2019 Multi-University Training Contest 3

#include<bits/stdc++.h>

using namespace std;
typedef long long ll;
const int S=8;

ll mult_mod(ll a,ll b,ll c)
{
    a%=c;
    b%=c;
    ll ret=0,tmp=a;
    while (b)
    {
        if (b&1)
        {
            ret+=tmp;
            if (ret>c)
            {
                ret-=c;
            }
        }
        tmp<<=1;
        if (tmp>c) tmp-=c;
        b>>=1;
    }
    return ret;
}

ll pow_mod(ll a,ll n,ll mod)
{
    ll ret=1;
    ll temp=a%mod;
    while (n)
    {
        if(n&1)
        {
            ret=mult_mod(ret,temp,mod);
        }
        temp=mult_mod(temp,temp,mod);
        n>>=1;
    }
    return ret;
}

bool check(ll a,ll n,ll x,ll t)
{
    ll ret=pow_mod(a,x,n);
    ll last=ret;
    for (int i=1; i<=t; i++)
    {
        ret=mult_mod(ret,ret,n);
        if (ret==1&&last!=1&&last!=n-1)
        {
            return 1;
        }
        last=ret;
    }
    if (ret!=1)
    {
        return 1;
    }
    return 0;
}

bool Miller_Rabin(ll n)
{
    if (n<2)
    {
        return 0;
    }
    if (n==2)
    {
        return 1;
    }
    if ((n&1)==0)
    {
        return 0;
    }
    ll x=n-1;
    ll t=0;
    while ((x&1)==0)
    {
        x>>=1;
        t++;
    }
    srand(time(NULL));
    for (int i=0; i<S; i++)
    {
        ll a=rand()%(n-1)+1;
        if (check(a,n,x,t))
        {
            return 0;
        }
    }
    return 1;
}

ll factor[100];
int tol;

ll gcd(ll a,ll b)
{
    if (!b)
    {
        return a;
    }
    return gcd(b,a%b);
}
ll pollard_rho(ll x,ll c)
{
    ll i=1,k=2;
    srand(time(NULL));
    ll x0=rand()%(x-1)+1;
    ll y=x0;
    while (1)
    {
        i++;
        x0=(mult_mod(x0,x0,x)+c)%x;
        ll d=gcd(y-x0,x);
        if (d!=1&&d!=x)
        {
            return d;
        }
        if (y==x0)
        {
            return x;
        }
        if (i==k)
        {
            y=x0;
            k+=k;
        }
    }
}

__int128 quick(__int128 a,__int128 b,__int128 p)
{
    __int128 ret=1%p;
    while (b)
    {
        if (b&1)
        {
            ret=ret*a%p;
        }
        b>>=1;
        a=a*a%p;
    }
    return ret;
}

void findfac(ll n,ll k)
{
    if (n==1)
    {
        return;
    }
    if (Miller_Rabin(n))
    {
        factor[tol++]=n;
        return;
    }
    ll p=n;
    ll c=k;
    while (p>=n)
    {
        p=pollard_rho(p,c--);
    }
    findfac(p,k);
    findfac(n/p,k);
}

__int128 inv(__int128 a,__int128 p){
    return quick(a,p-2,p);
}
int main()
{
    ll t,p,prime;
    __int128 ans;
    scanf("%lld",&t);
    while (t--)
    {
        scanf("%lld",&p);
        for (ll i=p-1; i>=2; i--)
        {
            if (Miller_Rabin(i))
            {
                prime=i;
                break;
            }
        }
        ans=p-1;
        for (__int128 i=p-1;i>prime;i--){
            ans=ans*inv(i,p)%p;
        }
        printf("%lld\n",(ll)ans);
    }
}

原文地址：https://www.cnblogs.com/Accpted/p/11265726.html