The base case clicked pretty fast once I realized removing a link and reconnecting is just prefix sums on the modified array.
First, clarify the problem constraints and edge cases. Then, derive an efficient algorithm using prefix sums and a hash map to track possible removal and cut positions. Finally, discuss time and space complexity and how to extend to the follow-up.
Pro tip: Mention that the total weight after removal must be even, and that the cut must split the reconnected chain into two contiguous segments. This shows you understand the core invariant and can quickly prune invalid cases.
Confirm the problem: remove one link, reconnect the two segments, then make one cut to split into two equal-weight pieces. Ask about constraints (e.g., array size, weight values) and edge cases (e.g., all zeros, negative weights).
Describe a naive O(n^2) approach: for each removal index, compute the reconnected chain and check all possible cut positions. This establishes correctness and helps identify inefficiencies.
Use prefix sums to compute segment weights in O(1). For each removal, the reconnected chain is the concatenation of two segments; the cut must split it into two equal halves. Track possible cut positions using a hash set of prefix sums.
To return all valid pairs, store removal indices and cut positions in a list. Ensure no duplicates and consider the order of removal and cut (cut can be before or after the removal point in the original array).
State time and space complexity: O(n) time with O(n) space using prefix sums and hash maps. Discuss trade-offs and potential optimizations for large inputs.
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