Find minimum-latency path across dependent services

You are given a set of services and directed dependencies between them. Each dependency edge represents a call from one service to another with a known latency.

• Services are labeled 0..N-1 .
• You are given a list of directed edges (u, v, latency) meaning service u can call service v and that hop adds latency milliseconds.
• Given a start service and a target service, compute the minimum total latency along any valid call chain from start to target .

If there is no route, return -1.

Input

• N : number of services
• edges : list of (u, v, w) with w > 0
• start , target

Output

• Integer minimum total latency (sum of edge weights), or -1 if unreachable.

Notes

• The dependency graph may contain cycles.
• Multiple edges between the same pair may exist; take the best one if helpful.