The base case (remove one element) is manageable once you realize that removing an index shifts the parity of everything after it, so you can precompute prefix sums for even and odd positions and check the balance in O(n).
For the single removal case, precompute prefix sums of even and odd positions, then iterate through each index to check if removing it makes the sums equal. For exactly k removals, use dynamic programming to track the difference between even and odd sums after removing k elements, considering the parity shift caused by removals.
Pro tip: Clarify with the interviewer whether 'remove' means deleting the element and shifting subsequent elements, as this affects parity. Also, discuss time/space complexity trade-offs and edge cases like k > array length.
Confirm that removing an element shifts all subsequent elements, changing their positions. Ask if k is guaranteed to be valid (k ≤ n) and if the array can be modified.
Compute prefix sums for even and odd indices. For each index i, calculate the new sums after removal using prefix sums and the parity shift, then check if they are equal.
Define DP state as (index, removals_used, current_parity_shift) and track the difference between even and odd sums. Transition by either keeping or removing the current element, updating the parity shift accordingly.
Discuss potential optimizations such as reducing state space or using greedy approaches if applicable. Analyze time and space complexity of the DP solution.
Walk through small examples, including cases where k=0, k=n, and arrays with all zeros. Verify correctness and handle edge cases.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.