Modifier and Type	Class and Description
private static enum	Combinations.IterationOrder Describes the type of iteration performed by the `iterator`.
private static class	Combinations.LexicographicComparator Defines the lexicographic ordering of combinations, using the `lexNorm(int[])` method.
private static class	Combinations.LexicographicIterator Lexicographic combinations iterator.
private static class	Combinations.SingletonIterator Iterator with just one element to handle degenerate cases (full array, empty array) for combination iterator.

Modifier and Type	Field and Description
private final Combinations.IterationOrder	iterationOrder Iteration order.
private final int	k Number of elements in each combination.
private final int	n Size of the set from which combinations are drawn.

Access	Constructor and Description
public	Combinations(int Size of the set from which subsets are selected. n, int Size of the subsets to be enumerated. k) Creates an instance whose range is the k-element subsets of {0, ..., n - 1} represented as `int[]` arrays.
private	Combinations(int Size of the set from which subsets are selected. n, int Size of the subsets to be enumerated. k, Combinations.IterationOrder Specifies the `iteration order`. iterationOrder) Creates an instance whose range is the k-element subsets of {0, ..., n - 1} represented as `int[]` arrays.

Modifier and Type	Method and Description
public Comparator<int[]>	Returns: a lexicographic comparator. comparator() Defines a lexicographic ordering of combinations.
public int	Returns: the size of the subsets to be enumerated. getK() Gets the number of elements in each combination.
public int	Returns: the size of the universe. getN() Gets the size of the set from which combinations are drawn.
public Iterator<int[]>	iterator() Implements java.lang.Iterable.iterator. Returns an iterator over elements of type `T`.

iterationOrder	back to summary
private final Combinations.IterationOrder iterationOrder Iteration order.

k	back to summary
private final int k Number of elements in each combination.

n	back to summary
private final int n Size of the set from which combinations are drawn.

Constructor Detail

Combinations back to summary

Combinations	back to summary
public Combinations(int n, int k) Creates an instance whose range is the k-element subsets of {0, ..., n - 1} represented as `int[]` arrays. The iteration order is lexicographic: the arrays returned by the `iterator` are sorted in descending order and they are visited in lexicographic order with significance from right to left. For example, `new Combinations(4, 2).iterator()` returns an iterator that will generate the following sequence of arrays on successive calls to `next()`: `[0, 1], [0, 2], [1, 2], [0, 3], [1, 3], [2, 3]` If `k == 0` an iterator containing an empty array is returned; if `k == n` an iterator containing [0, ..., n - 1] is returned. Parameters n:int Size of the set from which subsets are selected. k:int Size of the subsets to be enumerated. Exceptions NotPositiveException: if `n < 0`. NumberIsTooLargeException: if `k > n`.

public Combinations(int n, int k)

Creates an instance whose range is the k-element subsets of {0, ..., n - 1} represented as int[] arrays.

The iteration order is lexicographic: the arrays returned by the iterator are sorted in descending order and they are visited in lexicographic order with significance from right to left. For example, new Combinations(4, 2).iterator() returns an iterator that will generate the following sequence of arrays on successive calls to next():
[0, 1], [0, 2], [1, 2], [0, 3], [1, 3], [2, 3]

If k == 0 an iterator containing an empty array is returned; if k == n an iterator containing [0, ..., n - 1] is returned.

Parameters

n:int: Size of the set from which subsets are selected.
k:int: Size of the subsets to be enumerated.

Exceptions

NotPositiveException:: if n < 0.
NumberIsTooLargeException:: if k > n.

Combinations back to summary

Combinations	back to summary
private Combinations(int n, int k, Combinations.IterationOrder iterationOrder) Creates an instance whose range is the k-element subsets of {0, ..., n - 1} represented as `int[]` arrays. If the `iterationOrder` argument is set to `IterationOrder#LEXICOGRAPHIC`, the arrays returned by the `iterator` are sorted in descending order and they are visited in lexicographic order with significance from right to left. For example, `new Combinations(4, 2).iterator()` returns an iterator that will generate the following sequence of arrays on successive calls to `next()`: `[0, 1], [0, 2], [1, 2], [0, 3], [1, 3], [2, 3]` If `k == 0` an iterator containing an empty array is returned; if `k == n` an iterator containing [0, ..., n - 1] is returned. Parameters n:int Size of the set from which subsets are selected. k:int Size of the subsets to be enumerated. iterationOrder:Combinations.IterationOrder Specifies the `iteration order`. Exceptions NotPositiveException: if `n < 0`. NumberIsTooLargeException: if `k > n`.

private Combinations(int n, int k, Combinations.IterationOrder iterationOrder)

Creates an instance whose range is the k-element subsets of {0, ..., n - 1} represented as int[] arrays.

