The key insight is that the order of queries doesn't actually matter for whether it's possible.
Model the problem as a difference array where each query adds a constraint on the maximum cumulative decrement at each position. Use a sweep line to check if the required decrements can be satisfied without exceeding the query limits, ensuring that the total decrement at each index equals the original value.
Pro tip: Clarify that queries can be applied in any order and that each query's decrement is independent; this allows a greedy or difference-array approach. Mention that if the array has negative values or queries with negative values, the problem becomes infeasible, so handle edge cases explicitly.
Restate the problem: given an array and range-decrement queries with a max decrement per query, determine if we can reduce all elements to zero. Clarify that each query can decrement each element in its range by any amount up to the given value, independently.
For each query (L, R, V), it imposes that the total decrement at any index i in [L, R] cannot exceed V from this query alone. Use a difference array to track the maximum allowed decrement at each position from all queries.
Perform a left-to-right sweep, maintaining the current maximum allowed decrement from active queries. At each index, check if the array value is less than or equal to this limit; if not, return false.
Compute the total possible decrement at each index by summing V over all queries covering that index using a difference array. Then check if array[i] ≤ total possible decrement for all i. If any array[i] is negative or any V is negative, return false.
Time complexity O(n + q) with difference array, space O(n). Mention edge cases: empty array, no queries, queries with V=0, negative values, and overlapping queries.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.