Unique Paths II -- leetcode

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) {
        if (obstacleGrid.empty() || obstacleGrid[0].empty())
            return 0;

        vector<int> path(obstacleGrid[0].size());
        path[0] = 1;
        for (int i=0; i<obstacleGrid.size(); i++) {
            for (int j=0; j<path.size(); j++) {
                if (obstacleGrid[i][j])
                    path[j] = 0;
                else if (j)
                    path[j] += path[j-1];
            }
        }

        return path[path.size()-1];
    }
};