Nested List Weight Sum

When preparing for an interview, you should be familiar with fundamental graph traversal techniques because they are frequently used in technical interviews. As we live in an interconnected society with no isolated piece of information, the use of graphs is becoming more widespread. Today's prompt has one such graph traversal technique, Depth first search (DFS).

Prompt

You are given a nested list of integers nestedList. Each element is either an:

1. integer, or
2. a list whose elements may also be integers, or other lists

The depth of an integer is the number of lists that it is inside of. For example, the nested list [1,[2,2],[[3],2],1] has each integer's value set to its depth.

Return the sum of rach integer in nestedList by its **depth.

Expected Inputs and Outputs

Example 1

Input: [[1,1],2,[1,1]]
Output: 10 

Explanation: Four 1's at depth 2, one 2 at depth 1.

Example 2

Input: [1,[4,[6]]]
Output: 27 

Explanation: One 1 at depth 1, one 4 at depth 2, and one 6 at depth 3; 1 + 4*2 + 6*3 = 27.

Constraints

• nestedList.length <= 50
  
• The values of the integers in the nested list is in the range [-100, 100].
• The maximum depth of any integer is less than or equal to 50.