快速排序法03:双路快速排序法
作者:互联网
为了解决数组中重复元素过多导致的性能退化,重新思考partition()方法的逻辑,在原有的基础上,从两端分别进行比较大小
循环不变量:arr[left + 1, i - 1] <= v,arr[j + 1, right] >= v
import java.util.Arrays;
import java.util.Random;
public class Algorithm {
public static void main(String[] args) {
Integer[] arr = {3, 2, 5, 1, 0, 0};
QuickSort.sort2ways(arr);
System.out.println(Arrays.toString(arr));
}
}
class QuickSort {
private QuickSort(){}
public static<E extends Comparable<E>> void sort2ways(E[] arr){
Random random = new Random();
E temp = null;
sort2ways(arr, 0, arr.length - 1, temp, random);
}
public static<E extends Comparable<E>> void sort2ways(E[] arr, int left, int right, E temp, Random random){
if (left >= right){
return;
}
int p = partition2ways(arr, left, right, temp, random);
sort2ways(arr, left, p - 1, temp, random);
sort2ways(arr, p + 1, right, temp, random);
}
/**
* 循环不变量:arr[left + 1, i - 1] <= v,arr[j + 1, right] >= v
*/
public static <E extends Comparable<E>> int partition2ways(E[] arr, int left, int right, E temp, Random random){
/**
* 随机选择标定点,和第一个元素互换
*/
int p = random.nextInt(right - left + 1) + left;
temp = arr[p];
arr[p] = arr[left];
arr[left] = temp;
int i = left + 1;
int j = right;
/**
* i == j时有可能arr[i]还没有判断大小,所以不能结束循环
*/
while (i <= j){
/**
* 当左边元素小于arr[left]时继续向前,直到大于等于arr[left]
*/
if (arr[i].compareTo(arr[left]) < 0){
i++;
}
/**
* 当右边元素大于arr[left]时不动,直到小于等于arr[left]
*/
else if (arr[j].compareTo(arr[left]) > 0){
j--;
}
/**
* 此时两边的元素都不属于两侧,相互调换,直到i >= j
*/
else {
temp = arr[i];
arr[i] = arr[j];
arr[j] = temp;
i++;
j--;
}
}
/**
* 最后将j处元素和arr[left]互换
*/
temp = arr[j];
arr[j] = arr[left];
arr[left] = temp;
return j;
}
}
归并排序法、随机快速排序法和双路快速排序法性能比较
import java.util.Arrays;
import java.util.Random;
public class Algorithm {
public static void main(String[] args) {
Integer[] testScale = {10000, 100000};
for (Integer n : testScale){
Integer[] randomArr = ArrayGenerator.generatorRandomArray(n, 1);
Integer[] sortedArr = ArrayGenerator.generatorSortedArray(n, n);
Integer[] arr1 = Arrays.copyOf(randomArr, randomArr.length);
Integer[] arr3 = Arrays.copyOf(randomArr, randomArr.length);
Integer[] arr2 = Arrays.copyOf(sortedArr, sortedArr.length);
Integer[] arr4 = Arrays.copyOf(sortedArr, sortedArr.length);
System.out.println("测试随机数组排序性能");
System.out.println();
Verify.testTime("MergeSort", randomArr);
Verify.testTime("QuickSort", arr1);
Verify.testTime("QuickSort2Ways", arr3);
System.out.println();
System.out.println("测试有序数组排序性能");
System.out.println();
Verify.testTime("MergeSort", sortedArr);
Verify.testTime("QuickSort", arr2);
Verify.testTime("QuickSort2Ways", arr4);
System.out.println();
}
}
}
class QuickSort {
private QuickSort(){}
public static<E extends Comparable<E>> void sort2ways(E[] arr){
Random random = new Random();
E temp = null;
sort2ways(arr, 0, arr.length - 1, temp, random);
}
public static<E extends Comparable<E>> void sort2ways(E[] arr, int left, int right, E temp, Random random){
if (left >= right){
return;
}
int p = partition2ways(arr, left, right, temp, random);
sort2ways(arr, left, p - 1, temp, random);
sort2ways(arr, p + 1, right, temp, random);
}
public static <E extends Comparable<E>> int partition2ways(E[] arr, int left, int right, E temp, Random random){
int p = random.nextInt(right - left + 1) + left;
temp = arr[p];
arr[p] = arr[left];
arr[left] = temp;
int i = left + 1;
int j = right;
while (i <= j){
if (arr[i].compareTo(arr[left]) < 0){
i++;
}
else if (arr[j].compareTo(arr[left]) > 0){
j--;
}
else {
temp = arr[i];
arr[i] = arr[j];
arr[j] = temp;
i++;
j--;
