思路：
先遍历找到1，然后用bfs找到所有相连的1，并置成0，这一次遍历就是找到了一个岛屿。

代码：

import java.util.LinkedList;
import java.util.Queue;

public class Slution {
    public static void main(String[] args) {
//        char[][] grid = new char[][] {
//                {'1','1','1','1','0'},
//                {'1','1','0','1','0'},
//                {'1','1','0','0','0'},
//                {'0','0','0','0','0'}
//        };
//        char[][] grid = new char[][] {
//                {'1','1','0','0','0'},
//                {'1','1','0','0','0'},
//                {'0','0','1','0','0'},
//                {'0','0','0','1','1'}
//        };
        char[][] grid = new char[][]{
                {'0','1'},
                {'1','0'}
        };
        System.out.println(numIslands(grid));
    }

    public static int numIslands(char[][] grid) {
        int sum = 0;
        for (int i = 0; i < grid.length; i++) {
            for (int j = 0; j < grid[0].length; j++) {
                if (grid[i][j] == '1') {
                    bfs(grid, new Point(i,j));
                    sum++;
                }
            }
        }
        return sum;
    }

    public static void bfs(char[][] grid, Point start) {
        Queue<Point> queue = new LinkedList<>();
        queue.offer(start);
        while (!queue.isEmpty()) {
            Point point = queue.remove();
            grid[point.x][ point.y] = '0';
            if (point.x - 1 >= 0 && grid[point.x - 1][point.y] == '1') {
                queue.add(new Point(point.x-1, point.y));
                grid[point.x-1][point.y] = 0;
            }
            if (point.x + 1 < grid.length && grid[point.x + 1][point.y] == '1') {
                queue.add(new Point(point.x+1, point.y));
                grid[point.x+1][point.y] = 0;
            }
            if (point.y - 1 >= 0 && grid[point.x][point.y - 1] == '1') {
                queue.add(new Point(point.x, point.y - 1));
                grid[point.x][point.y-1] = 0;
            }
            if (point.y + 1 < grid[0].length && grid[point.x][point.y + 1] == '1') {
                queue.add(new Point(point.x, point.y + 1));
                grid[point.x][point.y+1] = 0;
            }
        }
    }

    public static class Point {
        int x;
        int y;

        public Point(int x, int y) {
            this.x = x;
            this.y = y;
        }
    }
}

Q.E.D.