LeetCode 63. Unique Paths II

Posted 2021-01-23 A-Little-Nut

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 3×3 grid as illustrated below.

[
  [0,0,0],
  [0,1,0],
  [0,0,0]
]

The total number of unique paths is 2.

分析

这道题和unique path I 没有本质区别，动态转移方程是dp[i][j]=obstacleGrid[i][j]==1?0:dp[i][j-1]+dp[i-1][j];

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