My first instinct was to just do a DFS and track depth, which is fine, but I didn't immediately clock that you need the max depth before you can assign any weights.
First, clarify the problem and edge cases, then discuss a recursive DFS approach that computes the maximum depth in one pass and the weighted sum in another (or combines both). Emphasize that the weight depends on the global max depth, so you need to know it before computing the sum. Alternatively, you can compute the sum of elements multiplied by their depth and the total sum, then use the formula: weighted sum = (max_depth + 1) * total_sum - sum_of_depth_times_value.
Pro tip: Mention that you can avoid a second traversal by computing both the max depth and the weighted sum in a single DFS if you first compute the max depth, or by using the formula with two accumulators (total sum and depth-weighted sum) in one pass, then combining after the max depth is known. This shows optimization awareness.
Ask about input size, nesting depth limits, and whether the list can be empty. Confirm that depth starts at 1 for top-level integers.
Decide between a two-pass DFS (first find max depth, then compute weighted sum) or a one-pass DFS that computes total sum and depth-weighted sum, then combines using the formula.
Write clean recursive code. For two-pass: first DFS to find max depth, second DFS to compute sum with weights. For one-pass: accumulate total sum and sum of value*depth, then compute weighted sum = (max_depth + 1) * total_sum - sum_depth_times_value.
Walk through a simple nested list like [1,[2,3]] and verify the output. Also test edge cases: empty list, single integer, deeply nested list.
State that time complexity is O(n) where n is total number of integers, and space complexity is O(d) for recursion stack where d is max depth.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.