题目链接: http://www.spoj.com/problems/VLATTICE/ 题意: 1≤x,y,z≤n,问有多少对(x,y,z)使得gcd(x,y,z)=1 分析: 欧拉搞不了了,我们用莫比乌斯来搞一搞. 同样,我们设 f(d):满足gcd(x,y,z)=d且x,y,z均在给定范围内的(x,y,z)的对数. F(d):满足d|gcd(x,y,z)且x,y,z均在给定范围内的(x,y,z)的对数. 显然F(d)=[n/d][n/d][n/d],反演后我们得到 f(x)=∑x|dμ(d…

题目链接:http://www.spoj.com/problems/VLATTICE/ 题意:求gcd(a, b, c) = 1    a,b,c <=N 的对数. 思路:我们令函数g(x)为gcd(a, b, c) = x的对数,那么这题就是要求g(1).我们令f(x)为x | gcd(a, b, c)的对数,显然f(n) = sigma(n | d, g(d)) .f(d) = (n/d) * (n/d) * (n/d),那么我们就可以用莫比乌斯反演公式了, g(n) = sigma(n |…

[BZOJ2226][Spoj 5971] LCMSum Description Given n, calculate the sum LCM(1,n) + LCM(2,n) + .. + LCM(n,n), where LCM(i,n) denotes the Least Common Multiple of the integers i and n. Input The first line contains T the number of test cases. Each of the n…

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. Inpu…

Code: #pragma GCC optimize(2) #include<bits/stdc++.h> #define setIO(s) freopen(s".in","r",stdin) #define maxn 1000006 #define M 1000004 #define ll long long using namespace std; char *p1,*p2,buf[100000]; #define nc() (p1==p2&…

SPOJ Problem Set (classical) 7001. Visible Lattice Points Problem code: VLATTICE 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…

http://www.spoj.com/problems/VLATTICE/ 明显,当gcd(x,y,z)=k,k!=1时,(x,y,z)被(x/k,y/k,z/k)遮挡,所以这道题要求的是gcd(x,y,z)==1的个数+{(x,y,0)|gcd(x,y)==1}的个数+3{(0,0,1),(0,1,0),(1,0,0)} 现在不去管最后的三个坐标轴上的点, 设f(i)=|{(x,y,0)|gcd(x,y)==i}|*3+|{(x,y,z)|gcd(x,y,z)==i}|,也就是不在坐标轴上且…

7001. Visible Lattice Points Problem code: VLATTICE 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 lat…

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 segmen…

7001. Visible Lattice Points Problem code: VLATTICE 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 lat…