Best Meeting Point

Try to solve the Best Meeting Point problem.

Statement

You are given a 2D grid of size m×nm \times n, where each cell contains either a 00 or a 11.

A 11 represents the home of a friend, and a 00 represents an empty space.

Your task is to return the minimum total travel distance to a meeting point. The total travel distance is the sum of the Manhattan distances between each friend’s home and the meeting point.

The Manhattan Distance between two points (x1, y1) and (x2, y2) is calculated as:
|x2 - x1| + |y2 - y1|.

Constraints:

  • m==m == grid.length

  • n==n== grid[i].length

  • 1≤m,n≤501 \leq m, n \leq 50

  • grid[i][j] is either 0 or 1.

  • There will be at least two friends in the grid.

Examples

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