Binary heap in data structures algorithms.pdf
- 1. Shri Ramswaroop Memorial University Deva Road , Barabanki Name : Aayush Tiwari Roll No: 202310101050052 Course: MCA Sem: 2nd Sem Subject: Data Structures and Algorithms Submitted To: Mr. Harendra Singh Kharwal
- 3. Binary Heap Tree: A Binary Heap is a complete Binary Tree which is used to store data efficiently to get the max or min element based on its structure. A Binary Heap is either Min Heap or Max Heap. In a Min Binary Heap, the key at the root must be minimum among all keys present in Binary Heap. The same property must be recursively true for all nodes in Binary Tree. Max Binary Heap is similar to MinHeap.
- 4. Complete Binary Tree A complete binary tree is a binary tree in which every level, except possibly the last, is completely filled, and all nodes in the last level are as far left as possible
- 5. Types of Heap There are two types of heap data structures Max Heap 1. Min Heap 2. 1.Max Heap In a Max Heap, the parent node is always greater than or equal to its child nodes 2.Min Heap In a Min Heap, the parent node is less than or equal to its child nodes.
- 8. Operations on Binary Heap: create-heap: create an empty heap heapify: create a heap out of given array of elements find-max or find-min: find a maximum item of a max-heap, or a minimum item of a min-heap insert. adding a new key to the heap delete-max or delete-min: removing the root node of a max- or min-heap, respectively size: return the number of items in the heap. merge (union): joining two heaps to form a valid new heap containing all the elements of both, preserving the original heaps
- 9. Application of Binary Heap Heapsort: One of the best sorting methods being in-place and with no quadratic worst- case scenarios. Finding the min, max, both the min and max, median, or even the k-th largest element can be done in linear time using heaps. Priority Queue:: Priority queues can be efficiently implemented using Binary Heap because it supports insert(), delete() and extractmax(), decreaseKey() operations in O(logn) time. Graph algorithms like Prim's Algorithm and Dijkstra's algorithm.
- 10. Thank you