29.cpp

/*

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 7 x 3 grid. How many possible unique paths are there?

 

Example 1:

Input: m = 3, n = 2
Output: 3
Explanation:
From the top-left corner, there are a total of 3 ways to reach the bottom-right corner:
1. Right -> Right -> Down
2. Right -> Down -> Right
3. Down -> Right -> Right
Example 2:

Input: m = 7, n = 3
Output: 28


Constraints:

1 <= m, n <= 100
It's guaranteed that the answer will be less than or equal to 2 * 10 ^ 9.
*/

class Solution {
public:
    int uniquePaths(int a, int b) {
        long long path = 1, m = a, n = b; 
        for (long long i = n; i < (m + n - 1); i++) { 
            path *= i; 
            path /= (i - n + 1); 
        } 
        return path;
    }
};