题目链接:hdu 2824 The Euler function 题意: 让你求一段区间的欧拉函数值. 题解: 直接上板子. 推导过程: 定义:对于正整数n,φ(n)是小于或等于n的正整数中,与n互质的数的数目. 例如:φ(8)=4,因为1,3,5,7均和8互质. 性质:1.若p是质数,φ(p)= p-1. 2.若n是质数p的k次幂,φ(n)=(p-1)*p^(k-1).因为除了p的倍数都与n互质 3.欧拉函数是积性函数,若m,n互质,φ(mn)= φ(m)φ(n). 根据这3条性质我们就可以推…

The Euler function Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)Total Submission(s): 5028    Accepted Submission(s): 2123 Problem Description The Euler function phi is an important kind of function in number theo…

The Euler function Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others) Problem Description The Euler function phi is an important kind of function in number theory, (n) represents the amount of the numbers which are sm…

The Euler function Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)Total Submission(s): 2986    Accepted Submission(s): 1221 Problem Description The Euler function phi is an important kind of function in number theo…

The Euler function Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others) Total Submission(s): 4507    Accepted Submission(s): 1872     Problem Description The Euler function phi is an important kind of function in number…

HDU - 2824 题意: 求[a,b]间的欧拉函数和.这道题卡内存,只能开一个数组. 思路: ϕ(n) = n * (p-1)/p * ... 可利用线性筛法求出所有ϕ(n) . #include <algorithm> #include <iterator> #include <iostream> #include <cstring> #include <iomanip> #include <cstdlib> #include…

如果打表的话会超内存,我想到了一种方法解决这个问题.题目给出的数据时3000000,我将三百万分成300个数据,将整万的数据存储下来,计算的时候,先计算x和y之间整万的数据,然后再计算零散数据. 想法很不错,但为啥就是通不过呢?而且看提交返回的时间来看,应该是卡在最后一两组数据上了. 我很疑惑. 代码中注释的部分是我之前的代码.最后这道题竟然是毫无美感的暴力过去了. #include<stdio.h> #include<string.h> #define N 3000005 int…

http://acm.hdu.edu.cn/showproblem.php?pid=2824 Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)Total Submission(s): 7752    Accepted Submission(s): 3217 Problem Description The Euler function phi is an important kin…

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…

欧拉函数: φ(n)=n*(1-1/p1)(1-1/p2)....(1-1/pk),其中p1.p2…pk为n的所有素因子.比如:φ(12)=12*(1-1/2)(1-1/3)=4.可以用类似求素数的筛法.(素数打表)先筛出n以内的所有素数,再以素数筛每个数的φ值.比如求10以内所有数的φ值:设一数组phi[11],赋初值phi[1]=1,phi[2]=2...phi[10]=10:然后从2开始循环,把2的倍数的φ值*(1-1/2),则phi[2]=2*1/2=1,phi[4]=4*1/2=2,p…

1.HDU 2824   The Euler function 2.链接:http://acm.hdu.edu.cn/showproblem.php?pid=2824 3.总结:欧拉函数 题意:求(a,b)间的欧拉函数值的和. #include<iostream> #include<cstring> #include<cmath> #include<queue> #include<algorithm> #include<cstdio>…

The Euler function phi is an important kind of function in number theory, (n) represents the amount of the numbers which are smaller than n and coprime to n, and this function has a lot of beautiful characteristics. Here comes a very easy question: s…

6322.Problem D. Euler Function 题意就是找欧拉函数为合数的第n个数是什么. 欧拉函数从1到50打个表,发现规律,然后勇敢的水一下就过了. 官方题解: 代码: //1004-欧拉函数水题 #include<iostream> #include<cstdio> #include<cstring> #include<algorithm> #include<cmath> using namespace std; typede…

题目: The Euler function Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others) Total Submission(s): 166 Accepted Submission(s): 96   Problem Description The Euler function phi is an important kind of function in number theory…

版权声明:本文为博主原创文章,未经博主同意不得转载. vasttian https://blog.csdn.net/u012860063/article/details/36426357 题目链接:http://acm.hdu.edu.cn/showproblem.php?pid=2824 欧拉函数性质: 1:(百科):http://baike.baidu.com/link?url=r-yneKCCyS9N6bhbQCqiZX0V2OCYq9r7iHSzHTSs03H7qRvu1OfUzlOxf…

素数筛 朴素算法 一般来说,可以用试除法判断某一个数是不是素数: bool isPrime(int n) { if(n < 2) return false; for(int i = 2; i < n; i++) if(n % i == 0) return false; return true; } 但其实我们只需要试除到根号n即可,因为对于任意的n,假设存在一个大于根号n的因数,那么肯定存在一个小于根号n的因数与之对应.那么有: bool isPrime(int n) { if(n <…

