Design & Analysis of Algorithms - Vol 2 | 9. Heaps by Abraham | Learn Smarter
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9. Heaps

The chapter focuses on the concept of heaps as a data structure for implementing priority queues. It explains how heaps facilitate efficient operations for inserting and deleting elements based on their priority, ensuring both operations can be executed in logarithmic time. The properties of valid heaps and their structures are also discussed, providing examples and guidelines for maintaining the heap characteristics.

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Sections

  • 9

    Heaps

    Heaps are specialized binary trees that provide efficient implementations of priority queues by ensuring a specific structure and value property.

    Learning Practice

  • 9.1

    Introduction To Heaps

    Heaps are specialized tree-based data structures used to implement priority queues efficiently, allowing for insertion and deletion of the maximum element in logarithmic time.

    Learning Practice

  • 9.2

    Heap Structure And Properties

    This section discusses heap structures and properties essential for implementing priority queues, focusing on operations like insert and delete max.

    Learning Practice

  • 9.2.1

    Binary Tree Definition

    A binary tree is a hierarchical structure where each node may have up to two children, and it plays a crucial role in implementing heaps used for priority queues.

    Learning Practice

  • 9.2.2

    Heap Shape And Value Property

    This section introduces the concept of heaps, a special type of binary tree used to implement priority queues, focusing on heap shapes and the value property that defines them.

    Learning Practice

  • 9.2.2.1

    Max Heap Property

    This section introduces the Max Heap property, a crucial element in managing data structures for priority queues.

    Learning Practice

  • 9.3

    Examples Of Heaps

    This section introduces heaps as a special tree structure used to efficiently implement priority queues.

    Learning Practice

  • 9.3.1

    Valid Heap Example 1

    This section introduces heaps as a data structure for efficient priority queue implementation, explaining their properties and how to insert elements while maintaining their structure.

    Learning Practice

  • 9.3.2

    Valid Heap Example 2

    This section explains the concept of heaps as a data structure used for priority queues, discussing its properties and operations.

    Learning Practice

  • 9.3.3

    Invalid Heap Example

    This section discusses the properties of heaps, including valid and invalid structures, and the max heap property, using examples to illustrate these concepts.

    Learning Practice

  • 9.4

    Insertion And Deletion In Heaps

    This section discusses how to insert and delete elements in a heap data structure, which is essential for implementing priority queues.

    Learning Practice

  • 9.4.1

    Inserting A Node Into The Heap

    This section discusses how to insert a node into a heap, outlining the important properties of heaps such as structure and value property.

    Learning Practice

  • 9.4.2

    Maintaining Heap Properties

    This section covers the fundamental properties of heaps, necessary for implementing a priority queue, and details the mechanisms for maintaining these properties through operations such as insert and delete max.

    Learning Practice

References

ch35 part a.pdf

Class Notes

Memorization

What we have learnt

  • Heaps are specialized binar...
  • The structure of a heap is ...
  • The heap property requires ...

Final Test

Revision Tests