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)

?

1 2 3 4 5 6 7 8 9 10 11 12 13

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];     } };