The greedy insight is pretty quick to get to since prices only go up, so you always want to buy left to right.
First, clarify that 'greedily moving rightward' means buying items in order from the starting position until the budget is exhausted. Then, explain that since the array is non-decreasing, the sum of any contiguous subarray can be computed efficiently, and for each query, you can use binary search on prefix sums to find the farthest index reachable within the budget. Finally, discuss time complexity and possible optimizations for multiple queries.
Pro tip: Mention that if there are many queries, you can precompute prefix sums and use binary search per query, achieving O(log n) per query after O(n) preprocessing. Also, note that if queries are offline, you might sort them and use two pointers to achieve O(n + q) total time.
Confirm that 'greedily moving rightward' means buying items sequentially from the starting index until the next item would exceed the remaining budget. Ensure you understand that the array is non-decreasing, which guarantees that prices increase or stay the same as you move right.
Compute a prefix sum array where prefix[i] is the sum of prices from index 0 to i-1. This allows O(1) calculation of the sum of any contiguous subarray.
For a query (start, budget), the total cost to buy items from start to index j is prefix[j+1] - prefix[start]. Use binary search to find the largest j such that this sum is ≤ budget. The number of items bought is j - start + 1.
State that preprocessing takes O(n) time and each query takes O(log n) time. Handle edge cases: budget insufficient for even the first item (answer 0), start index out of bounds, and large budgets that allow buying all remaining items.
If there are many queries, consider offline processing: sort queries by start index and use a sliding window or two pointers to achieve O(n + q) total time. Alternatively, if queries are online, the binary search approach is optimal.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.