If the iterationOrder argument is set to IterationOrder#LEXICOGRAPHIC, the arrays returned by the iterator are sorted in descending order and they are visited in lexicographic order with significance from right to left. For example, new Combinations(4, 2).iterator() returns an iterator that will generate the following sequence of arrays on successive calls to next():
[0, 1], [0, 2], [1, 2], [0, 3], [1, 3], [2, 3]

If k == 0 an iterator containing an empty array is returned; if k == n an iterator containing [0, ..., n - 1] is returned.

Parameters

n:int: Size of the set from which subsets are selected.
k:int: Size of the subsets to be enumerated.
iterationOrder:Combinations.IterationOrder: Specifies the iteration order.

Exceptions

NotPositiveException:: if n < 0.
NumberIsTooLargeException:: if k > n.

Method Detail

comparator back to summary

comparator	back to summary
public Comparator<int[]> comparator() Defines a lexicographic ordering of combinations. The returned comparator allows to compare any two combinations that can be produced by this instance's `iterator`. Its `compare(int[],int[])` method will throw exceptions if passed combinations that are inconsistent with this instance: `DimensionMismatchException` if the array lengths are not equal to `k`, `OutOfRangeException` if an element of the array is not within the interval [0, `n`). Returns:Comparator<int[]> a lexicographic comparator.

public Comparator<int[]> comparator()

Defines a lexicographic ordering of combinations. The returned comparator allows to compare any two combinations that can be produced by this instance's iterator. Its compare(int[],int[]) method will throw exceptions if passed combinations that are inconsistent with this instance:

DimensionMismatchException if the array lengths are not equal to k,
OutOfRangeException if an element of the array is not within the interval [0, n).

Returns:Comparator<int[]>: a lexicographic comparator.

getK	back to summary
public int getK() Gets the number of elements in each combination. Returns:int the size of the subsets to be enumerated.

getK

back to summary

public int getK()

Gets the number of elements in each combination.

Returns:int: the size of the subsets to be enumerated.

getN	back to summary
public int getN() Gets the size of the set from which combinations are drawn. Returns:int the size of the universe.

getN

back to summary

public int getN()

Gets the size of the set from which combinations are drawn.

Returns:int: the size of the universe.

iterator back to summary

iterator	back to summary
public Iterator<int[]> iterator() Implements java.lang.Iterable.iterator. Doc from java.lang.Iterable.iterator. Returns an iterator over elements of type `T`. Returns:Iterator<int[]> an Iterator.

public Iterator<int[]> iterator()

Implements java.lang.Iterable.iterator.

Doc from java.lang.Iterable.iterator.

Returns an iterator over elements of type T.

Returns:Iterator<int[]>: an Iterator.

org.apache.commons.math3.util back to summary

private final Enum Combinations.IterationOrder

Class Inheritance

extends Enum<Combinations.IterationOrder>

java.lang.Object
java.lang.Enum
org.apache.commons.math3.util.Combinations.IterationOrder

Describes the type of iteration performed by the iterator.

Field Summary

Modifier and Type	Field and Description
public static final Combinations.IterationOrder	LEXICOGRAPHIC Lexicographic order.

Constructor Summary

Access	Constructor and Description
private	IterationOrder()

Method Summary

Modifier and Type	Method and Description
public static Combinations.IterationOrder	valueOf(String name)
public static Combinations.IterationOrder[]	values()

Inherited from java.lang.Enum:: clone compareTo describeConstable equals finalize getDeclaringClass hashCode name ordinal toString valueOf

Field Detail

LEXICOGRAPHIC	back to summary
public static final Combinations.IterationOrder LEXICOGRAPHIC Lexicographic order.

