Staff Data Scientist Product, Google Play Games

Google

Given n pairs of parentheses, what is the total number of different, valid combinations of those parenthesis? For example: For n = 1, the only valid combination is (), so the answer is 1. For n = 2, the valid combinations are ()() and (()), so the answer is 2. For n = 3, the valid combinations are ((())), (()()), (())(), ()(()), and ()()(), so the answer is 5. Calculate the number of valid parenthesis combinations for a given n. Explain the formula or method used to arrive at the answer. What is the underlying mathematical concept at play here, and how does it ensure that we only count valid combinations, avoiding invalid ones such as )()(? Detail the relationship between this problem and Catalan numbers, and discuss how this relationship can be utilized to efficiently compute the number of valid combinations, even for relatively large values of n.

Google

Let's design a cache. Consider the following requirements: Basic Functionality: Implement a cache with put(key, value) and get(key) methods. Eviction Policy: Implement an LRU (Least Recently Used) eviction policy. When the cache is full, the least recently accessed item should be evicted to make space for the new item. Thread Safety: Ensure the cache is thread-safe to handle concurrent access from multiple threads. Generics: The cache should be able to store any type of key and value (using generics). Time Complexity: get and put operations should have an average time complexity of O(1). Example Usage: Cache cache = new Cache(5); // Cache with capacity 5 cache.put(1, one); cache.put(2, two); cache.get(1); // Access key 1, moves it to the most recently used cache.put(3, three); cache.put(4, four); cache.put(5, five); cache.put(6, six); // This will evict key 2 (LRU) System.out.println(cache.get(2)); // Output: null (because it was evicted) Discuss the data structures you would use, the implementation details for each method, and how you would address thread safety.

Google

Where do you see yourself in 5 years?