Question
A savings app lets users schedule deposits only in fixed amounts — for example 1, 2, and 5 dollars — with unlimited uses of each. Given the list of distinct positive deposit amounts and a savings goal, return how many different combinations of deposits reach the goal exactly. Two combinations are the same if they use each amount the same number of times; order does not matter. A goal of 0 has exactly one combination: deposit nothing.
count_deposit_mixes(amounts: list[int], goal: int) → int[[1,2,5],5]out4[[2,3],12]out3State your approach and its time/space complexity out loud before you optimize. Handle the edge cases (empty input, duplicates, overflow), and say why you chose this over the brute force. Green tests are the floor, not the grade.
Vibe coding: describe the solution in plain language (or narrate it) and the coach grades your approach. Generating runnable code from your description is coming next.