Nested List Weight Sum

Carry depth through the traversal

Assume each element is either an integer or a list with methods such as isInteger, getInteger, and getList. DFS starts at depth one. For an integer, add value * depth; for a list, recurse into its children at depth + 1. The recursive parameter is the important design choice because it makes each contribution local and auditable.

Every element is visited once, so time is O(n) for n integers and list nodes. Auxiliary space is O(d) for recursion depth, excluding the input, where d is maximum nesting depth. An iterative version stores (element, depth) pairs on a stack and has the same asymptotic cost. Test an empty list, one top-level integer, several sibling lists, deeply nested input, negative integers, and values that need a wider accumulator. Clarify whether the variation asks for inverse depth weights; that is a different problem and needs maximum depth or level sums.