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) {
        vector<vector<int> > grid(obstacleGrid.size(),vector<int>(obstacleGrid[0].size()));
        grid[0][0] = obstacleGrid[0][0] == 1 ? 0 : 1;
        for(int i=1;i<grid.size();i++)
            grid[i][0]=obstacleGrid[i][0] == 1 ? 0 : grid[i-1][0];
        for(int j=1;j<grid[0].size();j++)
            grid[0][j]=obstacleGrid[0][j]== 1 ? 0 : grid[0][j-1];
        for(int i=1;i<grid.size();i++)
            for(int j=1;j<grid[i].size();j++)
                grid[i][j]=obstacleGrid[i][j]==1 ? 0 : grid[i][j-1]+grid[i-1][j];
        return grid[grid.size()-1][grid[0].size()-1];
    }
};