}
}
temp = arr[j];
arr[j] = arr[left];
arr[left] = temp;
return j;
}
public static<E extends Comparable<E>> void sort(E[] arr){
Random random = new Random();
E temp = null;
sort(arr, 0, arr.length - 1, random, temp);
}
public static<E extends Comparable<E>> void sort(E[] arr, int left, int right, Random random, E temp){
if (left >= right){
return;
}
int p = partition(arr, left, right, random, temp);
sort(arr, left, p - 1, random, temp);
sort(arr, p + 1, right, random, temp);
}
public static <E extends Comparable<E>> int partition(E[] arr, int left, int right, Random random, E temp){
int p = random.nextInt(right - left + 1) + left;
temp = arr[p];
arr[p] = arr[left];
arr[left] = temp;
int j = left;
for (int i = left + 1; i <= right; i++) {
if (arr[i].compareTo(arr[left]) < 0){
j++;
temp = arr[i];
arr[i] = arr[j];
arr[j] = temp;
}
}
temp = arr[j];
arr[j] = arr[left];
arr[left] = temp;
return j;
}
}
class MergeSort {
private MergeSort(){}
public static<E extends Comparable<E>> void sort(E[] arr){
E[] temp = Arrays.copyOf(arr, arr.length);
sort(arr, 0, arr.length - 1, temp);
}
private static<E extends Comparable<E>> void sort(E[] arr, int left, int right, E[] temp){
if (left >= right){
return;
}
int mid = left + (right - left) / 2;
sort(arr, left, mid, temp);
sort(arr, mid + 1, right, temp);
if (arr[mid].compareTo(arr[mid + 1]) > 0) {
merge(arr, left, mid, right, temp);
}
}
public static<E extends Comparable<E>> void merge(E[] arr, int left, int mid, int right, E[] temp){
int i = left;
int j = mid + 1;
System.arraycopy(arr, left, temp, left, right - left + 1);
for (int n = left; n < right + 1; n++) {
if (i == mid + 1){
arr[n] = temp[j];
j++;
}
else if (j == right + 1) {
arr[n] = temp[i];
i++;
}
else if (temp[i].compareTo(temp[j]) <= 0) {
arr[n] = temp[i];
i++;
}
else{
arr[n] = temp[j];
j++;
}
}
}
}
class ArrayGenerator {
private ArrayGenerator (){}
public static Integer[] generatorRandomArray (Integer n, Integer maxBound){
Integer[] arr = new Integer[n];
Random random = new Random();
for (int i = 0; i < n; i++) {
arr[i] = random.nextInt(maxBound);
}
return arr;
}
public static Integer[] generatorSortedArray (Integer n, Integer maxBound){
Integer[] arr = new Integer[n];
for (int i = 0; i < n; i++) {
arr[i] = i;
}
return arr;
}
}
class Verify {
private Verify (){}
public static<E extends Comparable<E>> boolean isSorted(E[] arr){
for (int i = 0; i < arr.length - 1; i++) {
if (arr[i].compareTo(arr[i + 1]) > 0) {
return false;
}
}
return true;
}
public static<E extends Comparable<E>> void testTime(String AlgorithmName, E[] arr) {
long startTime = System.nanoTime();
if (AlgorithmName.equals("MergeSort")) {
MergeSort.sort(arr);
}
if (AlgorithmName.equals("QuickSort")) {
QuickSort.sort(arr);
}
if (AlgorithmName.equals("QuickSort2Ways")) {
QuickSort.sort2ways(arr);
}
long endTime = System.nanoTime();
if (!Verify.isSorted(arr)){
throw new RuntimeException(AlgorithmName + "算法排序失败!");
}
System.out.println(String.format("%s算法,测试用例为%d,执行时间:%f秒", AlgorithmName, arr.length, (endTime - startTime) / 1000000000.0));
}
}
快速排序法的复杂度分析
对于普通算法,如果能找到一组数据让它100%变成最坏的情况,那复杂度就看最坏的情况
而对于随机算法,没有一组数据可以让其100%发生性能恶化,因此更严谨的做法是使用期望来计算随机算法的复杂度
普通快速排序法,在数组元素相同时,性能下降概率为100%,因此复杂度为O(n^2)
而双路快速排序法是一个随机算法,它随机选择标定点,虽然在最坏的情况下复杂度为O(n^2),但概率极低。其递归层数期望值为O(logn),复杂度的期望值为O(nlogn)
双路快速排序法还有问题
双路快速排序法,对于元素完全一样的数组,性能得到了很大的提升,但每次拆分成子区间后还是要从头到尾遍历一遍元素,即使这些元素是相等的。
因此,如果可以在第一次遍历的时候,将相等的元素单独区分开,以后不再重复遍历这些元素,也会很好的对性能进行优化。
标签:03,arr,right,temp,int,双路,random,排序,left 来源: https://www.cnblogs.com/taoyuann/p/15442815.html