The Euler functionTime Limit: 2000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)Total Submission(s): 6018 Accepted Submission(s): 2539 Problem DescriptionThe Euler function phi is an important kind of function in number theory, (n)…

The Euler function Time Limit : 2000/1000ms (Java/Other)   Memory Limit : 32768/32768K (Java/Other) Total Submission(s) : 39   Accepted Submission(s) : 19 Font: Times New Roman | Verdana | Georgia Font Size: ← → Problem Description The Euler function…

/* 题意:(n)表示小于n与n互质的数有多少个,给你两个数a,b让你计算a+(a+1)+(a+2)+......+b; 初步思路:暴力搞一下,打表 #放弃:打了十几分钟没打完 #改进:欧拉函数:具体证明看po主的博客 ^0^ #超时:这里直接用欧拉函数暴力搞还是不可以的,用到线性筛欧拉函数,这里总和爆int,要用long long */ #include<bits/stdc++.h> #define ll long long using namespace std; /***********…

The Euler function Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)Total Submission(s): 3284    Accepted Submission(s): 1350 Problem Description The Euler function phi is an important kind of function in number theo…

Time Limit: 1000MS   Memory Limit: 32768KB   64bit IO Format: %I64d & %I64u Description The Euler function phi is an important kind of function in number theory, (n) represents the amount of the numbers which are smaller than n and coprime to n, and…

The Euler function Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)Total Submission(s): 5235    Accepted Submission(s): 2225 Problem Description The Euler function phi is an important kind of function in number theo…

The Euler function Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others) Total Submission(s): 4518    Accepted Submission(s): 1879 Problem Description The Euler function phi is an important kind of function in number the…

题目链接 快速求出a到b之间所有数的欧拉函数. 一个一个求肯定是不行的, 我们知道欧拉函数的公式为phi(n) = n*(1-1/i1)*(1-1/i2).......i1, i2为素因子. 那么我们就可以先将每一个数的欧拉函数值预处理出来. 具体看代码 #include<bits/stdc++.h> using namespace std; #define pb(x) push_back(x) #define ll long long #define mk(x, y) make_pair(x…

GTW likes function 题目连接: http://acm.hdu.edu.cn/showproblem.php?pid=5596 Description Now you are given two definitions as follows. f(x)=∑xk=0(−1)k22x−2kCk2x−k+1,f0(x)=f(x),fn(x)=f(fn−1(x))(n≥1) Note that φ(n) means Euler's totient function.(φ(n)is an…

链接:http://acm.hdu.edu.cn/showproblem.php?pid=6322 Problem Description In number theory, Euler's totient function φ(n) counts the positive integers up to a given integer n that are relatively prime to n . It can be defined more formally as the number…

题目链接: http://acm.hdu.edu.cn/showproblem.php?pid=5597 题意: http://bestcoder.hdu.edu.cn/contests/contest_chineseproblem.php?cid=658&pid=1003 题解: f0(1)=2;  f0(2)=3;  f0(3)=4; f1(1)=3;  f1(2)=4;  f1(3)=5; f2(1)=4;  ...... 所以归纳出:fn(x)=n+x+1;  orz 然后求euler(…

//题目链接:http://acm.hdu.edu.cn/showproblem.php?pid=6322 //题目大意:给定 k,求第 k 小的数 n,满足 φ(n) 是合数.显然 φ(1) = 1 不是合数,只考虑 n ≥ 2 的情况.//思路:得到题意之后,查到了一张表(https://en.wikipedia.org/wiki/Euler%27s_totient_function)//得知当且仅当 n = 1, 2, 3, 4, 6 时,φ(n) 不是合数.第1小的K值是5,第二小的K值…

题目求φ(a)+φ(a+1)+...+φ(b-1)+φ(b). 用欧拉筛选法O(n)计算出n以内的φ值,存个前缀和即可. φ(p)=p-1(p是质数),小于这个质数且与其互质的个数就是p-1: φ(p*a)=(p-1)*φ(a)(p是质数且p不能整除a),因为欧拉函数是积性函数,φ(p*a)=φ(p)*φ(a): φ(p*a)=p*φ(a)(p是质数且p|a),不知怎么理解.. #include<cstdio> #include<cstring> using namespace s…

裸题 O(nlogn): #include <cstdio> #include <iostream> #include <algorithm> using namespace std; typedef long long ll; const int maxn=3000000+100; int phi[maxn]; void init() { for(int i=2;i<maxn;i++) phi[i]=i; for(int i=2;i<maxn;i++) i…