题目大意: 给定n,m,求有多少组(a,b) 0<a<=n , 0<b<=m , 使得gcd(a,b)= p , p是一个素数 这里本来利用枚举一个个素数,然后利用莫比乌斯反演可以很方便得到答案,但是数据量过大,完全水不过去 题目分析过程(从别人地方抄来的) ans = sigma(p, sigma(d, μ(d) * (n/pd) * (m/pd))) Let s = pd, then ans = sigma(s, sigma(p, μ(s/p) * (n/s) * (m/s))…

http://www.spoj.com/problems/PGCD/en/ 题意: 给出a,b区间,求该区间内满足gcd(x,y)=质数的个数. 思路: 设f(n)为 gcd(x,y)=p的个数,那么F(n)为 p | gcd(x,y)的个数,显然可得F(n)=(x/p)*(y/p). 这道题目因为可以是不同的质数,所以需要枚举质数, 但是这样枚举太耗时,所以在这里令t=pk, 这样一来的话,我们只需要预处理u(t/p)的前缀和,之后像之前的题一样分块处理就可以了. #include<iostr…

BUPT2017 wintertraining(15) #5H HDU- 4947 题意 有一个长度为l的数组,现在有m个操作,第1种为1 n d v,给下标x 满足gcd(x,n)=d的\(a_x\)增加v.第2种为2 x,查询\(\sum_{i=1}^x a_i\). 数据范围:\(1\le n,d,v\le2\cdot 10^5,1\le x\le l\) 题解 设\(f_i\)满足\(a_i=\sum_{d|i} f_d\),用树状数组存储\(f_i\)的前缀和. \[a_x+=v\cd…

4491. Primes in GCD Table Problem code: PGCD Johnny has created a table which encodes the results of some operation -- a function of two arguments. But instead of a boring multiplication table of the sort you learn by heart at prep-school, he has cre…

SPOJ4491. Primes in GCD Table Problem code: PGCD Johnny has created a table which encodes the results of some operation -- a function of two arguments. But instead of a boring multiplication table of the sort you learn by heart at prep-school, he has…

[BZOJ2820]YY的GCD(莫比乌斯反演) 题面 讨厌权限题!!!提供洛谷题面 题解 单次询问\(O(n)\)是做过的一模一样的题目 但是现在很显然不行了, 于是继续推 \[ans=\sum_{d=1}^n[d\_is\_prime]\sum_{i=1}^{n/d}[\frac{n}{id}][\frac{m}{id}]\] 老套路了 令\(T=id\) \[ans=\sum_{T=1}^{n}[\frac{n}{T}][\frac{m}{T}]\sum_{d|T}[d\_is\_prim…

[BZOJ2818]Gcd(莫比乌斯反演) 题面 Description 给定整数N,求1<=x,y<=N且Gcd(x,y)为素数的 数对(x,y)有多少对. Input 一个整数N Output 如题 Sample Input 4 Sample Output 4 HINT 对于样例(2,2),(2,4),(3,3),(4,2) 1<=N<=10^7 题解 题目要求的: \[\sum_{i=1}^n\sum_{j=1}^n[gcd(i,j)\_is\_prime]\] 把因数提出来…

[HDU1695]GCD(莫比乌斯反演) 题面 题目大意 求\(a<=x<=b,c<=y<=d\) 且\(gcd(x,y)=k\)的无序数对的个数 其中,你可以假定\(a=c=1\) 所有数都\(<=100000\) 数据组数\(<=3000\) 题解 莫比乌斯反演 作为一道莫比乌斯反演的题目 首先我们要迈出第一步 如果有\(gcd(x,y)=k\) 那么,我们就有\(gcd(\frac{x}{k},\frac{y}{k})=1\) 所以,现在问题相当于转化为了求 \(…

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…

题意:求(1,b)区间和(1,d)区间里面gcd(x, y) = k的数的对数(1<=x<=b , 1<= y <= d). 知识点: 莫比乌斯反演/*12*/ 线性筛求莫比乌斯反演函数: void Init() { memset(vis,0,sizeof(vis)); mu[1] = 1; cnt = 0; for(int i=2; i<N; i++) { if(!vis[i]) { prime[cnt++] = i; mu[i] = -1; } for(int j=0;…