A Better Battle Plan

Computer Science Level pending

During a battle, Sheldor the conqueror notices that his cities are in the form of a Directed Acyclic Graph, i.e, all the roads are one-way and there is no sequence of roads starting from a city that comes back into it.

Because the roads are one way, Sheldor wants to order them in a fashion which will let him know in which order he should he should progress his troops, i.e, he needs a permutation of the cities such that if there is a road from $$u$$ to $$v$$, $$v$$ occurs after $$u$$ in the permutation.

Four of his ministers, Alice, Bob, Charles and David attempt this problem and produce these answers:

• Each line of the file contains two integers u v in that order. This means that there is a directed edge from u to v.