我已经实现了（在Java中）Insertion Sort，MergeSort，ModifiedMergeSort和Quick Sort：
ModifiedMergeSort有一个元素“绑定”的变量。当要排序的元素小于或等于“bound”时，请使用Insertion Sort对它们进行排序。
为什么版本1比版本3,4和5更好？
版本2和6的结果是否现实？
这是我的结果（以毫秒为单位）：
Version 1 - Insertion Sort: Run-Times over 50 test runs
Input Size Best-Case Worst-Case Average-Case
N = 10000 14 19 14.96
N = 20000 59 60 59.3
N = 40000 234 277 243.1
Version 2 - Merge Sort: Run-Times over 50 test runs
Input Size Best-Case Worst-Case Average-Case
N = 10000 1 15 1.78
N = 20000 3 8 3.4
N = 40000 6 9 6.7
Version 3 - Merge Sort and Insertion Sort on 15 elements: Run-Times over 50 test runs
Input Size Best-Case Worst-Case Average-Case
N = 10000 41 52 45.42
N = 20000 170 176 170.56
N = 40000 712 823 728.08
Version 4 - Merge Sort and Insertion Sort on 30 elements: Run-Times over 50 test runs
Input Size Best-Case Worst-Case Average-Case
N = 10000 27 33 28.04
N = 20000 113 119 114.36
N = 40000 436 497 444.2
Version 5 - Merge Sort and Insertion Sort on 45 elements: Run-Times over 50 test runs
Input Size Best-Case Worst-Case Average-Case
N = 10000 20 21 20.68
N = 20000 79 82 79.7
N = 40000 321 383 325.64
Version 6 - Quick Sort: Run-Times over 50 test runs
Input Size Best-Case Worst-Case Average-Case
N = 10000 1 9 1.18
N = 20000 2 3 2.06
N = 40000 4 5 4.26
这是我的代码：
package com.testing;
import com.sorting.InsertionSort;
import com.sorting.MergeSort;
import com.sorting.ModifiedMergeSort;
import com.sorting.RandomizedQuickSort;
/**
*
* @author mih1406
*/
public class Main {
private static final int R = 50; // # of tests
private static int N = 0; // Input size
private static int[] array; // Tests array
private static int[] temp; // Tests array
private static long InsertionSort_best = -1;
private static long InsertionSort_worst = -1;
private static double InsertionSort_average = -1.0;
private static long MergeSort_best = -1;
private static long MergeSort_worst = -1;
private static double MergeSort_average = -1.0;
private static long ModifiedMergeSort_V3_best = -1;
private static long ModifiedMergeSort_V3_worst = -1;
private static double ModifiedMergeSort_V3_average = -1.0;
private static long ModifiedMergeSort_V4_best = -1;
private static long ModifiedMergeSort_V4_worst = -1;
private static double ModifiedMergeSort_V4_average = -1.0;
private static long ModifiedMergeSort_V5_best = -1;
private static long ModifiedMergeSort_V5_worst = -1;
private static double ModifiedMergeSort_V5_average = -1.0;
private static long RandomizedQuickSort_best = -1;
private static long RandomizedQuickSort_worst = -1;
private static double RandomizedQuickSort_average = -1.0;
public static void main(String args[]) {
StringBuilder InsertionSort_text = new StringBuilder(
"Version 1 - Insertion Sort: Run-Times over 50 test runs\n");
StringBuilder MergeSort_text = new StringBuilder(
"Version 2 - Merge Sort: Run-Times over 50 test runs\n");
StringBuilder ModifiedMergeSort_V3_text = new StringBuilder(
"Version 3 - Merge Sort and Insertion Sort on 15 elements: Run-Times over 50 test runs\n");
StringBuilder ModifiedMergeSort_V4_text = new StringBuilder(
"Version 4 - Merge Sort and Insertion Sort on 30 elements: Run-Times over 50 test runs\n");
StringBuilder ModifiedMergeSort_V5_text = new StringBuilder(
"Version 5 - Merge Sort and Insertion Sort on 45 elements: Run-Times over 50 test runs\n");
