You Cant Pause

Toast Leon needs to make breakfast toast for the n members of his family. His toaster can accommodate one persons toast at a time, and each family member, j, wants their toast to spend tj seconds in the toaster. In Leons household, certain family members must have their toast before others (the precedence relationships form a directed acyclic graph). Violating precedence constraints is not an option, as it will make everything topsy turvy. Also, the amount of complaining that will be voiced by family member, j, if they receive their toast at time t is cj (t), where cj is a member-specific, non-negative, strictly increasing function. One thing Leon has learned is that you cannot pause toast. Pausing toast causes it to lose its essence. So, once Leon starts toasting someones toast, he cannot stop until it is done. Now, truth be told, Leon does not want to bring the ruckus to this breakfast. He asks you to develop a greedy algorithm that finds the ordering (schedule) that minimizes the maximum complaining among all valid toast schedules. Hint: start at the end