Design & Analysis of Algorithms - Vol 2 | 11. Heaps and Dijkstra's Algorithm by Abraham | Learn Smarter
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11. Heaps and Dijkstra's Algorithm

Heaps are a crucial data structure used in priority queues, enabling efficient operations such as insertion and deletion. The chapter discusses Dijkstra's algorithm, highlighting the importance of heaps for efficiently managing and updating distances in graphs. Additionally, it explores using heaps for sorting data and presents a methodology for achieving in-place sorting using heaps.

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Sections

  • 11.1

    Design And Analysis Of Algorithms

    This section covers the design and analysis of heaps in the context of Dijkstra's algorithm and sorting techniques.

    Learning Practice

  • 11.1.1

    Heaps And Dijkstra's Algorithm

    This section discusses the use of heaps in implementing Dijkstra's algorithm and their application in sorting techniques.

    Learning Practice

  • 11.1.2

    Using Heaps For Sorting

    This section covers the application of heaps in sorting algorithms, specifically detailing the process of heap sort and related complexities.

    Learning Practice

  • 11.2

    Dijkstra's Algorithm

    Dijkstra's Algorithm is a method for efficiently finding the shortest paths from a source vertex to all other vertices in a graph using heaps as priority queues.

    Learning Practice

  • 11.2.1

    Finding The Minimum Distance

    This section outlines Dijkstra’s algorithm and its implementation using heaps, discussing how to efficiently find the minimum distance in a graph.

    Learning Practice

  • 11.2.2

    Updating Heap Values

    This section discusses how to update values within heaps, focusing on the use of heaps in Dijkstra's algorithm and the implications of these updates.

    Learning Practice

  • 11.2.3

    Handling Value Changes

    This section discusses how to handle changes in values within heaps, focusing on Dijkstra's algorithm and heap-based sorting.

    Learning Practice

  • 11.3

    Complexity Analysis

    This section explores the complexity of heaps and Dijkstra's algorithm, emphasizing how heaps facilitate efficient operations in priority queues.

    Learning Practice

  • 11.3.1

    Time Complexity Of Dijkstra's Algorithm

    This section explains the time complexity of Dijkstra's algorithm using heaps, highlighting the efficient management of distances and updates within the algorithm.

    Learning Practice

  • 11.4

    Heaps As A Sorting Algorithm

    Heaps can be effectively used as a sorting algorithm, where building a heap and repeated extraction of maximum elements results in a sorted list.

    Learning Practice

  • 11.4.1

    Building And Maintaining A Heap

    This section discusses heaps as an implementation of priority queues, focusing on their construction, maintenance, and applications in algorithms like Dijkstra's.

    Learning Practice

  • 11.4.2

    In-Place Sorting With Heaps

    This section discusses the application of heaps in sorting algorithms, particularly how heaps can be used to achieve in-place sorting with a time complexity of O(n log n).

    Learning Practice

References

ch36.pdf

Class Notes

Memorization

What we have learnt

  • Heaps can be represented as...
  • Dijkstra's algorithm utiliz...
  • Heaps can be employed for s...

Final Test

Revision Tests