The core setup is basically a scheduling problem and I went straight to a min-heap because that felt right.
First, clarify the problem: are we assigning each request to a server, or are we summing the response times of all servers? Then, identify the core algorithmic pattern: if we need to minimize the total time by assigning requests to servers, this is a load balancing problem that can be solved with a min-heap (greedy) or binary search on the answer. If it's simply summing all response times, it's trivial. Discuss the chosen approach, its time and space complexity, and edge cases.
Pro tip: Always restate the problem in your own words and ask clarifying questions before diving into code. Interviewers at Google value clear communication and problem understanding as much as the solution itself.
Ask questions to understand the exact requirements: Are we assigning each request to a server? Is the goal to minimize the total time or just sum the given times? What are the constraints on n and the number of servers?
Recognize that if we need to distribute n requests among servers to minimize total processing time, this is a load balancing problem. Common approaches include using a min-heap to always assign the next request to the least loaded server, or binary searching on the answer if the assignment is more complex.
Outline the steps: initialize a min-heap with server response times (or zeros if servers start idle), for each request pop the smallest time, add the request's processing time, and push it back. After all requests, the total time is the maximum value in the heap (or sum, depending on problem).
State the time complexity: O(n log k) where k is the number of servers, and space O(k). Discuss edge cases: no servers, no requests, very large n, or servers with zero response time.
Walk through a small example to verify the approach, such as 3 servers with times [1,2,3] and 4 requests. Show how the heap updates and compute the final total time.
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