My first instinct was greedy: grab all the price-1 machines sorted by power descending, then fill in with price-2 if still short.
Recognize this as a knapsack-like problem where items have weights (power) and costs (1 or 2). Since costs are only 1 or 2, we can sort servers by power descending within each cost group and use a greedy approach: try all possible numbers of cost-2 servers, and for each, fill the remaining target with the highest-power cost-1 servers. Alternatively, use dynamic programming with state (index, power) but optimize using the small cost values.
Pro tip: Clarify constraints upfront (e.g., number of servers, target size) to choose the right approach. Mention that if the target is large, a greedy with sorting might not be optimal, but with costs 1 and 2, we can prove that taking the highest power per cost is optimal after sorting.
Restate the problem: select a subset of servers with total power >= target, minimizing total cost (each server costs 1 or 2). Ask about input size, target range, and whether powers are positive.
This is a variant of the knapsack problem (min cost to achieve at least a target). Since costs are only 1 or 2, we can group servers by cost and sort each group by power descending.
Use prefix sums of sorted powers for each cost group. Iterate over the number of cost-2 servers taken (from 0 to count2), compute the remaining power needed, and binary search or two-pointer to find the minimum number of cost-1 servers required. Track the minimum total cost.
If even taking all servers cannot meet the target, return -1. Also consider cases where target is 0 (cost 0) or no servers available.
Time complexity: O(n log n) for sorting plus O(n) for iteration. Space: O(n) for prefix sums. Discuss alternative DP approach and why greedy works here due to costs 1 and 2.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.