What is the least-cost solution for getting from point A to point B?

Shortest Paths Problem

Given a weighted, directed graph G = (V, E) with edge weights w and a path
definition of p =
<*v*_{0}, *v*_{1}, .., *v*_{k}> with weight
w(p) =
, find the shortest path weight from
vertex u to vertex v

Breadth-First Search worked on unweighted (unit weight) graphs.