/// <summary>
/// Make a new <see cref="Combination"/> from the supplied
/// <em>choices</em> and <em>picks</em> of <see cref="Rank"/> 0.
/// </summary>
/// <param name="choices">Number of values to pick from.</param>
/// <param name="picks">Number of elements in the sequence.</param>
/// <example>
/// <code source="Examples\Combination\CnExample01\CnExample01.cs" lang="cs" />
/// </example>
/// <exception cref="ArgumentOutOfRangeException">
/// When negative value supplied; when <em>picks</em> greater than <em>choices</em>.
/// </exception>
/// <exception cref="OverflowException">When the numbers are just too big.</exception>
public Combination(int choices, int picks)
{
if (choices < 0)
{
throw new ArgumentOutOfRangeException("choices", "Value is less than zero.");
}
if (picks < 0)
{
throw new ArgumentOutOfRangeException("picks", "Value is less than zero.");
}
if (picks > choices)
{
throw new ArgumentOutOfRangeException("picks", "Value is greater than choices.");
}
_data = new int[picks];
for (var ki = 0; ki < picks; ++ki)
{
_data[ki] = ki;
}
_choices = choices;
_rowCount = picks == 0 ? 0 : Combinatoric.BinomialCoefficient(choices, picks);
_rank = 0;
}
/// <summary>
/// Iterate thru all rows of all <see cref="Combination"/> tables for every
/// pick in the range (1..<see cref="Picks"/>).
/// </summary>
/// <returns>An iterator for a series of <see cref="Combination"/> tables.</returns>
/// <example>
/// <code source="Examples\Combination\CnExample02\CnExample02.cs" lang="cs" />
/// </example>
public IEnumerable <Combination> GetRowsForAllPicks()
{
for (var k = 1; k <= Picks; ++k)
{
var current = (Combination)MemberwiseClone();
current._data = new int[k];
for (var ei = 0; ei < current._data.Length; ++ei)
{
current._data[ei] = ei;
}
current._rowCount = Combinatoric.BinomialCoefficient(_choices, k);
current._rank = 0;
for (;;)
{
yield return(current);
current.Rank = current.Rank + 1;
if (current.Rank == 0)
{
break;
}
}
}
}
// On entry: elements & choices assumed valid, picks = elements.Length.
private static long CalcRank(int[] elements, int choices)
{
long result = 0;
var isUsed = new bool[choices];
//
// Perform ranking:
//
for (var ei1 = 0; ei1 < elements.Length; ++ei1)
{
isUsed[elements[ei1]] = true;
var digit = 0;
for (var ei2 = 0; ei2 < elements[ei1]; ++ei2)
{
if (!isUsed[ei2])
{
++digit;
}
}
result += digit * Combinatoric.Factorial(choices - ei1 - 1);
}
if (elements.Length < choices)
{
result = result / Combinatoric.Factorial(choices - elements.Length);
}
return(result);
}
/// <summary>
/// Make a new <see cref="Combination"/> from the supplied elements.
/// </summary>
/// <param name="choices">Number of values to pick from.</param>
/// <param name="source">Array of integers.</param>
/// <example>
/// <code source="Examples\Combination\CnExample04\CnExample04.cs" lang="cs" />
/// </example>
/// <exception cref="ArgumentNullException">When <em>source</em> is <b>null</b>.</exception>
/// <exception cref="ArgumentOutOfRangeException">
/// When length of <em>source</em> is greater than <em>picks</em>;
/// when <em>source</em> contains invalid data.
/// </exception>
public Combination(int choices, int[] source)
{
if (source == null)
{
throw new ArgumentNullException("source");
}
if (choices < 0)
{
throw new ArgumentOutOfRangeException("choices", "Value is less than zero.");
}
if (choices < source.Length)
{
throw new ArgumentOutOfRangeException("choices", "Value is less than picks.");
}
_data = new int[source.Length];
source.CopyTo(_data, 0);
Array.Sort(_data);
_choices = choices;
_rowCount = Picks == 0 ? 0 : Combinatoric.BinomialCoefficient(choices, Picks);
for (var ki = 0; ki < Picks; ++ki)
{
if (_data[ki] < 0 || _data[ki] >= choices)
{
throw new ArgumentOutOfRangeException("source", "Element is out of range.");
}
if (ki > 0)
{
if (_data[ki] == _data[ki - 1])
{
throw new ArgumentOutOfRangeException("source", "Elements must be unique.");
}
}
}
//
// Perform ranking:
//
_rank = 0;
var ji = 0;
for (var ki = 0; ki < Picks; ++ki)
{
for (; ji < _data[ki]; ++ji)
{
_rank += Combinatoric.BinomialCoefficient(Choices - ji - 1, Picks - ki - 1);
}
ji = _data[ki] + 1;
}
}
/// <summary>
/// Make a new <see cref="Multicombination"/> from the supplied
/// <em>choices</em> of the same <em>Picks</em>.
