Unique Paths II

Dynamic Programming

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.

在上一题的基础上，加入了障碍，只要将有障碍的地方的路径设置为0，就可以了。

C++实现代码：

#include<iostream>

#include<vector>

using namespace std;



class Solution

{

public:

    int uniquePathsWithObstacles(vector<vector<int> > &obstacleGrid)

    {

        if(obstacleGrid.empty()||obstacleGrid[0].empty())

            return 0;

        int m=obstacleGrid.size();

        int n=obstacleGrid[0].size();

        int path[m][n];

        int i,j;

        if(obstacleGrid[0][0]==1)

            return 0;

        path[0][0]=1;

        for(i=1; i<m; i++)

        {

            if(obstacleGrid[i][0]==1)

                path[i][0]=0;

            else

                path[i][0]=path[i-1][0];

        }

        for(j=1; j<n; j++)

        {

            if(obstacleGrid[0][j]==1)

                path[0][j]=0;

            else

                path[0][j]=path[0][j-1];

        }

        for(i=1; i<m; i++)

        {

            for(j=1; j<n; j++)

            {

                if(obstacleGrid[i][j]==1)

                    path[i][j]=0;

                else

                    path[i][j]=path[i-1][j]+path[i][j-1];

            }

        }

        return path[m-1][n-1];

    }

};



int main()

{

    Solution s;

    vector<vector<int> > vec= {{0,0,0},{0,1,0},{0,0,0}};

    cout<<s.uniquePathsWithObstacles(vec)<<endl;

}