Question $2$: Bellman$-$Ford Algorithm

Consider a city transportation network where roads between various districts have travel

costs that could sometimes be negative due to special subsidies. You need to determine

the shortest path from a central district to all other districts and check for the presence of

any negative weight cycles that might affect the feasibility of consistent travel costs.

Represent the network as a directed graph with the given data.

Use the Bellman$-$Ford algorithm starting from the central district $($node A$)$ to compute the

shortest paths to all other districts.

Identify if there is any negative weight cycle that could be reachable from the source.

Explain the implications of such a cycle on the network.

Provide the resulting shortest paths and discuss any districts that cannot be reached

optimally due to negative cycles.