如何在Java中实现多线程MergeSort

Question

我发现的大多数合并排序示例都运行在单个线程中。这首先克服了使用合并排序算法的一些优点。有人能说明用多线程在java中编写合并排序算法的正确方法吗？

该解决方案应在适用的情况下使用最新版本java的特性。许多已经在堆栈溢出上的解决方案使用普通线程。我正在寻找一个用RecursiveTask演示RecursiveTask的解决方案，这似乎是RecursiveTask类的主要用例。

重点应该是在可能的情况下，展示一种性能优越的算法，包括时间和空间复杂度。

注意到：建议的重复问题都不适用，因为它们都不提供使用递归任务的解决方案，这正是这个问题所要求的。

Answer 1

对于合并排序来说，最方便的多线程范例是叉-连接范例。这是Java 8及更高版本提供的。下面的代码演示了使用叉连接进行合并排序.

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);
    }
}

虽然更少直接向前，但是下面的代码变量消除了对ArrayList的过度复制。初始未排序列表只创建一次，对子列表的调用不需要自己执行任何复制。在每次算法分叉时复制数组列表之前。另外，现在，当合并列表而不是创建一个新列表并在其中复制值时，每次我们重用左列表并将我们的值插入其中时。通过避免额外的复制步骤，我们可以提高性能。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，这在ArrayList上也是很昂贵的。

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);
    }
}

我们还可以通过使用迭代器来进一步改进代码，而不是在执行合并时直接调用get。这样做的原因是，按索引访问LinkedList的时间性能(线性)很差，因此，通过使用迭代器，我们消除了在每个get上内部迭代链接列表所造成的减速。迭代器上对next的调用是常数时间，而不是调用获取的线性时间。下面的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，最复杂的版本的代码，这个迭代使用一个完全就地操作.只创建了初始的ArrayList，也没有创建任何额外的集合。因此，逻辑尤其难以遵循(因此，我将其保存到最后)。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);
    }
}