Graph Theory Questions Medium
The breadth-first search (BFS) algorithm is a graph traversal algorithm that explores all the vertices of a graph in breadth-first order. It starts at a given source vertex and systematically explores all the vertices that are reachable from the source vertex, visiting the vertices in increasing order of their distance from the source.
The algorithm works by maintaining a queue of vertices to be visited. It starts by enqueueing the source vertex and marking it as visited. Then, it repeatedly dequeues a vertex from the queue, visits it, and enqueues all its unvisited neighbors. This process continues until the queue becomes empty.
During the traversal, BFS also keeps track of the parent of each visited vertex, which allows us to reconstruct the shortest path from the source vertex to any other vertex in the graph.
BFS guarantees that all vertices will be visited, and it explores vertices in a level-by-level manner, meaning that it visits all the vertices at distance 1 from the source before moving on to vertices at distance 2, and so on. This property makes BFS useful for solving problems that involve finding the shortest path or exploring the graph in a systematic manner.
Overall, the breadth-first search algorithm is an efficient and widely used method for traversing and exploring graphs.