Circular Array — Multi-Query Distance Accumulation

Bus-stops-on-a-ring variant of LC 1184: prefix-sum the ring once, then answer a stream of (a, b) queries by accumulating the shorter of the two arc distances. Requirements Given n stops arranged on a ring with edge weights distance[i] between stop i and stop (i+1) % n. A query stream of pairs (start, end) arrives; for each pair return the shorter of the two arc distances between start and end. Total answer is the sum of all per-query distances. Optimize for many queries against the same ring. Notes Equivalent in shape to the LC 1184 "Distance Between Bus Stops" problem, but the interview variant runs many queries so an O(1) per query path is expected, not a per-query traversal. Standard recipe: build a prefix-sum P[i] = sum of distance[0..i-1] and let total = P[n]. For a query (a, b) with a < b, the forward arc is P[b] - P[a] and the answer is min(forward, total - forward). Watch for the common off-by-one when start > end — normalize by swapping or by using modular subtraction. The OA framing usually wraps this in a domain (deliveries / sightseeing route), so the under-specified part is mostly extracting the ring + edge weights from the input format. Preparation Solve LC 1184 cold, then re-solve with a query stream and measure that the prefix-sum path is O(1) per query. Hand-trace a 5-stop ring with two queries that straddle the wrap-around index to lock in the total - forward branch. Write the prefix-sum build in 90 seconds without looking — this is the kind of warm-up that buys time for the AI-debug second half of the OA.