org.apache.commons.math3.util

## Class CombinatoricsUtils

• public final class CombinatoricsUtils
extends Object
Combinatorial utilities.
Since:
3.3
• ### Method Summary

Methods
Modifier and Type Method and Description
static long binomialCoefficient(int n, int 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.
static double binomialCoefficientDouble(int n, int 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.
static double binomialCoefficientLog(int n, int 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.
static void checkBinomial(int n, int k)
Check binomial preconditions.
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.
static long factorial(int n)
Returns n!.
static double factorialDouble(int n)
Compute n!, the factorial of n (the product of the numbers 1 to n), as a double.
static double factorialLog(int n)
Compute the natural logarithm of the factorial of n.
static long stirlingS2(int n, int 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.
• ### Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
• ### Method Detail

• #### binomialCoefficient

public static long binomialCoefficient(int n,
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 - the size of the set
k - the size of the subsets to be counted
Returns:
n choose k
Throws:
NotPositiveException - if n < 0.
NumberIsTooLargeException - if k > n.
MathArithmeticException - if the result is too large to be represented by a long integer.
• #### binomialCoefficientDouble

public static double binomialCoefficientDouble(int n,
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 - the size of the set
k - the size of the subsets to be counted
Returns:
n choose k
Throws:
NotPositiveException - if n < 0.
NumberIsTooLargeException - if k > n.
MathArithmeticException - if the result is too large to be represented by a long integer.
• #### binomialCoefficientLog

public static double binomialCoefficientLog(int n,
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 - the size of the set
k - the size of the subsets to be counted
Returns:
n choose k
Throws:
NotPositiveException - if n < 0.
NumberIsTooLargeException - if k > n.
MathArithmeticException - if the result is too large to be represented by a long integer.
• #### factorial

public static long factorial(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 - argument
Returns:
n!
Throws:
MathArithmeticException - if the result is too large to be represented by a long.
NotPositiveException - if n < 0.
MathArithmeticException - if n > 20: The factorial value is too large to fit in a long.
• #### factorialDouble

public static double factorialDouble(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 - Argument.
Returns:
n!
Throws:
NotPositiveException - if n < 0.
• #### factorialLog

public static double factorialLog(int n)
throws NotPositiveException
Compute the natural logarithm of the factorial of n.
Parameters:
n - Argument.
Returns:
n!
Throws:
NotPositiveException - if n < 0.
• #### stirlingS2

public static long stirlingS2(int n,
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 - the size of the set
k - the number of non-empty subsets
Returns:
S(n,k)
Throws:
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
• #### combinationsIterator

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 - Size of the set from which subsets are selected.
k - Size of the subsets to be enumerated.
Returns:
an iterator over the k-sets in n.
Throws:
NotPositiveException - if n < 0.
NumberIsTooLargeException - if k > n.
• #### checkBinomial

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