I kept trying to simulate it directly at first, iterating over each range per query, which is obviously too slow.
Clarify the problem constraints and define the exact operation: each query specifies a range [l, r] and a max decrement value d, meaning you can decrement each element in the range by any integer between 0 and d, but you must apply all queries in order. Then, model the problem as a difference array or sweep line to track the cumulative decrements and check feasibility by ensuring that at each position, the total decrement applied so far does not exceed the original value, and that after all queries, the total decrement exactly equals the original value.
Pro tip: Mention that you would first confirm whether the decrement per element can be chosen independently per query (i.e., you can decrement different amounts for different elements within the same query) or if it's a uniform decrement across the range. This distinction drastically changes the solution and shows you think about edge cases.
Ask the interviewer to confirm the operation: for each query (l, r, d), you can decrement each element in arr[l..r] by any integer from 0 to d, independently per element, and queries must be applied in order. Also confirm that you cannot decrement below zero at any point.
Use a difference array or sweep line to track the total decrement applied to each index over all queries. Since queries are in order, you can process them sequentially and maintain the current total decrement at each position.
For each index, ensure that the total decrement applied so far never exceeds the original value, and that after all queries, the total decrement equals the original value. If any element would go negative or not reach zero, return false.
Use a difference array to apply range decrements in O(1) per query, then compute prefix sums to get the total decrement at each index. This yields O(n + q) time complexity.
Consider cases where queries overlap, where d is zero, where ranges are out of bounds, or where the array has negative numbers (if allowed). Also discuss if queries can be skipped or if all must be applied.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.