欧拉∮函数

2019-06-03 19:55:36 阅读：418 来源： 互联网

标签：bamboos 函数 int number Bi shoe bamboo 欧拉

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

1 2 3 4 5

10 11 12 13 14 15

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

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