Farey Sequence 题意:给定一个数n,求在[1,n]这个范围内两两互质的数的个数.(转化为给定一个数n,比n小且与n互质的数的个数) 知识点: 欧拉函数: 普通求法: int Euler(int n) { int ans=n; for(int i=0;i<cnt&&prime[i]<=n;i++) { if(n%prime[i]==0) { ans=ans-ans/prime[i]; while(n%prime[i]==0) n/=prime[i]; } } if(…

 名字是法雷数列其实是欧拉phi函数              Farey Sequence Time Limit: 1000MS   Memory Limit: 65536K Total Submissions: 11246   Accepted: 4363 Description The Farey Sequence Fn for any integer n with n >= 2 is the set of irreducible rational numbers a/b with 0 <…

Description The Farey Sequence Fn for any integer n with n >= 2 is the set of irreducible rational numbers a/b with 0 < a < b <= n and gcd(a,b) = 1 arranged in increasing order. The first few are  F2 = {1/2}  F3 = {1/3, 1/2, 2/3}  F4 = {1/4, 1…

A - Farey Sequence Time Limit:1000MS     Memory Limit:65536KB     64bit IO Format:%I64d & %I64u Submit Status Practice POJ 2478 Description The Farey Sequence Fn for any integer n with n >= 2 is the set of irreducible rational numbers a/b with 0 &l…

题目大意 直接看原文吧.... The Farey Sequence Fn for any integer n with n >= 2 is the set of irreducible rational numbers a/b with 0 < a < b <= n and gcd(a,b) = 1 arranged in increasing order. The first few areF2 = {1/2}F3 = {1/3, 1/2, 2/3}F4 = {1/4, 1/3…

The Farey Sequence Fn for any integer n with n >= 2 is the set of irreducible rational numbers a/b with 0 < a < b <= n and gcd(a,b) = 1 arranged in increasing order. The first few are F2 = {1/2} F3 = {1/3, 1/2, 2/3} F4 = {1/4, 1/3, 1/2, 2/3, 3…

UVA12995 Farey Sequence 欧拉函数 同仪仗队那题几乎相同,本质都是求欧拉函数的和 #include<cstdio> #define N 1000000 ],i,j,t; ],s[N+]; ]; int main(){ ;i<=N;++i){ ,pri[++cnt]=i; ;j<=cnt;++j){ t=i*pri[j]; if(t>N) break; v[t]=; ); else{phi[t]=phi[i]*pri[j];break;} } }//线性筛…

The Farey Sequence Fn for any integer n with n >= 2 is the set of irreducible rational numbers a/b with 0 < a < b <= n and gcd(a,b) = 1 arranged in increasing order. The first few are F2 = {1/2} F3 = {1/3, 1/2, 2/3} F4 = {1/4, 1/3, 1/2, 2/3, 3…

洛谷传送门 Farey Sequence (格式太难调,题面就不放了) 分析: 实际上求分数个数就是个幌子,观察可以得到,所求的就是$\sum^n_{i=2}\phi (i)$,所以直接欧拉筛+前缀和即可. Code: #include<cstdio> #include<cstring> #include<cstdlib> #include<cmath> #include<iostream> #include<iomanip> #in…

Farey Sequence Time Limit: 1000MS   Memory Limit: 65536K Total Submissions: 18507   Accepted: 7429 Description The Farey Sequence Fn for any integer n with n >= 2 is the set of irreducible rational numbers a/b with 0 < a < b <= n and gcd(a,b)…

题目链接:http://poj.org/problem?id=2478 Description The Farey Sequence Fn for any integer n with n >= 2 is the set of irreducible rational numbers a/b with 0 < a < b <= n and gcd(a,b) = 1 arranged in increasing order. The first few are F2 = {1/2}…

一.题目 The Farey Sequence Fn for any integer n with n >= 2 is the set of irreducible rational numbers a/b with 0 < a < b <= n and gcd(a,b) = 1 arranged in increasing order. The first few are F2 = {1/2} F3 = {1/3, 1/2, 2/3} F4 = {1/4, 1/3, 1/2, 2…

题目链接:http://poj.org/problem?id=2478 Farey Sequence Time Limit: 1000MS   Memory Limit: 65536K Total Submissions: 19736   Accepted: 7962 Description The Farey Sequence Fn for any integer n with n >= 2 is the set of irreducible rational numbers a/b with…

Farey Sequence Time Limit: 1000MS   Memory Limit: 65536K       Description The Farey Sequence Fn for any integer n with n >= 2 is the set of irreducible rational numbers a/b with 0 < a < b <= n and gcd(a,b) = 1 arranged in increasing order. Th…

题目链接: Farey Sequence Time Limit: 1000MS   Memory Limit: 65536K Total Submissions: 14230   Accepted: 5624 Description The Farey Sequence Fn for any integer n with n >= 2 is the set of irreducible rational numbers a/b with 0 < a < b <= n and gcd…

Time Limit: 1000MS   Memory Limit: 65536K Total Submissions: 15023   Accepted: 5962 Description The Farey Sequence Fn for any integer n with n >= 2 is the set of irreducible rational numbers a/b with 0 < a < b <= n and gcd(a,b) = 1 arranged in…

题目链接:https://vjudge.net/problem/POJ-2478 Farey Sequence Time Limit: 1000MS   Memory Limit: 65536K Total Submissions: 17753   Accepted: 7112 Description The Farey Sequence Fn for any integer n with n >= 2 is the set of irreducible rational numbers a/b…

http://poj.org/problem?id=2478 (题目链接) 题意 求分母小于等于n的真分数的个数. Solution 现在只能做做水题了,唉,思维僵化. 细节 前缀和开LL 代码 // poj2478 #include<algorithm> #include<iostream> #include<cstring> #include<cstdlib> #include<cstdio> #include<cmath> #d…

