Model the circular network as a graph where each hub is a node and edges represent travel times between adjacent hubs. Precompute the shortest travel time between any two hubs by considering both clockwise and counterclockwise paths around the circle. Then, sum the precomputed shortest times for each consecutive pair in the requested sequence, starting from hub 1.
Pro tip: Clarify whether the drone must visit hubs in the exact order given or if it can optimize the order; the problem states 'in order', so assume fixed order. Also, mention that the solution runs in O(m + n) time, which is optimal.
Restate the problem: a circular network of m hubs, start at hub 1, visit a sequence of requested hubs in order, minimize total travel time. Clarify that travel times are given for adjacent hubs and that the drone can move clockwise or counterclockwise.
Since the network is circular, the shortest path between any two hubs is the minimum of the clockwise and counterclockwise distances. Compute prefix sums of edge weights to quickly calculate these distances in O(1) per query.
Initialize total time to 0 and current hub to 1. For each requested hub in the given order, add the shortest distance from current hub to that hub, then update current hub to the requested hub.
Precomputing prefix sums takes O(m) time and O(m) space. Processing the sequence takes O(n) time, where n is the number of requests. Overall O(m + n) time, which is optimal.
Handle cases where the sequence is empty, contains hub 1, or has repeated hubs. Ensure the circular distance calculation correctly handles wrap-around (e.g., from hub m to hub 1).
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