最快的排序算法是什么

作者: 老瓦在霸都 | 来源:发表于2020-09-26 09:19 被阅读0次

最快的排序算法是什么，很多人的第一反应是快排，感觉QuickSort 当然应该最快了，其实并非如此，快排是不稳定的，最坏情况下，快排序并不是最优，Java7 中引入的 TimSort 就是一个结合了插入排序和归并排序的高效算法.

Timsort最早是 Tim Peters 于2001年为 Python 写的排序算法。自从发明该算法以来，它已被用作Python，Java，Android平台和GNU Octave中的默认排序算法。

关于此算法的详细描述参见 http://svn.python.org/projects/python/trunk/Objects/listsort.txt

看看它与另外两个高效排序算法的比较

相比之下， TimSort 的最佳，平均和最坏情况综合起来最佳。在数据量比较少（<=64）的情况下，它直接用 Insert Sort，否则使用 MergeSort + BinarySearch 来提高排序效率

下面写一个给扑克牌排序的例子，比较一下冒泡，插入，快排，归并排序，TimSort的性能:

扑克牌对象类如下

package com.github.walterfan.helloalgorithm;

import java.util.ArrayList;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.List;
import java.util.Map;

/**
 * @Author: Walter Fan
 **/
public class Poker {
    public static class Card {
        enum Suite {
            Spades(4), Hearts(3), Clubs(2), Diamonds(1);
            int value;

            Suite(int value) {
                this.value = value;

            }

            private static Map<Integer, Suite> valueMap = new HashMap<>();

            static {
                for (Suite suite : Suite.values()) {
                    valueMap.put(suite.value, suite);
                }
            }

            public static Suite valueOf(int pageType) {
                return valueMap.get(pageType);
            }

        }
        Suite suite;
        //1~13
        int point;

        public Card(int suiteValue, int point) {
            this.suite = Suite.valueOf(suiteValue);
            this.point = point;
        }

        public String toString() {
            String strPoint = Integer.toString(point);
            if (point > 10) {
                switch (point) {
                    case 11:
                        strPoint = "J";
                        break;
                    case 12:
                        strPoint = "Q";
                        break;
                    case 13:
                        strPoint = "K";
                        break;

                }
            }

            return suite.name() + ":" + strPoint;
        }

        public int getScore() {
            return suite.value * 100 + point;
        }
    }




    public static List<Card> createCardList(int suiteCount) {
        List<Card> cards = new ArrayList<>(52);
        for(int i = 1; i < 5; i++) {
            for(int j = 1; j < 14 ;++j) {
                cards.add(new Card(i, j));
            }
        }

        List<Card> totalCards = new ArrayList<>(suiteCount );

        for(int j = 0; j < suiteCount; j++) {
            totalCards.addAll(new ArrayList<>(cards));
        }

        Collections.shuffle(totalCards);
        return totalCards;
    }

    public static class CardComparator implements Comparator<Card> {

        @Override
        public int compare(Card o1, Card o2) {
            return o1.getScore() - o2.getScore();
        }
    }

}

各种排序算法的实现如下

package com.github.walterfan.helloalgorithm;

import com.google.common.base.Stopwatch;
import lombok.extern.slf4j.Slf4j;

import java.util.Collections;
import java.util.Comparator;
import java.util.List;
import java.util.concurrent.Callable;
import java.util.concurrent.atomic.AtomicInteger;
import java.util.stream.Collectors;

import static java.util.concurrent.TimeUnit.MILLISECONDS;


@Slf4j
public class SortCardTask implements Callable<Long> {
    public enum SortMethod { 
        BUBBLE_SORT, 
        INSERT_SORT, 
        QUICK_SORT, 
        MERGE_SORT, 
        TIM_SORT}

    private final List<Poker.Card> cards;
    private final SortMethod sortMethod;
    private final int taskNumber;

    private final AtomicInteger taskCounter;

    public SortCardTask(List<Poker.Card> cards, SortMethod method, int taskNumber, AtomicInteger taskCounter) {
        this.cards = cards;
        this.sortMethod = method;
        this.taskNumber = taskNumber;
        this.taskCounter = taskCounter;
    }

