Count closed islands in a grid

Q: Count closed islands in a grid

This question evaluates grid traversal and connected-component detection skills, focusing on 4-directional adjacency and boundary-condition reasoning in matrix-based maps.

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Question

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Problem

You are given an m x n 2D grid representing a map after flooding:

0 = water
1 = land

An island is a maximal 4-directionally connected component of land cells (1s), where connectivity is via up, down, left, right (not diagonals).

A closed island is an island that does not touch the grid boundary (i.e., none of its cells lie in the first/last row or first/last column). Any island that touches the boundary is not counted.

Task

Return the number of closed islands in the grid.

Input

grid : int[m][n]

Output

int : the number of closed islands

Notes / Assumptions

Use 4-directional adjacency.
You may assume m, n >= 1 .

Example

If an island is entirely surrounded by water but a land cell touches the border, it should not be counted as closed.