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White board Interview Questions

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Write a program that given 4 coin denominations and a dollar amount finds the best way to express that amount using the coins given. I.e. you have coins with denominations of 1c, 7c, 13c,19c and you have to express $2.12 with the least number of coins. There is always a 1c coin but the other 3 are arbitrary.

6 Answers

Turns out , this problem only has an elegant solution when the coin denominations are divisible by each other, such as the US coins (1, 5, 10, 25). Otherwise, it requires a (slightly optimized) brute force algorithm. I was told so by the interviewer after struggling with it using different approaches for about 40 minutes.

If you have a coin of value 1, you can use a greedy algorithm: always select the most valued coin, until you have less money left that this value. Remove the coin, try again with less coins and the money left. Otherwise, just bruteforce and memoization, to implement a simple dynamic programming approach where you want to minimize the number of coins used, caching on the amount of money left to divide.

Greedy algorithm is not right at all for general cases. This is a very classical questioin. If you fail on this question, I would say that it is probably your fault.

How would you implement an LRU Cache (LRU - Least Recently Used). What would your data structure look like. This was also a whiteboard problem.

2 Answers

Nothing was difficult. Some whiteboarding, and a small written test. Hardest was a whiteboard scripting task.

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