题意: 求前n项的欧拉函数之和 题解: 预处理出所有欧拉函数 赤裸裸的模版题- - 没什么好说的 代码: #include <cstdio> typedef long long ll; ; ll n,phi[N],pri[N],bo[N]; void makepri(){ ;i<=N;i++){ if (!bo[i]){ pri[++pri[]]=i; phi[i]=i-; } ;j<=pri[] && i*pri[j]<=N;j++){ bo[i*pri[j…

http://poj.org/problem?id=2478 求欧拉函数的模板. 初涉欧拉函数,先学一学它主要的性质. 1.欧拉函数是求小于n且和n互质(包含1)的正整数的个数. 记为φ(n). 2.欧拉定理:若a与n互质.那么有a^φ(n) ≡ 1(mod n),经经常使用于求幂的模. 3.若p是一个质数,那么φ(p) = p-1.注意φ(1) = 1. 4.欧拉函数是积性函数: 若m与n互质,那么φ(nm) = φ(n) * φ(m). 若n = p^k且p为质数,那么φ(n) = p^k…

洛谷题目传送门 分数其实就是一个幌子,实际上就是求互质数对的个数(除开一个特例\((1,1)\)).因为保证了\(a<b\),所以我们把要求的东西拆开看,不就是\(\sum_{i=2}^n\phi(i)\)吗? 关于通过筛素数线性求欧拉函数的一点思路总结在蒟蒻的blog里 剩下的就是记一个前缀和了. #include<cstdio> #define R register const int N=1000001; int pr[N],phi[N]; long long ans[N]; bo…

仔细看看题目,按照题目要求 其实就是 求 小于等于n的 每一个数的 欧拉函数值  的总和,为什么呢,因为要构成 a/b 然后不能约分  所以 gcd(a,b)==1,所以  分母 b的 欧拉函数值  就是 以b为分母的 这样的数有几个,分母b的范围 是小于等于n,所以 直接套一个模版就可以了 ,网上找的  说筛选的比较好,下面代码中有一个 注释掉的 模版 貌似 是错的,还不清楚为什么  弄清楚了 重新 注明一下  #include<iostream> #include<cstdio>…

题意:给出式子F F中分子分母互质,且分子小于分母 例: F2 = {1/2} F3 = {1/3, 1/2, 2/3} F4 = {1/4, 1/3, 1/2, 2/3, 3/4} F5 = {1/5, 1/4, 1/3, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5} 求解 fn的元素个数. 分析:本题就是求解欧拉函数值的前n项和,直接求解欧拉函数值的方法不行,由于用此法就是O(n^2)复杂度.採用递推式求解是O(nlogn)复杂度 代码例如以下: #include <set>…

http://poj.org/problem?id=2478 http://acm.hdu.edu.cn/showproblem.php?pid=2824 欧拉函数模板裸题,有两种方法求出所有的欧拉函数,一是筛法,而是白书上的筛法. 首先看欧拉函数的性质: 欧拉函数是求小于n且和n互质(包括1)的正整数的个数.记为φ(n). 欧拉定理:若a与n互质,那么有a^φ(n) ≡ 1(mod n),经常用于求乘法逆元. 若p是一个质数,那么φ(p) = p-1,注意φ(1) = 1. 欧拉函数是积性函数…

hdu1787,直接求欧拉函数 #include <iostream> #include <cstdio> using namespace std; int n; int phi(int n){ int ans=n; for(int i=2; i*i<=n; i++) if(n%i==0){ ans -= ans / i; while(n%i==0) n /= i; } if(n>1) ans -= ans / n; return ans; } int main(){…

[题目链接] 点击打开链接 [算法] 不难看出,ans = phi(2) + phi(3) + .... + phi(n-1) + phi(n) 线性筛筛出欧拉函数,预处理前缀和,即可 [代码] #include <algorithm> #include <bitset> #include <cctype> #include <cerrno> #include <clocale> #include <cmath> #include &…

题意:定义 Fn 序列表示一串 <1 的分数,分数为最简分数,且分母 ≤n .问该序列的个数.(2≤N≤10^6) 解法:先暴力找规律(代码见屏蔽处),发现 Fn 序列的个数就是 Φ(1)~Φ(n) 的和.于是用欧拉筛预处理就好了. 注意--求前缀和要用 long long 的类型. 1 #include<cstdio> 2 #include<cstdlib> 3 #include<cstring> 4 #include<iostream> 5 usi…

Farey Sequence Time Limit: 1000MS   Memory Limit: 65536K Total Submissions: 14291   Accepted: 5647 Description The Farey Sequence Fn for any integer n with n >= 2 is the set of irreducible rational numbers a/b with 0 < a < b <= n and gcd(a,b)…

Farey Sequence Time Limit: 1000MS   Memory Limit: 65536K Total Submissions: 17744   Accepted: 7109 Description The Farey Sequence Fn for any integer n with n >= 2 is the set of irreducible rational numbers a/b with 0 < a < b <= n and gcd(a,b)…

n阶的法里数列是0和1之间最简分数的数列,由小至大排列,每个分数的分母不大于n. Stern-Brocot树(SB Tree)可以生成这个序列 {0/1,1/1} {0/1,1/2,1/1} {0/1,1/3,1/2,2/3,1/1} {0/1,1/4,1/3,1/2,2/3,3/4,1/1} {0/1,1/5,1/4,1/3,2/5,1/2,3/5,2/3,3/4,4/5,1/1} {0/1,1/6,1/5,1/4,1/3,2/5,1/2,3/5,2/3,3/4,4/5,5/6,1/1} {0…