[LeetCode] 1254. Number of Closed Islands

Given a 2D grid consists of 0s (land) and 1s (water). An island is a maximal 4-directionally connected group of 0s and a closed island is an island totally (all left, top, right, bottom) surrounded by 1s.

Return the number of closed islands.

Example 1:

Input: grid = [[1,1,1,1,1,1,1,0],[1,0,0,0,0,1,1,0],[1,0,1,0,1,1,1,0],[1,0,0,0,0,1,0,1],[1,1,1,1,1,1,1,0]]
Output: 2
Explanation:
Islands in gray are closed because they are completely surrounded by water (group of 1s).

Example 2:

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

Example 3:
Input: grid = [[1,1,1,1,1,1,1],
[1,0,0,0,0,0,1],
[1,0,1,1,1,0,1],
[1,0,1,0,1,0,1],
[1,0,1,1,1,0,1],
[1,0,0,0,0,0,1],
[1,1,1,1,1,1,1]]
Output: 2

Constraints:
1 <= grid.length, grid[0].length <= 100
0 <= grid[i][j] <= 1

统计封闭岛屿的数目。

二维矩阵 grid 由 0 （土地）和 1 （水）组成。岛是由最大的4个方向连通的 0 组成的群，封闭岛是一个 完全 由1包围（左、上、右、下）的岛。

请返回 封闭岛屿 的数目。

来源：力扣（LeetCode）
链接：https://leetcode.cn/problems/number-of-closed-islands
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思路

思路还是跟岛屿类型的题一样，用 BFS 或者 DFS 做，需要遍历 input 矩阵两遍。BFS 或者 DFS 做时间空间复杂度相同。

注意这道题的规则，在 grid 边缘上的 0 是无法被完全包围的，所以我们第一轮遍历的时候先要把这些 0 变成 1。第二轮扫描的时候，剩下的 0 才是四面都被 1 包围的 0。

复杂度

时间O(mn)
空间O(mn)

DFS实现

Java实现

class Solution {
    int m;
    int n;

    public int closedIsland(int[][] grid) {
        m = grid.length;
        n = grid[0].length;
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                // 处理边界上的0
				if ((i == 0 || i == m - 1 || j == 0 || j == n - 1) && grid[i][j] == 0) {
					dfs(grid, i, j);
				}
            }
        }

        int count = 0;
		for (int i = 0; i < m; i++) {
			for (int j = 0; j < n; j++) {
				if (grid[i][j] == 0) {
					count++;
					dfs(grid, i, j);
				}
			}
		}
		return count;
    }

    private void dfs(int[][] grid, int i, int j) {
		if (i < 0 || i >= m || j < 0 || j >= n || grid[i][j] == 1) {
		    return;
		}
        grid[i][j] = 1;
		dfs(grid, i - 1, j);
		dfs(grid, i + 1, j);
		dfs(grid, i, j - 1);
		dfs(grid, i, j + 1);
	}
}

BFS实现

Java实现

class Solution {
    int m;
    int n;
    int[] dx = {-1, 1, 0, 0};
    int[] dy = {0, 0, -1, 1};
    
    public int closedIsland(int[][] grid) {
        m = grid.length;
        n = grid[0].length;
        // 把边界上所有的0变成1
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                if ((i == 0 || i == m - 1 || j == 0 || j == n - 1) && grid[i][j] == 0) {
                    bfs(grid, i, j);
                }
            }
        }

		int count = 0;
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                if (grid[i][j] == 0) {
                    count++;
                    bfs(grid, i, j);
                }
            }
        }
        return count;
    }
    
    private void bfs(int[][] grid, int i, int j) {
        Queue<int[]> queue = new LinkedList<>();
        queue.offer(new int[] { i, j });
        while (!queue.isEmpty()) {
            int[] cur = queue.poll();
            int x = cur[0];
            int y = cur[1];
            grid[x][y] = 1;
            for (int k = 0; k < 4; k++) {
                int newX = x + dx[k];
                int newY = y + dy[k];
                if (newX >= 0 && newX < m && newY >= 0 && newY < n && grid[newX][newY] == 0) {
                    queue.offer(new int[] { newX, newY });
                }
            }
        }
    }
}