# 63. Unique Paths II

## 刷题内容

• https://leetcode.com/problems/unique-paths-ii/

A robot is located at the top-left corner of a m x n grid (marked 'Start' in the diagram below).

The robot can only move either down or right at any point in time. The robot is trying to reach the bottom-right corner of the grid (marked 'Finish' in the diagram below).

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.

Note: m and n will be at most 100.

Example 1:

Input:
[
[0,0,0],
[0,1,0],
[0,0,0]
]
Output: 2
Explanation:
There is one obstacle in the middle of the 3x3 grid above.
There are two ways to reach the bottom-right corner:
1. Right -> Right -> Down -> Down
2. Down -> Down -> Right -> Right



**- 时间复杂度: O(n^2)*- 空间复杂度: O(n^2)***

class Solution {
public:
int uniquePathsWithObstacles(vector<vector<int>>& obstacleGrid) {
int length1 = obstacleGrid.size(),length2 = obstacleGrid[0].size();
long long dp[length1][length2];
memset(dp,0,sizeof(dp));
for(int i = length1 - 1;i >= 0;--i)
for(int j = length2 - 1;j >= 0;--j)
{
if(!obstacleGrid[i][j])
{
if(i == length1 - 1 && j == length2 - 1)
dp[i][j] = 1;
else
{
if(i == length1 - 1)
dp[i][j] = dp[i][j + 1];
else if(j == length2 - 1)
dp[i][j] = dp[i + 1][j];
else
dp[i][j] = dp[i][j + 1] + dp[i + 1][j];
}
}
}
return dp[0][0];
}
};