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My first instinct was just iterate through for each query, classic O(n*m) brute force.
Start by clarifying the problem: for each query, we need the maximum number of elements from the array whose sum is ≤ query value. The optimal strategy is to sort the array and use prefix sums, then for each query binary search the largest prefix sum ≤ query. This yields O(n log n + q log n) time, which is efficient and demonstrates strong algorithmic thinking.
Pro tip: Mention that sorting is key because selecting the smallest elements maximizes count for a given sum constraint. Also, discuss edge cases like negative numbers or empty arrays to show thoroughness.
Confirm that the subsequence can be any subset of elements (order doesn't matter) and that we want the maximum length. Ask about constraints: array size, query count, value ranges, and whether negative numbers are allowed.
Explain that to maximize count under a sum limit, we should pick the smallest elements first. Sorting the array allows us to consider prefixes, which are the smallest elements.
After sorting, compute prefix sums where prefix[i] is the sum of the first i elements. This allows O(1) sum retrieval for any prefix length.
For each query, binary search the largest index i such that prefix[i] ≤ query. The answer is i. If negative numbers are allowed, adjust by including all negatives first, then binary search on positives.
State time complexity: O(n log n) for sorting + O(q log n) for queries. Space: O(n) for prefix sums. Discuss edge cases: empty array, query smaller than smallest element, negative numbers, and large values causing overflow.
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