LEETCODE: Unique Paths

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于 2014-12-21 11:14:11 发布

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文章标签：排列 LEETCODE 算法

本文链接：https://blog.youkuaiyun.com/anyicheng2015/article/details/42059165

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本文探讨了一个机器人在限定网格中从起点到终点的不同路径数目计算问题。通过组合数学的方法，给出了一种高效的计算路径数目的算法实现。

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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?

幸亏long long 可以搞定，不过数量更多之后，还是需要其他办法。

class Solution {
public:
    int uniquePaths(int m, int n) {
        if(m == 1 || n == 1) return 1;
        
        int down = m + n - 2;
        int up = m < n ? m - 1 : n -1;
        long long totaldown = 1;
        long long totalup = 1;
        for(int ii = up; ii > 0; ii --) {
            totaldown *= down;
            totalup *= up;
            down --;
            up --;
        }
        
        return totaldown / totalup;
    }
};