HDU 3864 D_num Miller Rabin 質數判斷+Pollard Rho大整數分解

標籤：數學

連結：http://acm.hdu.edu.cn/showproblem.php?pid=3864

題意：給出一個數N（1<=N<10^18），如果N只有四個約數，就輸出除1外的三個約數。

思路：大數的質因數分解只能用隨機演算法Miller Rabin和Pollard_rho，在測試多的情況下正確率是由保證的。

代碼：

#include <iostream>#include <cstdio>#include <cstring>#include <cmath>#include <map>#include <cstdlib>#include <queue>#include <stack>#include <vector>#include <ctype.h>#include <algorithm>#include <string>#include <set>#include <ctime>#define PI acos(-1.0)#define INF 0x7fffffff#define eps 1e-8#define maxn 50005typedef __int64 LL;typedef unsigned long long ULL;using namespace std;LL Factor[100];int t=0;LL mul_mod(LL a,LL b,LL n){    a=a%n;    b=b%n;    LL s=0;    while(b)    {        if(b&1)            s=(s+a)%n;        a=(a<<1)%n;        b=b>>1;    }    return s;}LL pow_mod(LL a,LL b,LL n)//求a^b%n{    a=a%n;    LL s=1;    while(b)    {        if(b&1)            s=mul_mod(s,a,n);        a=mul_mod(a,a,n);        b=b>>1;    }    return s;}bool isPrime(LL n, LL times){    if(n==2)return 1;    if(n<2||!(n&1))return 0;    LL a, u=n-1, x, y;    int t=0;    while(u%2==0)    {        t++;        u/=2;    }    srand(100);    for(int i=0; i<times; i++)    {        a = rand() % (n-1) + 1;        x = pow_mod(a, u, n);        for(int j=0; j<t; j++)        {            y = mul_mod(x, x, n);            if ( y == 1 && x != 1 && x != n-1 )                return false; //must not            x = y;        }        if( y!=1) return false;    }    return true;}LL gcd(LL a,LL b){    if(a==0) return 1;    if(a<0) return gcd(-a,b);    return b==0?a:gcd(b,a%b);}LL Pollard_rho(LL n,LL c)//Pollard_rho演算法，找出n的因子{    LL i=1,j,k=2,x,y,d,p;    x=rand()%n;    y=x;    while(true)    {        i++;        x=(mul_mod(x,x,n)+c)%n;        if(y==x)return n;        if(y>x)p=y-x;        else p=x-y;        d=gcd(p,n);        if(d!=1&&d!=n)return d;        if(i==k)        {            y=x;            k+=k;        }    }}void factor(LL n){    if(isPrime(n,20))    {        Factor[t++]=n;        return;    }    LL p=n;    while(p>=n)p=Pollard_rho(p,rand()%(n-1)+1);    factor(p);    factor(n/p);}void solve(LL a){    if(a==1)    {        printf("is not a D_num\n");        return;    }    t=0;    factor(a);    sort(Factor,Factor+t);    if(t==2)    {        if(Factor[0]!=Factor[1])        {            printf("%I64d %I64d %I64d\n",Factor[0],Factor[1],a);        }        else            printf("is not a D_num\n");    }    else if(t==3)    {        if(Factor[0]==Factor[1]&&Factor[1]==Factor[2])            printf("%I64d %I64d %I64d\n",Factor[0],Factor[0]*Factor[1],a);        else printf("is not a D_num\n");    }    else printf("is not a D_num\n");}int main(){    LL a;    while(~scanf("%I64d",&a))    {        solve(a);    }    return 0;}