Internal Implementation of Min-Heap Data Structure
A Min heap is typically represented as an array.
- The root element will be at Arr[0].
- For any ith node Arr[i]:
- Arr[(i -1) / 2] returns its parent node.
- Arr[(2 * i) + 1] returns its left child node.
- Arr[(2 * i) + 2] returns its right child node.
The Internal Implementation of the Min-Heap requires 3 major steps:
- Insertion: To insert an element into the min heap, we first append the element to the end of the array and then adjust the heap property by repeatedly swapping the element with its parent until it is in the correct position.
- Deletion: To remove the minimum element from the min heap, we first swap the root node with the last element in the array, remove the last element, and then adjust the heap property by repeatedly swapping the element with its smallest child until it is in the correct position.
- Heapify: A heapify operation can be used to create a min heap from an unsorted array.
Introduction to Min-Heap – Data Structure and Algorithm Tutorials
A Min-Heap is defined as a type of Heap Data Structure in which each node is smaller than or equal to its children.
The heap data structure is a type of binary tree that is commonly used in computer science for various purposes, including sorting, searching, and organizing data.
Purpose and Use Cases of Min-Heap:
- Implementing Priority Queue: One of the primary uses of the heap data structure is for implementing priority queues.
- Dijkstra’s Algorithm: Dijkstra’s algorithm is a shortest path algorithm that finds the shortest path between two nodes in a graph. A min heap can be used to keep track of the unvisited nodes with the smallest distance from the source node.
- Sorting: A min heap can be used as a sorting algorithm to efficiently sort a collection of elements in ascending order.
- Median finding: A min heap can be used to efficiently find the median of a stream of numbers. We can use one min heap to store the larger half of the numbers and one max heap to store the smaller half. The median will be the root of the min heap.
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