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.

class Solution {public:    int uniquePaths(int m, int n) {        int d[111][111];        memset(d,0,sizeof(d));        for(int i=1;i<=m;i++)          d[i][1]=1;        for(int i=1;i<=n;i++)          d[1][i]=1;        for(int i=2;i<=m;i++)            for(int j=2;j<=n;j++)              d[i][j]=d[i-1][j]+d[i][j-1];        return d[m][n];    }};