Leetcode 63. Unique Paths II

63. Unique Paths II

• Total Accepted: 70691
• Total Submissions:237311
• Difficulty: Medium

 

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.

 

思路：
关于存储空间的优化，可以看姐妹题：Leetcode 62. Unique Paths

0<=i<m，0<=j<n：

1. obstacleGrid[i][j]==1，则(i,j)的路径数=0

2. obstacleGrid[i][j]==0时

2.1 j==0，(i,0)的路径数==(i-1,0)的路径数

2.2 i>0，(i,j)的路径数=(i-1,j)的路径数+(i,j-1)的路径数

 

代码：

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