org.cicirello.permutations.distance

Class LeeDistance

java.lang.Object

org.cicirello.permutations.distance.LeeDistance

All Implemented Interfaces:

NormalizedPermutationDistanceMeasurer, NormalizedPermutationDistanceMeasurerDouble, PermutationDistanceMeasurer, PermutationDistanceMeasurerDouble

public final class LeeDistance
extends Object

Lee Distance:

Lee Distance is closely related to deviation distance. However, Lee Distance considers the permutation to be a cyclic structure when computing positional deviations. That is, an element's deviation between permutations is the minimum of its deviation to the right or to the left (wrapping around ends cyclicly).

Consider p1 = [0, 1, 2, 3, 4, 5] and p2 = [5, 1, 0, 2, 3, 4]. Element 0 is 2 positions displaced (as in deviation distance). Elements 2, 3, and 4 are a 1 position displaced (as in deviation distance). Element 1 is stationary. Element 5 is 1 position displaced (for Lee Distance) whereas for Deviation Distance it would be 5 positions displaced. For Lee distance, the displacement is the minimum of how far it is displaced in either of the two directions. In this case element 5 is at the right most end in p1 and left most end of p2, which as a cyclic structure are adjacent positions.

Runtime: O(n), where n is the permutation length.

Described in:
C. Lee, "Some properties of nonbinary error-correcting codes," in IRE Transactions on Information Theory, vol. 4, no. 2, pp. 77-82, June 1958.

Since:

1.0

Constructor Summary

Constructors

Constructor and Description
LeeDistance() Constructs the distance measurer as specified in the class documentation.

Method Summary

Modifier and Type	Method and Description
int	distance(Permutation p1, Permutation p2) Measures the distance between two permutations.
double	distancef(Permutation p1, Permutation p2) Measures the distance between two permutations
int	max(int length) Computes the maximum possible distance between permutations of a specified length.
double	maxf(int length) Computes the maximum possible distance between permutations of a specified length.
double	normalizedDistance(Permutation p1, Permutation p2) Measures the distance between two permutations, normalized to the interval [0.0, 1.0].

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

LeeDistance

public LeeDistance()

Constructs the distance measurer as specified in the class documentation.

Method Detail

distance

public int distance(Permutation p1,
                    Permutation p2)

Measures the distance between two permutations.

Parameters:

p1 - first permutation

p2 - second permutation

Returns:

distance between p1 and p2

max

public int max(int length)

Computes the maximum possible distance between permutations of a specified length.

Parameters:

length - Permutation length.

Returns:

the maximum distance between a pair of permutations of the specified length.

distancef

public final double distancef(Permutation p1,
                              Permutation p2)

Measures the distance between two permutations

Specified by:

distancef in interface PermutationDistanceMeasurerDouble

Parameters:

p1 - first permutation

p2 - second permutation

Returns:

distance between p1 and p2

maxf

public final double maxf(int length)

Computes the maximum possible distance between permutations of a specified length.

Specified by:

maxf in interface NormalizedPermutationDistanceMeasurerDouble

Parameters:

length - Permutation length.

Returns:

the maximum distance between a pair of permutations of the specified length.

normalizedDistance

public final double normalizedDistance(Permutation p1,
                                       Permutation p2)

Measures the distance between two permutations, normalized to the interval [0.0, 1.0].

Specified by:

normalizedDistance in interface NormalizedPermutationDistanceMeasurerDouble

Parameters:

p1 - first permutation

p2 - second permutation

Returns:

distance between p1 and p2 normalized to the interval [0.0, 1.0]