Number of 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.

Java: Unique Paths

01 public int uniquePaths(int m, int n) {
02 
03   if(m<1 || n<1)
04     return 0;
05   int [][]matrix=new int[m][n];
06 
07   for(int i=0;i<m;i++)
08   {
09     matrix[i][0]=1;
10   }
11   for(int j=0;j<n;j++)
12   {
13     matrix[0][j]=1;
14   }
15 
16   for(int i=1;i<m;i++)
17   {
18     for(int j=1;j<n;j++)
19     {
20       matrix[i][j]=matrix[i-1][j]+matrix[i][j-1];
21     }
22   }
23 
24   return matrix[m-1][n-1];
25 }