org.apache.commons.math3.util
Class CombinatoricsUtils

java.lang.Object
  org.apache.commons.math3.util.CombinatoricsUtils

public final class CombinatoricsUtils
extends Object

Combinatorial utilities.

Since:

3.1

Version:

$Id: CombinatoricsUtils.java 14178 2015-10-12 06:11:28Z galpin $

Method Summary

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 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.

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 an ArithMeticException 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 < 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 IllegalArgumentException 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 IllegalArgumentException is thrown)
• The result is small enough to fit into a long. The largest value of n for which n! < Long.MAX_VALUE} is 20. If the computed value exceeds Long.MAX_VALUE an ArithMeticException 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! < 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.

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.