Compute maximum perimeter among islands

Problem

You are given an m x n binary grid grid where:

• grid[r][c] = 1 represents land
• grid[r][c] = 0 represents water

An island is a maximal set of land cells connected 4-directionally (up, down, left, right).

The perimeter of an island is the total number of unit edges of land cells that either:

• lie on the boundary of the grid, or
• border a water cell.

Return the maximum perimeter among all islands in the grid. If there is no land, return 0.

Input / Output

• Input: grid: List[List[int]]
• Output: int (maximum island perimeter)

Constraints (typical interview constraints)

• 1 <= m, n <= 1000 (or similar)
• grid[r][c] is 0 or 1
• Aim for O(mn) time

Example

Given:

grid = [
  [0,1,1,0],
  [0,1,0,0],
  [1,1,0,0]
]

There are two islands; return the larger island’s perimeter.