My first instinct was to just simulate it, sum up the total capacity per index and compare to nums[i].
Model the problem as a system of constraints: for each index, the sum of decrements from all queries covering it must equal the original value, and each query's decrement must be between 0 and its max. Use a difference array or sweep line to efficiently compute coverage and check feasibility, or reduce to a flow problem if queries can be partially applied.
Pro tip: Clarify whether queries must be applied fully or can be partially used; this changes the problem from a simple coverage check to a flow/matching problem. Also, mention that if the total maximum decrement per index is less than the array value, it's immediately impossible.
Ask whether each query must be applied exactly once with a fixed decrement, or if we can choose any amount up to the max per query. Also confirm if queries are independent and can be applied in any order.
For each index, the sum of decrements from all queries covering it must equal the array value. Each query contributes a variable between 0 and its max. This is a system of linear equations with bounds.
Compute for each index the total maximum possible decrement (sum of max values of covering queries). If any index's array value exceeds this, return false. Also check that total sum of array equals total sum of applied decrements.
If queries can be partially applied, model as a flow network: source to queries (capacity = max), queries to indices (infinite capacity if covers), indices to sink (capacity = array value). Check if max flow equals total array sum. Alternatively, use a greedy sweep with a priority queue if queries are intervals.
Analyze time/space complexity of your approach. Mention edge cases: empty array, queries with max=0, overlapping queries, and indices not covered by any query.
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