Bzoj2818: Gcd
发布日期:2021-08-26 11:01:55 浏览次数:2 分类:技术文章

本文共 1652 字,大约阅读时间需要 5 分钟。

题面

Sol

傻逼题

\(原式=\sum_{p质数}^{n}\sum_{i=1}^{\lfloor\frac{n}{p}\rfloor}\sum_{j=1}^{\lfloor\frac{m}{p}\rfloor}[gcd(i, j)==1]\)
\(设f(i) = \sum_{i=1}^{\lfloor\frac{n}{d}\rfloor}\sum_{j=1}^{\lfloor\frac{m}{d}\rfloor}[gcd(i, j)==1]\)
\(g(i) = \sum_{i|d} f(d) = \lfloor\frac{\lfloor\frac{n}{d}\rfloor}{i}\rfloor\lfloor\frac{\lfloor\frac{m}{d}\rfloor}{j}\rfloor\)
质数就把质数的bool求前缀和就好了,数论分块

# include 
# define RG register# define IL inline# define Fill(a, b) memset(a, b, sizeof(a))using namespace std;typedef long long ll;const int _(1e7 + 1);IL ll Read(){ char c = '%'; ll x = 0, z = 1; for(; c > '9' || c < '0'; c = getchar()) if(c == '-') z = -1; for(; c >= '0' && c <= '9'; c = getchar()) x = x * 10 + c - '0'; return x * z;}int prime[_], mu[_], num, s[_];bool isprime[_];IL void Prepare(){ isprime[1] = 1; mu[1] = 1; for(RG int i = 2; i < _; ++i){ if(!isprime[i]) prime[++num] = i, mu[i] = -1; for(RG int j = 1; j <= num && i * prime[j] < _; ++j){ isprime[i * prime[j]] = 1; if(i % prime[j]) mu[i * prime[j]] = -mu[i]; else{ mu[i * prime[j]] = 0; break; } } mu[i] += mu[i - 1]; s[i] = s[i - 1] + (!isprime[i]); }}IL ll Calc(RG ll n){ RG ll f = 0; for(RG ll i = 1, j; i <= n; i = j + 1) j = n / (n / i), f += 1LL * (mu[j] - mu[i - 1]) * (n / i) * (n / i); return f;}int main(RG int argc, RG char *argv[]){ Prepare(); RG int n = Read(); RG ll ans = 0; for(RG ll d = 1, j; d <= n; d = j + 1) j = n / (n / d), ans += 1LL * (s[j] - s[d - 1]) * Calc(n / d); printf("%lld\n", ans); return 0;}

转载于:https://www.cnblogs.com/cjoieryl/p/8260773.html

转载地址:https://blog.csdn.net/weixin_33882452/article/details/93665082 如侵犯您的版权,请留言回复原文章的地址,我们会给您删除此文章,给您带来不便请您谅解!

上一篇:复现Spark2.2.0快速入门
下一篇:拓扑排序

发表评论

最新留言

很好
[***.229.124.182]2024年03月22日 13时17分35秒