Unique Paths 不同的路径 DP

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 i,j,dp[101][101];
        memset(dp,0,sizeof(dp));
        
        for(i=1;i<=n;i++)
            dp[1][i]=1;
        for(i=1;i<=m;i++)
            dp[i][1]=1;
        for(i=2;i<=m;i++)
        {
            for(j=2;j<=n;j++)
              dp[i][j]=dp[i-1][j]+dp[i][j-1];
        }
        return dp[m]
;
    }
};