Compute nested depth sum and grid distance

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.

Input:

• grid : m x n integer matrix

Output:

• Minimum possible sum distance, or -1

Example:

• grid = [[1,0,2,0,1],[0,0,0,0,0],[0,0,1,0,0]] → output 7 (one optimal empty cell has total distance 7)

Constraints (typical):

• 1 <= m,n <= 50