BZOJ4802 欧拉函数 （Pollard-Rho Miller-Robin）

题目

求大数的欧拉函数$varphi$

题解

Pollard-Rho 板子

CODE

#pragma GCC optimize (3)
#include <bits/stdc++.h>
using namespace std;
typedef long long LL;
 
inline LL mul(LL a, LL b, LL p) {
    a=(a%p+p)%p, b=(b%p+p)%p;
    return (((a*b)-(LL)((long double)a*b/p)*p)%p+p)%p;
}
 
inline LL qpow(LL a, LL b, LL p) {
    LL re=1;
    for(; b; b>>=1, a=mul(a,a,p))
        if(b&1) re=mul(re,a,p);
    return re;
}
 
namespace Pollard_Rho {
    int bs[5] = { 2, 3, 7, 31, 61 };
    bool Miller_Robin(LL x) {
        for(int i = 0; i < 5; ++i) if(x == bs[i]) return 1;
        LL res = x-1, k = 0;
        for(; !(res&1); res>>=1, ++k);
        for(int i = 0; i < 5; ++i) {
            LL pre = qpow(bs[i], res, x), now;
            for(int t = k; t--; swap(now, pre))
                if((now=mul(pre, pre, x)) == 1 && pre != 1 && pre != x-1)
                    return 0;
            if(pre != 1) return 0;
        }
        return 1;
    }
    LL Rho(LL x, LL c) {
        LL i = 1, j = 0, sum = 1, a = rand()%(x-1) + 1, b = a, d = 1;
        while(d == 1) {
            sum = mul(sum, abs((a=(mul(a,a,x)+c)%x)-b), x);
            if(++j == i) i<<=1, b = a, d = __gcd(sum, x);
            if(!(j&1023)) d = __gcd(sum, x);
        }
        return d == x ? Rho(x, c+1) : d;
    }
    map<LL, int>mp;
    map<LL, int>::iterator it;
    void Pollard(LL x) {
        if(x == 1) return;
        if(Miller_Robin(x)) { ++mp[x]; return; }
        LL tmp = Rho(x, 3);
        Pollard(tmp), Pollard(x/tmp);
    }
    vector<pair<LL,int> > Solve(LL x) {
        mp.clear(); Pollard(x);
        vector<pair<LL,int> > re;
        for(it = mp.begin(); it != mp.end(); ++it)
            re.push_back(make_pair(it->first, it->second));
        return re;
    }
}
LL n;
vector<pair<LL,int> >vec;
int main() {
    srand(19260817);
    scanf("%lld", &n);
    vec = Pollard_Rho::Solve(n);
    for(int i = vec.size()-1; i >= 0; --i)
        n = n / vec[i].first * (vec[i].first-1);
    printf("%lld
", n);
}