Breadth First Search(BFS)

This is simpler way to present BFS, which we showed in class.

The Q is a First In First Out queue.

 Complexity: O(N^2) for an adjacency  matrix representation

                      O(N+E) for an adjacency list representation.

Properties:

1. each nodes is visited exactly once if the graph is connected.

2. Each edges is "explored" twice, once from each node.

    ·       Initialize: Color all vertices white

        For all v Î V,

                               c[v]  = white                :color

                              parent[v] = none                  :parent

                               d[v]  = -100                 :distance

    ·       Source s:

                               c[s]  = grey

                              parent[s] = none

                               d[s] = 0

    ·       Add s to queue: Q

    ·       While Q is not empty

        Do

                  u = Get head of Q   (remove it from Q)

                  For all adjacent nodes,w, of u

                  Do

                           If c[w] == white

                           Then

                                     Color[w] = grey

                                            d[w] = d[u] + 1

                                           parent[w] = u

                                     add w to Q

                           End if

                  End for

               c[u] = black

        End while