My first instinct was brute force and I actually started coding it before catching myself.
First, restate the problem and clarify constraints (e.g., array size, element range). Then, derive an O(n) solution by counting even and odd elements at even and odd indices, since the conditions depend only on parity. Finally, compute the valid pairs using combinatorics and verify with a brute-force check on small examples.
Pro tip: Mention that you can solve it in O(n) time and O(1) space by counting parities, which is optimal. Also, proactively discuss edge cases like empty arrays or all odd numbers to show thoroughness.
Confirm the problem: count pairs (i, j) with i < j, (arr[i] * arr[j]) even, and (j - i) odd. Ask about input size and element range to determine if O(n^2) is acceptable.
Note that product is even if at least one element is even. Distance odd means indices have opposite parity (one even, one odd). So valid pairs are those where one index is even and the other odd, and at least one element is even.
Traverse the array once, counting the number of even and odd elements at even indices and at odd indices. Let E_even, O_even, E_odd, O_odd be these counts.
Total pairs with opposite index parity = (E_even + O_even) * (E_odd + O_odd). Subtract pairs where both elements are odd: O_even * O_odd. Result = (E_even + O_even)*(E_odd + O_odd) - O_even*O_odd.
Test with small examples (e.g., [1,2,3,4]) to ensure correctness. Discuss time O(n) and space O(1), and mention that this is optimal since we must read the array.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.