题目链接: GTW likes function Time Limit: 4000/2000 MS (Java/Others)     Memory Limit: 131072/131072 K (Java/Others) Problem 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 th…

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(…

题意:问从(0,0)到(x,y)(0≤x, y≤N)的线段没有与其他整数点相交的点数. 解法:只有 gcd(x,y)=1 时才满足条件,问 N 以前所有的合法点的和,就发现和上一题-- [poj 2478]Farey Sequence(数论--欧拉函数 找规律求前缀和) 求 x/y,gcd(x,y)=1 且 x<y 很像.   而由于这里 x可等于或大于y,于是就求 欧拉函数的前缀和*2+边缘2个点+对角线1个点. 1 #include<cstdio> 2 #include<cst…

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…

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…

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…

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…

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…

A Simple Stone Game Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 262144/262144 K (Java/Others)Total Submission(s): 0    Accepted Submission(s): 0 Problem Description After he has learned how to play Nim game, Bob begins to try another ston…

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…