Given n cities with m one$-$way train connections

between cities, we can follow a sequence of connections $($a $$route$)$ to travel from one city

to another. Given connections a $->$ b and b $->$ c between cities a$,$ b and c$,$ for example, we can

travel from a to c through b$.$ We assume there are no cycles, i$.$e$.$ there is no route containing at

least one connection from any city to itself. Design a dynamic programming algorithm to compute

the number of distinct routes from city s to any city v$.$

a$)$ Define subproblems.

b$)$ Write a recurrence describing the relationship between subproblems defined in a$).$

c$)$ Give the pseudo$-$code of the algorithm.