数据结构时间复杂度冒泡排序选择排序插入排序

Posted 2021-04-07 wxtRelax

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时间复杂度的计算方式：

1、O(1)：常数

只要没有循环语句，不论代码有多少行，时间复杂度都是O(1)。

2、O(log2n)：对数复杂度，底数不一定是2，可以是任何数

int i = 20;while(i < n){    i = i * 2;}

3、O(n)：线性阶

for(int i = 0; i < n; i++){}

4、O(nlogn) : 线性对数阶

for(int i = 0; i < n; i++){  int j = 20; while(j < n){            i = i * 2; }}

5、O(n2) : 平方阶

for(int i = 0; i < n; i++){    for(int j = 0 ; j < n;j ++){}}

1

冒泡排序：其时间复杂度为O(n2)

原理：从左往右依次进行对比，如果左边比右边大就进行交换，第一次交换后会将最后一个放置为最大的元素。然后依次，再将倒数第二个元素放置为次之的元素。下面兑现代码：

Java实现：

import java.text.SimpleDateFormat;import java.util.Date;
/** * @Author junkle * @Date 2020/4/21 - 16:02 * @Version 1.0 **/public class BubbleSort { public static void main(String[] args) { final int MAXSIZE = 80000; //这是一个即将要排序得数组 int[] arr = new int[MAXSIZE]; for (int i = 0;i < MAXSIZE;i++){ arr[i] = (int) (Math.random() * 70000 % 101); } Date date = new Date(); SimpleDateFormat simpleDateFormat = new SimpleDateFormat("yyyy-MM-dd hh：mm：ss"); String format1 = simpleDateFormat.format(date); System.out.println("排序前的时间是" + format1);// for (int i : arr){// System.out.print(i + " ");// }// System.out.println(); bSort(arr);// for (int i : arr){// System.out.print(i + " ");// } Date date1 = new Date(); String format = simpleDateFormat.format(date1); System.out.println("排序后的时间是" + format); }
 public static void bSort(int[] array){ int size = array.length; for (int i = 0; i < size - 1 ; i++){ for (int j = 0; j < size - 1 - i; j++){ if (array[j] > array[j + 1]){ int tmp = array[j + 1]; array[j + 1] = array[j]; array[j] = tmp; } } } }}

C++实现：

#include <iostream>#include <ctime>#include <cstdlib>using namespace std;constexpr int MAXSIZE = 80000;void bSort(int* array, int size){ int tmp = 0; for (int i = 0; i < size - 1; i++) { //cout << "即将进行第 " << i + 1 <<" 次排序..."<< endl; bool flag = false; for (int j = 0;j < size - 1 - i;j++) { if (array[j] > array[j + 1]) { flag = true; tmp = array[j]; array[j] = array[j + 1 ]; array[j + 1] = tmp; } } if (!flag) { break; } }}

int mainmp(){ srand(time(NULL)); int* array = new int[MAXSIZE]; for (int i = 0; i < MAXSIZE; i++) { array[i] = rand() * 70000 % 101; } /*for (int i = 0; i < MAXSIZE; i++) { cout << array[i] << " "; }*/ cout << endl; cout << "排序之前的时间是："; time_t start = clock(); cout << start; cout << endl; bSort(array, MAXSIZE); cout << "排序之后的时间是是："; time_t end = clock(); cout << end << endl; /*for (int i = 0; i < MAXSIZE; i++) { cout << array[i] << " "; }*/ cout << endl; return 0;}

