如何用Java实现多线程归并排序

Question

我发现的大多数归并排序示例都在单个线程中运行。这首先就抵消了使用合并排序算法的一些优势。有人可以展示使用多线程在 java 中编写合并排序算法的正确方法吗？

该解决方案应使用最新版本的 java 的适用功能。Stackoverflow 上已有的许多解决方案都使用普通线程。我正在寻找一个演示 ForkJoin 与 RecursiveTask 的解决方案，这似乎是 RecursiveTask 类的主要用例。

重点应该是展示一种具有卓越性能特征的算法，包括尽可能的时间和空间复杂度。

注意：所提议的重复问题都不适用，因为两者都没有提供使用递归任务的解决方案，而这正是该问题所要求的。

Answer 1

合并排序最方便的多线程范例是分叉连接范例。这是从 Java 8 及更高版本提供的。以下代码演示了使用 fork-join 的归并排序。

import java.util.*;
import java.util.concurrent.*;

public class MergeSort<N extends Comparable<N>> extends RecursiveTask<List<N>> {
    private List<N> elements;

    public MergeSort(List<N> elements) {
        this.elements = new ArrayList<>(elements);
    }

    @Override
    protected List<N> compute() {
        if(this.elements.size() <= 1)
            return this.elements;
        else {
            final int pivot = this.elements.size() / 2;
            MergeSort<N> leftTask = new MergeSort<N>(this.elements.subList(0, pivot));
            MergeSort<N> rightTask = new MergeSort<N>(this.elements.subList(pivot, this.elements.size()));

            leftTask.fork();
            rightTask.fork();

            List<N> left = leftTask.join();
            List<N> right = rightTask.join();

            return merge(left, right);
        }
    }

    private List<N> merge(List<N> left, List<N> right) {
        List<N> sorted = new ArrayList<>();
        while(!left.isEmpty() || !right.isEmpty()) {
            if(left.isEmpty())
                sorted.add(right.remove(0));
            else if(right.isEmpty())
                sorted.add(left.remove(0));
            else {
                if( left.get(0).compareTo(right.get(0)) < 0 )
                    sorted.add(left.remove(0));
                else
                    sorted.add(right.remove(0));
            }
        }

        return sorted;
    }

    public static void main(String[] args) {
        ForkJoinPool forkJoinPool = ForkJoinPool.commonPool();
        List<Integer> result = forkJoinPool.invoke(new MergeSort<Integer>(Arrays.asList(7,2,9,10,1)));
        System.out.println("result: " + result);
    }
}

虽然不太直接，但以下代码变体消除了 ArrayList 的过度复制。初始未排序列表仅创建一次，并且对子列表的调用不需要本身执行任何复制。在每次算法分叉时我们都会复制数组列表。另外，现在，当合并列表时，而不是创建一个新列表并在每次重用左侧列表并将值插入其中时复制其中的值。通过避免额外的复制步骤，我们提高了性能。我们在这里使用 LinkedList，因为与 ArrayList 相比，插入相当便宜。我们还消除了对remove的调用，这对于ArrayList来说也可能很昂贵。

import java.util.*;
import java.util.concurrent.*;

public class MergeSort<N extends Comparable<N>> extends RecursiveTask<List<N>> {
    private List<N> elements;

    public MergeSort(List<N> elements) {
        this.elements = elements;
    }

    @Override
    protected List<N> compute() {
        if(this.elements.size() <= 1)
            return new LinkedList<>(this.elements);
        else {
            final int pivot = this.elements.size() / 2;
            MergeSort<N> leftTask = new MergeSort<N>(this.elements.subList(0, pivot));
            MergeSort<N> rightTask = new MergeSort<N>(this.elements.subList(pivot, this.elements.size()));

            leftTask.fork();
            rightTask.fork();

            List<N> left = leftTask.join();
            List<N> right = rightTask.join();

            return merge(left, right);
        }
    }

    private List<N> merge(List<N> left, List<N> right) {
        int leftIndex = 0;
        int rightIndex = 0;
        while(leftIndex < left.size() || rightIndex < right.size()) {
            if(leftIndex >= left.size())
                left.add(leftIndex++, right.get(rightIndex++));
            else if(rightIndex >= right.size())
                return left;
            else {
                if( left.get(leftIndex).compareTo(right.get(rightIndex)) < 0 )
                    leftIndex++;
                else
                    left.add(leftIndex++, right.get(rightIndex++));
            }
        }

        return left;
    }

    public static void main(String[] args) {
        ForkJoinPool forkJoinPool = ForkJoinPool.commonPool();
        List<Integer> result = forkJoinPool.invoke(new MergeSort<Integer>(Arrays.asList(7,2,9,-7,777777,10,1)));
        System.out.println("result: " + result);
    }
}

