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) {
        //Note: robot move right || down 
        int N = m + n - 2;  //total step 
        int x = m - 1; 
        //res = (N choose x) = N*(N-1)*...*(N-x+1)/x!
        double res = 1;
        for (int i = 1; i <= x; i++) {
            //a single (N-x+i)/i could be non-integer
            res = res*(N-x+i)/i;
        }
        return (int)res;
    }
}
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