Knew the sliding window trick going in, so I coded it up pretty fast.
Start by clarifying the problem and edge cases, then propose an efficient sliding window approach that computes the sum of the first window and slides it by subtracting the outgoing element and adding the incoming element. Finally, analyze the time and space complexity, emphasizing the O(n) time and O(1) space.
Pro tip: At Apple, interviewers value clean, efficient code and clear communication. Mention that this approach is optimal because it processes each element once, and relate it to real-time analytics where low latency is critical.
Confirm that the array contains positive integers, k is positive and less than or equal to the array length, and discuss handling of edge cases like k=1 or k=n.
Explain that you will compute the sum of the first k elements, then slide the window by subtracting the element leaving the window and adding the new element entering, keeping track of the maximum sum.
Demonstrate the algorithm on a small example to show how the window slides and the maximum is updated, ensuring clarity.
State that the time complexity is O(n) because each element is processed once, and space complexity is O(1) as only a few variables are used.
Mention that this is optimal for a single query; if multiple queries with different k are needed, consider prefix sums or other data structures.
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