Unicorns / VO Interview Question: Integer to Binary String and Reverse Depth Sum

Given a non-negative integer, produce a string representation of it in binary.

For example:

• 4 => "100"
• 15 => "1111"
• 38 => "100110"

Given a nested list of integers, return the sum of all integers in the list weighted by their reversed level.

For example, given the list {{1,1},2,{1,1}}, the deepest level is 2. Thus the function should return 8 (four 1s with weight 1, one 2 with weight 2).

Given the list {1,{4,{6,2}}}, the function should return 19 (1 with weight 3, 4 with weight 2, 6 with weight 1, 2 with weight 1).

It is the "reverse depth" of the item in the list. For the above item:

1 (reverse-depth 3) = 1 * 3 = 3
{4} (reverse-depth 2) = 4 * 2 = 8
{6,2} (reverse-depth 1) = 6 * 1 + 2 * 1 = 8
Total = 3 + 8 + 8 = 19

This set combines two classic interview tasks: converting a non-negative integer to its binary string, and computing the reverse-depth weighted sum of a nested integer list. The binary conversion can be solved by repeated division or bit operations, while the nested-list problem is usually handled by first finding the maximum depth and then traversing the structure with DFS or BFS to apply the correct weight to each integer. The key interview focus is handling recursive nested data, tracking depth accurately, and turning reverse depth into a simple formula during accumulation.