The ring structure is what makes it click.
First clarify the problem constraints and assumptions, then design an efficient algorithm using prefix sums to compute distances in O(1) per query. Explain how to handle the circular nature by comparing clockwise and counterclockwise distances, and analyze time and space complexity.
Pro tip: Mention that you would precompute prefix sums of corridor lengths to answer each distance query in constant time, and discuss edge cases like when the route has only one hub or when the shorter arc is ambiguous (equal distances).
Ask questions to confirm: Are the hubs numbered 0 to n-1 in order? Are corridor lengths positive? Can the route contain repeated hubs? Is the drone allowed to pass through other hubs? Confirm that 'shorter arc' means the minimum of clockwise and counterclockwise distances.
Compute prefix sums of the corridor lengths around the ring so that the clockwise distance between any two hubs can be found in O(1). Also compute the total perimeter length.
For each pair of consecutive hubs in the route, calculate the clockwise distance using prefix sums, then the counterclockwise distance as total perimeter minus clockwise. Take the minimum of the two.
Accumulate the minimum distances for all consecutive pairs to get the total minimum distance the drone travels. Handle edge cases such as a route with fewer than two hubs (return 0).
State that preprocessing takes O(n) time and O(n) space, and each query takes O(1), so total time is O(n + m) where m is the route length. Walk through a small example to verify correctness.
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