Problem $2.$ We have an undirected graph G$=($V$,$E$)$ and two vertices s and t$.$ Additionally, we are given a list of new edges F which do not belong to the graph G$.$ For any edge f in F$,$ we define the graph G$\_($f$)$ as the graph obtained by adding the edge f to the original graph G$.$ Design an algorithm that in time O$($n$+$m$+|$F$|)$ finds the edge f in F such that the distance from s to t in G$\_($f$)$ is minimized among all choices of an edge from F$.$

Please write out the algorithm and give an analysis of its runtime.