[leetcode] 63. 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).

How many possible unique paths are there?

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 3x3 grid as illustrated below.

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

The total number of unique paths is 2.

Note: m and n will be at most 100.

解法一：

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