糟糕!我刚刚把这个程序放进去,然后才意识到你的问题标记了C#。这是C ++,我几年前写的Pollard Rho版本,并在此处发布以帮助其他人理解它。与试除法相比,它在分解半素数时快得多。正如我所说,我很遗憾它不是C#,但你应该能够理解概念,甚至可以轻松移植它。作为奖励,.NET库具有用于处理任意大整数的命名空间,我的C ++实现需要我查找第三方库来使用它们。无论如何,即使在C#中,以下程序也将在不到1秒钟的时间内将一个2^63阶半素数分解成2个质数。有比这更快的算法,但它们要复杂得多。
#include <string>
#include <stdio.h>
#include <iostream>
#include "BigIntegerLibrary.hh"
typedef BigInteger BI;
typedef BigUnsigned BU;
using std::string;
using std::cin;
using std::cout;
BU pollard(BU &numberToFactor);
BU gcda(BU differenceBetweenCongruentFunctions, BU numberToFactor);
BU f(BU &x, BU &numberToFactor, int &increment);
void initializeArrays();
BU getNumberToFactor ();
void factorComposites();
bool testForComposite (BU &num);
BU primeFactors[1000];
BU compositeFactors[1000];
BU tempFactors [1000];
int primeIndex;
int compositeIndex;
int tempIndex;
int numberOfCompositeFactors;
bool allJTestsShowComposite;
int main ()
{
while(1)
{
primeIndex=0;
compositeIndex=0;
tempIndex=0;
initializeArrays();
compositeFactors[0] = getNumberToFactor();
cout<<"\n\n";
if (compositeFactors[0] == 0) return 0;
numberOfCompositeFactors = 1;
factorComposites();
}
}
void initializeArrays()
{
for (int i = 0; i<1000;i++)
{
primeFactors[i] = 0;
compositeFactors[i]=0;
tempFactors[i]=0;
}
}
BU getNumberToFactor ()
{
std::string s;
std::cout<<"Enter the number for which you want a prime factor, or 0 to quit: ";
std::cin>>s;
return stringToBigUnsigned(s);
}
void factorComposites()
{
while (numberOfCompositeFactors!=0)
{
compositeIndex = 0;
tempIndex = 0;
while (compositeIndex < 1000)
{
if(compositeFactors[compositeIndex] == 0)
{
compositeIndex++;
continue;
}
if(testForComposite(compositeFactors[compositeIndex]) == false)
{
tempFactors[tempIndex] = compositeFactors[compositeIndex];
compositeFactors[compositeIndex] = 0;
tempIndex++;
compositeIndex++;
}
else
{
tempFactors[tempIndex] = pollard (compositeFactors[compositeIndex]);
compositeFactors[compositeIndex] /= tempFactors[tempIndex];
tempIndex++;
compositeIndex++;
}
}
compositeIndex = 0;
while (compositeIndex < 1000)
{
if (compositeFactors[compositeIndex] != 0)
{
tempFactors[tempIndex] = compositeFactors[compositeIndex];
compositeFactors[compositeIndex] = 0;
tempIndex++;
compositeIndex++;
}
else compositeIndex++;
}
compositeIndex = 0;
tempIndex = 0;
while (tempIndex<1000)
{
if(tempFactors[tempIndex] == 0)
{
tempIndex++;
continue;
}
if(testForComposite(tempFactors[tempIndex]) == false)
{
primeFactors[primeIndex] = tempFactors[tempIndex];
cout<<primeFactors[primeIndex]<<"\n";
tempFactors[tempIndex]=0;
primeIndex++;
tempIndex++;
}
else
{
compositeFactors[compositeIndex] = tempFactors[tempIndex];
tempFactors[tempIndex]=0;
compositeIndex++;
tempIndex++;
}
}
compositeIndex=0;
numberOfCompositeFactors=0;
while(compositeIndex<1000)
{
if(compositeFactors[compositeIndex]!=0) numberOfCompositeFactors++;
compositeIndex ++;
}
}
return;
}
bool testForComposite (BU &num)
{
BU confidenceFactor = 101;
if (confidenceFactor >= num) confidenceFactor = num-1;
BU a,d,s, nMinusOne;
nMinusOne=num-1;
d=nMinusOne;
s=0;
while(modexp(d,1,2)==0)
{
d /= 2;
s++;
}
allJTestsShowComposite = true;
for (BI i = 2 ; i<=confidenceFactor;i++)
{
if (modexp(i,d,num) == 1)
continue;
if (modexp(i,d,num) == nMinusOne)
{
allJTestsShowComposite = false;
continue;
}
BU exponent(1);
for (BU j(0); j.toInt()<=s.toInt()-1;j++)
{
exponent *= 2;
if (modexp(i,exponent*d,num) == nMinusOne)
{
allJTestsShowComposite = false;
continue;
}
}
if (allJTestsShowComposite == true) return true;
}
return false;
}
BU pollard(BU &n)
{
if (n == 4) return 2;
BU x = 2;
BU y = 2;
BU d = 1;
int increment = 1;
while(d==1||d==n||d==0)
{
x = f(x,n, increment);
y = f(y,n, increment);
y = f(y,n, increment);
if (y>x)
{
d = gcda(y-x, n);
}
else
{
d = gcda(x-y, n);
}
if (d==0)
{
x = 2;
y = 2;
d = 1;
increment++;
}
}
return d;
}
BU gcda(BU a, BU b)
{
if (a==b||a==0)
return 0;
BU currentGCD = 1;
while (currentGCD!=0)
{
currentGCD = b % a;
b=a;
a=currentGCD;
}
return b;
}
BU f(BU &x, BU &n, int &increment)
{
return (x * x + increment) % n;
}