2

选择排序

原理：选择出最小的与第一个进行交换，选择次小和第二个元素进行交换。依次..... 其时间复杂度为O(n2) 。下面看兑现代码：

Java实现：

import javax.imageio.stream.ImageInputStreamImpl;import java.text.SimpleDateFormat;import java.util.Date;import java.util.zip.CheckedOutputStream;
/** * @Author junkle * @Date 2020/4/21 - 18:30 * @Version 1.0 **/public class SelectSort { public static void sort(int[] array){ int size = array.length; int min = 0; int index = 0; for (int i = 0; i < size; i++) { min = array[i]; index = i; for (int j = i + 1; j < size;j++) { if (min > array[j]) { min = array[j]; index = j; } } if (index != i) { array[index] = array[i]; array[i] = min; } } } public static void main(String[] args) { final int MAXSIZE = 8; //这是一个即将要排序得数组 int[] arr = new int[MAXSIZE]; for (int i = 0;i < MAXSIZE;i++){ arr[i] = (int) (Math.random() * 70000 % 101); } Date date = new Date(); SimpleDateFormat simpleDateFormat = new SimpleDateFormat("yyyy-MM-dd hh：mm：ss"); String format1 = simpleDateFormat.format(date); System.out.println("排序前的时间是" + format1); for (int i : arr){ System.out.print(i + " "); } System.out.println(); sort(arr); for (int i : arr){ System.out.print(i + " "); } Date date1 = new Date(); String format = simpleDateFormat.format(date1); System.out.println("排序后的时间是" + format); }}

C++实现：

#include <iostream>#include <ctime>#include <cstdlib>using namespace std;constexpr int MAXSIZE = 80000;void chooseSort(int *array,int size){ int tmp = 0; int minIndex = 0; for (int i = 0; i < size - 1; i++) { tmp = array[i]; minIndex = i; for (int j = i + 1; j < size; j++) { if (tmp > array[j]) { tmp = array[j]; minIndex = j; } } if (minIndex != i) { array[minIndex] = array[i]; array[i] = tmp; } }}

int mainxz(){ srand(time(NULL)); int* array = new int[MAXSIZE]; for (int i = 0; i < MAXSIZE; i++) { array[i] = rand() % 101; } /*for (int i = 0; i < MAXSIZE; i++) { cout << array[i] << " "; }*/ cout << endl; cout << "排序之前的时间是："; time_t start = clock(); cout << start; cout << endl; chooseSort(array, MAXSIZE); cout << "排序之后的时间是是："; time_t end = clock(); cout << end << endl; /*for (int i = 0; i < MAXSIZE; i++) { cout << array[i] << " "; }*/ cout << endl; delete []array; return 0;}

3

插入排序

原理：从第二个元素开始依次向回查找该元素合适插入的位置。需要用一个变量来记录要插入的元素，然后如果元素不适合，依次向后排。其时间复杂度为O(n2)

 下面看对兑现代码：

Java实现：

import java.util.SortedMap;
/** * @Author junkle * @Date 2020/4/21 - 21:55 * @Version 1.0 **/public class InsertSort { public static void main(String[] args) { int[] array = new int[]{1,8,-1,10,2}; for (int i = 0; i < 5;i++){ System.out.print(array[i] + " "); } System.out.println(); sort(array); for (int i = 0; i < 5;i++){ System.out.print(array[i] + " "); } System.out.println(); } public static void sort(int[] array){ int size = array.length; int insertValue = 0; int insertIndex = 0; for (int i = 1; i < size; i++) { insertValue = array[i]; insertIndex = i - 1; while (insertIndex >= 0 && insertValue < array[insertIndex]) { array[insertIndex + 1] = array[insertIndex]; insertIndex--; } if (insertIndex != i - 1) { array[insertIndex + 1] = insertValue; } } }}

C++实现：

#include <iostream>#include <ctime>#include <cstdlib>constexpr int MAXSIZE = 80000;

using namespace std;

void insertSort(int* array, int size){ for (int i = 1; i < size; i++) { int insertValue = array[i]; int insertIndex = i - 1; while (insertIndex >= 0 && insertValue < array[insertIndex]) { array[insertIndex + 1] = array[insertIndex]; insertIndex--; } if (insertIndex != i - 1) { array[insertIndex + 1] = insertValue; } }}int main(){ srand(time(NULL)); int* array = new int[MAXSIZE]; for (int i = 0; i < MAXSIZE; i++) { array[i] = rand() * 70000 % 101; } /*for (int i = 0; i < MAXSIZE; i++) { cout << array[i] << " "; }*/ /*cout << endl;*/ cout << "排序之前的时间是："; time_t start = clock(); cout << start; cout << endl; insertSort(array, MAXSIZE); cout << "排序之后的时间是是："; time_t end = clock(); cout << end << endl; //for (int i = 0; i < MAXSIZE; i++) //{ // cout << array[i] << " "; //} cout << endl; return 0;}