Leetcode之Unique Paths

題目：

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?

Note: m and n will be at most 100.

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

代碼：

class Solution {
public:
    int uniquePaths(int m, int n) {
       if (m <= 0 || n <= 0)return 0;
	if (m == 1 || n == 1)return 1;
	int rights = m - 1;
	int downs = n - 1;
	int total = rights + downs;
	int min = rights < downs ? rights : downs;
	int minn = min;
	long int mm = 1, nn = 1;
	for (int i = 1; i <= min; i++) {
		mm *= total;
		total -= 1;
		nn *= minn;
		minn -= 1;
	}
	return mm / nn;
    }
};

感想：

使用數學的思路解答問題