莫比乌斯习题讲解

VLATTICE - Visible Lattice Points

Consider a N*N*N lattice. One corner is at (0,0,0) and the opposite one is at (N,N,N). How many lattice points are visible from corner at (0,0,0) ? A point X is visible from point Y iff no other lattice point lies on the segment joining X and Y.
 
Input :
The first line contains the number of test cases T. The next T lines contain an interger N
 
Output :
Output T lines, one corresponding to each test case.
 
Sample Input :
3
1
2
5
 
Sample Output :
7
19
175
 
Constraints :
T <= 50
1 <= N <= 1000000

 

然后这个问题就是比较基础的莫比乌斯函数的应用,我们这时候我们需要用到的公式,

有了这个公式,我们可以f(d)看成gcd(a,b,c)=d的方案数,那么显而易见的是F(n)代表的含义就是gcd(a,b,c)%n==0的gcd(a,b,c)数量的总和,我们可以有公式很好的看出来,那么这个问题就显而易见了,我的思路就是就是先算出来空间中存在的点,然后再算出每个平面存在的合法的点,然后再加3就行了。很简单的一道题。

 

posted @ 2017-02-20 23:19  Heilce  阅读(266)  评论(0编辑  收藏  举报