63. Unique Paths II 动态规划

description:

https://leetcode.com/problems/unique-paths/
机器人从一堆方格的左上角走到右下角，只能往右或者往下走 ，问有几种走法，这个加了难度，在矩阵中加了障碍物
Note:

Example:

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

answer:

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)); //比实际大一圈是为了处理左边和上边两个边的边缘问题
        dp[0][1] = 1; // 初始化
        for (int i = 1; i <= m; ++i) {
            for (int j = 1; j <= n; ++j) {
                if (obstacleGrid[i - 1][j - 1] != 0) continue; //如果是障碍则略过
                dp[i][j] = dp[i - 1][j] + dp[i][j - 1];
            }
        }
        return dp[m][n];
    }
};

relative point get√：

hint :

动态规划