岛屿问题

岛屿个数问题

1 是陆地, 0 是水, 只考虑上下左右四个方向相邻

例如:

输入:
11110
11010
11000
00000

输出: 1

思路: 遍历二维数组, 如果是 1, 就把它上下左右都感染为 2, 岛屿个数 +1

遍历完成, 最后返回岛屿个数

感染的时候可以用递归

class Solution {
public:
    int numIslands(vector<vector<char>>& grid) {
        int h = (int)grid.size();
        if(h == 0)
            return 0;
        int w = (int)grid[0].size();

        int count = 0;

        int i, j;
        for(i=0; i<h; i++)
        {
            for(j=0; j<w; j++)
            {
                if(grid[i][j] == '1')
                {
                    count++;
                    infect(grid, i, j, w, h);
                }
            }
        }
        return count;        
    }

    void infect(vector<vector<char>>& grid, int i, int j, int w, int h)
    {
        if(i < 0 || i >= h || j < 0 || j >= w || grid[i][j] != '1')
            return ;
        grid[i][j] = '0';

        infect(grid, i-1, j, w, h);
        infect(grid, i+1, j, w, h);
        infect(grid, i, j-1, w, h);
        infect(grid, i, j+1, w, h);
    }
};

最大岛屿的面积

class Solution {
public:
    int maxAreaOfIsland(vector<vector<int>>& grid) {

        int row = grid.size();
        if(row == 0)
            return 0;
        int col = grid[0].size();
        int max_num = 0;
        for(int i=0; i<row; i++) {
            for(int j=0; j<col; j++) {
                if(grid[i][j] == 1) {
                    max_num = max(max_num, dfs(grid, i, j, row, col));
                }
            }
        }
        return max_num;
    }
    int dfs(vector< vector<int> >& grid, int i, int j, int row, int col) {
        if(i >= 0 && i < row && j >= 0 && j < col && grid[i][j] == 1) {
            grid[i][j] = 0;
            return 1 + dfs(grid, i-1, j, row, col) 
                     + dfs(grid, i+1, j, row, col)
                     + dfs(grid, i, j-1, row, col)
                     + dfs(grid, i, j+1, row, col);
        }
        return 0;
    }
};

岛屿的周长

[[0,1,0,0],
 [1,1,1,0],
 [0,1,0,0],
 [1,1,0,0]]

答案: 16
解释: 它的周长是下面图片中的 16 个黄色的边：

class Solution {
public:
    int islandPerimeter(vector<vector<int>>& grid) {
        int row = grid.size();
        if(row == 0)
            return 0;
        int col = grid[0].size();

        int count = 0;

        for(int i=0; i<row; i++)
        {
            for(int j=0; j<col; j++)
            {
                if(grid[i][j] == 1)
                {
                    count += 4;
                    if(i > 0 && grid[i-1][j] == 1)
                        count -= 2;
                    if(j > 0 && grid[i][j-1] == 1)
                        count -= 2;
                }
            }
        }
        return count;    
    }      
};

结合版, 同时求岛屿个数和最大岛屿面积

class Solution {
public:
    int maxAreaOfIsland(vector<vector<int>>& grid) {
        int h = (int)grid.size();
        if(h == 0)
            return 0;
        int w = (int)grid[0].size();

        int count = 0;
        int max = 0;

        int i, j;
        for(i=0; i<h; i++)
        {
            for(j=0; j<w; j++)
            {
                if(grid[i][j] == 1)
                {
                    count++;
                    int tmp = infect(grid, i, j, w, h);
                    if(tmp > max)
                        max = tmp;
                }
            }
        }      
        cout << count << "," << max << endl;           
    }

    int infect(vector<vector<int>>& grid, int i, int j, int w, int h)
    {
       if(i < 0 || i >= h || j < 0 || j >= w || grid[i][j] != 1)
            return 0;
        grid[i][j] = 0;

        return 1 + infect(grid, i-1, j, w, h)
                 + infect(grid, i+1, j, w, h)
                 + infect(grid, i, j-1, w, h)
                 + infect(grid, i, j+1, w, h);
    }
};