Amazon interviews often include problems that test a candidate's ability to design efficient algorithms. This article presents a detailed breakdown of a real Amazon interview question and demonstrates how a candidate can excel with the support of csoahelp.
Problem Statement
Amazon wants to build a lottery system. When a customer purchases items worth between $1 and $100, they are entered into the lottery. Customers that purchase an item for $10 should be 10 times more likely to win the lottery than customers who have purchased an item for $1 (i.e., there is a linear relationship between the amount a customer purchased an item for and their probability of winning). Write a function that takes a list of customers and purchase price as input. As output, it should return K winners.
The Interview Walkthrough
Interviewer: Here’s the problem: Amazon wants to build a lottery system where customers who purchase items worth between $1 and $100 are entered into a lottery. The probability of winning is directly proportional to the purchase amount. For example, a customer who spends $10 is 10 times more likely to win than a customer who spends $1. Please write a function that takes a list of customers and their purchase prices and returns K winners. Do you understand the problem?
Candidate: I believe I understand the problem, but I’d like to clarify a few details to ensure we’re on the same page:
- Are we guaranteed that all purchase prices are between $1 and $100?
- Can the same customer win multiple times?
- What should happen if the number of customers is less than K?
Interviewer: Yes, all purchase prices will always be between $1 and $100, so you don’t need to handle edge cases. Yes, a customer can win multiple times. And if there are fewer customers than K, you can just return all customers as winners.
csoahelp (prompt): "Ask if the probabilities need to be normalized. This will help clarify whether the total sum of probabilities should add up to 1, which can guide your implementation."
Candidate: One more question: Do the probabilities need to be normalized? For example, should the total probability sum up to 1?
Interviewer: No, normalization is not required. You just need to maintain the proportional relationship between the purchase price and the probability of winning.
Candidate: Here’s my initial thought process:
- I will calculate the weight for each customer based on their purchase price. The weight will be directly proportional to the purchase price.
- Using these weights, I will either build a weighted lottery pool where each customer appears multiple times or use a prefix sum array to efficiently map random numbers to customers.
- Finally, I will randomly select K winners based on the weights.
Interviewer: That’s a reasonable plan. However, constructing a weighted pool could be memory-intensive, especially if there are many customers. How would you optimize this?
csoahelp (prompt): "Suggest using a prefix sum array to map random numbers to customers. This avoids creating a large pool while maintaining proportional probabilities."
Candidate: You’re absolutely right. Instead of constructing a weighted pool, I can use a prefix sum array. Here’s how it would work:
- First, compute the cumulative sum of the weights for all customers.
- Generate a random number between 0 and the total weight.
- Use binary search on the prefix sum array to determine which customer the random number maps to.
This approach avoids the need for a large memory allocation and keeps the algorithm efficient.
Interviewer: Great! What’s the time complexity of your approach?
Candidate: The time complexity can be broken down as follows:
- Constructing the prefix sum array takes O(n), where n is the number of customers.
- Selecting K winners involves generating K random numbers and performing binary search for each. Since binary search is O(log n), the total complexity for this step is O(K * log n).
Thus, the overall complexity is O(n + K * log n).
csoahelp (prompt): "Mention that this approach also optimizes memory usage since the prefix sum array requires only O(n) space, compared to a weighted pool which could require significantly more."
Candidate: Additionally, this method is memory-efficient. The prefix sum array only requires O(n) space, while a weighted pool would require significantly more memory, especially if weights are large.
Interviewer: Good. Now, let’s consider some edge cases. What happens if all customers have the same purchase price?
Candidate: If all customers have the same purchase price, all weights will be equal, resulting in a uniform distribution of probabilities. The random selection process will ensure each customer has an equal chance of being chosen, which aligns with the problem requirements.
Interviewer: Great. Now let’s shift gears. Can you tell me about a time when you solved a challenging problem in a project?
Candidate: Sure. During an internship, I worked on a recommendation system where latency was a significant issue due to large-scale user data. I identified that the bottleneck was in a set of nested database queries. I optimized the queries by adding indices and batching smaller queries into a single large query. Additionally, I introduced caching for frequently accessed data, which reduced query load. As a result, the recommendation system’s latency decreased by 50%.
csoahelp (prompt): "Add details about how you measured the improvement and validated the results, such as using A/B testing or monitoring tools."
Candidate: To ensure the optimizations were effective, I conducted A/B testing with a subset of users. I also used monitoring tools to track response times and server load before and after the changes. These validated that our optimizations significantly improved performance.
Interviewer: That’s impressive! Thank you for your time. Do you have any questions for me?
Candidate: Thank you! I’d like to know more about how your team approaches collaborative problem-solving, especially when dealing with high-pressure situations.
How csoahelp Enhances Interview Performance
In this interview, csoahelp provided the following critical support:
- Clarification Prompts: Guided the candidate to ask about normalization, showing a thorough understanding of the problem requirements.
- Algorithm Optimization Tips: Suggested using a prefix sum array to replace a memory-intensive weighted pool, enabling a more efficient solution.
- Complexity Analysis Guidance: Helped the candidate articulate both time and space complexity, emphasizing the benefits of their approach.
- Behavioral Question Refinement: Encouraged the candidate to include A/B testing and monitoring tools when describing project outcomes, showcasing a strong problem-solving process.
By leveraging real-time assistance from csoahelp, the candidate demonstrated clear thinking, technical expertise, and effective communication, leaving a strong impression on the interviewer.
Whether you’re preparing for a technical interview at Amazon or any other top tech company, csoahelp is your ultimate partner for real-time guidance and preparation. Try it today and take your interview performance to the next level!
经过csoahelp的面试辅助，候选人获取了良好的面试表现。如果您需要面试辅助或面试代面服务，帮助您进入梦想中的大厂，请随时联系我。
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