Spent the first few minutes overcomplicating it.
Start by clarifying the problem: we need to select the maximum number of distinct products whose total price does not exceed the budget. The optimal strategy is to sort the prices in ascending order and greedily pick the cheapest products until the budget is exhausted, which is a classic greedy algorithm. Then discuss time complexity, edge cases, and potential optimizations.
Pro tip: Mention that this is a special case of the knapsack problem where all items have equal value (1), so the greedy approach is optimal. Also, note that if the product list is huge, you can use a min-heap or quickselect to avoid full sorting, but sorting is usually fine.
Confirm that each product can be bought at most once, we want to maximize the count of distinct products, and the budget is a hard constraint. Ask if prices are positive integers and if the list is static.
Recognize that to maximize the number of items under a sum constraint, we should prioritize cheaper items. This leads to a greedy strategy: sort prices ascending and take as many as possible.
Describe the steps: sort the price list, initialize a counter and remaining budget, iterate through sorted prices, and for each price, if it fits, subtract from budget and increment counter; otherwise stop.
State time complexity O(n log n) due to sorting, space O(1) or O(n) depending on sort. Discuss edge cases: empty list, budget zero, prices exceeding budget, duplicate prices (distinct products but same price).
Mention that if we only need the count, we can use a min-heap to extract the smallest prices one by one, or use quickselect to find the k smallest sum. Also note that if values were not equal, it would be the knapsack problem.
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