Light OJ 1370 Party All the Time （欧拉函数 +素数打表）

Time Limit: 2 second(s)Memory Limit: 32 MB

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：

 给你一些数，把每一个数，看成一个数的欧拉函数值。如一个欧拉函数值为x，那么他对应这初始值为y因为很多数有相同的欧拉函数值，即一个x对应着很多个y，我们求出数Y欧拉函数不小于x。问：这些y值和最小为多少。

解题思路：

要求和最小，我们可以让每个数都尽量小，那么我们最后得到的肯定就是一个最小值。

给定一个数的欧拉函数值ψ(N)，我们怎么样才能求得最小的N?

我们知道，一个素数P的欧拉函数值ψ(P)=P-1。所以如果我们知道ψ(N)，那么最小的N就是最接近ψ(N)，并且大于ψ(N)的素数。我们把所有素数打表之后再判断就可以了。

[cpp] view plain copy

print?

1. #include<iostream>  
2. #include<cstdio>  
3. #include<cstring>  
4. #include<algorithm>  
5. using namespace std;  
6. typedef long long LL;  
7. const int maxn=1000000+1000;  
8. int is_prime[maxn];  
9. int n;  
10. void init()  
11. {  
12.     memset(is_prime,0,sizeof(is_prime));  
13.     is_prime[1]=1;  
14.     for(LL i=2;i<maxn;i++)  
15.     {  
16.         if(!is_prime[i])  
17.         {  
18.             for(LL j=i*i;j<maxn;j+=i)  
19.                 is_prime[j]=1;  
20.         }  
21.     }  
22. }  
23. int main()  
24. {  
25.     init();  
26.     int t,x;  
27.     int cas=0;  
28.     scanf(”%d”,&t);  
29.     while(t–)  
30.     {  
31.         long long ans=0;  
32.         scanf(”%d”,&n);  
33.         for(int i=0;i<n;i++)  
34.         {  
35.             scanf(”%d”,&x);  
36.             for(int j=x+1;;j++)  
37.             {  
38.                 if(!is_prime[j]){  
39.                     ans+=j;  
40.                     break;  
41.                 }  
42.             }  
43.         }  
44.         printf(”Case %d: %lld Xukha\n”,++cas,ans);  
45.     }  
46.     return 0;  
47. }