Permutation Class

Represents a specific arrangement of distinct picks from a supplied range.

Inheritance Hierarchy

SystemObject
Kaos.CombinatoricsPermutation

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

Syntax

Copy

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

The Permutation type exposes the following members.

Constructors

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

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Properties

	Name	Description
	Choices	Number of available choices for the elements of the Permutation.
	Item	Get an element of the Permutation at the supplied column.
	MaxChoices	Returns the maximum number of elements that may be in a Permutation.
	Picks	Number of elements in the Permutation.
	PlainRank	Row index of the sequence in the plain ordered Permutation table.
	Rank	Row index of the sequence in the lexicographically ordered Permutation table.
	RowCount	Returns number of distinct possible arrangements of this Permutation.
	Swaps	Returns number of element swaps needed to transform this Permutation into Rank 0.

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Methods

	Name	Description
	Backtrack	Advance Rank a minimum while changing element at nodeIndex.
	CompareTo(Object)	Compare 2 Permutations.
	CompareTo(Permutation)	Compare 2 Permutations.
	CopyTo	Copy the entire sequence to the supplied destination.
	Equals(Object)	Indicate whether two Permutations have the same value. (Overrides ObjectEquals(Object).)
	Equals(Permutation)	Indicate whether two Permutations 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 Permutation.
	GetHashCode	Get the hash oode of the Permutation. (Overrides ObjectGetHashCode.)
	GetRows	Iterate thru all rows of the Permutation table for every Rank ascending.
	GetRowsForAllChoices	Iterate thru all rows of all Permutation tables for every Choices value in the range (1..Choices).
	GetRowsForAllPicks	Iterate thru all rows of all Permutation tables for every Picks value in the range (1..Picks).
	GetRowsOfPlainChanges	Iterate thru all rows of the Permutation table while swapping only two values in each result.
	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 Permutation sequence to rearrange the supplied list or array.
	ToString	Provide a readable form of the Permutation sequence. (Overrides ObjectToString.)

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Operators

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

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Remarks

The defining variables of a permutation 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-permutation also known as a variation. Permutations are contrasted to combinations where the arrangement is generally not significant (except for ranking).

The Permutation class uses the inherent sequencing of the elements to arrange the rows into an lexicographically ordered table. Support for k-permutations is provided by supplying a picks value that is less than the supplied choices value to the appropriate constructors.

Use the Choices property to get the number of elements to choose from. Use the Picks property to get the number of elements of a Permutation. Use the RowCount property to get the number of distinct possible sequences of a Permutation. Use the indexer to get a specified element of the sequence. Use the default enumerator to iterate thru the elements of a Permutation. Use the Permute method to rearrange a supplied array based on the current sequence.

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

Use the PlainRank property to get or set the row index in a table ordered for plain changes where adjacent rows differ by only a single swap of 2 adjacent elements. Use GetRowsOfPlainChanges to iterate thru all possible sequences of a Permutation ordered by PlainRank.

Use the Swaps property to get the number of element swaps that would transform a row into the sequence of Rank 0. Use the Backtrack method to minimally advance Rank while changing a specified element.

The default appearance of a Permutation 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 Permutation and override ToString(). (See GetRowsForAllPicks for an example.)

For more information about permutations and k-permutations, see:

https://en.wikipedia.org/wiki/Permutation
https://en.wikipedia.org/wiki/Eight_queens_puzzle

Examples

Iterating thru new Permutation (4).GetRows() produces:

{ 0, 1, 2, 3 }
{ 0, 1, 3, 2 }
{ 0, 2, 1, 3 }
{ 0, 2, 3, 1 }
{ 0, 3, 1, 2 }
{ 0, 3, 2, 1 }
{ 1, 0, 2, 3 }
{ 1, 0, 3, 2 }
{ 1, 2, 0, 3 }
{ 1, 2, 3, 0 }
{ 1, 3, 0, 2 }
{ 1, 3, 2, 0 }
{ 2, 0, 1, 3 }
{ 2, 0, 3, 1 }
{ 2, 1, 0, 3 }
{ 2, 1, 3, 0 }
{ 2, 3, 0, 1 }
{ 2, 3, 1, 0 }
{ 3, 0, 1, 2 }
{ 3, 0, 2, 1 }
{ 3, 1, 0, 2 }
{ 3, 1, 2, 0 }
{ 3, 2, 0, 1 }
{ 3, 2, 1, 0 }

Iterating thru new Permutation (4, 3).GetRows() produces:

{ 0, 1, 2 }
{ 0, 1, 3 }
{ 0, 2, 1 }
{ 0, 2, 3 }
{ 0, 3, 1 }
{ 0, 3, 2 }
{ 1, 0, 2 }
{ 1, 0, 3 }
{ 1, 2, 0 }
{ 1, 2, 3 }
{ 1, 3, 0 }
{ 1, 3, 2 }
{ 2, 0, 1 }
{ 2, 0, 3 }
{ 2, 1, 0 }
{ 2, 1, 3 }
{ 2, 3, 0 }
{ 2, 3, 1 }
{ 3, 0, 1 }
{ 3, 0, 2 }
{ 3, 1, 0 }
{ 3, 1, 2 }
{ 3, 2, 0 }
{ 3, 2, 1 }

Iterating thru new Permutation (4).GetRowsOfPlainChanges() produces:

{ 0, 1, 2, 3 }
{ 0, 1, 3, 2 }
{ 0, 3, 1, 2 }
{ 3, 0, 1, 2 }
{ 3, 0, 2, 1 }
{ 0, 3, 2, 1 }
{ 0, 2, 3, 1 }
{ 0, 2, 1, 3 }
{ 2, 0, 1, 3 }
{ 2, 0, 3, 1 }
{ 2, 3, 0, 1 }
{ 3, 2, 0, 1 }
{ 3, 2, 1, 0 }
{ 2, 3, 1, 0 }
{ 2, 1, 3, 0 }
{ 2, 1, 0, 3 }
{ 1, 2, 0, 3 }
{ 1, 2, 3, 0 }
{ 1, 3, 2, 0 }
{ 3, 1, 2, 0 }
{ 3, 1, 0, 2 }
{ 1, 3, 0, 2 }
{ 1, 0, 3, 2 }
{ 1, 0, 2, 3 }

Reference

Kaos.Combinatorics Namespace