BreadthFirstSearch

Breadth-first search

DFS is called "depth first" because it descends into the graph as quickly as possible.

Breadth-search first, in contrast, explores nodes by following a "wave front". It explores in order of their distance from the start vertex.

BFS(graph G, vertex v)

   FIFO_Queue Q;
   Array<int> distance(-1);
   
   distance[v] = 0;
   insert vertex v into the queue Q.

   while (Q is not empty)
      take the next vertex W off the front of the queue Q
      for each neighbor X of W do
         if (distance[X] == -1) then
            distance[X] = distance[W] + 1
            add vertex X to the tail of the queue Q
end

(example here)

Prove that BFS runs in time O(N+M) on any graph with N vertices and M edges.

References

• GoodrichAndTomassia section 6.3.3.