[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;
}
};