lightOJ1370 Euler function Properties

D-(example) Euler function properties

crawling in process ... crawling failed Time limit:2000MS Memory Limit:32768KB 64bit IO Format:%lld &%llu

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Description

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

3

5

1 2 3) 4 5

6

10 11 12 13 14 15

2

1 1

Sample Output

Case 1:22 Xukha

Case 2:88 Xukha

Case 3:4 Xukha

The main idea of this problem is to give you a number N, so that you find the smallest K meet & (k) >=n (& refers to Euler function)

Analysis of Ideas: the simple properties of Euler functions are investigated, that is, the first prime number that satisfies & (k) >=n is n+1z.

Code:

#include <iostream>#include<cstdio>#include<algorithm>#include<cstring>#include<cmath>using namespaceStd;typedefLong Longll;Const intmaxn=1e6+ -;intPHI[MAXN];intPRIME[MAXN];BOOLCHECK[MAXN];inttot;voidMake_phi () {tot=0; memset (check,true,sizeof(check)); phi[1]=1;  for(intI=2; i<=maxn;i++)    {        if(Check[i]) {Prime[tot++]=i; Phi[i]=i-1; }         for(intj=0; j<tot&&i*prime[j]<=maxn;j++) {Check[i*prime[j]]=false; if(i%prime[j]==0) {Phi[i*prime[j]]=phi[i]*Prime[j];  Break; }            Elseprime[i*prime[j]]=phi[i]* (prime[j]-1); }    }}intKase;intMain () {intT;    Make_phi (); scanf ("%d",&T); Kase=0;    ll num;  while(t--)    {        intN; scanf ("%d",&N); ll ans=0;  while(n--) {scanf ("%lld",&num); ll K=num+1;  for(ll i=k;; i++)            {                if(Check[i]) {ans+=i;  Break; }}} printf ("Case %d:%lld xukha\n",++Kase,ans); }}

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lightOJ1370 Euler function Properties