    @Override
    public Long call() {
        Stopwatch stopwatch = Stopwatch.createStarted();
        log.info("* {} begin to sort {} cards ({} suite） by {}", this.taskNumber, cards.size(), cards.size()/52, sortMethod);
        Comparator<Poker.Card> comparator = new Poker.CardComparator();
        switch(sortMethod) {
            case BUBBLE_SORT:
                bubbleSort(cards, comparator);
                break;
            case INSERT_SORT:
                insertSort(cards, comparator);
                break;
            case QUICK_SORT:
                quickSort(cards, comparator);
                break;
            case MERGE_SORT:
                mergeSort(cards, comparator);
                break;
            case TIM_SORT:
                timSort(cards, comparator);
                break;
        }

        stopwatch.stop();

        long millis = stopwatch.elapsed(MILLISECONDS);
        log.info("* {} end to sort {} cards ({} suite）sort by {} spend {} milliseconds - {}" , this.taskNumber, cards.size(), cards.size()/52, sortMethod, millis, stopwatch); // formatted string like "12.3 ms"
        taskCounter.incrementAndGet();
        return millis;
    }

    public static <T> void bubbleSort(List<T> aList, Comparator<T> comparator) {
        boolean sorted = false;
        int loopCount = aList.size() - 1;
        while (!sorted) {
            sorted = true;
            for (int i = 0; i < loopCount; i++) {
                if (comparator.compare(aList.get(i), aList.get(i + 1)) > 0) {
                    Collections.swap(aList, i, i + 1);
                    sorted = false;
                }
            }
        }
    }

    public static <T> void insertSort(List<T> aList, Comparator<T> comparator) {
        int size = aList.size();
        for (int i = 1; i < size; ++i) {
            T selected = aList.get(i);

            if (size < 10) {
                log.info("{} insert to {}", selected, aList.subList(0, i).stream().map(String::valueOf).collect(Collectors.joining(", ")));
            }

            int j = i - 1;
            //find a position for insert currentElement in the left sorted collection
            while (j >= 0 && comparator.compare(selected, aList.get(j)) < 0) {
                //it does not overwrite existed element because the j+1=i that is currentElement at beginging
                aList.set(j + 1, aList.get(j));
                j--;
            }
            aList.set(j + 1, selected);

        }
    }

    public static <T> void timSort(List<T> aList, Comparator<T> comparator) {
        //aList.parallelStream().sorted(comparator).collect(Collectors.toList());
        aList.sort(comparator);
    }

    public static <T> void quickSort(List<T> aList, Comparator<T> comparator) {
        T[] arr = (T[]) aList.toArray();
        quickSort(arr, comparator, 0, aList.size() - 1);
    }

    public static <T> void quickSort(T[] arr, Comparator<T> comparator, int begin, int end) {
        if (begin < end) {
            int partitionIndex = partition(arr, comparator, begin, end);

            quickSort(arr, comparator, begin, partitionIndex-1);
            quickSort(arr, comparator, partitionIndex+1, end);
        }
    }

    private static <T> int partition(T[] arr, Comparator<T> comparator, int begin, int end) {

        T pivot = arr[end];
        int i = (begin-1);

        for (int j = begin; j < end; j++) {
            if (comparator.compare(arr[j], pivot) <= 0) { //arr[j] <= pivot
                i++;

                T swapTemp = arr[i];
                arr[i] = arr[j];
                arr[j] = swapTemp;
            }
        }

