63 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.

Solution

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