Constructor Detail

IterationOrder	back to summary
private IterationOrder()

Method Detail

valueOf	back to summary
public static Combinations.IterationOrder valueOf(String name)

values	back to summary
public static Combinations.IterationOrder[] values()

org.apache.commons.math3.util back to summary

private Class Combinations.LexicographicComparator

Class Inheritance

extends Object
implements Comparator<int[]>, Serializable

java.lang.Object
org.apache.commons.math3.util.Combinations.LexicographicComparator

All Implemented Interfaces

java.io.Serializable, java.util.Comparator

Defines the lexicographic ordering of combinations, using the lexNorm(int[]) method.

Field Summary

Modifier and Type	Field and Description
private final int	k Number of elements in each combination.
private final int	n Size of the set from which combinations are drawn.
private static final long	serialVersionUID Serializable version identifier.

Constructor Summary

Access	Constructor and Description
pack-priv	LexicographicComparator(int Size of the set from which subsets are selected. n, int Size of the subsets to be enumerated. k)

Method Summary

Modifier and Type	Method and Description
public int	compare(int[] the first object to be compared. c1, int[] the second object to be compared. c2) Implements java.util.Comparator.compare. Compares its two arguments for order.
private long	Returns: the lexicographic norm. lexNorm(int[] Input array. c) Computes the value (in base 10) represented by the digit (interpreted in base `n`) in the input array in reverse order.

Inherited from java.lang.Object:: clone equals finalize getClass hashCode notify notifyAll toString wait wait wait

Field Detail

k	back to summary
private final int k Number of elements in each combination.

n	back to summary
private final int n Size of the set from which combinations are drawn.

serialVersionUID	back to summary
private static final long serialVersionUID Serializable version identifier.

Constructor Detail

LexicographicComparator	back to summary
pack-priv LexicographicComparator(int n, int k) Parameters n:int Size of the set from which subsets are selected. k:int Size of the subsets to be enumerated.

Method Detail

compare back to summary

compare	back to summary
public int compare(int[] c1, int[] c2) Implements java.util.Comparator.compare. Doc from java.util.Comparator.compare. Compares its two arguments for order. Returns a negative integer, zero, or a positive integer as the first argument is less than, equal to, or greater than the second. The implementor must ensure that `signum(compare(x, y)) == -signum(compare(y, x))` for all `x` and `y`. (This implies that `compare(x, y)` must throw an exception if and only if `compare(y, x)` throws an exception.) The implementor must also ensure that the relation is transitive: `((compare(x, y)>0) && (compare(y, z)>0))` implies `compare(x, z)>0`. Finally, the implementor must ensure that `compare(x, y)==0` implies that `signum(compare(x, z))==signum(compare(y, z))` for all `z`. Parameters c1:int[] the first object to be compared. c2:int[] the second object to be compared. Returns:int a negative integer, zero, or a positive integer as the first argument is less than, equal to, or greater than the second. Exceptions DimensionMismatchException: if the array lengths are not equal to `k`. OutOfRangeException: if an element of the array is not within the interval [0, `n`).

public int compare(int[] c1, int[] c2)

Implements java.util.Comparator.compare.

Doc from java.util.Comparator.compare.

Compares its two arguments for order. Returns a negative integer, zero, or a positive integer as the first argument is less than, equal to, or greater than the second.

The implementor must ensure that signum(compare(x, y)) == -signum(compare(y, x)) for all x and y. (This implies that compare(x, y) must throw an exception if and only if compare(y, x) throws an exception.)

The implementor must also ensure that the relation is transitive: ((compare(x, y)>0) && (compare(y, z)>0)) implies compare(x, z)>0.

Finally, the implementor must ensure that compare(x, y)==0 implies that signum(compare(x, z))==signum(compare(y, z)) for all z.

Parameters

c1:int[]: the first object to be compared.
c2:int[]: the second object to be compared.

Returns:int

a negative integer, zero, or a positive integer as the first argument is less than, equal to, or greater than the second.

