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As Far from Land as Possible

Given an n x n grid containing only values 0 and 1, where 0 represents water and 1 represents land, find a water cell such that its distance to the nearest land cell is maximized,...

Given an n x n grid containing only values 0 and 1, where 0 represents water and 1 represents land, find a water cell such that its distance to the nearest land cell is maximized, and return the distance. If no land or water exists in the grid, return -1.

The distance used in this problem is the Manhattan distance: the distance between two cells (x0, y0) and (x1, y1) is |x0 - x1| + |y0 - y1|.

As Far from Land as Possible diagram

Example 1

Input: grid = [[1,0,1],[0,0,0],[1,0,1]]

Output: 2

Explanation: The cell (1, 1) is as far as possible from all the land with distance 2.

Example 2

Input: grid = [[1,0,0],[0,0,0],[0,0,0]]

Output: 4

Explanation: The cell (2, 2) is as far as possible from all the land with distance 4.

Constraints

  • n == grid.length
  • n == grid[i].length
  • 1 <= n <= 100
  • grid[i][j] is 0 or 1

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