Design & Analysis of Algorithms - Vol 2 | 10. Height of the Heap by Abraham | Learn Smarter
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10. Height of the Heap

Heaps are data structures designed for efficiently implementing priority queues, offering logarithmic time complexity for insertions and deletions. By contrasting max heaps with min heaps, the chapter highlights their respective roles in prioritizing maximum and minimum values. Additionally, the process of building heaps via bottom-up approaches is introduced, demonstrating a more efficient O(N) method compared to the naive O(N log N) approach.

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Sections

  • 10.1

    Height Of The Heap

    This section discusses the relationship between a tree's height and its complexity, mentioning operations such as insertion and deletion in heaps.

    Learning Practice

  • 10.1.1

    Height Of The Tree And Complexity

    This section discusses the relationship between a tree's height and its complexity, mentioning operations such as insertion and deletion in heaps.

    Learning Practice

  • 10.1.2

    Insert Operation Complexity

    This section discusses the complexity of the insert operation in heaps and outlines the algorithm for inserting elements and deleting the maximum element in a priority queue.

    Learning Practice

  • 10.2

    Delete Maximum Operation

    This section discusses the delete maximum operation in heaps, explaining its efficiency and implementation.

    Learning Practice

  • 10.2.1

    Finding And Removing The Maximum

    This section explains how to find and remove the maximum value in a heap data structure, emphasizing the operations' efficiency and complexity.

    Learning Practice

  • 10.2.2

    Restoring Heap Property

    This section discusses how to restore the heap property after operations like insertion and deletion in a heap data structure.

    Learning Practice

  • 10.3

    Heap Representation

    This section explains the properties and operations of heap data structures, particularly focusing on their representation and how insertion and deletion operations maintain the heap properties.

    Learning Practice

  • 10.3.1

    Array Representation Of Heap

    This section covers the structure and behavior of heaps, particularly their array representation, operations of insertion and deletion, and how they maintain the heap property.

    Learning Practice

  • 10.3.2

    Child And Parent Node Calculation

    This section explains the relationship between parent and child nodes in a heap, focusing on the height of the tree and the operations required for inserting and deleting elements.

    Learning Practice

  • 10.4

    Building A Heap

    This section discusses the process of building a heap structure, focusing on insertion and deletion operations and the time complexity associated with them.

    Learning Practice

  • 10.4.1

    Naive Heap Construction

    This section explains how naive heap construction works, including the processes for inserting elements and deleting the maximum in a heap, along with their time complexities.

    Learning Practice

  • 10.4.2

    Optimized Heap Construction

    This section covers the efficient construction and operations of heaps, focusing on insertion and deletion processes, their time complexity, and methods to construct heaps from a set of data.

    Learning Practice

  • 10.5

    Heap Operations Summary

    This section summarizes heap operations, focusing on insertion, deletion, and the underlying structure that allows for efficient priority queue management.

    Learning Practice

  • 10.5.1

    Priority Queue Implementation

    This section details the implementation of priority queues using heaps, focusing on insertion and deletion operations.

    Learning Practice

  • 10.5.2

    Types Of Heaps

    This section explores different types of heaps, including max heaps and min heaps, along with their properties and operations such as insert and delete.

    Learning Practice

References

ch35 part b.pdf

Class Notes

Memorization

What we have learnt

  • Heap structures allow effic...
  • Understanding max heaps and...
  • The bottom-up method for he...

Final Test

Revision Tests