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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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.
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