Introduction to Heap in Data Structure and Algorithm from sandesh's blog

What is Heap in Data Structure?

A heap is a binary tree structure wherein every member complies with a specific heap property. Every level of a complete binary tree is full save the last level, meaning that every node in every level but the last level will have two children. From the left, the final level will be filled. Each node in the heap is stored with a value key that indicates its position in relation to other nodes.

• Max-Heap: In a Max-Heap, the root node's key must rank highest among its children's keys. Every sub-tree in that binary Tree must have the same recursively 

true property.

• Min-Heap:In a Min-Heap, the root node's key must rank lowest among all the keys found at all of its descendants. All of the sub-trees in the Binary Tree must share the same property in a recursive manner. You can learn these concepts in detail via an online data structures and algorithms course, offered by Learnbay. 

The attributes of the heap are as follows:

• The system assigns a special heap identifier for each heap in the activation group. The default heap always has the heap identifier zero. The heap identifier is used to identify the heap on which a storage management-bindable API is to function when a programme or procedure invokes it. The activation group in which the bindable API owns the heap must be active.

• To accommodate allocation demands, a heap's size is dynamically increased. (4GB - 512KB) is the heap's maximum size. This is the maximum heap size if no more than 128 000 allocations (at any given time) are made overall.

• A heap can only hold (16MB - 64KB) for any given allocation.

1. Heapify: The elements are rearranged to retain the heap data structure's properties. When one node's operations on another node cause the heap to become unbalanced, it is necessary to perform this action. Balancing the Tree requires O(log N) time. 

1. Insertion:If we add a new element to the heap because we are doing so, it will change its properties, so we must conduct the heapify operation to keep the heap's properties intact.

1. Deletion: The root element of the Tree is always deleted when an element from the heap is deleted, and the Tree's last element always replaces it.

Since removing the root element from the heap will change its properties, heapify procedures must be performed to keep its properties intact. 

• An array that captures the parent-child connection in its indices can represent a binary heap. Assuming A[] is a heap array of length n

• The binary heap's root is kept at A[0]. 

• If there are any offspring of an element A[i], they are stored in A[2i + 1] and A[2i + 2], respectively.

• The parent of A[i] is stored in A[(i1)/2]. The left child of i is denoted as left(i) = A[2i + 1], if 2i + 1 n. The right child of i is denoted as right(i) = A[2i + 2], if 2i + 2 n.

Priority queues: Priority queues are frequently implemented using the heap data structure, where components are stacked on top of one another and sorted by priority. This enables constant-time access to the element with the highest priority, making it an effective data structure for handling tasks or events that must be prioritized.

Heapsort algorithm: An effective sorting technique with a worst-case time complexity of O(n log n), the heap data structure is the foundation for the heapsort algorithm. Database indexing and numerical analysis are just two uses for the heapsort method.

Memory management: In memory management systems, dynamic memory allocation and deallocation are accomplished using the heap data structure. The memory blocks are kept in a heap, and the heap data structure is utilized to efficiently manage them and assign them to other programmes as needed. 

Graph algorithms: Several graph algorithms, including the Dijkstra, Prim, and Kruskal algorithms, employ the heap data structure. These algorithms call for an effective priority queue implementation, which the heap data structure can provide.

Job scheduling: In algorithms for job scheduling, tasks are planned according to their priority or deadline using the heap data structure. The heap data structure is helpful for applications that involve job scheduling because it enables quick access to the task with the highest priority.

Effective element insertion and deletion are possible using the heap data structure. The heapify procedure transfers an element that has been added to the heap from the bottom of the heap to the right position. Similarly, the heap is reformed using the heapify operation when an element is removed from the heap; the bottom element then replaces the deleted element.

Effective priority queue:A priority queue with the highest priority element at the top is often implemented using the heap data structure. The heap is a useful data structure for building priority queues since it offers constant-time access to the element with the highest priority.

Access to the highest or lowest element is assured since the highest element in a max-heap is always the highest, and the highest element in a min-heap is always the lowest. This makes it handy for algorithms that need access to extreme values because it guarantees access to the highest or lowest element in a heap.

Due to the fact that it keeps elements in a complete binary tree structure, the heap data structure uses less memory than other data structures like linked lists or arrays.

The heap data structure is the foundation for the heap-sort algorithm, an effective sorting method with a worst-case time complexity of O(n log n).

• Lack of flexibility:Because the heap data structure is intended to preserve a particular order of components, it is not very versatile. This implies that it might not be appropriate for some applications that require more flexible data structures.

The heap data structure allows for rapid access to the top element, but it is not the best option for searching for a specific piece within the heap. A heap search involves traversing the entire Tree, which takes O(n) time to complete.

The relative order of equal elements may not be retained when the heap is formed or updated since the heap data structure is unstable.

• Memory management:Because the heap data structure involves dynamic memory allocation, using it on systems with little available memory can be difficult. Managing the RAM allotted to the heap can also be challenging and error-prone.

The heap data structure has a worst-case time complexity of O(n log n), which may not be ideal for some applications that call for quicker algorithms, despite providing for efficient insertion, deletion, and priority queue implementation.

To effectively organize and retrieve elements according to their priority, heaps are employed in a number of algorithms and data structures. 

• Priority Queues: Priority queues can be implemented using heaps, where items with higher priorities are retrieved before items with lower priorities.

• Sorting:A comparison-based method called heapsort may efficiently sort an array in O(n log n) time.

• Graph algorithms: Algorithms for graphs, like Dijkstra's shortest path algorithm, use heaps to effectively locate the node closest to the source.

• Median Maintenance: The median of an ever-changing group of numbers can be easily maintained by heaps.

• Task Scheduling:In real-time operating systems, heaps can be used to schedule jobs in accordance with their priority. 

Heaps are typically employed when it is necessary to efficiently retrieve and manage components according to their priority. Because they can obtain, insert, and delete elements faster than a linear search can—in O(log n) time—heaps are efficient. A linear search would take O(n) time. Various algorithms and data structures can easily employ heaps because they are simple to implement. For detailed explanations of different types of Data structures, refer to an online DSA course, and prepare yourself for a competitive world.