Physical Design Methodology CAD Engineer

Apple

Let's explore dynamic programming with a classic problem: the knapsack problem. Imagine you have a knapsack with a limited weight capacity, and a collection of items, each with its own weight and value. Your goal is to select the items to put into the knapsack to maximize the total value, without exceeding the weight capacity. Specifically: Problem Statement: You are given a knapsack with a maximum weight capacity W. You are also given n items. Each item i has a weight wi and a value vi. Determine the maximum total value of items that can be placed in the knapsack without exceeding its weight capacity. Example: Knapsack capacity W = 10 Items: Item 1: weight = 6, value = 30 Item 2: weight = 3, value = 14 Item 3: weight = 4, value = 16 Item 4: weight = 2, value = 9 What is the maximum value you can obtain by putting items into the knapsack, and which items should you choose? Explain how you would approach this problem using dynamic programming. Be sure to define the subproblems, the recurrence relation, and the base cases. Also, discuss the time and space complexity of your dynamic programming solution.

Apple

Let's design a system for URL shortening, like TinyURL. Assume a large-scale service. Please consider the following aspects in your design: Functional Requirements: The system should generate shorter URLs (a.k.a. short links) given longer URLs. Users should be able to navigate to the original URL by entering the short link in their browser. The system should be highly available. Non-Functional Requirements: The system should have low latency for both URL shortening and redirection. Short links should be relatively short (e.g., 6-8 characters). The system should be able to handle a large number of URL shortening and redirection requests. Capacity Estimation: Assume 100 million URLs are shortened per day. Assume 1 billion URL redirections per day. Estimate storage requirements for 5 years. Design Considerations: How would you generate unique short links? What data structures and databases would you use to store the URL mappings? How would you handle collisions when generating short links? How would you optimize for low latency redirection? How would you scale the system to handle the expected traffic? Walk me through your design, explaining your choices and the trade-offs you considered. Provide diagrams where necessary to illustrate the architecture.

Apple

Let's explore your interest in Apple. To help me understand your motivations, please provide a detailed explanation of why you are specifically interested in working at Apple, rather than another technology company. Your answer should include specific examples related to Apple's products, services, culture, or values that resonate with you. For instance, you could discuss a particular Apple product that you admire and explain how its design or functionality aligns with your own interests and skills. Alternatively, you could talk about a specific initiative or project that Apple is undertaking and why you find it compelling. Furthermore, elaborate on how you believe your skills and experiences would contribute to Apple's success and how working here would support your professional growth and aspirations. Finally, please articulate how you see yourself fitting into Apple's culture and how you would embody the company's values in your day-to-day work. Please provide concrete examples to illustrate your points and demonstrate a deep understanding of Apple's unique position in the technology landscape.