Types of heaps

Introduction to Heap:

Binary heap is a complete binary tree where the root of any subtree has a higher (or lower based on the type of heap) value than all the nodes in its subtree....

Types of heaps:

There are 2 types of heaps:...

Representation of Binary Heap:

A Binary Heap is a Complete Binary Tree. A binary heap is typically represented as an array....

Operations on Binary Heaps:

The common operation involved using heaps are:...

Advantages of Heap Data Structure:

Efficient insertion and deletion: The heap data structure allows efficient insertion and deletion of elements. When a new element is added to the heap, it is placed at the bottom of the heap and moved up to its correct position using the heapify operation. Similarly, when an element is removed from the heap, it is replaced by the bottom element, and the heap is restructured using the heapify operation.Efficient priority queue: The heap data structure is commonly used to implement a priority queue, where the highest priority element is always at the top of the heap. The heap allows constant-time access to the highest priority element, making it an efficient data structure for implementing priority queues.Guaranteed access to the maximum or minimum element: In a max-heap, the top element is always the maximum element, and in a min-heap, the top element is always the minimum element. This provides guaranteed access to the maximum or minimum element in the heap, making it useful in algorithms that require access to the extreme values.Space efficiency: The heap data structure requires less memory compared to other data structures, such as linked lists or arrays, as it stores elements in a complete binary tree structure.Heap-sort algorithm: The heap data structure forms the basis for the heap-sort algorithm, which is an efficient sorting algorithm that has a worst-case time complexity of O(n log n)....

Disadvantages of Heap Data Structure:

Lack of flexibility: The heap data structure is not very flexible, as it is designed to maintain a specific order of elements. This means that it may not be suitable for some applications that require more flexible data structures.Not ideal for searching: While the heap data structure allows efficient access to the top element, it is not ideal for searching for a specific element in the heap. Searching for an element in a heap requires traversing the entire tree, which has a time complexity of O(n).Not a stable data structure: The heap data structure is not a stable data structure, which means that the relative order of equal elements may not be preserved when the heap is constructed or modified.Memory management: The heap data structure requires dynamic memory allocation, which can be a challenge in some systems with limited memory. In addition, managing the memory allocated to the heap can be complex and error-prone.Complexity: While the heap data structure allows efficient insertion, deletion, and priority queue implementation, it has a worst-case time complexity of O(n log n), which may not be optimal for some applications that require faster algorithms....

Previously Asked GATE Questions on Binary Heap

Question 1: The elements 32, 15, 20, 30, 12, 25, 16 are inserted one by one in the given order into a Max Heap. The resultant Max Heap is....