/// <summary>
/// Liczy ilosc potege podzielnika, aktualizuje liczbe.
/// Jezeli ostatnim podzielnikiem jest liczba pierwsza to zwraca true, w przeciwnym wypadku false.
/// </summary>
/// <param name="n"></param>
/// <param name="factor"></param>
/// <param name="newn"></param>
/// <param name="primeFactors"></param>
/// <param name="pcheck"></param>
/// <returns></returns>
private bool GetPrimeFactorPowerAndUpdateList(long n, long factor, out long newn, Dictionary <long, long> primeFactors, PrimeNumbersCheck pcheck)
{
long cnt = GetFactorPower(n, factor, out newn);
if (cnt > 0)
{
primeFactors[factor] = cnt;
//ostatni dzielnik jest liczba pierwsza
if (pcheck.IsPrimeMRTest(newn))
{
primeFactors[newn] = 1;
newn = 1;
return(true);
}
}
return(false);
}
public void TestPrimesMillerRabinCheck()
{
_pobj.IsPrimeMRTest(2).ShouldBeTrue();
_pobj.IsPrimeMRTest(3).ShouldBeTrue();
_pobj.IsPrimeMRTest(5).ShouldBeTrue();
_pobj.IsPrimeMRTest(7).ShouldBeTrue();
_pobj.IsPrimeMRTest(4).ShouldBeFalse();
_pobj.IsPrimeMRTest(2000000000).ShouldBeFalse();
_pobj.IsPrimeMRTest(2000000011).ShouldBeTrue();
//piewsze 3 liczby Carmichaela
_pobj.IsPrimeMRTest(561).ShouldBeFalse();
_pobj.IsPrimeMRTest(1105).ShouldBeFalse();
_pobj.IsPrimeMRTest(1729).ShouldBeFalse();
_pobj.IsPrimeMRTest(2147483647).ShouldBeTrue(); //2^31 - 1
}
/// <summary>
/// Metoda faktoryzacji na czynniki pierwsze z wykorzystaniem algorytmu Rho Pollarda
/// dziala dla liczb 32bit
///
/// https://www.cs.colorado.edu/~srirams/courses/csci2824-spr14/pollardsRho.html
/// http://www.geeksforgeeks.org/pollards-rho-algorithm-prime-factorization/
/// https://en.wikipedia.org/wiki/Pollard%27s_rho_algorithm
/// https://pl.wikipedia.org/wiki/Algorytm_faktoryzacji_rho_Pollarda
///
/// opierajac sie na pierwszym znalezionym dzielniku dziala ok 2,5x szybciej niz w przypadku listy z ograniczona iloscia iteracji (1200ms do 3000ms)
/// </summary>
/// <param name="n"></param>
/// <returns>zwraca słownik w postaci (czynnik, ilość)</returns>
public Dictionary <long, long> PollardRhoPrimeFactors(long n)
{
PrimeNumbersCheck pcheck = new PrimeNumbersCheck();
Dictionary <long, long> primeFactors = new Dictionary <long, long>();
if (pcheck.IsPrimeMRTest(n))
{
return(primeFactors);
}
//okreslenie poteg 2
if (GetPrimeFactorPowerAndUpdateList(n, 2, out n, primeFactors, pcheck))
{
return(primeFactors);
}
Random gen = new Random();
List <long> toCheck = new List <long>()
{
n
};
long nv = n;
while (nv > 1)
{
long v = nv;
if (toCheck.Count > 0)
{
v = toCheck[0];
toCheck.RemoveAt(0);
}
//long c = gen.Next(2, (int)v);
//long startx = gen.Next(1, (int)v);
long c = RandomLong(2, v, gen);
long startx = RandomLong(1, v, gen);
//List<long> factors = GetPollardRhoFactorsList(v, startx, c);
List <long> factors = GetPollardRhoSingleFactor(v, startx, c); //singlefactor ok 2,5x szybciej niz z lista i ograniczeniem petli
foreach (long factor in factors)
{
if (pcheck.IsPrimeMRTest(factor))
{
if (!primeFactors.ContainsKey(factor))
{
if (GetPrimeFactorPowerAndUpdateList(nv, factor, out nv, primeFactors, pcheck))
{
break;
}
}
}
else
{
if (!toCheck.Contains(factor))
{
toCheck.Add(factor);
}
long d = n / factor;
if (!toCheck.Contains(d))
{
toCheck.Add(d);
}
}
}
}
return(primeFactors);
}