        T swapTemp = arr[i+1];
        arr[i+1] = arr[end];
        arr[end] = swapTemp;

        return i+1;
    }

    public static <T> void mergeSort(List<T> aList, Comparator<T> comparator) {
        T[] arr = (T[]) aList.toArray();
        mergeSort(arr, 0, aList.size() - 1, comparator);
    }

    public static <T> void mergeSort(T arr[], int l, int r, Comparator<T> comparator)
    {
        if (l < r) {
            // Same as (l+r)/2, but avoids overflow for
            // large l and h
            int m = l + (r - l) / 2;

            // Sort first and second halves
            mergeSort(arr, l, m, comparator);
            mergeSort(arr, m + 1, r, comparator);

            merge(arr, l, m, r, comparator);
        }
    }

    public static <T> void  merge(T arr[], int l, int m, int r, Comparator<T> comparator)
    {
        int i, j, k;
        int n1 = m - l + 1;
        int n2 = r - m;

        /* create temp arrays */
        T[] L = (T[])new Object[n1];
        T[] R = (T[])new Object[n2];

        /* Copy data to temp arrays L[] and R[] */
        for (i = 0; i < n1; i++)
            L[i] = arr[l + i];
        for (j = 0; j < n2; j++)
            R[j] = arr[m + 1 + j];

        /* Merge the temp arrays back into arr[l..r]*/
        i = 0; // Initial index of first subarray
        j = 0; // Initial index of second subarray
        k = l; // Initial index of merged subarray
        while (i < n1 && j < n2) {
            if (comparator.compare(L[i], R[j]) <= 0) {
                arr[k] = L[i];
                i++;
            }
            else {
                arr[k] = R[j];
                j++;
            }
            k++;
        }

    /* Copy the remaining elements of L[], if there
       are any */
        while (i < n1) {
            arr[k] = L[i];
            i++;
            k++;
        }

    /* Copy the remaining elements of R[], if there
       are any */
        while (j < n2) {
            arr[k] = R[j];
            j++;
            k++;
        }
    }



    @Override
    public String toString() {
        return "SortCardTask{" +
                "taskNumber=" + taskNumber +
                ", sortMethod=" + sortMethod +
                '}';
    }
}

然后分别用以上5种排序方法来做下性能比较

package com.github.walterfan.helloalgorithm;

import com.google.common.base.Stopwatch;
import com.google.common.util.concurrent.Uninterruptibles;
import lombok.extern.slf4j.Slf4j;

import java.time.Duration;
import java.util.ArrayList;
import java.util.Collections;
import java.util.List;
import java.util.concurrent.Callable;
import java.util.concurrent.ExecutorService;
import java.util.concurrent.Executors;
import java.util.concurrent.Future;
import java.util.concurrent.TimeUnit;
import java.util.concurrent.atomic.AtomicInteger;

@Slf4j
public class SortAlgorithmDemo {
    public static final int SORT_TIMEOUT_SEC = 30;
    private static AtomicInteger finishCounter = new AtomicInteger(0);

    private AtomicInteger taskNumber = new AtomicInteger(0);

    private ExecutorService executorService =Executors.newSingleThreadExecutor();

    public Callable<Long> createTask(int cardSuiteCount, SortCardTask.SortMethod method) {
        List<Poker.Card> cards = Poker.createCardList(cardSuiteCount);
        return new SortCardTask(cards, method, taskNumber.incrementAndGet(), finishCounter);

    }

    public List<Future<Long>> exeucteTasks(List<Callable<Long>> tasks, Duration waitTime)  {
        try {
            return this.executorService.invokeAll(tasks, waitTime.toMillis(), TimeUnit.MILLISECONDS);
        } catch (InterruptedException e) {
            log.warn("invokeAll interrupt", e);
            return Collections.emptyList();
        }
    }

    private void runTasks(int cardSuiteCount, SortCardTask.SortMethod sortMethod) {

        List<Callable<Long>> tasks = new ArrayList<>();

        tasks.add(this.createTask(cardSuiteCount, sortMethod));

