Design & Analysis of Algorithms - Vol 1 | 22. Applications of BFS and DFS by Abraham | Learn Smarter
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22. Applications of BFS and DFS

The chapter explores the applications and properties of graph traversal techniques such as Breadth-First Search (BFS) and Depth-First Search (DFS). It discusses how these methods can identify connected components, determine cycles, and reveal important structural features in both undirected and directed graphs. Additionally, the chapter highlights the classification of edges and presents the concept of strongly connected components in directed graphs.

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Sections

  • 22.1

    Applications Of Bfs And Dfs

    This section explores various applications of Breadth First Search (BFS) and Depth First Search (DFS) algorithms, focusing on their roles in identifying graph properties such as connectivity and cycles.

    Learning Practice

  • 22.2

    Connected Components

    This section introduces connected components in graphs, explaining how BFS and DFS can identify these components and the significance of graph connectivity.

    Learning Practice

  • 22.2.1

    Identifying Connected Components

    This section covers how to identify connected components in undirected graphs using Breadth-First Search (BFS) and Depth-First Search (DFS).

    Learning Practice

  • 22.3

    Cycles In Graphs

    This section explores how to use Breadth First Search (BFS) and Depth First Search (DFS) to analyze graph structures, particularly focusing on identifying cycles and connected components.

    Learning Practice

  • 22.3.1

    Acyclic Graphs And Trees

    This section discusses the concepts of acyclic graphs and trees, highlighting their properties and applications in graph theory.

    Learning Practice

  • 22.4

    Understanding Bfs And Dfs In Cycle Detection

    This section discusses how Breadth-First Search (BFS) can be used to detect cycles in graphs, differentiating between properties of undirected and directed graphs.

    Learning Practice

  • 22.4.1

    Using Bfs For Cycle Detection

    This section discusses how Breadth-First Search (BFS) can be used to detect cycles in graphs, differentiating between properties of undirected and directed graphs.

    Learning Practice

  • 22.4.2

    Using Dfs For Cycle Detection

    This section discusses how Depth First Search (DFS) can be used to detect cycles in graphs, both undirected and directed.

    Learning Practice

  • 22.4.2.1

    Types Of Edges In Directed Graphs

    This section elaborates on different types of edges in directed graphs and their implications for understanding graph cycles and connectivity.

    Learning Practice

  • 22.4.2.2

    Classifying Non-Tree Edges

    This section explores the classification of non-tree edges in graphs using BFS and DFS.

    Learning Practice

  • 22.5

    Strongly Connected Components In Directed Graphs

    This section explores the identification and significance of strongly connected components in directed graphs using depth-first search (DFS).

    Learning Practice

  • 22.5.1

    Definition Of Strongly Connected Components

    Strongly connected components in directed graphs are defined such that every vertex can reach every other vertex in the component.

    Learning Practice

  • 22.5.2

    Using Dfs For Strongly Connected Components

    This section explores how Depth-First Search (DFS) can be applied to identify strongly connected components in directed graphs.

    Learning Practice

  • 22.6

    Applications Of Bfs And Dfs

    This section explores the applications of Breadth-First Search (BFS) and Depth-First Search (DFS) in analyzing the structure of graphs, including identifying connected components and detecting cycles.

    Learning Practice

  • 22.6.1

    Articulation Points

    This section explores the concepts of articulation points in graphs, highlighting their importance in maintaining graph connectivity.

    Learning Practice

  • 22.6.2

    Critical Edges

    This section explores the essential concepts of graph traversal, particularly focusing on Breadth First Search (BFS) and Depth First Search (DFS) to analyze the structural properties of graphs.

    Learning Practice

References

ch22.pdf

Class Notes

Memorization

What we have learnt

  • BFS and DFS can be used to ...
  • Connected components can be...
  • Different types of edges, s...

Final Test

Revision Tests