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…

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))…

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…

这题肝了三四天,其他啥也没做... 传送门 然后...双倍经验 简单版 不知道为什么会脑抽去帮 LZ_101 大佬验题... 题目和被 A 穿的 PGCD 一样,数据范围变成大概 2e11 ... 于是我们就要考虑用更加优秀的做法去解决这道题了 首先我们得想到 PGCD 中最优秀的解法: \[ANS=\sum_{i=1}^{n} \lfloor {n\over d}\rfloor \lfloor {m\over d} \rfloor \sum_{p∈ prime ,p|d} \mu({p\ove…

题目链接:https://vjudge.net/problem/SPOJ-PGCD 题目大意: 给定 \(N\) 和 \(M\),求满足 \((1 \le x \le N), (1 \le y \le M)\),且 \(gcd(x,y)\) 为素数的 \((x,y)\) 的对数. 知识点: 莫比乌斯反演 解题思路: 设 \(g(p)\) 表示满足 \((1 \le x \le N), (1 \le y \le M)\),且 \(gcd(x,y) = p\) 的 \((x,y)\) 的对数.直接求…

传送门:Primes in GCD Table 题意:给定两个数和,其中,,求为质数的有多少对?其中和的范围是. 分析:这题不能枚举质数来进行莫比乌斯反演,得预处理出∑υ(n/p)(n%p==0). #pragma comment(linker,"/STACK:1024000000,1024000000") #include <cstdio> #include <cstring> #include <string> #include <cmat…

C. GCD Table The GCD table G of size n × n for an array of positive integers a of length n is defined by formula Let us remind you that the greatest common divisor (GCD) of two positive integers x and y is the greatest integer that is divisor of both…

A. GCD Table time limit per test 2 seconds memory limit per test 256 megabytes input standard input output standard output The GCD table G of size n × n for an array of positive integers a of length n is defined by formula Let us remind you that the…

C. GCD Table Time Limit: 1 Sec Memory Limit: 256 MB 题目连接 http://codeforces.com/contest/583/problem/C Description The GCD table G of size n × n for an array of positive integers a of length n is defined by formula Let us remind you that the greatest c…