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?

Note

m and n will be at most 100.

Example

1,1	1,2	1,3	1,4	1,5	1,6	1,7
2,1
3,1						3,7

Above is a 3 x 7 grid. How many possible unique paths are there

class Solution {
public:
    /**
     * @param n, m: positive integer (1 <= n ,m <= 100)
     * @return an integer
     */
    int uniquePaths(int m, int n) {
        vector<vector<int>> UP(m, vector<int>(n, 1));
        
        for(int i = m-2; i >= 0; i--)
          for(int j = n-2; j >= 0; j--)
              UP[i][j] = UP[i+1][j] + UP[i][j + 1];
        return UP[0][0];
        
    }
};

class Solution {
public:
    /**
     * @param n, m: positive integer (1 <= n ,m <= 100)
     * @return an integer
     */
    int uniquePaths(int m, int n) {
        vector<int> UP(n, 1);
        
        for(int i = m-2; i >= 0; i--)
          for(int j = n-2; j >= 0; j--)
              UP[j] = UP[j] + UP[j + 1];
        return UP[0];
        
    }
};