[LeetCode]20. Unique Paths II唯一路径

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.

解法：还是使用动态规划。不同的是若遇到障碍，则说明到此位置后面就行不通了，路径数目为0。注意初始化不能再是path[i][0]=1，path[0][j]=1(0<=i<m，0<=j<n)，而是path[0][0]=1，因为第一行和第一列上就有可能有障碍。

class Solution {
public:
    int uniquePathsWithObstacles(vector<vector<int>>& obstacleGrid) {
        int res = 0;
        if(obstacleGrid.empty() || obstacleGrid[0].empty())
            return res;
        int m = obstacleGrid.size();
        int n = obstacleGrid[0].size();

        vector<int> path(n, 0);
        path[0] = 1;
        for(int i = 0; i < m; i++)
        {
            for(int j = 0; j < n; j++)
            {
                if(obstacleGrid[i][j] == 1)
                    path[j] = 0;
                else if(j > 0)
                    path[j] += path[j - 1];
            }
        }
        
        res = path[n - 1];
        return res;
    }
};