Apache Commons Math 3.6.1 · org.apache.commons.math3.util.CombinatoricsUtils

Modifier and Type	Field and Description
pack-priv static final long[]	FACTORIALS All long-representable factorials
pack-priv static final AtomicReference<long[][]>	STIRLING_S2 Stirling numbers of the second kind.

Access	Constructor and Description
private	CombinatoricsUtils() Private constructor (class contains only static methods).

Method Summary

Modifier and Type	Method and Description
public static long	Returns: `n choose k` binomialCoefficient(final int the size of the set n, final int the size of the subsets to be counted k) Returns an exact representation of the Binomial Coefficient, "`n choose k`", the number of `k`-element subsets that can be selected from an `n`-element set.
public static double	Returns: `n choose k` binomialCoefficientDouble(final int the size of the set n, final int the size of the subsets to be counted k) Returns a `double` representation of the Binomial Coefficient, "`n choose k`", the number of `k`-element subsets that can be selected from an `n`-element set.
public static double	Returns: `n choose k` binomialCoefficientLog(final int the size of the set n, final int the size of the subsets to be counted k) Returns the natural `log` of the Binomial Coefficient, "`n choose k`", the number of `k`-element subsets that can be selected from an `n`-element set.
public static void	checkBinomial(final int Size of the set. n, final int Size of the subsets to be counted. k) Check binomial preconditions.
public static Iterator<int[]>	Returns: an `iterator` over the k-sets in n. combinationsIterator(int Size of the set from which subsets are selected. n, int Size of the subsets to be enumerated. k) Returns an iterator whose range is the k-element subsets of {0, ..., n - 1} represented as `int[]` arrays.
public static long	Returns: `n!` factorial(final int argument n) Returns n!.
public static double	Returns: `n!` factorialDouble(final int Argument. n) Compute n!, the factorial of `n` (the product of the numbers 1 to n), as a `double`.
public static double	Returns: `n!` factorialLog(final int Argument. n) Compute the natural logarithm of the factorial of `n`.
public static long	Returns: `S(n,k)` stirlingS2(final int the size of the set n, final int the number of non-empty subsets k) Returns the Stirling number of the second kind, "`S(n,k)`", the number of ways of partitioning an `n`-element set into `k` non-empty subsets.

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

FACTORIALS	back to summary
pack-priv static final long[] FACTORIALS All long-representable factorials

STIRLING_S2	back to summary
pack-priv static final AtomicReference<long[][]> STIRLING_S2 Stirling numbers of the second kind.

CombinatoricsUtils	back to summary
private CombinatoricsUtils() Private constructor (class contains only static methods).

Method Detail

binomialCoefficient back to summary

binomialCoefficient	back to summary
public static long binomialCoefficient(final int n, final int k) throws NotPositiveException, NumberIsTooLargeException, MathArithmeticException Returns an exact representation of the Binomial Coefficient, "`n choose k`", the number of `k`-element subsets that can be selected from an `n`-element set. Preconditions: `0 <= k <= n` (otherwise `MathIllegalArgumentException` is thrown) The result is small enough to fit into a `long`. The largest value of `n` for which all coefficients are `< Long.MAX_VALUE` is 66. If the computed value exceeds `Long.MAX_VALUE` a `MathArithMeticException` is thrown. Parameters n:int the size of the set k:int the size of the subsets to be counted Returns:long `n choose k` Exceptions NotPositiveException: if `n < 0`. NumberIsTooLargeException: if `k > n`. MathArithmeticException: if the result is too large to be represented by a long integer.

public static long binomialCoefficient(final int n, final int k) throws NotPositiveException, NumberIsTooLargeException, MathArithmeticException

Returns an exact representation of the Binomial Coefficient, "n choose k", the number of k-element subsets that can be selected from an n-element set.

Preconditions:

0 <= k <= n (otherwise MathIllegalArgumentException is thrown)
The result is small enough to fit into a long. The largest value of n for which all coefficients are < Long.MAX_VALUE is 66. If the computed value exceeds Long.MAX_VALUE a MathArithMeticException is thrown.

