Package org.hipparchus.util

Class CombinatoricsUtils

java.lang.Object
org.hipparchus.util.CombinatoricsUtils
public final class CombinatoricsUtils extends Object
Combinatorial utilities.

  • Field Details

    • MAX_BELL

      public static final int MAX_BELL
      Maximum index of Bell number that fits into a long.
      Since:
      2.2
      See Also:

  • Method Details

    • 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