Took me longer than I'd like to admit to see why this reduces to two states.
Clarify the problem constraints and edge cases, then propose a dynamic programming solution that tracks the maximum alternating sum ending at each index with a positive or negative sign. Explain the recurrence and optimize space to O(1) if possible.
Pro tip: Discuss how the problem relates to stock trading with cooldown or maximum subarray sum, showing pattern recognition. Also, mention that the greedy approach of picking local extrema works for the maximum alternating sum of the entire array but not for subsequences, so DP is necessary.
Ask about constraints (array size, element range), whether the subsequence must be non-empty, and if the alternating sum can start with either sign. Confirm that subsequence means preserving order but not necessarily contiguous.
Let dp[i][0] be the maximum alternating sum of a subsequence ending at index i where the last operation was addition (i.e., the element is added). Let dp[i][1] be the maximum alternating sum where the last operation was subtraction (i.e., the element is subtracted).
For each element, dp[i][0] = max(dp[i-1][0], dp[i-1][1] + arr[i], arr[i]) and dp[i][1] = max(dp[i-1][1], dp[i-1][0] - arr[i]). The answer is max(dp[n-1][0], dp[n-1][1]).
Observe that only the previous state is needed, so we can reduce space to O(1) by keeping two variables: max_add and max_sub.
Time complexity is O(n) and space O(1). Walk through examples like [1,2,3] and [1,-2,3,-4] to verify correctness, and discuss edge cases like all negative numbers.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.