欧拉∮函数
作者:互联网
题目:LightOJ 1370 - Bi-shoe and Phi-shoe (欧拉函数思想)
Bamboo Pole-vault is a massively popular sport in Xzhiland. And Master Phi-shoe is a very popular coach for his success. He needs some bamboos for his students, so he asked his assistant Bi-Shoe to go to the market and buy them. Plenty of Bamboos of all possible integer lengths (yes!) are available in the market. According to Xzhila tradition,
Score of a bamboo = Φ (bamboo's length)
(Xzhilans are really fond of number theory). For your information, Φ (n) = numbers less than n which are relatively prime (having no common divisor other than 1) to n. So, score of a bamboo of length 9 is 6 as 1, 2, 4, 5, 7, 8 are relatively prime to 9.
The assistant Bi-shoe has to buy one bamboo for each student. As a twist, each pole-vault student of Phi-shoe has a lucky number. Bi-shoe wants to buy bamboos such that each of them gets a bamboo with a score greater than or equal to his/her lucky number. Bi-shoe wants to minimize the total amount of money spent for buying the bamboos. One unit of bamboo costs 1 Xukha. Help him.
Input
Input starts with an integer T (≤ 100), denoting the number of test cases.
Each case starts with a line containing an integer n (1 ≤ n ≤ 10000) denoting the number of students of Phi-shoe. The next line contains n space separated integers denoting the lucky numbers for the students. Each lucky number will lie in the range [1, 106].
Output
For each case, print the case number and the minimum possible money spent for buying the bamboos. See the samples for details.
Sample Input |
Output for Sample Input |
3 5 1 2 3 4 5 6 10 11 12 13 14 15 2 1 1 |
Case 1: 22 Xukha Case 2: 88 Xukha Case 3: 4 Xukha |
题意:
给n个数,对于这n个数依次求某个数x的欧拉函数值不小于这个数的x最小值
数论基础:
1.1与任何数互素
2.∮(n)定义为不超过n且与n互素正整数个数
3.如果p是素数,∮(p)= p-1,有最大值,对于合数or1 ,∮(p)<=p-2 。
证明:如果p为素数,任意小于p的正整数与其互素
如果p为合数,p至少有一因子d满足1<d<p,显然p,d不互素故 ∮(p)<=p-2
如果p为1,∮(p)≠p-1
代码:
#include<bits/stdc++.h> using namespace std; const int maxn=1e6+10; int prime[maxn]={1,1,0}; void db() //埃式筛 { for(int i=2;i<maxn;i++) { if(!prime[i]) { for(int j=i+i;j<=maxn;j+=i) { prime[j]=1; } } } } int main() { db(); int t; cin>>t; for(int j=1;j<=t;j++) { int n; cin>>n; long long sum=0; int x; while(n--) { cin>>x; for(int i=x+1;;i++) { if(!prime[i]) { sum+=i; break; } } } cout<<"Case "<<j<<": "<<sum<<" Xukha"<<endl; } return 0; }
标签:bamboos,函数,int,number,Bi,shoe,bamboo,欧拉 来源: https://www.cnblogs.com/BYBL/p/10969592.html