My first instinct was prefix sums and I think that's the right move.
First, clarify the problem constraints and define what 'partition' means (e.g., contiguous subarrays or subsets). Then, reduce the problem to finding a subset with sum equal to half the total sum, and discuss algorithmic approaches like dynamic programming or greedy with sorting, analyzing time and space complexity.
Pro tip: Always check if the total sum is odd; if so, equal partition is impossible. Also, mention that for contiguous subarrays, a linear-time prefix sum approach works, but for arbitrary subsets, it's NP-complete (subset sum), so discuss trade-offs.
Ask whether the partition must be into contiguous subarrays or arbitrary subsets, and whether the subarrays must cover the entire array. Also confirm if elements can be negative.
Compute the total sum. If it's odd, return false immediately. Otherwise, the target sum for each partition is total_sum / 2.
For contiguous subarrays, use prefix sums to find a split point in O(n). For arbitrary subsets, use dynamic programming (subset sum) with O(n * target) time and O(target) space, or meet-in-the-middle for large n.
Write clean code for the chosen approach, handle edge cases (empty array, single element, zeros), and discuss potential optimizations like early termination or bitset DP.
State time and space complexity, and discuss trade-offs between approaches, especially if the problem is NP-complete for arbitrary subsets.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.