Lightoj Bi-shoe and Phi-shoe 1370 "Euler function + prime number playing 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:

To some number of AI (number i), AI these numbers represent the value of a certain number of Euler functions, we require that the number of the Euler function of Ni is not less than the AI. And what we're asking for is these Ni and sum sums, and we want the sum to be the smallest, to find out how much the sum is.

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.

AC Code:

#include <stdio.h> #include <math.h> #include <vector> #include <queue> #include <string> #include <string.h> #include <stdlib.h> #include <iostream> #include <algorithm>using Namespace Std;typedef long Long ll;const int maxn = 1000000+100; LL IS_PRIME[MAXN]; LL prime[maxn];void Find_prime () {    is_prime[1]=1;    for (int i=2;i<maxn;i++) {        if (!is_prime[i]) {for            (int j=i*2;j<maxn;j+=i)                is_prime[j]=1;}}    } int main () {    find_prime ();    int t;    scanf ("%d", &t);    int xp=1;    while (t--) {        int n;        scanf ("%d", &n);        int num;        LL ans=0;        for (int i=0;i<n;i++) {            scanf ("%d", &num);            for (int j=num+1;; J + +)                if (!is_prime[j]) {                    ans+=j;                    break;                }        }        printf ("Case%d:%lld xukha\n", Xp++,ans);    }    return 0;}

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Lightoj Bi-shoe and Phi-shoe 1370 "Euler function + prime number playing table"