我们还可以在执行合并时使用迭代器而不是直接调用 get 来进一步改进代码。其原因是通过索引获取 LinkedList 的时间性能较差（线性），因此通过使用迭代器，我们消除了因在每次获取时内部迭代链表而导致的速度减慢。迭代器上对 next 的调用是常数时间，而不是对 get 的调用的线性时间。以下代码被修改为使用迭代器。

import java.util.*;
import java.util.concurrent.*;

public class MergeSort<N extends Comparable<N>> extends RecursiveTask<List<N>> {
    private List<N> elements;

    public MergeSort(List<N> elements) {
        this.elements = elements;
    }

    @Override
    protected List<N> compute() {
        if(this.elements.size() <= 1)
            return new LinkedList<>(this.elements);
        else {
            final int pivot = this.elements.size() / 2;
            MergeSort<N> leftTask = new MergeSort<N>(this.elements.subList(0, pivot));
            MergeSort<N> rightTask = new MergeSort<N>(this.elements.subList(pivot, this.elements.size()));

            leftTask.fork();
            rightTask.fork();

            List<N> left = leftTask.join();
            List<N> right = rightTask.join();

            return merge(left, right);
        }
    }

    private List<N> merge(List<N> left, List<N> right) {
        ListIterator<N> leftIter = left.listIterator();
        ListIterator<N> rightIter = right.listIterator();
        while(leftIter.hasNext() || rightIter.hasNext()) {
            if(!leftIter.hasNext()) {
                leftIter.add(rightIter.next());
                rightIter.remove();
            }
            else if(!rightIter.hasNext())
                return left;
            else {
                N rightElement = rightIter.next();
                if( leftIter.next().compareTo(rightElement) < 0 )
                    rightIter.previous();
                else {
                    leftIter.previous();
                    leftIter.add(rightElement);
                }
            }
        }

        return left;
    }

    public static void main(String[] args) {
        ForkJoinPool forkJoinPool = ForkJoinPool.commonPool();
        List<Integer> result = forkJoinPool.invoke(new MergeSort<Integer>(Arrays.asList(7,2,9,-7,777777,10,1)));
        System.out.println("result: " + result);
    }
}

最后是最复杂的代码版本，此迭代使用完全就地操作。仅创建初始 ArrayList，并且不会创建其他集合。因此，逻辑特别难以遵循（所以我把它留到最后）。但应该尽可能接近理想的实现。

import java.util.*;
import java.util.concurrent.*;

public class MergeSort<N extends Comparable<N>> extends RecursiveTask<List<N>> {
    private List<N> elements;

    public MergeSort(List<N> elements) {
        this.elements = elements;
    }

    @Override
    protected List<N> compute() {
        if(this.elements.size() <= 1)
            return this.elements;
        else {
            final int pivot = this.elements.size() / 2;
            MergeSort<N> leftTask = new MergeSort<N>(this.elements.subList(0, pivot));
            MergeSort<N> rightTask = new MergeSort<N>(this.elements.subList(pivot, this.elements.size()));

            leftTask.fork();
            rightTask.fork();

            List<N> left = leftTask.join();
            List<N> right = rightTask.join();

            merge(left, right);
            return this.elements;
        }
    }

    private void merge(List<N> left, List<N> right) {
        int leftIndex = 0;
        int rightIndex = 0;
        while(leftIndex < left.size() ) {
            if(rightIndex == 0) {
                if( left.get(leftIndex).compareTo(right.get(rightIndex)) > 0 ) {
                    swap(left, leftIndex++, right, rightIndex++);
                } else {
                    leftIndex++;
                }
            } else {
                if(rightIndex >= right.size()) {
                    if(right.get(0).compareTo(left.get(left.size() - 1)) < 0 )
                        merge(left, right);
                    else
                        return;
                }
                else if( right.get(0).compareTo(right.get(rightIndex)) < 0 ) {
                    swap(left, leftIndex++, right, 0);
                } else {
                    swap(left, leftIndex++, right, rightIndex++);
                }
            }
        }

        if(rightIndex < right.size() && rightIndex != 0)
            merge(right.subList(0, rightIndex), right.subList(rightIndex, right.size()));
    }

    private void swap(List<N> left, int leftIndex, List<N> right, int rightIndex) {
        //N leftElement = left.get(leftIndex);
        left.set(leftIndex, right.set(rightIndex, left.get(leftIndex)));
    }

    public static void main(String[] args) {
        ForkJoinPool forkJoinPool = ForkJoinPool.commonPool();
        List<Integer> result = forkJoinPool.invoke(new MergeSort<Integer>(new ArrayList<>(Arrays.asList(5,9,8,7,6,1,2,3,4))));
        System.out.println("result: " + result);
    }
}