StringBuilder RandomizedQuickSort_text = new StringBuilder(
"Version 6 - Quick Sort: Run-Times over 50 test runs\n");
InsertionSort_text.append("Input Size\t\t"
+ "Best-Case\t\tWorst-Case\t\tAverage-Case\n");
MergeSort_text.append("Input Size\t\t"
+ "Best-Case\t\tWorst-Case\t\tAverage-Case\n");
ModifiedMergeSort_V3_text.append("Input Size\t\t"
+ "Best-Case\t\tWorst-Case\t\tAverage-Case\n");
ModifiedMergeSort_V4_text.append("Input Size\t\t"
+ "Best-Case\t\tWorst-Case\t\tAverage-Case\n");
ModifiedMergeSort_V5_text.append("Input Size\t\t"
+ "Best-Case\t\tWorst-Case\t\tAverage-Case\n");
RandomizedQuickSort_text.append("Input Size\t\t"
+ "Best-Case\t\tWorst-Case\t\tAverage-Case\n");
// Case N = 10000
N = 10000;
fillArray();
testing_InsertionSort();
testing_MergeSort();
testing_ModifiedMergeSort(15);
testing_ModifiedMergeSort(30);
testing_ModifiedMergeSort(45);
testing_RandomizedQuickSort();
InsertionSort_text.append("N = " + N + "\t\t" + InsertionSort_best
+ "\t\t\t" + InsertionSort_worst + "\t\t\t"
+ InsertionSort_average + "\n");
MergeSort_text.append("N = " + N + "\t\t" + MergeSort_best
+ "\t\t\t" + MergeSort_worst + "\t\t\t"
+ MergeSort_average + "\n");
ModifiedMergeSort_V3_text.append("N = " + N + "\t\t" + ModifiedMergeSort_V3_best
+ "\t\t\t" + ModifiedMergeSort_V3_worst + "\t\t\t"
+ ModifiedMergeSort_V3_average + "\n");
ModifiedMergeSort_V4_text.append("N = " + N + "\t\t" + ModifiedMergeSort_V4_best
+ "\t\t\t" + ModifiedMergeSort_V4_worst + "\t\t\t"
+ ModifiedMergeSort_V4_average + "\n");
ModifiedMergeSort_V5_text.append("N = " + N + "\t\t" + ModifiedMergeSort_V5_best
+ "\t\t\t" + ModifiedMergeSort_V5_worst + "\t\t\t"
+ ModifiedMergeSort_V5_average + "\n");
RandomizedQuickSort_text.append("N = " + N + "\t\t" + RandomizedQuickSort_best
+ "\t\t\t" + RandomizedQuickSort_worst + "\t\t\t"
+ RandomizedQuickSort_average + "\n");
// Case N = 20000
N = 20000;
fillArray();
testing_InsertionSort();
testing_MergeSort();
testing_ModifiedMergeSort(15);
testing_ModifiedMergeSort(30);
testing_ModifiedMergeSort(45);
testing_RandomizedQuickSort();
InsertionSort_text.append("N = " + N + "\t\t" + InsertionSort_best
+ "\t\t\t" + InsertionSort_worst + "\t\t\t"
+ InsertionSort_average + "\n");
MergeSort_text.append("N = " + N + "\t\t" + MergeSort_best
+ "\t\t\t" + MergeSort_worst + "\t\t\t"
+ MergeSort_average + "\n");
ModifiedMergeSort_V3_text.append("N = " + N + "\t\t" + ModifiedMergeSort_V3_best
+ "\t\t\t" + ModifiedMergeSort_V3_worst + "\t\t\t"
+ ModifiedMergeSort_V3_average + "\n");
ModifiedMergeSort_V4_text.append("N = " + N + "\t\t" + ModifiedMergeSort_V4_best
+ "\t\t\t" + ModifiedMergeSort_V4_worst + "\t\t\t"
+ ModifiedMergeSort_V4_average + "\n");
ModifiedMergeSort_V5_text.append("N = " + N + "\t\t" + ModifiedMergeSort_V5_best
+ "\t\t\t" + ModifiedMergeSort_V5_worst + "\t\t\t"
+ ModifiedMergeSort_V5_average + "\n");
RandomizedQuickSort_text.append("N = " + N + "\t\t" + RandomizedQuickSort_best
+ "\t\t\t" + RandomizedQuickSort_worst + "\t\t\t"
+ RandomizedQuickSort_average + "\n");
// Case N = 40000
N = 40000;
fillArray();
testing_InsertionSort();
testing_MergeSort();
testing_ModifiedMergeSort(15);
testing_ModifiedMergeSort(30);
testing_ModifiedMergeSort(45);
testing_RandomizedQuickSort();
InsertionSort_text.append("N = " + N + "\t\t" + InsertionSort_best
+ "\t\t\t" + InsertionSort_worst + "\t\t\t"
