Monte Carlo_素数

蒙特卡罗算法--判断素数

 

// 素数.cpp : 定义控制台应用程序的入口点。
//

// MonteCarlo.cpp : 定义控制台应用程序的入口点。
#include "stdafx.h"
#include "targetver.h"
#include <stdio.h>
#include <tchar.h>
#include "stdafx.h"
#include"iostream"
#include<math.h>
#include<time.h>
#include<iomanip>
using namespace std;
const unsigned long maxshort=65535L;
const unsigned long multiplier=1194211693L;
const unsigned long adder=12345L;
class RandomNumber{
private:
 //当前种子
 unsigned long randSeed;
public:
 //构造函数
 RandomNumber(unsigned long s=0);
 unsigned short Random(unsigned long n);
 double fRandom();
};

RandomNumber::RandomNumber(unsigned long s)
{
 if(s==0)
  randSeed=time(0);
 else
  randSeed=s;
}

double RandomNumber::fRandom()
{
 return Random(maxshort)/double(maxshort);
}

unsigned short RandomNumber::Random(unsigned long n)
{
 randSeed=multiplier*randSeed+adder;
 return (unsigned short)((randSeed>>16)%n);
}

 

void power(unsigned int a,unsigned int p,unsigned int n,unsigned int &result,bool &composite)
{
 unsigned int x;
 if(p==0) result=1;
 else
 {
  power(a,p/2,n,x,composite);//递归计算
  result=(x*x)%n;
  if((result==1)&&(x!=1)&&(x!=n-1))
   composite=true;
  if((p%2)==1)              //p是奇数
   result=(result*a)%n;
 }
}

bool Prime(unsigned int n)
{
 //素数测试的蒙特卡罗算法
 RandomNumber rnd;
 unsigned int a,result;
 bool composite=false;
 a=rnd.Random(n-3)+2;
 power(a,n-1,n,result,composite);
 if(composite||(result!=1))
  return false;
 else
  return true;
}

bool  PrimeMC(unsigned int n,unsigned int k)
{
 //重复调用k次Prime算法的蒙特卡罗算法
 RandomNumber rnd;
 unsigned int a,result;
 bool composite=false;
 for(int i=1;i<=k;i++)
 {
  a=rnd.Random(n-3)+2;
  power(a,n-1,n,result,composite);
  if(composite||(result!=1))
   return false;
 }
 return true;
}

int _tmain(int argc, _TCHAR* argv[])
{
 cout<<PrimeMC(1105,4);
 int x;
 cin>>x;
}