Parameters

n:int: the size of the set
k:int: the size of the subsets to be counted

Returns:long

n choose k

Exceptions

NotPositiveException:: if n < 0.
NumberIsTooLargeException:: if k > n.
MathArithmeticException:: if the result is too large to be represented by a long integer.

binomialCoefficientDouble back to summary

binomialCoefficientDouble	back to summary
public static double binomialCoefficientDouble(final int n, final int k) throws NotPositiveException, NumberIsTooLargeException, MathArithmeticException Returns a `double` representation of the Binomial Coefficient, "`n choose k`", the number of `k`-element subsets that can be selected from an `n`-element set. Preconditions: `0 <= k <= n` (otherwise `IllegalArgumentException` is thrown) The result is small enough to fit into a `double`. The largest value of `n` for which all coefficients are less than Double.MAX_VALUE is 1029. If the computed value exceeds Double.MAX_VALUE, Double.POSITIVE_INFINITY is returned Parameters n:int the size of the set k:int the size of the subsets to be counted Returns:double `n choose k` Exceptions NotPositiveException: if `n < 0`. NumberIsTooLargeException: if `k > n`. MathArithmeticException: if the result is too large to be represented by a long integer.

public static double binomialCoefficientDouble(final int n, final int k) throws NotPositiveException, NumberIsTooLargeException, MathArithmeticException

Returns a double representation of the Binomial Coefficient, "n choose k", the number of k-element subsets that can be selected from an n-element set.

Preconditions:

0 <= k <= n (otherwise IllegalArgumentException is thrown)
The result is small enough to fit into a double. The largest value of n for which all coefficients are less than Double.MAX_VALUE is 1029. If the computed value exceeds Double.MAX_VALUE, Double.POSITIVE_INFINITY is returned

Parameters

n:int: the size of the set
k:int: the size of the subsets to be counted

Returns:double

n choose k

Exceptions

NotPositiveException:: if n < 0.
NumberIsTooLargeException:: if k > n.
MathArithmeticException:: if the result is too large to be represented by a long integer.

binomialCoefficientLog back to summary

binomialCoefficientLog	back to summary
public static double binomialCoefficientLog(final int n, final int k) throws NotPositiveException, NumberIsTooLargeException, MathArithmeticException Returns the natural `log` of the Binomial Coefficient, "`n choose k`", the number of `k`-element subsets that can be selected from an `n`-element set. Preconditions: `0 <= k <= n` (otherwise `MathIllegalArgumentException` is thrown) Parameters n:int the size of the set k:int the size of the subsets to be counted Returns:double `n choose k` Exceptions NotPositiveException: if `n < 0`. NumberIsTooLargeException: if `k > n`. MathArithmeticException: if the result is too large to be represented by a long integer.

public static double binomialCoefficientLog(final int n, final int k) throws NotPositiveException, NumberIsTooLargeException, MathArithmeticException

Returns the natural log of the Binomial Coefficient, "n choose k", the number of k-element subsets that can be selected from an n-element set.

Preconditions:

0 <= k <= n (otherwise MathIllegalArgumentException is thrown)

Parameters

n:int: the size of the set
k:int: the size of the subsets to be counted

Returns:double

n choose k

Exceptions

NotPositiveException:: if n < 0.
NumberIsTooLargeException:: if k > n.
MathArithmeticException:: if the result is too large to be represented by a long integer.

checkBinomial back to summary

checkBinomial	back to summary
public static void checkBinomial(final int n, final int k) throws NumberIsTooLargeException, NotPositiveException Check binomial preconditions. Parameters n:int Size of the set. k:int Size of the subsets to be counted. Exceptions NumberIsTooLargeException: if `k > n`. NotPositiveException: if `n < 0`.

public static void checkBinomial(final int n, final int k) throws NumberIsTooLargeException, NotPositiveException

Check binomial preconditions.

Parameters

n:int: Size of the set.
k:int: Size of the subsets to be counted.

Exceptions

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

combinationsIterator back to summary

combinationsIterator	back to summary
public static Iterator<int[]> combinationsIterator(int n, int k) Returns an iterator whose range is the k-element subsets of {0, ..., n - 1} represented as `int[]` arrays. 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, combinationsIterator(4, 2) 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 and 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. Returns:Iterator<int[]> an `iterator` over the k-sets in n. Exceptions NotPositiveException: if `n < 0`. NumberIsTooLargeException: if `k > n`.

public static Iterator<int[]> combinationsIterator(int n, int k)

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

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, combinationsIterator(4, 2) 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 and 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.

Returns:Iterator<int[]>

an iterator over the k-sets in n.

