# 63. Unique Paths II

You are given an `m x n` integer array `grid`. There is a robot initially located at the top-left corner (i.e., `grid[0][0]`). The robot tries to move to the bottom-right corner (i.e., `grid[m - 1][n - 1]`). The robot can only move either down or right at any point in time.

An obstacle and space are marked as `1` or `0` respectively in `grid`. A path that the robot takes cannot include any square that is an obstacle.

Return the number of possible unique paths that the robot can take to reach the bottom-right corner.

The testcases are generated so that the answer will be less than or equal to `2 * 109`.

Example 1:

``````Input: obstacleGrid = [[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
``````

Example 2:

``````Input: obstacleGrid = [[0,1],[0,0]]
Output: 1
``````

Constraints:

• `m == obstacleGrid.length`
• `n == obstacleGrid[i].length`
• `1 <= m, n <= 100`
• `obstacleGrid[i][j]` is `0` or `1`.

dp[i][j] = dp[i-1][j] + dp[i][j-1]

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

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

Github 同步地址：

https://github.com/grandyang/leetcode/issues/63

Unique Paths

Unique Paths III

Minimum Path Cost in a Grid

Paths in Matrix Whose Sum Is Divisible by K

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

https://leetcode.com/problems/unique-paths-ii/discuss/23250/Short-JAVA-solution

https://leetcode.com/problems/unique-paths-ii/discuss/23248/My-C%2B%2B-Dp-solution-very-simple!

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