Design & Analysis of Algorithms - Vol 2 | 4. Dijkstra's Algorithm and Prim's Algorithm by Abraham | Learn Smarter
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4. Dijkstra's Algorithm and Prim's Algorithm

This chapter discusses Prim's algorithm, a greedy algorithm used for finding the minimum spanning tree of a graph. It highlights the similarities and differences between Prim's and Dijkstra's algorithms, particularly in their update functions and overall approach. The chapter also covers the complexity analysis of Prim's algorithm, explaining how the use of data structures can optimize performance.

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Sections

  • 4.1

    Dijkstra's Algorithm And Prim's Algorithm

    This section explores Dijkstra's and Prim's algorithms, highlighting their similarities and differences in finding shortest paths and minimum spanning trees in graphs.

    Learning Practice

  • 4.1.1

    Introduction To Algorithm Comparison

    This section introduces Prim's algorithm, explaining it as a variant of Dijkstra's algorithm specifically for minimum spanning trees.

    Learning Practice

  • 4.1.2

    Executing Prim's Algorithm

    This section explains Prim's algorithm for finding a minimum spanning tree, comparing it with Dijkstra's algorithm and detailing its execution steps.

    Learning Practice

  • 4.1.3

    Update Mechanism In Prim's Algorithm

    This section discusses the update mechanism used in Prim's algorithm for generating minimum spanning trees and its comparison with Dijkstra's algorithm.

    Learning Practice

  • 4.1.4

    Complexity Analysis

    This section explains the complexity analysis of algorithms, particularly Prim's and Dijkstra's algorithms, showcasing the similarities and differences in their operations.

    Learning Practice

  • 4.1.5

    Handling Ties In Edge Weights

    This section examines how Prim's algorithm handles ties in edge weights, emphasizing the algorithm's flexibility in selecting edges and the implications for minimum spanning trees.

    Learning Practice

  • 4.1.6

    Conclusion On Spanning Trees

    This section concludes the discussion on spanning trees, specifically focusing on Prim's algorithm and its similarities with Dijkstra's algorithm.

    Learning Practice

  • 4.2

    Complexity Analysis

    This section discusses the complexity involved in Prim's algorithm and its relationship with Dijkstra’s algorithm, emphasizing the differences in how updates are managed.

    Learning Practice

  • 4.2.1

    Update Performance Improvement With Heap

    This section delves into the application of heap structures in Prim's algorithm for efficient tree formation.

    Learning Practice

References

ch30 part b.pdf

Class Notes

Memorization

What we have learnt

  • Prim's algorithm is a greed...
  • The algorithm operates simi...
  • To improve efficiency, usin...

Final Test

Revision Tests