Exceptions

DimensionMismatchException:: if the array lengths are not equal to k.
OutOfRangeException:: if an element of the array is not within the interval [0, n).

lexNorm back to summary

lexNorm	back to summary
private long lexNorm(int[] c) Computes the value (in base 10) represented by the digit (interpreted in base `n`) in the input array in reverse order. For example if `c` is `{3, 2, 1}`, and `n` is 3, the method will return 18. Parameters c:int[] Input array. Returns:long the lexicographic norm. Exceptions OutOfRangeException: if an element of the array is not within the interval [0, `n`).

private long lexNorm(int[] c)

Computes the value (in base 10) represented by the digit (interpreted in base n) in the input array in reverse order. For example if c is {3, 2, 1}, and n is 3, the method will return 18.

Parameters

c:int[]: Input array.

Returns:long

the lexicographic norm.

Exceptions

OutOfRangeException:: if an element of the array is not within the interval [0, n).

org.apache.commons.math3.util back to summary

private Class Combinations.LexicographicIterator

Class Inheritance

extends Object
implements Iterator<int[]>

java.lang.Object
org.apache.commons.math3.util.Combinations.LexicographicIterator

All Implemented Interfaces

java.util.Iterator

Lexicographic combinations iterator.

Implementation follows Algorithm T in The Art of Computer Programming Internet Draft (PRE-FASCICLE 3A), "A Draft of Section 7.2.1.3 Generating All Combinations, D. Knuth, 2004.

The degenerate cases k == 0 and k == n are NOT handled by this implementation. If constructor arguments satisfy k == 0 or k >= n, no exception is generated, but the iterator is empty.

Field Summary

Modifier and Type	Field and Description
private final int[]	c c[1], ..., c[k] stores the next combination; c[k + 1], c[k + 2] are sentinels.
private int	j Marker: smallest index such that c[j + 1] > j
private final int	k Size of subsets returned by the iterator
private boolean	more Return value for `hasNext()`

Constructor Summary

Access	Constructor and Description
pack-priv	LexicographicIterator(int size of the set from which subsets are enumerated n, int size of the subsets to enumerate k) Construct a CombinationIterator to enumerate k-sets from n.

Method Summary

Modifier and Type	Method and Description
public boolean	hasNext() Implements java.util.Iterator.hasNext. Returns `true` if the iteration has more elements.
public int[]	next() Implements java.util.Iterator.next. Returns the next element in the iteration.
public void	remove() Overrides default java.util.Iterator.remove. Not supported.

Inherited from java.lang.Object:: clone equals finalize getClass hashCode notify notifyAll toString wait wait wait

Field Detail

c	back to summary
private final int[] c c[1], ..., c[k] stores the next combination; c[k + 1], c[k + 2] are sentinels. Note that c[0] is "wasted" but this makes it a little easier to follow the code.

back to summary

private final int[] c

c[1], ..., c[k] stores the next combination; c[k + 1], c[k + 2] are sentinels.

Note that c[0] is "wasted" but this makes it a little easier to follow the code.

j	back to summary
private int j Marker: smallest index such that c[j + 1] > j

k	back to summary
private final int k Size of subsets returned by the iterator

more	back to summary
private boolean more Return value for `hasNext()`

Constructor Detail

LexicographicIterator back to summary

LexicographicIterator	back to summary
pack-priv LexicographicIterator(int n, int k) Construct a CombinationIterator to enumerate k-sets from n. Note If `k === 0` or `k >= n`, the Iterator will be empty (that is, `hasNext()` will return `false` immediately. Parameters n:int size of the set from which subsets are enumerated k:int size of the subsets to enumerate

pack-priv LexicographicIterator(int n, int k)

Construct a CombinationIterator to enumerate k-sets from n.

Note

If k === 0 or k >= n, the Iterator will be empty (that is, hasNext() will return false immediately.

Parameters

n:int: size of the set from which subsets are enumerated
k:int: size of the subsets to enumerate

Method Detail

hasNext back to summary

hasNext	back to summary
public boolean hasNext() Implements java.util.Iterator.hasNext. Doc from java.util.Iterator.hasNext. Returns `true` if the iteration has more elements. (In other words, returns `true` if `next` would return an element rather than throwing an exception.) Returns:boolean `true` if the iteration has more elements

public boolean hasNext()

Implements java.util.Iterator.hasNext.

Doc from java.util.Iterator.hasNext.

Returns true if the iteration has more elements. (In other words, returns true if next would return an element rather than throwing an exception.)

