LeetCode Problem : Unique Paths

Problem

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.

Code

int uniquePaths(int m, int n) {
    // IMPORTANT: Please reset any member data you declared, as
    // the same Solution instance will be reused for each test case.
    vector<vector<int> > M(m,vector<int>(n,1));
    for(int i = 1;i < m;++i)
        M[i][0] = 1;
    for(int j = 1;j < n;++j)
        M[0][j] = 1;
    for(int i = 1;i < m;++i){
        for(int j = 1;j < n;++j){
            M[i][j] = M[i - 1][j] + M[i][j - 1];
        }
    }
    return M[m - 1][n - 1];
}