LightOJ 1370 Bi-shoe and Phi-shoe(素数筛)
2016-03-14 19:42
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A - Bi-shoe and Phi-shoe
Time Limit:2000MS Memory Limit:32768KB 64bit IO Format:%lld & %llu
Submit
Status
Practice
LightOJ 1370
Description
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
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
题目大意:
首先给出T组数据,给一些数ai(第 i 个数),ai这些数代表的是某个数欧拉函数的值,我们要求出数 pi 的欧拉函数值不小于ai。而我们要求的就是这些 pi 这些数字的和sum,而且我们想要sum最小,求出sum至少是多少。
解题思路:
要想找到最小的和 只要我们考虑的是每个pi最小 因为素数的欧拉函数值是素数-1,所以我们只需要找到比ai大的第一个素数就行啦,然后我们就想到素数筛啦 哈哈~~ 其实数据范围是1e6,并不是很大 所以可以直接存下
详见代码:
A - Bi-shoe and Phi-shoe
Time Limit:2000MS Memory Limit:32768KB 64bit IO Format:%lld & %llu
Submit
Status
Practice
LightOJ 1370
Description
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
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
题目大意:
首先给出T组数据,给一些数ai(第 i 个数),ai这些数代表的是某个数欧拉函数的值,我们要求出数 pi 的欧拉函数值不小于ai。而我们要求的就是这些 pi 这些数字的和sum,而且我们想要sum最小,求出sum至少是多少。
解题思路:
要想找到最小的和 只要我们考虑的是每个pi最小 因为素数的欧拉函数值是素数-1,所以我们只需要找到比ai大的第一个素数就行啦,然后我们就想到素数筛啦 哈哈~~ 其实数据范围是1e6,并不是很大 所以可以直接存下
详见代码:
#include <iostream> #include <cstring> using namespace std; typedef long long LL; const int MAXN = 1e6+5; int prime[MAXN];///存素数的 int cnt;///素数的个数 bool p[MAXN];///判断素数滴 void isprime()///素数筛 { cnt = 0; memset(p, true, sizeof(p)); p[1] = false; for(LL i=2; i<MAXN; i++) { if(p[i]) { prime[cnt++] = i; for(LL j=i*i; j<MAXN; j+=i) p[j] = false; } } } ///没有用的欧拉函数 白写了~~ ///int Eular(int m) ///{ /// int ret = m; /// for(int i=2; i<m; i++) /// { /// if(m%i == 0) /// { /// ret -= ret/i; /// while(m%i) /// m /= i; /// } /// } /// if(m > 1) /// ret -= ret/m; /// return ret; ///} int main() { isprime(); ///cout<<prime[cnt-1]<<endl; LL T, m, num; cin>>T; for(int cas=1; cas<=T; cas++) { cin>>m; LL sum = 0; while(m--) { cin>>num; for(int i=num+1; ; i++)///找到第一个素数 { if(p[i]) { sum += i; break; } } } cout<<"Case "<<cas<<": "<<sum<<" Xukha\n"; } return 0; }
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