Solution: Shortest Distance from All Buildings

Statement

Given an m x n integer grid grid, where each cell contains one of three values:

• $0$ represents empty land that can be freely traversed,

• $1$ represents a building that cannot be passed through,

• $2$ represents an obstacle that cannot be passed through.

You want to place a house on an empty land cell ($0$) such that the sum of shortest distances from the house to all buildings is minimized. Movement is restricted to four directions: up, down, left, and right.

Return the minimum total travel distance for such a placement. If no valid empty land cell can reach all buildings, return $-1$.

Note: The total travel distance is the sum of the shortest path distances from the chosen empty land cell to every building in the grid.

Constraints:

• m == grid.length

• n == grid[i].length

• $1 \leq$ m, n $\leq 50$

• grid[i][j] is either $0$, $1$, or $2$ ...