Unique Paths

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.

思路：本题意思是通过向下走或者向右走到达Finish，我们可以抽象一下，到达(i,j)点必通过(i-1,j)或者(i,j-1).所以使用result[i][j]表示到达(i,j)有多少中方法，故result[i][j]=result[i-1][j]+result[i][j-1];

class Solution {

public:

    int uniquePaths(int m, int n) {

        int result[m][n];

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

            result[i][0]=1;

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

            result[0][j]=1;

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

        {

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

            {

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

            }

        }

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

    }

};