Exceptions

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

factorial back to summary

factorial	back to summary
public static long factorial(final int n) throws NotPositiveException, MathArithmeticException Returns n!. Shorthand for `n` Factorial, the product of the numbers `1,...,n`. Preconditions: `n >= 0` (otherwise `MathIllegalArgumentException` is thrown) The result is small enough to fit into a `long`. The largest value of `n` for which `n!` does not exceed Long.MAX_VALUE} is 20. If the computed value exceeds `Long.MAX_VALUE` an `MathArithMeticException` is thrown. Parameters n:int argument Returns:long `n!` Exceptions NotPositiveException: if `n < 0`. MathArithmeticException: if the result is too large to be represented by a `long`. if `n > 20`: The factorial value is too large to fit in a `long`.

public static long factorial(final int n) throws NotPositiveException, MathArithmeticException

Returns n!. Shorthand for n Factorial, the product of the numbers 1,...,n.

Preconditions:

n >= 0 (otherwise MathIllegalArgumentException is thrown)
The result is small enough to fit into a long. The largest value of n for which n! does not exceed Long.MAX_VALUE} is 20. If the computed value exceeds Long.MAX_VALUE an MathArithMeticException is thrown.

Parameters

n:int: argument

Returns:long

n!

Exceptions

NotPositiveException:

if n < 0.

MathArithmeticException:

if the result is too large to be represented by a long.
if n > 20: The factorial value is too large to fit in a long.

factorialDouble back to summary

factorialDouble	back to summary
public static double factorialDouble(final int n) throws NotPositiveException Compute n!, the factorial of `n` (the product of the numbers 1 to n), as a `double`. The result should be small enough to fit into a `double`: The largest `n` for which `n!` does not exceed `Double.MAX_VALUE` is 170. If the computed value exceeds `Double.MAX_VALUE`, `Double.POSITIVE_INFINITY` is returned. Parameters n:int Argument. Returns:double `n!` Exceptions NotPositiveException: if `n < 0`.

public static double factorialDouble(final int n) throws NotPositiveException

Compute n!, the factorial of n (the product of the numbers 1 to n), as a double. The result should be small enough to fit into a double: The largest n for which n! does not exceed Double.MAX_VALUE is 170. If the computed value exceeds Double.MAX_VALUE, Double.POSITIVE_INFINITY is returned.

Parameters

n:int: Argument.

Returns:double

n!

Exceptions

NotPositiveException:: if n < 0.

factorialLog back to summary

factorialLog	back to summary
public static double factorialLog(final int n) throws NotPositiveException Compute the natural logarithm of the factorial of `n`. Parameters n:int Argument. Returns:double `n!` Exceptions NotPositiveException: if `n < 0`.

public static double factorialLog(final int n) throws NotPositiveException

Compute the natural logarithm of the factorial of n.

Parameters

n:int: Argument.

Returns:double

n!

Exceptions

NotPositiveException:: if n < 0.

stirlingS2 back to summary

stirlingS2	back to summary
public static long stirlingS2(final int n, final int k) throws NotPositiveException, NumberIsTooLargeException, MathArithmeticException Returns the Stirling number of the second kind, "`S(n,k)`", the number of ways of partitioning an `n`-element set into `k` non-empty subsets. The preconditions are `0 <= k <= n` (otherwise `NotPositiveException` is thrown) Parameters n:int the size of the set k:int the number of non-empty subsets Returns:long `S(n,k)` Exceptions NotPositiveException: if `k < 0`. NumberIsTooLargeException: if `k > n`. MathArithmeticException: if some overflow happens, typically for n exceeding 25 and k between 20 and n-2 (S(n,n-1) is handled specifically and does not overflow) Since 3.1

public static long stirlingS2(final int n, final int k) throws NotPositiveException, NumberIsTooLargeException, MathArithmeticException

Returns the Stirling number of the second kind, "S(n,k)", the number of ways of partitioning an n-element set into k non-empty subsets.

The preconditions are 0 <= k <= n (otherwise NotPositiveException is thrown)

Parameters

n:int: the size of the set
k:int: the number of non-empty subsets

Returns:long

S(n,k)

Exceptions

NotPositiveException:: if k < 0.
NumberIsTooLargeException:: if k > n.
MathArithmeticException:: if some overflow happens, typically for n exceeding 25 and k between 20 and n-2 (S(n,n-1) is handled specifically and does not overflow)

Since

3.1

public final Class CombinatoricsUtils

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