Took me longer than it should have to realize the non-decreasing property was the whole key.
First, clarify the problem constraints and edge cases, then propose an efficient algorithm using prefix sums and binary search to answer each query in O(log n) time. Explain how to compute the maximum number of items by finding the furthest booth reachable within the budget from the starting position.
Pro tip: Mention that since the array is non-decreasing, the cost to buy from a contiguous subarray is simply the sum of prices, and prefix sums allow O(1) range sum queries. This demonstrates you recognize the monotonicity and can optimize beyond brute force.
Ask clarifying questions about input format, constraints (e.g., n and number of queries), and whether prices are integers. Confirm that Alex must buy from consecutive booths starting at the given index and cannot skip booths.
Compute a prefix sum array of the prices so that the sum of any contiguous subarray can be calculated in O(1) time. This is crucial for handling multiple queries efficiently.
For a query (start, budget), use binary search to find the largest index end such that the sum from start to end is ≤ budget. The number of items is end - start + 1.
Consider cases where the budget is less than the first price (answer 0), or where the budget is enough to buy all remaining items. Also handle large inputs with efficient I/O.
State that preprocessing takes O(n) time, and each query takes O(log n) time due to binary search. Overall time complexity is O(n + q log n), which is optimal for this problem.
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