$4.$ In a directed network with $\backslash ($ N $\backslash )$ nodes and non$-$negative link costs, how to find the shortest path between a pair of source$-$destination nodes $\backslash ($ S $\backslash )$ and $\backslash ($ D $\backslash ),$ subject to the constraints that the transmission from S has to go through a node A $,$ say, for security inspection, before it finally reaches D $.$ Note that we do not allow the path from S to D go through any node twice.

$(25$ marks$)$