Unique Paths

Dynamic Programming

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?

Above is a 3 x 7 grid. How many possible unique paths are there?

Note: m and n will be at most 100.

C++代码：

#include<iostream>

using namespace std;



class Solution {

public:

    int uniquePaths(int m, int n) {

        if(m==0||n==0)

            return 0;

        int path[m][n];

        path[0][0]=0;

        int i,j;

        for(i=0;i<m;i++)

            path[i][0]=1;

        for(j=0;j<n;j++)

            path[0][j]=1;

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

        {

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

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

        }

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

    }

};



int main()

{

    Solution s;

    cout<<s.uniquePaths(3,7)<<endl;

}