695. Max Area of Island（python+cpp）

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题目：

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.)
Example 1:

[
[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.
Example 2:

[[0,0,0,0,0,0,0,0]] 
Given the above grid, return 0. 

Note: The length of each dimension in the given grid does not exceed 50.

解释：
经典dfs的题目，遍历过的位置要学会标记，在开始递归之前判断条件，速度更快。
python代码：

class Solution(object):
    def maxAreaOfIsland(self, grid):
        """
        :type grid: List[List[int]]
        :rtype: int
        """
        m=len(grid)
        n=len(grid[0])
        def dfs(i,j):
            grid[i][j]=0
            result=1
            if i+1<m and grid[i+1][j]:
                result+=dfs(i+1,j)
            if i-1>=0 and grid[i-1][j]:
                result+=dfs(i-1,j)
            if j+1<n and grid[i][j+1]:
                result+=dfs(i,j+1)
            if j-1>=0 and grid[i][j-1]:
                result+=dfs(i,j-1)
            return result
        maxIsland=0
        for i in xrange(m):
            for j in xrange(n):
                if grid[i][j]:
                    maxIsland=max(maxIsland,dfs(i,j))
        return maxIsland

c++代码：

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