        List<Future<Long>> results = this.exeucteTasks(tasks, Duration.ofSeconds(SORT_TIMEOUT_SEC));

        results.stream().filter(x -> !x.isDone()).forEach(x -> log.info("{} is not done", x));
    }

    private void waitAndstop(int seconds) {
        Uninterruptibles.sleepUninterruptibly(seconds, TimeUnit.SECONDS);
        this.executorService.shutdownNow();
    }

    public static void main(String[] args) {

        SortAlgorithmDemo demo = new SortAlgorithmDemo();

        int cardSuiteCount = 1000;

        demo.runTasks(cardSuiteCount, SortCardTask.SortMethod.BUBBLE_SORT);

        demo.runTasks(cardSuiteCount, SortCardTask.SortMethod.INSERT_SORT);

        demo.runTasks(cardSuiteCount, SortCardTask.SortMethod.QUICK_SORT);

        demo.runTasks(cardSuiteCount, SortCardTask.SortMethod.MERGE_SORT);

        demo.runTasks(cardSuiteCount, SortCardTask.SortMethod.TIM_SORT);

        demo.waitAndstop(30);
    }
}

将1000 副牌打乱顺序的扑克牌排序下来，结果如下

冒泡排序：23.77 秒
插入排序：1.231 秒
快速排序： 135 毫秒
归并排序： 23.96 毫秒
TimSort: 18.98 毫秒

09:06:35.315: c.g.w.h.SortCardTask * 1 begin to sort 52000 cards (1000 suite） by BUBBLE_SORT
09:06:59.082: c.g.w.h.SortCardTask * 1 end to sort 52000 cards (1000 suite）sort by BUBBLE_SORT spend 23769 milliseconds - 23.77 s
09:06:59.151: c.g.w.h.SortCardTask * 2 begin to sort 52000 cards (1000 suite） by INSERT_SORT
09:07:00.382: c.g.w.h.SortCardTask * 2 end to sort 52000 cards (1000 suite）sort by INSERT_SORT spend 1230 milliseconds - 1.231 s
09:07:00.388: c.g.w.h.SortCardTask * 3 begin to sort 52000 cards (1000 suite） by QUICK_SORT
09:07:00.523: c.g.w.h.SortCardTask * 3 end to sort 52000 cards (1000 suite）sort by QUICK_SORT spend 135 milliseconds - 135.0 ms
09:07:00.525: c.g.w.h.SortCardTask * 4 begin to sort 52000 cards (1000 suite） by MERGE_SORT
09:07:00.549: c.g.w.h.SortCardTask * 4 end to sort 52000 cards (1000 suite）sort by MERGE_SORT spend 23 milliseconds - 23.96 ms
09:07:00.551: c.g.w.h.SortCardTask * 5 begin to sort 52000 cards (1000 suite） by TIM_SORT
09:07:00.570: c.g.w.h.SortCardTask * 5 end to sort 52000 cards (1000 suite）sort by TIM_SORT spend 18 milliseconds - 18.98 ms

但是 TimSort 也有一个问题，在 JDK7 的描述中提到它有如下兼容性问题

Area: API: Utilities
Synopsis: Updated sort behavior for Arrays and Collections may throw an IllegalArgumentException
Description: The sorting algorithm used by java.util.Arrays.sort and (indirectly) by java.util.Collections.sort has been replaced. The new sort implementation may throw an IllegalArgumentException if it detects a Comparable that violates the Comparable contract. The previous implementation silently ignored such a situation. If the previous behavior is desired, you can use the new system property, java.util.Arrays.useLegacyMergeSort, to restore previous mergesort behavior.
Nature of Incompatibility: behavioral
RFE: 6804124

所以在JDK7以后，实现Comparable接口的比较器需要满足以下三个约束条件：
1）自反性：x，y 的比较结果和 y，x 的比较结果相反。
2）传递性：x>y, y>z,则 x>z。
3）对称性：x=y,则 x,z 比较结果和 y，z 比较结果相同。

