My first instinct was greedy and I spent a while convincing myself it was correct.
Clarify the problem definition and constraints, then propose a dynamic programming solution that tracks the maximum sum ending at each index with either a positive or negative sign. Explain the recurrence relations and optimize space to O(1) if possible, while analyzing time and space complexity.
Pro tip: Demonstrate Amazon's leadership principles by discussing trade-offs between different approaches and considering edge cases like empty arrays or single elements. Also, mention how you would test the solution and handle large inputs.
Ask questions to confirm the definition of alternating subsequence, whether the subsequence must be contiguous, and if the first operation is always addition. Also, check constraints on array size and element range.
Let dp_plus[i] be the maximum alternating sum of a subsequence ending at index i where the last operation is addition, and dp_minus[i] where the last operation is subtraction. Initialize with the first element.
For each i, dp_plus[i] = max(dp_plus[i-1], dp_minus[i-1] + arr[i]) and dp_minus[i] = max(dp_minus[i-1], dp_plus[i-1] - arr[i]). Update the global maximum.
Observe that only the previous states are needed, so reduce space to O(1). Time complexity is O(n) and space O(1).
Walk through examples like [1,2,3] and edge cases like empty array, single element, and all negative numbers to verify correctness.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.