+ InsertionSort_average + "\n");
MergeSort_text.append("N = " + N + "\t\t" + MergeSort_best
+ "\t\t\t" + MergeSort_worst + "\t\t\t"
+ MergeSort_average + "\n");
ModifiedMergeSort_V3_text.append("N = " + N + "\t\t" + ModifiedMergeSort_V3_best
+ "\t\t\t" + ModifiedMergeSort_V3_worst + "\t\t\t"
+ ModifiedMergeSort_V3_average + "\n");
ModifiedMergeSort_V4_text.append("N = " + N + "\t\t" + ModifiedMergeSort_V4_best
+ "\t\t\t" + ModifiedMergeSort_V4_worst + "\t\t\t"
+ ModifiedMergeSort_V4_average + "\n");
ModifiedMergeSort_V5_text.append("N = " + N + "\t\t" + ModifiedMergeSort_V5_best
+ "\t\t\t" + ModifiedMergeSort_V5_worst + "\t\t\t"
+ ModifiedMergeSort_V5_average + "\n");
RandomizedQuickSort_text.append("N = " + N + "\t\t" + RandomizedQuickSort_best
+ "\t\t\t" + RandomizedQuickSort_worst + "\t\t\t"
+ RandomizedQuickSort_average + "\n");
System.out.println(InsertionSort_text);
System.out.println(MergeSort_text);
System.out.println(ModifiedMergeSort_V3_text);
System.out.println(ModifiedMergeSort_V4_text);
System.out.println(ModifiedMergeSort_V5_text);
System.out.println(RandomizedQuickSort_text);
}
private static void fillArray() {
// (re)creating the array
array = new int[N];
// filling the array with random numbers
// using for-loop and the given random generator instruction
for(int i = 0; i < array.length; i++) {
array[i] = (int)(1 + Math.random() * (N-0+1));
}
}
private static void testing_InsertionSort() {
// run-times arrays
long [] run_times = new long[R];
// start/finish times
long start;
long finish;
for(int i = 0; i < R; i++) {
copyArray();
// recording start time
start = System.currentTimeMillis();
// testing the algorithm
InsertionSort.sort(temp);
// recording finish time
finish = System.currentTimeMillis();
run_times[i] = finish-start;
}
InsertionSort_best = findMin(run_times);
InsertionSort_worst = findMax(run_times);
InsertionSort_average = findAverage(run_times);
}
private static void testing_MergeSort() {
// run-times arrays
long [] run_times = new long[R];
// start/finish times
long start;
long finish;
for(int i = 0; i < R; i++) {
copyArray();
// recording start time
start = System.currentTimeMillis();
// testing the algorithm
MergeSort.sort(temp);
// recording finish time
finish = System.currentTimeMillis();
run_times[i] = finish-start;
}
MergeSort_best = findMin(run_times);
MergeSort_worst = findMax(run_times);
MergeSort_average = findAverage(run_times);
}
private static void testing_ModifiedMergeSort(int bound) {
// run-times arrays
long [] run_times = new long[R];
// setting the bound
ModifiedMergeSort.bound = bound;
// start/finish times
long start;
long finish;
for(int i = 0; i < R; i++) {
copyArray();
// recording start time
start = System.currentTimeMillis();
// testing the algorithm
ModifiedMergeSort.sort(temp);
// recording finish time
finish = System.currentTimeMillis();
run_times[i] = finish-start;
}
if(bound == 15) {
ModifiedMergeSort_V3_best = findMin(run_times);
ModifiedMergeSort_V3_worst = findMax(run_times);
ModifiedMergeSort_V3_average = findAverage(run_times);
}
if(bound == 30) {
ModifiedMergeSort_V4_best = findMin(run_times);
ModifiedMergeSort_V4_worst = findMax(run_times);
ModifiedMergeSort_V4_average = findAverage(run_times);
}
if(bound == 45) {
ModifiedMergeSort_V5_best = findMin(run_times);
