This question evaluates algorithmic proficiency with interval overlap counting and concurrent event aggregation, emphasizing correctness reasoning and time/space complexity analysis. It falls under the Coding & Algorithms domain and is commonly asked to assess practical algorithm implementation and complexity-analysis skills rather than purely conceptual understanding.
You are given N bus routes, each defined by a start time (inclusive) and an end time (exclusive). Compute the maximum number of routes running simultaneously. Clarify your algorithm, justify correctness, and analyze time and space complexity.