Ligh OJ 1370 Party all the time (Euler function + prime number table)

1370-bi-shoe and Phi-shoe

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Time Limit: 2 second (s)

Memory Limit: MB

Bamboo Pole-vault is a massively popular sport in Xzhiland. And Master Phi-shoe is a very popular coaches 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!) is available in the market. According to Xzhila tradition,

Score of a bamboo = Φ (bamboo ' s length)

(Xzhilans is really fond of number theory). For your information, Φ (n) = numbers less than n which is relatively prime (having no common divisor o Ther than 1) to N. So, score of a bamboo of length 9 is 6 as 1, 2, 4, 5, 7, 8 were relatively prime to 9.

The assistant Bi-shoe have to buy one bamboo for each student. As a twist, each pole-vault student of Phi-shoe have a lucky number. Bi-shoe wants to buy bamboos such, each of them gets a bamboo with a score greater than or equal to his/her lucky numb Er. 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 would 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

Test instructions

Give you some numbers, and take each number as a number of Euler function values. If the value of a Euler function is x, then he corresponds to this initial value y because many numbers have the same Euler function value, that is, an x corresponds to a number of Y, we find that the Y Euler function is not less than X. Q: What are these y values and the minimum?

Problem Solving Ideas:

Requirements and minimum, we can make every number as small as possible, then we finally get a minimum value is definitely.

Given a number of Euler function values ψ (n), how can we find the smallest n?

We know that the Euler function value of a prime P is ψ (p) =p-1. So if we know Ψ (n), then the smallest n is the prime number closest to Ψ (n) and greater than ψ (n). We put all the primes on the table before we can judge.

#include <iostream> #include <cstdio> #include <cstring> #include <algorithm>using namespace Std;typedef Long Long ll;const int maxn=1000000+1000;int is_prime[maxn];int n;void init () {    memset (is_prime,0, sizeof (Is_prime));    Is_prime[1]=1;    for (ll i=2;i<maxn;i++)    {        if (!is_prime[i])        {for            (ll j=i*i;j<maxn;j+=i)                is_prime[j]=1;        }    }}int Main () {    init ();    int t,x;    int cas=0;    scanf ("%d", &t);    while (t--)    {        long long ans=0;        scanf ("%d", &n);        for (int i=0;i<n;i++)        {            scanf ("%d", &x);            for (int j=x+1;; J + +) {                if (!is_prime[j]) {                    ans+=j;                    Break        ;        }}} printf ("Case%d:%lld xukha\n", ++cas,ans);    }    return 0;}

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Ligh OJ 1370 Party all the time (Euler function + prime number table)