java中数组的所有可能的组合和子集

给定一个可变维度的数组...... 例如。数组={1,2,4,5}

我需要一种方法来概括数组的所有可能组合和子集。

给定一个包含 n 个元素的数组，我需要拥有所有子集（1 个元素的所有子集、2 个元素的所有子集、n 个元素的所有子集）以及每个子集的所有可能排列。

例如结果应该是：

{1}
{2}
{4}
{5}
{1,2}
{1,4}
{1,5}
{2,1}
{2,4}
{2,5}
....
....
{1,2,4,5}
{1,2,5,4}
{1,4,2,5}
{1,5,2,4}
{1,5,4,2}
{2,1,4,5}
{2,1,5,4}
....
....
{5,1,4,2}
{5,1,2,4}
{5,2,4,1}
....
....
etc...

所有组合！

有没有快速的方法呢？ 我不知道....

您应该应用 2 个步骤：

1. 您需要找到给定输入的所有子集。这组子集称为电源组 http://en.wikipedia.org/wiki/Power_set.
2. 对于这个幂集的每个元素（即每个子集），您需要所有排列 http://en.wikipedia.org/wiki/Permutation.

该实现使用了一些实用程序类组合学 https://github.com/javagl/Combinatorics项目。输出还包含空集{}并且不按尺寸排序，但这可以作为后处理步骤轻松完成。

import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Iterator;
import java.util.List;
import java.util.NoSuchElementException;

public class AllCombinations {
    public static void main(String[] args) {
        List<Integer> list = Arrays.asList(1,2,4,5);

        PowerSetIterable<Integer> powerSet = 
            new PowerSetIterable<Integer>(list);
        for (List<Integer> subset : powerSet)
        {
            PermutationIterable<Integer> permutations = 
                new PermutationIterable<Integer>(subset);
            for (List<Integer> permutation : permutations) {
                System.out.println(permutation);
            }
        }

    }
}

//From https://github.com/javagl/Combinatorics
class PowerSetIterable<T> implements Iterable<List<T>> {
    private final List<T> input;
    private final int numElements;
    public PowerSetIterable(List<T> input) {
        this.input = input;
        numElements = 1 << input.size();
    }

    @Override
    public Iterator<List<T>> iterator() {
        return new Iterator<List<T>>() {
            private int current = 0;

            @Override
            public boolean hasNext() {
                return current < numElements;
            }

            @Override
            public List<T> next() {
                if (!hasNext()) {
                    throw new NoSuchElementException("No more elements");
                }
                List<T> element = new ArrayList<T>();
                for (int i = 0; i < input.size(); i++) {
                    long b = 1 << i;
                    if ((current & b) != 0) {
                        element.add(input.get(i));
                    }
                }
                current++;
                return element;
            }

            @Override
            public void remove() {
                throw new UnsupportedOperationException(
                        "May not remove elements from a power set");
            }
        };
    }
}
//From https://github.com/javagl/Combinatorics
class PermutationIterable<T> implements Iterable<List<T>> {
    public static int factorial(int n) {
        int f = 1;
        for (int i = 2; i <= n; i++) {
            f = f * i;
        }
        return f;
    }
    private final List<T> input;
    private final int numPermutations;
    public PermutationIterable(List<T> input) {
        this.input = input;
        numPermutations = factorial(input.size());
    }

    @Override
    public Iterator<List<T>> iterator() {
        if (input.size() == 0) {
            return Collections.<List<T>> singletonList(
                    Collections.<T> emptyList()).iterator();
        }
        return new Iterator<List<T>>() {
            private int current = 0;

            @Override
            public boolean hasNext() {
                return current < numPermutations;
            }

            @Override
            public List<T> next() {
                if (!hasNext()) {
                    throw new NoSuchElementException("No more elements");
                }
                // Adapted from http://en.wikipedia.org/wiki/Permutation
                List<T> result = new ArrayList<T>(input);
                int factorial = numPermutations / input.size();
                for (int i = 0; i < result.size() - 1; i++) {
                    int tempIndex = (current / factorial) % (result.size() - i);
                    T temp = result.get(i + tempIndex);
                    for (int j = i + tempIndex; j > i; j--) {
                        result.set(j, result.get(j - 1));
                    }
                    result.set(i, temp);
                    factorial /= (result.size() - (i + 1));
                }
                current++;
                return result;
            }

            @Override
            public void remove() {
                throw new UnsupportedOperationException(
                        "May not remove elements from a permutation");
            }
        };
    }
}