Compute inverse-depth weighted sum of a nested list

Problem

You are given a nested list of integers, where each element is either:

• an integer, or
• a list that follows the same rule (i.e., a nested list).

Define the depth of an integer as the number of lists that contain it.

• Example: In [1,[2,[3]]] , the integer 1 has depth 1, 2 has depth 2, and 3 has depth 3.

Let D be the maximum depth among all integers in the structure. Compute the inverse-depth weighted sum where each integer with depth d is weighted by:

$weight(d) = D - d + 1$

Return the total weighted sum.

Examples

• Input: [1,[2,[3]]]
  • Maximum depth D=3
  • Sum = 1*(3-1+1) + 2*(3-2+1) + 3*(3-3+1) = 1*3 + 2*2 + 3*1 = 10
  • Output: 10
• Input: [[1,1],2,[1,1]]
  • Maximum depth D=2
  • Output: 8

Constraints (reasonable interview constraints)

• Total number of integers N up to ~1e4.
• Total nested list elements (including lists) up to ~1e4.
• Integers fit in 32-bit signed range.

Function Signature (language-agnostic)

int inverseDepthSum(NestedList nested)