How does a Breadth-First Search work when looking for Shortest Path?

Question

I\'ve done some research, and I seem to be missing one small part of this algorithm. I understand how a Breadth-First Search works, but I don\'t understand how exactly it wi

Answer 1

Visiting this thread after some period of inactivity, but given that I don't see a thorough answer, here's my two cents.

Breadth-first search will always find the shortest path in an unweighted graph. The graph may be cyclic or acyclic.

See below for pseudocode. This pseudocode assumes that you are using a queue to implement BFS. It also assumes you can mark vertices as visited, and that each vertex stores a distance parameter, which is initialized as infinity.

mark all vertices as unvisited
set the distance value of all vertices to infinity
set the distance value of the start vertex to 0
if the start vertex is the end vertex, return 0
push the start vertex on the queue
while(queue is not empty)   
    dequeue one vertex (we’ll call it x) off of the queue
    if x is not marked as visited:
        mark it as visited
        for all of the unmarked children of x:
            set their distance values to be the distance of x + 1
            if the value of x is the value of the end vertex: 
                return the distance of x
            otherwise enqueue it to the queue
if here: there is no path connecting the vertices

Note that this approach doesn't work for weighted graphs - for that, see Dijkstra's algorithm.