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HomeBlogWeb DevelopmentWhat is Binary Heap? Types, Operations, Implementation
Efficiency is paramount in computer science. From massive datasets to complex tasks, quickly accessing and organizing information is key. Enter the Binary Heap, a powerful data structure used for everything from algorithms to priority queues. This article dives into Binary Heaps, exploring their types, operations, and implementation. Programmers of all levels will benefit from understanding this fundamental data structure.
A Binary Heap is a full binary tree-based data structure that has the heap property. In layman's words, it's a tree structure in which each parent node has at most two children and the tree is filled on all levels except the lowest, which is filled from left to right.
Binary heaps are especially handy for priority queue implementations, and they are widely utilized in algorithms like Dijkstra's shortest path method and the heap sort algorithm. Their ability to insert, delete, and retrieve the minimum or maximum element makes them helpful in a variety of applications requiring fast data organization and processing.
Here's an example that will help you understand better. Consider a hospital emergency room with a long line of patients. The priority queue can be modelled as a binary heap in the following way.
Binary heaps are expressed as arrays. Arrays are containers that hold elements in a predefined order that satisfies the attribute. Below is the binary heap example, an ascending array stores values in ascending (increasing) order.
Because heap elements are kept in an array, you'll require an index. The root or initial value is stored in the first place. For any other element 'i' in the array:
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The attributes of a binary heap are as follows:
Binary heaps are classified into two types: max and min-heaps.
In a minimum binary heap structure, for each node 'x' (other than the root), the key (value) stored in children is less than or equal to x's key (values). In other words, the root always contains the smallest element, and the value of each parent node is less than or equal to the values of its children.
In contrast to a min-heap, every node 'x' (except the root) should have a key (value) that is less than or equal to the keys (values) contained in its offspring. Simply put, the greatest element is always at the root, and the value of each parent node exceeds or equals the values of its children.
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Criteria | Binary Min Heap | Binary Max Heap |
Definition | For any node ‘x,’ the key (value) in ‘x’ is less than or equal to the keys (values) in its children. | For any node ‘x,’ the key (value) in ‘x’ is greater than or equal to the keys (values) in its children. |
Root Key (or Value) | Minimum | Maximum |
Sorting | Ascending | Descending |
Insertion | A new element to be inserted is placed at the appropriate position to maintain the min-heap property. | The new element is placed at the appropriate position without disturbing the max-heap property. |
Deletion | The minimum value (root value) is removed and the last element in the heap replaces it. | The entire heap is then accommodated to satisfy the min-heap property. The maximum value (root value) is deleted |
Application | It uses where the minimum is to be assessed | It is uses where the maximum is to be assessed. |
When evaluating the minimum/maximum and priority in sorting-based applications, binary heaps are frequently utilized. Consequently, you may perform a wide range of operations on binary heap arrays. The heap operations that are most frequently utilized are listed below.
The minimal value, or root element, of a binary min heap is returned by the getMin() function. On the other hand, a binary max heap's maximum value, or root, is returned by getMax().
The insert() function allows you to insert new items. To preserve the entire tree property, the new element is often placed at the bottom right of the heap. Once the newly inserted value has been compared with its parent, the order property is restored through suitable swapping.
The root (min in min-heap and max in max-heap) is deleted during this process. After that, the heap's final element is shifted to the root location, and the heap is modified to meet the necessary order property. By contrasting the new root value with its children's value, the adjustment is made.
To eliminate the root, or minimum element, from a binary min heap, use the extractMin() command. On the other hand, to remove the maximum (root) from a binary max heap, use the extractMax() command.
Binary heaps are very important because they improve the efficiency with which sorting and prioritizing algorithms may be implemented. These are a few typical uses.
Priority queues, in which items have corresponding priorities and must be handled in accordance with those priorities, are one of the most popular uses for binary heaps. Task scheduling, event simulations, graph algorithms like Dijkstra and Prim's, and other applications employ these queues.
Binary heaps are used by the effective sorting algorithm known as heap sort. Using the input array, this algorithm creates an ascending max-heap and a descending min-heap, from which the corresponding max and min are extracted. There is a sorted array as the result. Heap is frequently utilized in situations that require in-place sorting with a worst-case performance guarantee (where items must be sifted along the whole heap's length).
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Here are some of the common ways to implement Binary Heap:
Using arrays is the most effective technique to express binary heaps. These properties apply to a binary heap represented as an array:
Heapify algorithms must be used if you have an array and want to transform it into a proper binary heap. In order to construct a heap or to restore the heap property following an insertion or deletion, this step is crucial. Sift-down and sift-up are the two main variants of the heapify algorithms, often known as heap sort.
There are many applications for binary heaps in the real world. Here are a few illustrations.
An evolved form of binary heaps known as D-ary heaps allow each internal node to have up to 'D' children rather than just one or two at most. Especially for big D values, they provide lower tree height and better cache performance when compared to binary heaps.
A more sophisticated type of heap data structure that allows for more complex operations like key merging and key shrinking is called a fibonacci heap. These operations now have a constant time complexity that is much lower, which makes them compatible with some algorithms, such Dijkstra's algorithm.
Binary Heaps are a cornerstone of data structures, providing a tremendous combination of efficiency, adaptability, and simplicity. Their complete binary tree structure and adherence to the heap order property keep them balanced and capable of enabling quick operations such as insertion, deletion, and retrieval of the minimum or maximum element.
Binary Heaps' efficiency makes them ideal for building priority queues, which provide quick access to elements based on their priority level or value. Furthermore, their space-efficient array-based representations and capacity to allow modifications such as d-ary heaps contribute to their extensive use in a variety of computational applications.
A memory heap is a region of a program's memory for dynamic memory allocation, whereas a binary heap is a specific data structure used for implementing priority queues. The former manages memory allocation, while the latter organizes data in a hierarchical manner for efficient priority-based operations.
A heap size in a binary heap refers to the maximum number of elements that can be stored in the underlying array representing the heap structure.
The use of a binary heap is for implementing priority queues, where elements are stored in a hierarchical order based on their priority, allowing for efficient insertion, deletion, and retrieval of the highest (or lowest) priority element.
The runtime of common operations in a binary heap, such as insertion, deletion, and retrieval of the highest (or lowest) priority element, typically achieves logarithmic time complexity, O(log n), where n is the number of elements in the heap.
Yes, a binary heap can contain duplicate elements.
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