Compute nested depth sum and grid distance

Q: Compute nested depth sum and grid distance

This pair of problems evaluates algorithmic proficiency with nested data structures and grid-based graph traversal, covering concepts such as depth-weighted aggregation and shortest-path computation under obstacles.

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Coding & Algorithms questions require understanding of core concepts and practice. PracHub provides solutions with explanations to help you master coding & algorithms interviews.

Q: What difficulty level is this interview question?

This is a medium difficulty Coding & Algorithms question, commonly asked during Onsite rounds at Meta.

Q: What role is this question designed for?

This question is commonly asked for Machine Learning Engineer candidates at Meta during technical interviews.

Question

Problem A: Weighted sum of integers in a nested list

You are given a nested list structure that may contain integers or other nested lists. Define the depth of top-level elements as 1, their children as depth 2, etc.

Task: Compute the sum of each integer multiplied by its depth.

Input:

A nested list, e.g. [1, [4, [6]]]

Output:

An integer weighted sum

Example:

Input: [1, [4, [6]]]
- 1 at depth 1 → 1*1
- 4 at depth 2 → 4*2
- 6 at depth 3 → 6*3
- Total = 1 + 8 + 18 = 27

Constraints (typical):

Total number of integers across all nesting: up to ~1e5
Nesting depth may be up to ~1e3

Problem B: Best empty cell minimizing distance to all buildings

You are given an m x n grid with values:

0 = empty land (you may start here)
1 = building
2 = obstacle (cannot pass)

Movement is 4-directional (up/down/left/right). Distance is the number of steps along empty cells (you cannot pass through obstacles or buildings).

Task: Choose an empty cell 0 such that the sum of shortest path distances from that cell to every building is minimized. Return that minimum sum.

If there is no empty cell from which all buildings are reachable, return -1.