POJ 2407 Relatives(欧拉函数)

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题目:

Given n, a positive integer, how many positive integers less than n are relatively prime to n? Two integers a and b are relatively prime if there are no integers x > 1, y > 0, z > 0 such that a = xy and b = xz.

Input:

There are several test cases. For each test case, standard input contains a line with n <= 1,000,000,000. A line containing 0 follows the last case.

Output:

For each test case there should be single line of output answering the question posed above.

Sample Input:

7
12
0

Sample Output:

6
4

题目链接

直接求欧拉函数值。

AC代码:

//#include <bits/stdc++.h>
#include <iostream>
#include <cstdio>
#include <cmath>
#include <cstring>
using namespace std;
#define mem(a,b) memset(a,b,sizeof(a))
#define pb push_back
#define mp make_pair
#define lowbit(x) (x&(-x))
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int> PII;
typedef pair<double,double> PDD;
typedef pair<ll,ll> PLL;
const int INF = 0x3f3f3f3f;
const int maxn = 1e6 + 5;
const int mod = 1e9 + 7;
const double eps = 1e-8;
const double pi = asin(1.0) * 2;
const double e = 2.718281828459;
bool Finish_read;
template<class T>inline void read(T &x) {
    Finish_read = 0;
    x = 0;
    int f = 1;
    char ch = getchar();
    while (!isdigit(ch)) {
        if (ch == '-') {
            f = -1;
        }
        if (ch == EOF) {
            return;
        }
        ch = getchar();
    }
    while (isdigit(ch)) {
        x = x * 10 + ch - '0';
        ch = getchar();
    }
    x *= f;
    Finish_read = 1;
};

ull Phi(ull x) {
    ull res = x;
    for (int i = 2; i <= int(sqrt(x * 1.0)); ++i) {
        if (!(x % i)) {
            res = res / i * (i - 1);
            while (!(x % i)) {
                x /= i;
            }
        }
    }
    if (x > 1) {
        res = res / x * (x - 1);
    }
    return res;
}

int main(int argc, char *argv[]) {
#ifndef ONLINE_JUDGE
    freopen("in.txt", "r", stdin);
    freopen("out.txt", "w", stdout);
#endif
    ull n;
    while (~scanf("%llu", &n) && n) {
        printf("%llu\n", Phi(n));
    }
#ifndef ONLINE_JUDGE
    fclose(stdin);
    fclose(stdout);
    system("gedit out.txt");
#endif
    return 0;
}