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.

 

Code: (Dynamic Programming)

class Solution {
public:
    int uniquePaths(int m, int n) {
        int mat[101][101] = {0};
        mat[0][1] = 1;
    
        for (int i = 1; i <= m; i++)
            for (int j = 1; j <= n; j++)
                mat[i][j] = mat[i-1][j] + mat[i][j-1];
    
        return mat[m][n];
    }
};