/// <summary>
/// Returns a copy of this prime factorization object.
/// </summary>
public PrimeFactorization Copy()
{
var result = new PrimeFactorization();
foreach (var entry in entriesList)
{
result.AddEntry(entry.Prime, entry.Power);
}
return(result);
}
/// <summary>
/// Calculates all positive divisors of the integer provided.
/// <example>For example, 18 returns IEnumerable<1, 2, 3, 6, 9, 18>.</example>
/// </summary>
/// <param name="n">The integer to calculate divisors for.</param>
/// <param name="proper">If true, the integer n will be excluded.</param>
/// <returns>All positive divisors of the integer n.</returns>
public static IEnumerable <long> Divisors(long n, bool proper = false)
{
var factorization = PrimeFactorization(n);
var divisorFactorization = new PrimeFactorization();
foreach (var item in factorization.Entries)
{
divisorFactorization.AddEntry(item.Prime, 0);
}
var product = 1L;
while (true)
{
if (!proper || product != n)
{
yield return(product);
}
var incremented = false;
foreach (var item in divisorFactorization.Entries)
{
if (item.Power < factorization.Entry(item.Prime).Power)
{
product *= item.Prime;
++item.Power;
incremented = true;
break;
}
else
{
for (var i = 0; i < item.Power; ++i)
{
product /= item.Prime;
}
item.Power = 0;
}
}
if (!incremented)
{
break;
}
}
}
/// <summary>
/// Returns true if this factorization is equivalent to the other factorization provided, false otherwise.
/// </summary>
public bool Equals(PrimeFactorization other)
{
if (other != null)
{
foreach (var entry1 in entriesList)
{
if (!entry1.Equals(other.Entry(entry1.Prime)))
{
return(false);
}
}
foreach (var entry2 in other.entriesList)
{
if (!entry2.Equals(Entry(entry2.Prime)))
{
return(false);
}
}
return(true);
}
return(false);
}
/// <summary>
/// Constructs a prime factorization of the integer provided.
/// <example>For example, 60 = 2^2 * 3 * 5.</example>
/// </summary>
/// <param name="n">The integer for which a prime factorization will be constructed.</param>
public static PrimeFactorization PrimeFactorization(long n)
{
var result = new PrimeFactorization();
var power = 0;
while (n % 2L == 0)
{
n /= 2L;
++power;
}
if (power > 0)
{
result.AddEntry(2L, power);
}
for (var i = 3L; i <= System.Math.Sqrt(n); i += 2L)
{
power = 0;
while (n % i == 0)
{
n /= i;
++power;
}
if (power > 0)
{
result.AddEntry(i, power);
}
}
if (n > 2)
{
result.AddEntry(n, 1);
}
return(result);
}