HDOJ/HDU 3864 多校联合 D_num 数论

题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=3864

题目：

D_num

Time Limit: 2000/1000 MS (Java/Others)Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 921Accepted Submission(s): 249

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

题目意思很简单了主要难的地方在于数据量太大，所以必须用随机算法

但是要注意一种特殊情况，及某质数的三次方。

我的代码：

#include<stdio.h>
#include<algorithm>
#include<iostream>
#include<time.h>
#include<math.h>
#include<stdlib.h>
#include<string.h>
#define MAX_VAL __int64(1)<<60
#define TIMES 40
#define MAX_L 64n 
#define CVAL 200
typedef __int64 LL;

using namespace std;

LL minfactor;

LL multandmod(LL a,LL b,LL n)
{
    a=a%n;
    LL res=0;
    while(b)
    {
        if(b&1)
        {
            res=res+a;
            if(res>=n)
                res=res-n;
        }    
        a=a<<1;
        if(a>=n)
            a=a-n;
        b=b>>1;
    }
    return res;
}

LL modandexp(LL a,LL b,LL n)
{
    a=a%n;
    LL res=1;
    while(b>=1)
    {
        if(b&1)
            res=multandmod(res,a,n);
        a=multandmod(a,a,n);
        b=b>>1;
    }
    return res;
}

bool millerRobin(LL a,LL n)
{
    LL u=0,cur=n-1;
    int t=0;
    bool find1=false;
    while(cur!=0)
    {
        if(!find1)
        {
            int pb=cur%2;
            if(pb==0)
                t++;
            else
                find1=true;
        }
        if(find1)
            break;
        cur=cur/2;
    }
    u=cur;
    cur=modandexp(a,u,n);
    LL now;
    for(int p=1;p<=t;p++)
    {
        now=modandexp(cur,2,n);
        if(cur!=1&&now==1&&cur!=n-1)
        {
            return false;
        }
        cur=now;
    }
    if(cur!=1)
        return false;
    return true;
}

bool testprime(int times,LL n)
{
    if(n==2)
        return true;
    if(n%2==0)
        return false;
    LL a;int t;
    srand(time(NULL));
    for(t=1;t<=times;t++)
    {
        a=rand()%(n-1)+1;
        if(!millerRobin(a,n))
            return false;
    }
    return true;
}

LL gcd(LL a,LL b)
{
    if(b==0)
        return a;
    else
        return gcd(b,a%b);
}

LL pollardrho(LL n,int c)
{
    int i=1;
    srand(time(NULL));
    LL x=rand()%n;
    LL y=x;
    int k=2;
    while(true)
    {
        i=i+1;
        x=(modandexp(x,2,n)+c)%n;
        LL d=gcd(y-x,n);
        if(1<d&&d<n)
            return d;
        if(y==x)
            return n;
        if(i==k)
        {
            y=x;
            k=k*2;
        }
    }
}

void getsmallst(LL n,int c)
{
    if(n==1)
        return;
    if(testprime(TIMES,n))
    {
        if(n<minfactor)
            minfactor=n;
        return;
    }
    LL val=n;
    while(val==n)
        val=pollardrho(n,c--);
    getsmallst(val,c);
    getsmallst(n/val,c);
}

int main()
{
    LL n;
    while(scanf("%I64d",&n)!=EOF)                                                                       
    {
        minfactor=MAX_VAL;
        if(n==1)
        {
            printf("is not a D_num\n");
            continue;
        }
        if(testprime(TIMES,n))
            printf("is not a D_num\n");
        else
        {
            getsmallst(n,CVAL);
            if(minfactor*minfactor*minfactor==n)
            {
                printf("%I64d %I64d %I64d\n",minfactor,minfactor*minfactor,n);
                continue;
            }
            if(minfactor*minfactor==n)
            {
                printf("is not a D_num\n");
                continue;
            }
            if(testprime(TIMES,n/minfactor))
                printf("%I64d %I64d %I64d\n",minfactor,n/minfactor,n);
            else
                printf("is not a D_num\n");
        }
    }
    return 0;
}