Question：
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) {
long x = 1;
long y = 1;
if(m>n){
for (int i = 1; i <= n - 1; i++) {
y *= i;
}
for (int i = m; i <= m + n - 2; i++) {
x *= i;
}
}else {
for (int i = 1; i <= m - 1; i++) {
y *= i;
}
for (int i = n; i <= m + n - 2; i++) {
x *= i;
}
}
return (int) (x/y);
}
}