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 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].
For each case, print the case number and the minimum possible money spent for buying the bamboos. See the samples for details.
题目大意： Φ (n)表示长度为小于数字n的和n互质的数的个数，也就是欧拉函数。现在给出n个幸运数字，对于每一个幸运数字，要求的x，使Φ (x)的值大于等于这个幸运数字，求这些x和的最小值。 解题思路：可以先把题目数据范围内的欧拉函数求解出来，欧拉函数的求法可以自己写。然后再对比输入的数据进行选择。 参考代码：
#include <iostream> #include <algorithm> #include <string> #include <vector> #include <stack> #include <queue> #include <map> #include <set> #include <cstdio> #include <cstdlib> #include <cstring> #include <cmath> using namespace std; #define ll long long #define clean(arrays) memset(arrays, 0, sizeof(arrays)) #define N 1000006 int prime[N], mark[N]; // prime 为素数数组， mark 标记是否为素数 int phi[N], indexs = 0; // phi[i] 为φ(i), indexs 为出现素数的个数 //欧拉函数线性筛 void line_phi(int n) { clean(phi); clean(prime); phi[1] = 1; // φ(1) = 1； for (int i = 2; i <= n; i++) { if (! mark[i]) { // 如果是素数(为0) prime[++indexs] = i; //进素数数组，指针加 1 phi[i] = i - 1; } for (int j = 1; j <= indexs; j++) { if (i * prime[j] > n) break; mark[i * prime[j]] = 1; // 标记 i * prime[j] 不是素数 if (i % prime[j] == 0) { //应用性质 1 phi[i * prime[j]] = phi[i] * prime[j]; break; } else { phi[i * prime[j]] = phi[i] * (prime[j] - 1); //应用性质 3 } } } } int a[1000005]; int main() { line_phi(N); //先把欧拉函数求出来 int t, m; cin >> t; for (int i = 1; i <= t; i++) { cin >> m; for (int j = 1; j <= m; j++) cin >> a[j]; sort(a + 1, a + m + 1); // 对数组进行排序，避免以后的重复计算 int x = 2; ll ans = 0; // 最后累加的和是个比较大的数 for (int j = 1; j <= m; j++) { while (phi[x] < a[j]) x++; ans += x; } cout <<"Case " << i << ": " << ans << " " <<"Xukha"<<endl; } }