Returns:boolean: true if the iteration has more elements

next	back to summary
public int[] next() Implements java.util.Iterator.next. Doc from java.util.Iterator.next. Returns the next element in the iteration. Returns:int[] the next element in the iteration

back to summary

public int[] next()

Implements java.util.Iterator.next.

Doc from java.util.Iterator.next.

Returns the next element in the iteration.

Returns:int[]: the next element in the iteration

remove	back to summary
public void remove() Overrides default java.util.Iterator.remove. Not supported.

remove

back to summary

public void remove()

Overrides default java.util.Iterator.remove.

Not supported.

org.apache.commons.math3.util back to summary

private Class Combinations.SingletonIterator

Class Inheritance

extends Object
implements Iterator<int[]>

java.lang.Object
org.apache.commons.math3.util.Combinations.SingletonIterator

All Implemented Interfaces

java.util.Iterator

Iterator with just one element to handle degenerate cases (full array, empty array) for combination iterator.

Field Summary

Modifier and Type	Field and Description
private boolean	more True on initialization, false after first call to next
private final int[]	singleton Singleton array

Constructor Summary

Access	Constructor and Description
pack-priv	SingletonIterator(final int[] array returned by the iterator singleton) Create a singleton iterator providing the given array.

Method Summary

Modifier and Type	Method and Description
public boolean	Returns: True until next is called the first time, then false hasNext() Implements java.util.Iterator.hasNext. Returns `true` if the iteration has more elements.
public int[]	Returns: the singleton in first activation; throws NSEE thereafter next() Implements java.util.Iterator.next. Returns the next element in the iteration.
public void	remove() Overrides default java.util.Iterator.remove. Not supported

Inherited from java.lang.Object:: clone equals finalize getClass hashCode notify notifyAll toString wait wait wait

Field Detail

more	back to summary
private boolean more True on initialization, false after first call to next

singleton	back to summary
private final int[] singleton Singleton array

Constructor Detail

SingletonIterator	back to summary
pack-priv SingletonIterator(final int[] singleton) Create a singleton iterator providing the given array. Parameters singleton:int[] array returned by the iterator

SingletonIterator

back to summary

pack-priv SingletonIterator(final int[] singleton)

Create a singleton iterator providing the given array.

Parameters

singleton:int[]: array returned by the iterator

Method Detail

hasNext back to summary

hasNext	back to summary
public boolean hasNext() Implements java.util.Iterator.hasNext. Doc from java.util.Iterator.hasNext. Returns `true` if the iteration has more elements. (In other words, returns `true` if `next` would return an element rather than throwing an exception.) Returns:boolean True until next is called the first time, then false

public boolean hasNext()

Implements java.util.Iterator.hasNext.

Doc from java.util.Iterator.hasNext.

Returns true if the iteration has more elements. (In other words, returns true if next would return an element rather than throwing an exception.)

Returns:boolean: True until next is called the first time, then false

next	back to summary
public int[] next() Implements java.util.Iterator.next. Doc from java.util.Iterator.next. Returns the next element in the iteration. Returns:int[] the singleton in first activation; throws NSEE thereafter

back to summary

public int[] next()

Implements java.util.Iterator.next.

Doc from java.util.Iterator.next.

Returns the next element in the iteration.

Returns:int[]: the singleton in first activation; throws NSEE thereafter

remove	back to summary
public void remove() Overrides default java.util.Iterator.remove. Not supported

remove

back to summary

public void remove()

Overrides default java.util.Iterator.remove.

Not supported

public Class Combinations

Nested and Inner Type Summary

Field Summary

Constructor Summary

Method Summary

Field Detail

Constructor Detail

Method Detail

private final Enum Combinations.IterationOrder

Field Summary

Constructor Summary

Method Summary

Field Detail

Constructor Detail

Method Detail

private Class Combinations.LexicographicComparator

Field Summary

Constructor Summary

Method Summary

Field Detail

Constructor Detail

Method Detail

private Class Combinations.LexicographicIterator

Field Summary

Constructor Summary

Method Summary

Field Detail

Constructor Detail

Method Detail

private Class Combinations.SingletonIterator

Field Summary

Constructor Summary

Method Summary

Field Detail

Constructor Detail

Method Detail