java.lang.Object
- org.hipparchus.util.CombinatoricsUtils

public final class CombinatoricsUtils
extends Object

Combinatorial utilities.

Nested Class Summary

Nested Classes
Modifier and Type Class Description

static class CombinatoricsUtils.FactorialLog
Class for computing the natural logarithm of the factorial of n.

Field Summary

Fields
Modifier and Type Field Description

static int MAX_BELL
Maximum index of Bell number that fits into a long.

Method Summary

All Methods Static Methods Concrete Methods
Modifier and Type	Method	Description
`static long`	`bellNumber(int n)`	Compute the Bell number (number of partitions of a set).
`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!
`static double`	`factorialLog(int n)`	Compute the natural logarithm of the factorial of `n`.
`static <T> Stream<List<T>[]>`	`partitions(List<T> list)`	Generate a stream of partitions of a list.
`static <T> Stream<List<T>>`	`permutations(List<T> list)`	Generate a stream of permutations of a list.
`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

- Field Detail
  - MAX_BELL
```
public static final int MAX_BELL
```
    Maximum index of Bell number that fits into a long.
    
    Since:
    
    2.2
    
    See Also:
    
    Constant Field Values
- Method Detail
  - binomialCoefficient
```
public static long binomialCoefficient(int n,
                                       int k)
                                throws MathIllegalArgumentException,
                                       MathRuntimeException
```
    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 MathRuntimeException is thrown.
    Parameters:
    
    n - the size of the set
    
    k - the size of the subsets to be counted
    
    Returns:
    
    n choose k
    
    Throws:
    
    MathIllegalArgumentException - if n < 0.
    
    MathIllegalArgumentException - if k > n.
    
    MathRuntimeException - if the result is too large to be represented by a long integer.
  - binomialCoefficientDouble
```
public static double binomialCoefficientDouble(int n,
                                               int k)
                                        throws MathIllegalArgumentException,
                                               MathRuntimeException
```
    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:
    
    MathIllegalArgumentException - if n < 0.
    
    MathIllegalArgumentException - if k > n.
    
    MathRuntimeException - if the result is too large to be represented by a long integer.
  - binomialCoefficientLog
```
public static double binomialCoefficientLog(int n,
                                            int k)
                                     throws MathIllegalArgumentException,
                                            MathRuntimeException
```
    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:
    
    MathIllegalArgumentException - if n < 0.
    
    MathIllegalArgumentException - if k > n.
    
    MathRuntimeException - if the result is too large to be represented by a long integer.
  - factorial
```
public static long factorial(int n)
                      throws MathIllegalArgumentException
```
    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 MathRuntimeException is thrown.
    Parameters:
    
    n - argument
    
    Returns:
    
    n!
    
    Throws:
    
    MathRuntimeException - if the result is too large to be represented by a long.
    
    MathIllegalArgumentException - if n < 0.
    
    MathIllegalArgumentException - if n > 20: The factorial value is too large to fit in a long.
  - factorialDouble
```
public static double factorialDouble(int n)
                              throws MathIllegalArgumentException
```
    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:
    
    MathIllegalArgumentException - if n < 0.
  - factorialLog
```
public static double factorialLog(int n)
                           throws MathIllegalArgumentException
```
    Compute the natural logarithm of the factorial of n.
    
    Parameters:
    
    n - Argument.
    
    Returns:
    
    log(n!)
    
    Throws:
    
    MathIllegalArgumentException - if n < 0.
  - stirlingS2
```
public static long stirlingS2(int n,
                              int k)
                       throws MathIllegalArgumentException,
                              MathRuntimeException
```
    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 MathIllegalArgumentException is thrown)
    
    Parameters:
    
    n - the size of the set
    
    k - the number of non-empty subsets
    
    Returns:
    
    S(n,k)
    
    Throws:
    
    MathIllegalArgumentException - if k < 0.
    
    MathIllegalArgumentException - if k > n.
    
    MathRuntimeException - 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)
  - 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:
    
    MathIllegalArgumentException - if n < 0.
    
    MathIllegalArgumentException - if k > n.
  - checkBinomial
```
public static void checkBinomial(int n,
                                 int k)
                          throws MathIllegalArgumentException
```
    Check binomial preconditions.
    
    Parameters:
    
    n - Size of the set.
    
    k - Size of the subsets to be counted.
    
    Throws:
    
    MathIllegalArgumentException - if n < 0.
    
    MathIllegalArgumentException - if k > n.
  - bellNumber
```
public static long bellNumber(int n)
```
    Compute the Bell number (number of partitions of a set).
    
    Parameters:
    
    n - number of elements of the set
    
    Returns:
    
    Bell number Bₙ
    
    Since:
    
    2.2
  - partitions
```
public static <T> Stream<List<T>[]> partitions(List<T> list)
```
    Generate a stream of partitions of a list.
    This method implements the iterative algorithm described in Short Note: A Fast Iterative Algorithm for Generating Set Partitions by B. Djokić, M. Miyakawa, S. Sekiguchi, I. Semba, and I. Stojmenović (The Computer Journal, Volume 32, Issue 3, 1989, Pages 281–282, https://doi.org/10.1093/comjnl/32.3.281
    
    Type Parameters:
    
    T - type of the list elements
    
    Parameters:
    
    list - list to partition
    
    Returns:
    
    stream of partitions of the list, each partition is an array or parts and each part is a list of elements
    
    Since:
    
    2.2
  - permutations
```
public static <T> Stream<List<T>> permutations(List<T> list)
```
    Generate a stream of permutations of a list.
    This method implements the Steinhaus–Johnson–Trotter algorithm with Even's speedup Steinhaus–Johnson–Trotter algorithm
    
    Type Parameters:
    
    T - type of the list elements
    
    Parameters:
    
    list - list to permute
    
    Returns:
    
    stream of permutations of the list
    
    Since:
    
    2.2

Class CombinatoricsUtils

Nested Class Summary

Field Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

MAX_BELL

Method Detail

binomialCoefficient

binomialCoefficientDouble

binomialCoefficientLog

factorial

factorialDouble

factorialLog

stirlingS2

combinationsIterator

checkBinomial

bellNumber

partitions

permutations