use cases of heaps?

- Heaps are commonly used in algorithms that require efficient access to the minimum or maximum element in a collection, such as Dijkstra’s shortest path algorithm and the heap sort algorithm.

- What are the advantages of using heaps?

- The main advantage of using heaps is their efficiency in accessing the minimum or maximum element in a collection. They are also efficient in adding and removing elements.

## Related Topics

- Tree
- Binary Tree
- Heaps
- Hashing
- Advanced Data Structures
- Max Heap and Min Heap
- Heapify Operation
- Heap Sort Algorithm
- Binary Heap Data Structure
- Applications of Heaps
- Fibonacci Heap
- Binomial Heap
- D-ary Heap
- Pairing Heap
- Leftist Heap
- Skew Heap
- Binary Heap vs. BST (Binary Search Tree)