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();
        
        vector<int> row(n,0);
        vector<vector<int>> record(m,row);
        
        bool obstacle = false;
        for(int i = n-1; i >= 0; i--){
            if(obstacle)
                record[m-1][i] = 0;
            else if(obstacleGrid[m-1][i] == 1){
                obstacle = true;
                record[m-1][i] = 0;
            }else record[m-1][i] = 1;
        }
        obstacle = false;
        for(int i = m-1; i >= 0; i--){
            if(obstacle)
                record[i][n-1] = 0;
            else if(obstacleGrid[i][n-1] == 1){
                obstacle = true;
                record[i][n-1] = 0;
            }else record[i][n-1] = 1;
            
        }
        for(int i = m-2; i >= 0; i--)
            for(int j = n-2; j >= 0; j--){
                if(obstacleGrid[i][j] == 1) record[i][j] = 0;
                else record[i][j] = record[i+1][j] + record[i][j+1];
            }
        return record[0][0];
    }
};

动态规划，时间复杂度O(m*n), 空间复杂度O(m*n)。