Unique Paths II

Follow up for "Unique Paths":

Now consider if some obstacles are added to the grids. How many unique paths would there be?

An obstacle and empty space is marked as 1 and 0 respectively in the grid.

For example,

There is one obstacle in the middle of a 3x3 grid as illustrated below.

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

The total number of unique paths is 2.

Note: m and n will be at most 100.

class Solution {
public:
    int uniquePathsWithObstacles(vector<vector<int> > &obstacleGrid) 
    {
        int m=obstacleGrid.size();
        if(m==0) return 0;
        
        int n=obstacleGrid[0].size();
        int path[n];
        path[0]=1-obstacleGrid[0][0];
        for(int i=1;i<n;i++) 
            if(obstacleGrid[0][i]==1) path[i]=0;
            else path[i]=path[i-1];
        
        for(int i=1;i<m;i++)
        {
            if(obstacleGrid[i][0]==1) path[0]=0;
            for(int j=1;j<n;j++)
                if(obstacleGrid[i][j]==1) path[j]=0;
                else path[j]=path[j-1]+path[j];
        }
        return path[n-1];
    }
};