My first instinct was brute force, just track every pair of matching values and sum between them.
First, clarify the problem constraints and edge cases, then propose an efficient algorithm using a hash map to track the first and last occurrence of each value, and prefix sums to compute subarray sums in O(1). Compare this with a brute-force approach to highlight the optimization.
Pro tip: Mention that you would handle large inputs by using a hash map and prefix sums to achieve O(n) time, and discuss potential integer overflow issues with large sums.
Ask questions to confirm details: Are indices inclusive? Can the array be empty? What if no pairs exist? Should we consider negative numbers? This ensures you understand the requirements.
Explain a simple O(n^2) solution: for each pair of indices with equal values, compute the sum by iterating the subarray. This shows you can start simple but also recognize inefficiency.
Use a hash map to store the first occurrence of each value and a prefix sum array to compute subarray sums in O(1). Iterate through the array, and for each value, if it's seen before, compute the sum between the first occurrence and current index, updating the maximum.
State that the optimized solution runs in O(n) time and O(n) space. Discuss edge cases: no pairs, all elements same, negative numbers, and large sums causing overflow.
Walk through a small example to verify correctness, such as [1,2,1,3,1] and show how the algorithm finds the maximum sum.
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