Combination Class

Represents an ascending sequence of distinct picks from a supplied range.

Inheritance Hierarchy

SystemObject
Kaos.CombinatoricsCombination

Namespace: Kaos.Combinatorics
Assembly: KaosCombinatorics (in KaosCombinatorics.dll) Version: 6.0.0.0

Syntax

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public class Combination : IComparable, 
	IEnumerable, IComparable<Combination>, IEquatable<Combination>, 
	IEnumerable<int>

The Combination type exposes the following members.

Constructors

	Name	Description
	Combination	Initializes an empty combination instance.
	Combination(Int32)	Initializes a new combination of Rank 0 with the supplied number of elements.
	Combination(Combination)	Initializes a new instance that is copied from the supplied combination.
	Combination(Int32, Int32)	Initializes a new combination of Rank 0 with the supplied number of picks from the supplied number of choices.
	Combination(Int32, Int32)	Initializes a new combination from elements supplied in source picked from the supplied number of choices.
	Combination(Int32, Int32, Int64)	Initializes a new combination of the supplied rank with the supplied number of picks from the supplied number of choices.

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Properties

	Name	Description
	Choices	The available number of integers to choose from.
	Item	Get a element of the Combination at the supplied column.
	Picks	Number of elements in the Combination.
	Rank	Row index in the ordered Combination table.
	RowCount	Count of distinct sequences in the Combination table.

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Methods

	Name	Description
	CompareTo(Object)	Compare two Combinations.
	CompareTo(Combination)	Compare two Combinations.
	CopyTo	Copy the entire sequence to the supplied destination.
	Equals(Object)	Indicate whether two Combinations have the same value. (Overrides ObjectEquals(Object).)
	Equals(Combination)	Indicate whether two Combinations have the same value.
	Finalize	Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object.)
	GetEnumerator	Enumerate all elements of a Combination.
	GetHashCode	Get the hash oode of the Combination. (Overrides ObjectGetHashCode.)
	GetRows	Iterate thru all rows of the Combination table for every Rank ascending.
	GetRowsForAllPicks	Iterate thru all rows of all Combination tables for every pick in the range (1..Picks).
	GetType	Gets the Type of the current instance. (Inherited from Object.)
	MemberwiseClone	Creates a shallow copy of the current Object. (Inherited from Object.)
	PermuteT	Apply a Combination sequence to rearrange the supplied list or array.
	ToString	Provide a readable form of the Combination sequence. (Overrides ObjectToString.)

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Operators

	Name	Description
	Equality	Indicate whether 2 Combinations are equal.
	GreaterThan	Indicate whether the left Combination is greater than the right Combination.
	GreaterThanOrEqual	Indicate whether the left Combination is greater than or equal to the right Combination.
	Inequality	Indicate whether 2 Combinations are not equal.
	LessThan	Indicate whether the left Combination is less than the right Combination.
	LessThanOrEqual	Indicate whether the left Combination is less than or equal to the right Combination.

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Remarks

The defining variables of a combination are n which is the number of possible choices and k which is the number of distinct picks from those choices. When k is less than n, this is a k-combination also known as a pick-combination. Combinations are contrasted to multicombinations where the values in the sequence may repeat.

The Combination class produces k-combinations with ascending elements. While sequence order of the elements is not a general requirement of combinations, producing an ascending sequence allows ranking the sequences into an ordered table.

Use the Picks property to get the number of elements (k) of a Combination taken from a possible number of Choices (n). Use the RowCount property to get the number of distinct possible Combination sequences. Use the indexer to get a specified element of the sequence. Use the default enumerator to iterate thru the elements of a Combination. Use the Permute method to pick objects from a supplied array of choices based on the current sequence.

Use the Rank property to get or set the row index in a lexicographically ordered Combination table of all possible sequences in an ascending order. Use GetRows to iterate thru all possible sequences of the Combination ordered by Rank. Use GetRowsForAllPicks to iterate thru every table of all picks in the range (1..Picks).

The default appearance of a Combination row is a list of integers (starting at 0) enclosed in braces. The appearance may be tailored 3 ways:

Map each element to a different value using the default enumerator or the indexer.
Use the Permute method and output the rearranged values.
Define a subclass of Combination and override ToString(). (See GetRowsForAllPicks for an example.)

For more information about k-combinations, see:

https://en.wikipedia.org/wiki/Combination

Examples

Iterating thru new Combination (6, 3).GetRows() produces:

{ 0, 1, 2 }
{ 0, 1, 3 }
{ 0, 1, 4 }
{ 0, 1, 5 }
{ 0, 2, 3 }
{ 0, 2, 4 }
{ 0, 2, 5 }
{ 0, 3, 4 }
{ 0, 3, 5 }
{ 0, 4, 5 }
{ 1, 2, 3 }
{ 1, 2, 4 }
{ 1, 2, 5 }
{ 1, 3, 4 }
{ 1, 3, 5 }
{ 1, 4, 5 }
{ 2, 3, 4 }
{ 2, 3, 5 }
{ 2, 4, 5 }
{ 3, 4, 5 }

Reference

Kaos.Combinatorics Namespace