description:

https://leetcode.com/problems/unique-paths/
机器人从一堆方格的左上角走到右下角,只能往右或者往下走 ,问有几种走法
Note:

Example:

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

answer:

class Solution {
public:
    int uniquePaths(int m, int n) {
        double sum = 1, up = 1;  // 这里一定是 double 
        int mi = m < n ? m : n;  // 必须先找出最小的,虽然数学上两个排列相等,但是程序里因为数的范围限制神马的不清楚,会超时
        for (int i = 0; i < mi - 1; i++) {
            sum *= m + n - 2 - i;
            up *= i + 1;
        }
        return (int)(sum / up); // 最后要把double 变到 integer
    }
};

relative point get√:

hint :

就是在总步数 m + n - 2 里选 n-1 步 (m - 1)是往下走(右)