Introduction to the framework of mathematical combination in the Java class library

Introduction to the framework of mathematical combination in the Java class library In the Java class library, there are many powerful frameworks for mathematical computing and processing.One of the important parts is the related features of the mathematical combination.The combination is the method of selecting elements from a given collection, instead of considering the order of the element.The Java class library provides several classes and methods to handle combinations, and we will introduce them one by one. 1. `java.util.collections` Class:` Collections' is an important tool class in the Java class library. It provides a variety of static methods for operating sets.`Static <T> List <T >> Combinations (List <T> List, Int Size) method in the` collections` class, you can find all combinations specified in the given list.The following is an example code: import java.util.Collections; import java.util.List; public class CombinationExample { public static void main(String[] args) { List<Integer> list = List.of(1, 2, 3); List<List<Integer>> combinations = Collections.combinations(list, 2); for (List<Integer> combination : combinations) { System.out.println(combination); } } } Output results: [1, 2] [1, 3] [2, 3] 2. ORG.APACHE.COMMONS.MATH3.UTIL.COMBINATORSUTILS `Class: Apache Commons Math is a popular Java library for various mathematical calculations.`Combinatoricsutils' provides a method of processing combination.Among them, the method of `CombiningSitrator (int n, int k)` method returns an iterator that can be used to obtain all combinations of specified size.The following is an example code: import org.apache.commons.math3.util.CombinatoricsUtils; import java.util.Iterator; public class CombinationExample { public static void main(String[] args) { int n = 3; int k = 2; Iterator<int[]> iterator = CombinatoricsUtils.combinationsIterator(n, k); while (iterator.hasNext()) { int[] combination = iterator.next(); for (int num : combination) { System.out.print(num + " "); } System.out.println(); } } } Output results: 0 1 0 2 1 2 3. ORG.APACHE.COMMONS.MATH3.complex.Complexutils Class: If a combination of complex number is required, you can use the `Complexutils` class in the Apache Commons Math library.This class provides the method of `CombinevariationSitrator (int [] n, int K, Boolean Repetition) method, which can generate all combinations of plural.The following is an example code: import org.apache.commons.math3.complex.Complex; import org.apache.commons.math3.complex.ComplexUtils; import java.util.Iterator; public class CombinationExample { public static void main(String[] args) { Complex[] complexNumbers = { new Complex(1, 2), new Complex(3, 4), new Complex(5, 6) }; int k = 2; Iterator<Complex[]> iterator = ComplexUtils.combineVariationsIterator(complexNumbers, k, false); while (iterator.hasNext()) { Complex[] combination = iterator.next(); for (Complex num : combination) { System.out.print(num + " "); } System.out.println(); } } } Output results: (1.0,2.0) (3.0,4.0) (1.0,2.0) (5.0,6.0) (3.0,4.0) (5.0,6.0) By using these combination frameworks in the Java class library, we can easily generate and handle different combinations of sets.Whether it is through the `Commons Math Library of Apache Commons Math Library, or by processing the plural combination, the Java class library provides us with a powerful mathematical combination function.