Design & Analysis of Algorithms - Vol 1 | 20. Breadth First Search (BFS) by Abraham | Learn Smarter
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20. Breadth First Search (BFS)

20. Breadth First Search (BFS)

This chapter discusses the Breadth First Search (BFS) algorithm for exploring graphs, emphasizing the methods for systematically finding paths between vertices. It explains the representation of graphs, the data structures used in BFS, and the way BFS operates, including complexities and how to track the shortest path between nodes. BFS is shown to efficiently explore graphs while providing distance information when needed.

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Sections

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  1. 20.1
    Breadth First Search (Bfs)

    Breadth First Search (BFS) is an algorithm used to explore graphs...

  2. 20.2
    Graph Representation

    This section discusses the representation of graphs using data structures...

  3. 20.2.1
    Adjacency Matrix

    This section introduces the concept of an adjacency matrix, a way to...

  4. 20.2.2
    Adjacency List

    This section explains how to represent graphs using adjacency lists and how...

  5. 20.3
    Bfs Algorithm

    The Breadth First Search (BFS) algorithm systematically explores a graph...

  6. 20.3.1
    Exploration Strategy

    This section introduces the Breadth-First Search (BFS) algorithm, detailing...

  7. 20.3.2
    Data Structures For Bfs

    This section covers the data structures essential for implementing the...

  8. 20.3.3
    Pseudo Code For Bfs

    This section introduces the algorithm for Breadth-First Search (BFS),...

  9. 20.3.4
    Example Of Bfs Execution

    This section discusses the concept of Breadth First Search (BFS) for...

  10. 20.3.5
    Formal Code For Bfs

    This section provides an in-depth explanation of the Breadth First Search...

  11. 20.3.6
    Complexity Analysis Of Bfs

    This section covers the complexity analysis of the Breadth-First Search...

  12. 20.3.7
    Input Size In Graphs

    This section discusses the representation of graphs, focusing on...

  13. 20.4
    Path Reconstruction In Bfs

    This section discusses the breadth-first search (BFS) algorithm, focusing on...

  14. 20.4.1
    Tracking Parent Vertices

    The section explores the Breadth First Search (BFS) algorithm for exploring...

  15. 20.4.2
    Tracking Levels

    This section discusses the breadth-first search algorithm for graph...

  16. 20.4.3
    Reconstructing Paths In Bfs

    This section discusses the Breadth-First Search (BFS) algorithm, focusing on...

  17. 20.5
    Shortest Path In Unweighted Graphs

    This section introduces the concept of finding the shortest path in...

  18. 20.5.1
    Shortest Path Properties

    This section discusses the properties of the shortest path in graphs using...

What we have learnt

  • Graphs can be represented using adjacency matrices or adjacency lists.
  • The BFS algorithm explores vertices level by level, marking each visited vertex.
  • BFS can be utilized to reconstruct paths and compute distances in unweighted graphs.

Key Concepts

-- Graph
A collection of vertices and edges representing connections.
-- Breadth First Search (BFS)
An algorithm for traversing or searching tree or graph data structures, exploring all neighbors at the present depth prior to moving on to vertices at the next depth level.
-- Adjacency Matrix
A square matrix used to represent a finite graph, where the elements indicate whether pairs of vertices are adjacent or not.
-- Adjacency List
A collection of lists or arrays that represent which vertices are adjacent to each vertex.
-- Queue
A data structure used in BFS to keep track of the vertices that need to be explored.
-- Path Reconstruction
The process of determining the route taken to reach a specific vertex in a graph, often achieved by keeping track of parent vertices.

Additional Learning Materials

Supplementary resources to enhance your learning experience.