System Dependency Load Factor

You are building an application that consists of many different services that can depend on each other. One of these services is the entrypoint which receives user requests and then makes requests to each of its dependencies, which will in turn call each of their dependencies and so on before returning.

Given a directed acyclic graph that contains these dependencies, you are tasked with determining the "load factor" for each of these services to handle this load. The load factor of a service is defined as the number of units of load it will receive if the entrypoint receives a 1 unit of load. Note that we are interested in the worst case capacity. For a given downstream service, its load factor is the number of units of load it is required to handle if all upstream services made simultaneous requests.

For example, in the following dependency graph where A is the entrypoint: Each query to A will generate one query to B which will pass it on to C and from there to D. A will also generate a query to C which will pass it on to D, so the worst case (maximum) load factors for each service is A:1, B:1, C:2, D:2.