leetcode - 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?

class Solution {
public:
int uniquePaths(int m, int n) {
std::vector<std::vector<int>> dp(m,std::vector<int>(n,0));
for (int i = 0; i < m; i++)
{
dp[i][0] = 1;
}
for (int i = 0; i < n; i++)
{
dp[0][i] = 1;
}
for (int i = 1; i < m; i++)
{
for (int j = 1; j < n; j++)
{
dp[i][j] = dp[i-1][j] + dp[i][j-1];
}
}
return dp[m-1][n-1];
}
};