/// </summary>
/// <param name="choices">Number of elements in the sequence.</param>
/// <exception cref="ArgumentOutOfRangeException">
/// When <em>choices</em> less than 0.
/// </exception>
public Multicombination(int choices)
{
if (choices < 0)
{
throw new ArgumentOutOfRangeException("choices", "Value is less than zero.");
}
_data = new int[choices];
_choices = choices;
_rowCount = choices == 0 ? 0 : Combinatoric.BinomialCoefficient(Picks + choices - 1, Picks);
_rank = 0;
}
// On entry: elements allocated for choices.
// On exit: result will be in elements.
private static void CalcPlainUnrank(int[] elements, long plainRank)
{
elements[0] = 0;
for (var ei = 1; ei < elements.Length; ++ei)
{
var yd = (int)(Combinatoric.Factorial(elements.Length) / Combinatoric.Factorial(ei + 1));
var yi = (int)((plainRank / yd) % ((ei + 1) * 2));
var ip = yi <= ei ? ei - yi : yi - ei - 1;
for (var si = ei; si > ip; --si)
{
elements[si] = elements[si - 1];
}
elements[ip] = ei;
}
}
// On entry: choices, picks assumed valid.
private static long CalcCount(int choices, int picks)
{
if (picks == 0)
{
return(0);
}
var result = Combinatoric.Factorial(choices);
if (picks < choices)
{
result = result / Combinatoric.Factorial(choices - picks);
}
return(result);
}
/// <summary>
/// Make a new <see cref="Combination"/> from the supplied
/// <em>choices</em> and <em>picks</em> of the supplied <em>rank</em>.
/// </summary>
/// <remarks>
/// If the supplied <em>rank</em> is out of the range (0..<see cref="RowCount"/>-1),
/// it will be normalized to the valid range. For example, a value of -1 will
/// produce the last row in the ordered table.
/// </remarks>
/// <param name="choices">Number of values to pick from.</param>
/// <param name="picks">Number of elements in the sequence.</param>
/// <param name="rank">Initial row index in the ordered <see cref="Combination"/> table.</param>
/// <example>
/// <code source="Examples\Combination\CnExample05\CnExample05.cs" lang="cs" />
/// </example>
/// <exception cref="ArgumentOutOfRangeException">
/// When negative value supplied; when <em>picks</em> greater than <em>choices</em>.
/// </exception>
/// <exception cref="OverflowException">When too many <em>choices</em>.</exception>
public Combination(int choices, int picks, long rank)
{
if (choices < 0)
{
throw new ArgumentOutOfRangeException("choices", "Value is less than zero.");
}
if (picks < 0)
{
throw new ArgumentOutOfRangeException("picks", "Value is less than zero.");
}
if (picks > choices)
{
throw new ArgumentOutOfRangeException("picks", "Value is greater than choices.");
}
_data = new int[picks];
_choices = choices;
_rowCount = picks == 0 ? 0 : Combinatoric.BinomialCoefficient(choices, picks);
Rank = rank;
}
/// <summary>
/// Make a new <see cref="Multicombination"/> from the supplied
/// <em>choices</em> and <em>picks</em> of the supplied <em>rank</em>.
/// </summary>
/// <remarks>
/// If the supplied <em>rank</em> is out of the range (0..<see cref="RowCount"/>-1),
/// it will be normalized to the valid range. For example, a value of -1 will
/// produce the last row in the ordered table.
/// </remarks>
/// <param name="choices">Number of values to pick from.</param>
/// <param name="picks">Number of elements in the sequence.</param>
/// <param name="rank">Initial row index in the ordered <see cref="Multicombination"/> table.</param>
/// <example>
/// <code source="Examples\Multicombination\McExample05\McExample05.cs" lang="cs" />
/// </example>
/// <exception cref="ArgumentOutOfRangeException">
/// When negative value supplied; when <em>choices</em> is 0 and <em>picks</em> is not 0.
