Heapify operation on Max-heap Data Structure

A heapify operation can be used to create a max heap from an unsorted array. This is done by starting at the last non-leaf node and repeatedly performing the “bubble down” operation until all nodes satisfy the heap property. The time complexity of heapify in a max heap is O(n).

Heapify Operations in Max-Heap

Introduction to Max-Heap – Data Structure and Algorithm Tutorials

A Max-Heap is defined as a type of Heap Data Structure in which each internal node is greater 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.

Introduction to Max-Heap Data Structure

Purpose and Use Cases of Max-Heap:

  • Priority Queue: One of the primary uses of the heap data structure is for implementing priority queues. 
  • Heap Sort: The heap data structure is also used in sorting algorithms.  
  • Memory Management: The heap data structure is also used in memory management. When a program needs to allocate memory dynamically, it uses the heap data structure to keep track of the available memory. 
  • Graph Algorithms: The heap data structure is used in various graph algorithms. For example, Dijkstra’s shortest path algorithm uses a heap data structure to keep track of the vertices with the shortest path from the source vertex. 

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Max-Heap Data structure in Different languages:

1. Max-Heap in C++...

Difference between Max and Min Heap

Min Heap Max Heap 1. In a Min-Heap the key present at the root node must be less than or equal to among the keys present at all of its children. In a Max-Heap the key present at the root node must be greater than or equal to among the keys present at all of its children. 2. In a Min-Heap the minimum key element present at the root. In a Max-Heap the maximum key element present at the root. 3. A Min-Heap uses the ascending priority. A Max-Heap uses the descending priority. 4. In the construction of a Min-Heap, the smallest element has priority. In the construction of a Max-Heap, the largest element has priority. 5. In a Min-Heap, the smallest element is the first to be popped from the heap. In a Max-Heap, the largest element is the first to be popped from the heap....

Internal Implementation of Max-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]. left child is stored at index 2i+1 Right child is stored at index 2i+2 Parent is stored at index floor((i-1)/2)...

Operations on Max-heap Data Structure and their Implementation:

Here are some common operations that can be performed on a Heap Data Structure data structure,...

1. Insertion in Max-Heap Data Structure:

Elements can be inserted to the heap following a similar approach as discussed above for deletion. The idea is to:...

2. Deletion in Max-Heap Data Structure:

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3. Peek operation on Max-heap Data Structure:

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4. Heapify operation on Max-heap Data Structure:

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5. Search operation on Max-heap Data Structure:

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Applications of Max-Heap Data Structure:

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Advantages of Max-Heap Data Structure:

Deleting an element at any intermediary position in the heap can be costly, so we can simply replace the element to be deleted with the last element and delete the last element of the Heap....

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