Find minimum shuttle transfers
Overview
This question evaluates a candidate's ability to model connectivity and minimize transfers in networked systems, testing graph-based reasoning, algorithm design, data-structure selection, and complexity analysis within the Coding & Algorithms domain.
You are given a collection of shuttle loops, each represented by a list of stop IDs that the loop visits in perpetuity. You may board a shuttle at any stop it serves and remain on it until any later stop on the same loop. Transferring from one shuttle loop to another counts as boarding a new shuttle. Given a source stop s and a target stop t, determine the minimum number of shuttles you must board to travel from s to t; return -1 if it is impossible. Describe the data structures you would use, outline the algorithm step by step, and analyze time and space complexity for inputs with up to 100,000 total stops across all loops. Discuss edge cases such as s == t, isolated loops, and multiple loops sharing the same stop. Follow-ups: how would you output an actual sequence of shuttles taken; how would you handle weighted transfer penalties or restricted operating hours; how can you reduce memory and avoid building an explicit route-to-route graph when the number of loops is very large?