/// </exception>
/// <exception cref="OverflowException">When too many <em>choices</em>.</exception>
public Multicombination(int choices, int picks, long rank)
{
if (choices < 0)
{
throw new ArgumentOutOfRangeException("choices", "Value is less than zero.");
}
if (picks < 0)
{
throw new ArgumentOutOfRangeException("picks", "Value is less than zero.");
}
if (choices == 0 && picks > 0)
{
throw new ArgumentOutOfRangeException("choices", "Value is zero and picks is nonzero.");
}
_data = new int[picks];
_choices = choices;
_rowCount = picks == 0 ? 0 : Combinatoric.BinomialCoefficient(picks + choices - 1, picks);
Rank = rank;
}
/// <summary>
/// Iterate thru all rows of all <see cref="Multicombination"/> tables for every
/// pick in the range (<em>startPicks</em>..<em>stopPicks</em>).
/// </summary>
/// <returns>An iterator for a series of <see cref="Multicombination"/> tables.</returns>
/// <remarks>
/// Unlike <see cref="Picks"/>, <see cref="Choices"/> may exceed <see cref="Choices"/>.
/// </remarks>
/// <param name="startPicks">Number of picks for first table.</param>
/// <param name="stopPicks">Number of picks for last table.</param>
/// <example>
/// <code source="Examples\Multicombination\McExample02\McExample02.cs" lang="cs" />
/// </example>
/// <exception cref="Combination">
/// When <em>startPicks</em> is less than 0 or greater than <em>stopPicks</em>.
/// </exception>
public IEnumerable <Multicombination> GetRowsForPicks(int startPicks, int stopPicks)
{
if (startPicks < 0 || startPicks > stopPicks)
{
throw new ArgumentOutOfRangeException("startPicks", "Pick range is not valid.");
}
if (Choices == 0)
{
yield break;
}
if (startPicks == 0)
{
startPicks = 1;
}
for (var k = startPicks; k <= stopPicks; ++k)
{
var current = (Multicombination)MemberwiseClone();
current._data = new int[k];
current._rowCount = Combinatoric.BinomialCoefficient(k + _choices - 1, k);
current._rank = 0;
for (;;)
{
yield return(current);
current.Rank = current.Rank + 1;
if (current.Rank == 0)
{
break;
}
}
}
}
/// <summary>
/// Make a new <see cref="Multicombination"/> from the supplied elements.
/// </summary>
/// <param name="choices">Number of values to pick from.</param>
/// <param name="source">Array of integers.</param>
/// <example>
/// <code source="Examples\Multicombination\McExample04\McExample04.cs" lang="cs" />
/// </example>
/// <exception cref="ArgumentNullException">When <em>source</em> is <b>null</b>.</exception>
/// <exception cref="ArgumentOutOfRangeException">
/// When <em>source</em> contains invalid data;
/// when <em>choices</em> is 0 and <em>source</em> is not empty.
/// </exception>
public Multicombination(int choices, int[] source)
{
if (source == null)
{
throw new ArgumentNullException("source");
}
if (choices < 0)
{
throw new ArgumentOutOfRangeException("choices", "Value is less than zero.");
}
if (choices == 0 && source.Length > 0)
{
throw new ArgumentOutOfRangeException("choices", "Value is zero and picks is nonzero.");
}
_data = new int[source.Length];
source.CopyTo(_data, 0);
Array.Sort(_data);
_choices = choices;
_rowCount = Picks == 0 ? 0 : Combinatoric.BinomialCoefficient(Picks + choices - 1, Picks);
for (var ki = 0; ki < Picks; ++ki)
{
if (_data[ki] < 0 || _data[ki] >= choices)
{
throw new ArgumentOutOfRangeException("source", "Element is out of range.");
}
}
//
// Perform ranking:
//
_rank = 0;
if (RowCount == 0)
{
return;
}
var comboElement = _data[0];
var ji = 0;
for (var ki = 0;;)
{
for (; ji < comboElement; ++ji)
{
_rank += Combinatoric.BinomialCoefficient(Choices + Picks - ji - 2, Picks - ki - 1);
}
++ki;
if (ki >= Picks)
{
break;
}
ji = comboElement + 1;
comboElement = _data[ki] - _data[ki - 1] + ji;
}
}