ModifiedMergeSort_V5_worst = findMax(run_times);
ModifiedMergeSort_V5_average = findAverage(run_times);
}
}
private static void testing_RandomizedQuickSort() {
// run-times arrays
long [] run_times = new long[R];
// start/finish times
long start;
long finish;
for(int i = 0; i < R; i++) {
copyArray();
// recording start time
start = System.currentTimeMillis();
// testing the algorithm
RandomizedQuickSort.sort(temp);
// recording finish time
finish = System.currentTimeMillis();
run_times[i] = finish-start;
}
RandomizedQuickSort_best = findMin(run_times);
RandomizedQuickSort_worst = findMax(run_times);
RandomizedQuickSort_average = findAverage(run_times);
}
private static long findMax(long[] times) {
long max = times[0];
for(int i = 1; i < times.length; i++) {
if(max < times[i]) {
max = times[i];
}
}
return max;
}
private static long findMin(long[] times) {
long min = times[0];
for(int i = 1; i < times.length; i++) {
if(min > times[i]) {
min = times[i];
}
}
return min;
}
private static double findAverage(long[] times) {
long sum = 0;
double avg;
for(int i = 0; i < times.length; i++) {
sum += times[i];
}
avg = (double)sum/(double)times.length;
return avg;
}
private static void copyArray() {
temp = new int[N];
System.arraycopy(array, 0, temp, 0, array.length);
}
}
答案 0 :(得分：2)
您目前正在采取的方法似乎存在一些系统性错误。我将陈述您面临的一些最明显的实验性问题，即使它们可能不会直接成为您实验结果的罪魁祸首。
正如我之前在评论中所述，JVM默认会以解释模式运行您的代码。这意味着在您的方法中找到的每个字节码指令将在现场解释，然后运行。
这种方法的优点是，它允许您的应用程序比在每次运行启动时编译为本机代码的Java程序具有更快的启动时间。
缺点是虽然没有启动性能，但是你会得到一个性能较慢的程序。
为了改善这两个问题，JVM团队进行了权衡。最初您的程序将被解释，但JVM将收集有关哪些方法（或方法的一部分）被密集使用的信息，并将仅编译那些似乎被大量使用的方法。在编译时，你会获得很小的性能，但是代码会比以前更快。
进行测量时，您必须考虑这一事实。
标准方法是“预热JVM”，即稍微运行算法以确保JVM完成它需要执行的所有编译。让JVM变暖的代码与您想要进行基准测试的代码相同非常重要，否则在您对代码进行基准测试时可能会进行一些编译。
测量时间时，您应使用System.nanoTime()代替System.currentTimeMillis。我不会详细介绍，可以访问here。
你也应该小心。以下代码块可能在开始时看起来相同，但在大多数情况下会产生不同的结果：
totalDuration = 0;
for (i = 0; i < 1000; ++i)
startMeasure = now();
algorithm();
endMeasure = now();
duration = endMeasure - startMeasure;
totalDuration += duration;
}
//...
TRIALS_COUNT = 1000;
startMeasure = now();
for (i = 0; i < TRIALS_COUNT; ++i)
algorithm();
}
endMeasure = now();
duration = endMeasure - startMeasure / TRIALS_COUNT;
为什么呢？因为特别是对于更快algorithm()的实现，它们越快，获得准确结果就越困难。
渐近符号有助于理解不同算法如何针对n的大值进行升级。将它们应用于小输入值通常是荒谬的，因为在这种程度上，您通常需要的是计算精确的操作次数及其相关成本（类似于Jakub所做的那样）。 Big O表示法大多数时候只对大Os有意义。 Big O将告诉您算法如何处理难以忍受的输入值大小，而不是它如何处理小数字。规范示例例如是QuickSort，对于大数组而言，它将是王者，但对于大小为4或5的数组而言，这通常比选择或插入排序更慢。不过，您的输入大小似乎足够大。
如前所述，由Jakub完成的数学练习是完全错误的，不应该被考虑在内。
答案 1 :(得分：0)
自己计算复杂性。我假设10000个样本用于以下计算：
插入排序： O（n ^ 2），10 000 * 10 000 = 100 000 000。
合并排序： O（nlogn），10 000 * log10 000 = 140 000。
与插入（15）合并： 15介于9（大小为20的数组）和10（大小为10的数组）之间 2 ^ 10插入排序（大小为10），然后2 ^ 10 * 10 000合并：1 024 * 10 * 10（插入）+ 1 024 * 10 000（合并）= 10 342 400
与插入（30）合并： 30介于8（大小为40的数组）和9（大小为20的数组）之间 2 ^ 9插入排序（大小为20），然后2 ^ 9 * 10 000合并：512 * 20 * 20（插入）+ 512 * 10 000（合并）= 5 324 800
与插入（45）合并： 45介于7（大小为80的数组）和8（大小为40的数组）之间 2 ^ 8插入排序（大小40），然后2 ^ 8 * 10 000合并：256 * 40 * 40（插入）+ * 10 000（合并）= 2 969 600
Quicksort：，而最坏情况的快速排序需要O（n ^ 2），最坏的情况必须经过精心设计才能达到这个限制。大多数情况下，使用radomly生成的算法，平均为O（nlogn）：10 000 * log10 000 = 140 000.
测量排序算法性能会变得非常痛苦，因为您需要在尽可能广泛的输入数据上有效地进行测量。
您在插入排序中看到的数字可能会因输入数字而大幅偏差。如果您在数组中仅使用0和1，并且数组是随机生成的，那么实际上您可以更容易地解决算法问题。对于给定的情况，平均一半的数组已经排序，并且您不需要将0和1相互比较。问题是减少到向左传输所有0，平均只需要（log（n / 2））！+ n时间。对于10 000，实际时间是5 000！+10 000 = 133 888。