选择排序随机平均情况低于预期

Question

具有2,000个数组元素的插入排序的最坏情况是4,000,000个交换，最好的情况是0个交换。为什么我的随机排序数组的平均情况大约有4,000个交换？它不应该在0到4,000,000之间波动吗？

我正在使用各种排序函数记录算法的比较数和交换次数。

import java.io.*;
import java.util.*;
public class SortAlgorithm
{
    public static void main(String[] args) throws IOException
    {
        int sort1[] = new int[2000];//sorted
        int sort2[] = new int[2000];//reverse sorted
        int sort3[] = new int[2000];//random sorted
        Random rand = new Random();
        String str;
        BufferedWriter writer = new BufferedWriter(new FileWriter("C:\\Users\\Colin\\Desktop\\Test.txt"));


        for(int i = 0; i < sort1.length; i++) //sorted
        {
            sort1[i] = i;
        }
        str = "Bubble Sort in sorted order: ";
        str += bubbleSort(sort1);
        writer.write(str);
        writer.newLine();
        for(int i = 0; i < sort1.length; i++) //sorted
        {
            sort1[i] = i;
        }
        str = "Selection Sort in sorted order: ";
        str += selectionSort(sort1);
        writer.write(str);
        writer.newLine();
        for(int i = 0; i < sort1.length; i++) //sorted
        {
            sort1[i] = i;
        }
        str = "Insertion Sort in sorted order: ";
        str += insertionSort(sort1);
        writer.write(str);
        writer.newLine();
        writer.newLine();





        for(int i = 0, j = sort2.length - 1; i < sort2.length; i++, j--)//reverse sorted
        {
            sort2[i] = j;
        }
        str = "Bubble Sort in reverse sorted order: ";
        str += bubbleSort(sort2);
        writer.write(str);
        writer.newLine();
        for(int i = 0, j = sort2.length - 1; i < sort2.length; i++, j--)//reverse sorted
        {
            sort2[i] = j;
        }
        str = "Selection Sort in reverse sorted order: ";
        str += selectionSort(sort2);
        writer.write(str);
        writer.newLine();
        for(int i = 0, j = sort2.length - 1; i < sort2.length; i++, j--)//reverse sorted
        {
            sort2[i] = j;
        }
        str = "Insertion Sort in reverse sorted order: ";
        str += insertionSort(sort2);
        writer.write(str);
        writer.newLine();
        writer.newLine();





        for(int i = 0; i < sort3.length; i++)//random sorted
        {
            sort3[i] = rand.nextInt(2000) + 1;
        }
        str = "Bubble Sort in random sorted order: ";
        str += bubbleSort(sort3);
        writer.write(str);
        writer.newLine();
        for(int i = 0; i < sort3.length; i++)//random sorted
        {
            sort3[i] = rand.nextInt(2000) + 1;
        }
        str = "Selection Sort in random sorted order: ";
        str += selectionSort(sort3);
        writer.write(str);
        writer.newLine();
        for(int i = 0; i < sort3.length; i++)//random sorted
        {
            sort3[i] = rand.nextInt(2000) + 1;
        }
        str = "Insertion Sort in random sorted order: ";
        str += insertionSort(sort3);
        writer.write(str);
        writer.newLine();
        writer.close();
    }

    static String selectionSort(int sort[])
    {
        int comparisons = 0, exchanges = 0;
        String str;
        int n = sort.length;

        for(int i = 0; i < n; i++)
        {
            int small = sort[i];
            int pos = i;
            comparisons++;
            for(int j = i + 1; j < n; j++)
            {
                comparisons++;
                if(sort[j] < small)
                {
                    small = sort[j];
                    pos = j;
                    exchanges++;
                }
                comparisons++;
            }

            int temp = sort[pos];
            sort[pos] = sort[i];
            sort[i] = temp;

        }
        str = "Number of comparisons: " + (comparisons) + " , number of exchanges: " + (exchanges);
        return str;
    }

    static String insertionSort(int sort[])
    {
        int comparisons = 0, exchanges = 0;
        String str = "";
        int n = sort.length;
        for(int i = 1; i < n; i++)
        {
            int j = i - 1;
            int temp = sort[i];
            comparisons++;
            while(j >= 0 && temp < sort[j])
            {
                sort[j + 1] = sort[j];
                j--;
                exchanges++;
            }
            sort[j + 1] = temp;
            comparisons++;
        }
        str = "Number of comparisons: " + (comparisons) + " , number of exchanges: " + (exchanges);
        return str;
    }

    static String bubbleSort(int sort[])
    {
        String str;
        int comparisons = 0, exchanges = 0;
        int n = sort.length;
        for (int i = 0; i < n; i++)
        {
            comparisons++;
            for (int j = 0; j < n - i - 1; j++)
            {
                comparisons++;
                if (sort[j] > sort[j + 1])
                {
                    int temp = sort[j];
                    sort[j] = sort[j + 1];
                    sort[j + 1] = temp;
                    exchanges++;
                }
                comparisons++;
            }
        }
        str = "Number of comparisons: " + (comparisons) + " , number of exchanges: " + (exchanges);
        return str;
    }
}

这是输出：

Bubble Sort in sorted order: Number of comparisons: 4000000 , number of exchanges: 0
Selection Sort in sorted order: Number of comparisons: 4000000 , number of exchanges: 0
Insertion Sort in sorted order: Number of comparisons: 3998 , number of exchanges: 0

Bubble Sort in reverse sorted order: Number of comparisons: 4000000 , number of exchanges: 1999000
Selection Sort in reverse sorted order: Number of comparisons: 4000000 , number of exchanges: 1000000
Insertion Sort in reverse sorted order: Number of comparisons: 3998 , number of exchanges: 1999000

Bubble Sort in random sorted order: Number of comparisons: 4000000 , number of exchanges: 1005056
Selection Sort in random sorted order: Number of comparisons: 4000000 , number of exchanges: 11590
Insertion Sort in random sorted order: Number of comparisons: 3998 , number of exchanges: 970272