Max Area of Island问题及解法

问题描述：

Given a non-empty 2D array grid of 0's and 1's, an island is a group of 1's (representing land) connected 4-directionally (horizontal or vertical.) You may assume all four edges of the grid are surrounded by water.

Find the maximum area of an island in the given 2D array. (If there is no island, the maximum area is 0.)

示例:

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

Given the above grid, return 6. Note the answer is not 11, because the island must be connected 4-directionally.

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

Given the above grid, return 0.

问题分析：

统计出现island区域中1的个数，出现最多的即为答案，我们可以利用dfs来求解该问题。

过程详见代码：

class Solution {public:    int maxAreaOfIsland(vector<vector<int>>& grid) {int res = 0;for (int i = 0; i < grid.size(); i++){for (int j = 0; j < grid[0].size(); j++){if (grid[i][j]){res = max(res, dfs(grid, i, j));}}}return res;}int dfs(vector<vector<int>>& grid,int i,int j){if (i < 0 || i >= grid.size() || j < 0 || j >= grid[0].size()) return 0;if (grid[i][j]){grid[i][j] = 0;return  1 + dfs(grid, i, j + 1) + dfs(grid, i + 1, j)+ dfs(grid, i, j - 1) + dfs(grid, i - 1, j);}return 0;}};