Given: a sequence of activities $\backslash (1,\backslash$ldots$,$ n $\backslash ),$ where each activity $\backslash ($ i $\backslash )$ has with an execution time $\backslash ($ c$\_\{$i$\}\backslash )$ and with a list of prerequisite activities that needs to be completed before activity is started.

Find: The time required to complete all activities. Problem $4$: Consider the Project Management problem seen in class: we are given a sequence of activities $\backslash (1,\backslash$ldots$,$ n $\backslash ),$ where each activity $\backslash ($ i $\backslash )$ has an execution time $\backslash ($ c$\_\{$i$\}\backslash )$ and a list of prerequisite activities that needs to be completed before activity $\backslash ($ i $\backslash )$ is started. The completion time of the project is the time needed to complete all activities, assuming that we can do in parallel as many activities as we want as long as none is a prerequisite of the other.

We say that an activity is in a critical path if any delay in its completion will cause the completion time of the project to be delayed. Give an algorithm to compute which activities are in the critical path.