LeetCode 62: 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.

public class Solution {
    public int uniquePaths(int m, int n) {
        // DP problem
        // Number of unique paths at (m, n) S[m-1][n-1] = S[m-1][n-2] + S[m-2][n-1]
        if (m<=0 || n<=0)
            return 0;
        
        int[][] S = new int[m][n];
        
        S[0][0] = 1;
        
        // Note: The first row only has one way.
        if (n > 1)
            for (int i = 1; i < n; i++)
                S[0][i] = 1;
        
        // Note: The first column only has one way.   
        if (m > 1)
            for (int i = 1; i < m; i++)
                S[i][0] = 1;   
        
        for (int i = 1; i < m; i++)
            for (int j = 1; j < n; j++)
                S[i][j] = S[i][j-1] + S[i-1][j];
                
        return S[m-1][n-1];
    }
}