Clarify the problem constraints and define 'value' (likely total price or count of items). Then, if the goal is to maximize the number of items, sort the array by price and greedily pick the cheapest items until the budget is exhausted; if maximizing total value, use dynamic programming (0/1 knapsack). Discuss time and space complexity and consider edge cases.
Pro tip: At Amazon, interviewers value candidates who ask clarifying questions and discuss trade-offs. Explicitly state your assumptions and compare greedy vs. DP approaches, showing you understand when each is appropriate.
Ask questions to confirm whether 'value' means total price, number of items, or another metric. Also confirm if items can be partially purchased (fractional) or only whole items (0/1).
If maximizing count, sorting and greedy works. If maximizing total value with indivisible items, use dynamic programming (0/1 knapsack). Explain why the chosen approach is optimal.
For greedy: sort prices ascending, iterate and add to total until budget exceeded. For DP: create a table of size budget+1, iterate items, update max value for each capacity.
State time and space complexity (e.g., O(n log n) for sorting, O(nB) for DP). Discuss edge cases: empty array, budget zero, all items too expensive, duplicate prices.
Walk through a small example to verify correctness, such as prices [2,3,4], budget 5. Show how the algorithm produces the expected result.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
This tripped me up more than it should have.
Treat the 'spend exactly' constraint as a variant of the knapsack problem where you must hit the target sum exactly, and discuss how to adapt your algorithm to handle exactness (e.g., DP with exact sum, backtracking, or meet-in-the-middle). Then, connect it to Amazon's leadership principles by emphasizing customer obsession and frugality—explaining that spending exactly is about maximizing value, not wasting resources. Finally, outline trade-offs in time/space complexity and propose a practical solution.
Pro tip: Acknowledge that in real-world engineering, exact budget spending is often a proxy for maximizing ROI; show you understand the business context by suggesting that you'd first clarify whether 'exact' means strictly equal or at least the budget, and whether unused budget has penalties.
Ask clarifying questions: Is the budget a hard constraint (must spend exactly) or a soft one (can spend up to)? Are there penalties for under/over-spending? What are the item costs—discrete or continuous?
Formalize as: given a set of items with costs, select a subset that sums exactly to the budget while maximizing value (or minimizing cost if value is fixed). This is the subset sum or 0/1 knapsack with exact weight.
Discuss DP (O(n*B) time, O(B) space) for small budgets, meet-in-the-middle for large n, or approximation if NP-hard. Mention that exact sum may be infeasible; then consider adding dummy items or adjusting.
If no exact subset exists, propose fallback: spend as close as possible, or negotiate with stakeholders. Discuss how to detect infeasibility early (e.g., GCD of costs doesn't divide budget).
Tie back to Amazon's Leadership Principles: Customer Obsession (maximize customer value), Frugality (avoid waste), and Ownership (think long-term). Emphasize that exact spending should serve a business goal, not be an end in itself.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
First, clarify that this is a bounded knapsack problem where each item has a maximum quantity. Then, discuss efficient transformations like binary splitting or monotonic queue optimization to reduce the problem to 0/1 knapsack, and analyze the time and space complexity trade-offs.
Pro tip: Mention that binary splitting is often preferred in interviews due to its simplicity and O(sum log c_i * W) complexity, but also note that monotonic queue optimization can achieve O(nW) if the interviewer pushes for optimality.
Confirm that each item i has a maximum quantity c_i, and the goal is to maximize value under a weight capacity. Ensure you understand if quantities are integers and if items are indivisible.
Recognize this as the bounded knapsack problem, a variation of the classic 0/1 knapsack where items can be taken multiple times up to a limit.
Discuss options: naive DP with O(W * sum c_i) time, binary splitting to convert to 0/1 knapsack, or monotonic queue optimization for O(nW) time. Explain the trade-offs.
Walk through the chosen approach step-by-step, including state definition, transition, and initialization. For binary splitting, show how to decompose c_i into powers of 2.
State time and space complexity, and discuss edge cases like zero capacity, zero quantities, or large c_i values.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Use the STAR method to structure your answer, focusing on a specific situation where you had to adapt to changing requirements or ambiguous information. Emphasize your actions and the positive outcome, and explicitly connect it to Amazon's Leadership Principles like 'Learn and Be Curious' and 'Deliver Results'.
Pro tip: Quantify the impact of your actions whenever possible (e.g., reduced deployment time by 30%) and show how you turned ambiguity into a structured plan. Also, reflect on what you learned and how you applied it to future situations.
Briefly describe the project, your role, and the specific challenge or ambiguity you faced. Keep it concise to focus on your actions.
Detail why the situation was ambiguous or required adaptability—e.g., unclear requirements, shifting priorities, or incomplete information.
Walk through the steps you took to navigate the ambiguity: how you gathered information, made decisions, and adapted your approach.
Share the results of your actions, including any metrics or positive feedback. Emphasize how your adaptability led to success.
Summarize what you learned and how it aligns with Amazon's Leadership Principles, especially those related to adaptability and ambiguity.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.