HDU 3864 D_num （pollard_rho大数素数分解）

D_num

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 2046    Accepted Submission(s): 573

Problem Description

Oregon Maple was waiting for Bob When Bob go back home. Oregon Maple asks Bob a problem that as a Positive number N, if there are only four Positive number M makes Gcd(N, M) == M then we called N is a D_num. now, Oregon Maple has some Positive numbers, and if a Positive number N is a D_num , he want to know the four numbers M. But Bob have something to do, so can you help Oregon Maple?
Gcd is Greatest common divisor.

 

 

Input

Some cases (case < 100);
Each line have a numeral N（1<=N<10^18）

 

 

Output

For each N, if N is a D_NUM, then output the four M (if M > 1) which makes Gcd(N, M) = M. output must be Small to large, else output “is not a D_num”.

 

 

Sample Input

6 10 9

 

 

Sample Output

2 3 6 2 5 10 is not a D_num

 

 

Source

2011 Multi-University Training Contest 3 - Host by BIT

 

 

Recommend

lcy

 

 

就是判断一个long long的数的约数是不是有4个。

用pollard_rho，练习了下模板；

//============================================================================

// Name        : HDU3864.cpp

// Author      : 

// Version     :

// Copyright   : Your copyright notice

// Description : Hello World in C++, Ansi-style

//============================================================================



#include <iostream>

#include <stdio.h>

#include <stdlib.h>

#include <algorithm>

#include <string.h>

#include <time.h>

using namespace std;

const int S=2;

long long mult_mod(long long a,long long b,long long c)

{

    a%=c;

    b%=c;

    long long ret=0;

    while(b)

    {

        if(b&1){ret+=a;ret%=c;}

        a<<=1;

        if(a>=c)a%=c;

        b>>=1;

    }

    return ret;

}

long long pow_mod(long long x,long long n,long long mod)

{

    if(n==1)return x%mod;

    x%=mod;

    long long tmp=x;

    long long ret=1;

    while(n)

    {

        if(n&1)ret=mult_mod(ret,tmp,mod);

        tmp=mult_mod(tmp,tmp,mod);

        n>>=1;

    }

    return ret;

}

long long check(long long a,long long n,long long x,long long t)

{

    long long ret=pow_mod(a,x,n);

    long long last=ret;

    for(int i=1;i<=t;i++)

    {

        ret=mult_mod(ret,ret,n);

        if(ret==1 && last!=1 &&last!=n-1)return true;

        last=ret;

    }

    if(ret!=1)return true;

    return false;

}

bool Miller_Rabin(long long n)

{

    if(n<2)return false;

    if(n==2)return true;

    if((n&1)==0)return false;

    long long x=n-1;

    long long t=0;

    while((x&1)==0){x>>=1;t++;}

    for(int i=0;i<S;i++)

    {

        long long a=rand()%(n-1)+1;

        if(check(a,n,x,t))

            return false;

    }

    return true;

}



long long factor[100];

int tol;

long long gcd(long long a,long long b)

{

    if(a==0)return 1;

    if(a<0)return gcd(-a,b);

    while(b)

    {

        long long t=a%b;

        a=b;

        b=t;

    }

    return a;

}



long long Pollard_rho(long long x,long long c)

{

    long long i=1,k=2;

    long long x0=rand()%x;

    long long y=x0;

    while(1)

    {

        i++;

        x0=(mult_mod(x0,x0,x)+c)%x;

        long long d=gcd(y-x0,x);

        if(d!=1&&d!=x)return d;

        if(y==x0)return x;

        if(i==k)

        {

            y=x0;

            k+=k;

        }

    }

}



void findfac(long long n)

{

    if(Miller_Rabin(n))

    {

        factor[tol++]=n;

        return;

    }

    long long p=n;

    while(p>=n)p=Pollard_rho(p,rand()%(n-1)+1);

    findfac(p);

    findfac(n/p);

}



int main()

{

    srand(time(NULL));

    long long n;

    while(scanf("%I64d",&n)==1)

    {

        if(n==1)

        {

            printf("is not a D_num\n");

            continue;

        }

        tol=0;

        findfac(n);

        if(tol!=2 && tol!=3)

        {

            printf("is not a D_num\n");

            continue;

        }

        sort(factor,factor+tol);

        if(tol==2)

        {

            if(factor[0]!=factor[1])

            {

                printf("%I64d %I64d %I64d\n",factor[0],factor[1],factor[0]*factor[1]);

                continue;

            }

            else

            {

                printf("is not a D_num\n");

                continue;

            }

        }

        if(tol==3)

        {

            if(factor[0]==factor[1]&&factor[1]==factor[2])

            {

                printf("%I64d %I64d %I64d\n",factor[0],factor[0]*factor[1],factor[0]*factor[1]*factor[2]);

                continue;

            }

            else

            {

                printf("is not a D_num\n");

                continue;

            }

        }

    }

    return 0;

}