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.

Solution

public class Solution {
     public int uniquePaths(int m, int n) {
        int[][] result = new int[m + 1][n + 1];

        for(int i = 1; i < m+1; i ++)
            result[i][1] = 1;

        for(int i = 1; i < n+1; i ++) {
            result[1][i] = 1;
        }

        for(int i = 2; i < m+1; i ++) {
            for(int j = 2; j < n + 1; j ++) {
                result[i][j] = result[i-1][j] + result[i][j-1];
            }
        }

        return result[m][n];
    }
}