# [LeetCode] 63. Unique Paths II 不同的路径之二

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 space is marked as 1 and 0 respectively in the grid.

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) {
if (obstacleGrid.empty() || obstacleGrid[0].empty() || obstacleGrid[0][0] == 1) return 0;
int m = obstacleGrid.size(), n = obstacleGrid[0].size();
vector<vector<long>> dp(m + 1, vector<long>(n + 1, 0));
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) {
if (obstacleGrid.empty() || obstacleGrid[0].empty() || obstacleGrid[0][0] == 1) return 0;
int m = obstacleGrid.size(), n = obstacleGrid[0].size();
vector<long> dp(n, 0);
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

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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posted @ 2015-03-20 15:13  Grandyang  阅读(14538)  评论(5编辑  收藏  举报