如果你的比较方法违反了以上的约束，要么你不使用这个新的算法，还是回到传统的归并排序

System.setProperty("java.util.Arrays.useLegacyMergeSort", "true");

要么修改你的比较器以符合上述的约束条件。

举两个例子如下

例一: 违反了传递性

package com.github.walterfan.helloalgorithm;


import lombok.extern.slf4j.Slf4j;

import java.util.Arrays;
import java.util.Comparator;
import java.util.LinkedList;
import java.util.List;
import java.util.stream.Collectors;

/**
 * @Author: Walter Fan
 **/
@Slf4j
public class TimSortExam {
    public static class WorkLoadComparator implements Comparator<WorkNode> {

        @Override
        public int compare(WorkNode o1, WorkNode o2) {
            double ratio1 = o1.getRatio();
            double ratio2 = o2.getRatio();

            double distance = ratio1 - ratio2;
            if(Double.compare(Math.abs(distance), 0.02) < 0) {

                int ret =  Long.compare(o1.getConnections(), o2.getConnections());
                log.info("o1={}, o2={}, distance={}, ret={}" , ratio1, ratio2, distance, ret);
                return ret;
            }

            return Double.compare(ratio1, ratio2);
        }
    }
   public static void main(String[] args) {
       WorkNode node1 = new WorkNode(100, 20, 30);
       WorkNode node2 = new WorkNode(100, 22, 20);
       WorkNode node3 = new WorkNode(100, 23, 10);
       WorkNode node4 = new WorkNode(100, 25, 50);

       Comparator<WorkNode> comparator = new  WorkLoadComparator();

       int ret = comparator.compare(node1, node2); log.info("node1 {} node2 ", ret > 0? ">":"<=");
       ret = comparator.compare(node2, node3); log.info("node2 {} node3",  ret > 0? ">":"<=");
       ret = comparator.compare(node1, node3); log.info("node1 {} node3",  ret > 0? ">":"<=");

       List<WorkNode> aList = new LinkedList<>();
       for(int i = 0; i < 1; ++i) {
           aList.addAll(Arrays.asList(node1, node2, node3, node4));
       }
       List<WorkNode> sortedList = aList.stream().sorted(comparator).collect(Collectors.toList());
       log.info("~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~");
       sortedList.stream().forEach(x -> log.info("{}", x));
   }
}

例二: 违反了对称性

package com.github.walterfan.helloalgorithm;

import java.util.ArrayList;
import java.util.Collections;
import java.util.Comparator;
import java.util.List;

import org.apache.commons.lang3.StringUtils;

import java.util.Random;

public class TimSortDemo {

    public static void sortMessageError(List<String> list) {
        System.out.println("this is error comparator");
        Collections.sort(list, new Comparator<String>() {
            public int compare(String arg1, String arg2) {

                if (StringUtils.isBlank(arg1) || StringUtils.isBlank(arg2)) {
                    return 0;
                }

                return arg1.compareTo(arg2);
            }
        });

    }

    public static void sortMessageCorrect(List<String> list) {
        System.out.println("this is correct comparator");
        Collections.sort(list, new Comparator<String>() {
            public int compare(String arg1, String arg2) {

                if(StringUtils.isBlank(arg1) ) {
                    if(StringUtils.isBlank(arg2)) {
                        return 0;
                    }else {
                        return -1;
                    }

                }else if(StringUtils.isBlank(arg2)){
                    return 1;
                }

                return arg1.compareTo(arg2);

            }
        });

    }

    public static List<String> createList() {
        List<String> list = new ArrayList<String>();
        Random random = new Random();
        for (int i = 10000; i > 0; i--) {
            if (i % 5000 != 0) {
                list.add(random.nextInt(1000) + "");
            } else {
                list.add("");
            }

        }
        return list;
    }

    public static void main(String[] args) throws InterruptedException {

        sortMessageCorrect(createList());
        sortMessageError(createList());
    }

}

最快的排序算法是什么

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