概述
在計(jì)算器科學(xué)與數(shù)學(xué)中，一個(gè)排序算法（英語(yǔ)：Sorting algorithm）是一種能將一串?dāng)?shù)據(jù)依照特定排序方式進(jìn)行排列的一種算法。本文將總結(jié)幾類常用的排序算法，包括冒泡排序、選擇排序、插入排序、快速排序和歸并排序，分別使用JAVA代碼實(shí)現(xiàn)，簡(jiǎn)要使用圖例方式介紹其實(shí)現(xiàn)原理。
算法原理及實(shí)現(xiàn)
1、冒泡排序
- 原理圖
- 理解
通過(guò)重復(fù)地遍歷要排序的列表，比較每對(duì)相鄰的項(xiàng)目，并在順序錯(cuò)誤的情況下交換它們。
- Java Code
public class BubbleSort {
// logic to sort the elements
public static void bubble_srt(int array[]) {
int n = array.length;
int k;
for (int m = n; m >= 0; m--) {
for (int i = 0; i < n - 1; i++) {
k = i + 1;
if (array[i] > array[k]) {
swapNumbers(i, k, array);
}
}
printNumbers(array);
}
}
private static void swapNumbers(int i, int j, int[] array) {
int temp;
temp = array[i];
array[i] = array[j];
array[j] = temp;
}
private static void printNumbers(int[] input) {
for (int i = 0; i < input.length; i++) {
System.out.print(input[i] + ", ");
}
System.out.println("n");
}
public static void main(String[] args) {
int[] input = { 4, 2, 9, 6, 23, 12, 34, 0, 1 };
bubble_srt(input);
}
}
2、選擇排序
- 原理圖
- 理解
內(nèi)部循環(huán)查找下一個(gè)最小（或最大）值，外部循環(huán)將該值放入其適當(dāng)?shù)奈恢谩?/p>
- Java Code
public class SelectionSort {
public static int[] doSelectionSort(int[] arr){
for (int i = 0; i < arr.length - 1; i++)
{
int index = i;
for (int j = i + 1; j < arr.length; j++)
if (arr[j] < arr[index])
index = j;
int smallerNumber = arr[index];
arr[index] = arr[i];
arr[i] = smallerNumber;
}
return arr;
}
public static void main(String a[]){
int[] arr1 = {10,34,2,56,7,67,88,42};
int[] arr2 = doSelectionSort(arr1);
for(int i:arr2){
System.out.print(i);
System.out.print(", ");
}
}
}
冒泡排序和選擇排序的區(qū)別
1、冒泡排序是比較相鄰位置的兩個(gè)數(shù)，而選擇排序是按順序比較，找最大值或者最小值； 2、冒泡排序每一輪比較后，位置不對(duì)都需要換位置，選擇排序每一輪比較都只需要換一次位置； 3、冒泡排序是通過(guò)數(shù)去找位置，選擇排序是給定位置去找數(shù)。
3、插入排序
- 原理圖
- 理解
每一步將一個(gè)待排序的記錄，插入到前面已經(jīng)排好序的有序序列中去，直到插完所有元素為止。
- Java Code
public class InsertionSort {
public static void main(String a[]){
int[] arr1 = {10,34,2,56,7,67,88,42};
int[] arr2 = doInsertionSort(arr1);
for(int i:arr2){
System.out.print(i);
System.out.print(", ");
}
}
public static int[] doInsertionSort(int[] input){
int temp;
for (int i = 1; i < input.length; i++) {
for(int j = i ; j > 0 ; j--){
if(input[j] < input[j-1]){
temp = input[j];
input[j] = input[j-1];
input[j-1] = temp;
}
}
}
return input;
}
}
4、快速排序
- 原理圖
- 理解
將原問(wèn)題分解為若干個(gè)規(guī)模更小，但結(jié)構(gòu)與原問(wèn)題相似的子問(wèn)題，遞歸地解這些子問(wèn)題，然后將這些子問(wèn)題的解組合為原問(wèn)題的解。
- Java Code
public class QuickSort {
private int array[];
private int length;
public void sort(int[] inputArr) {
if (inputArr == null || inputArr.length == 0) {
return;
}
this.array = inputArr;
length = inputArr.length;
quickSort(0, length - 1);
}
private void quickSort(int lowerIndex, int higherIndex) {
int i = lowerIndex;
int j = higherIndex;
// calculate pivot number, I am taking pivot as middle index number
int pivot = array[lowerIndex+(higherIndex-lowerIndex)/2];
// Divide into two arrays
while (i <= j) {
/**
* In each iteration, we will identify a number from left side which
* is greater then the pivot value, and also we will identify a number
* from right side which is less then the pivot value. Once the search
* is done, then we exchange both numbers.
*/
while (array[i] < pivot) {
i++;
}
while (array[j] > pivot) {
j--;
}
if (i <= j) {
exchangeNumbers(i, j);
//move index to next position on both sides
i++;
j--;
}
}
// call quickSort() method recursively
if (lowerIndex < j)
quickSort(lowerIndex, j);
if (i < higherIndex)
quickSort(i, higherIndex);
}
private void exchangeNumbers(int i, int j) {
int temp = array[i];
array[i] = array[j];
array[j] = temp;
}
public static void main(String a[]){
MyQuickSort sorter = new MyQuickSort();
int[] input = {24,2,45,20,56,75,2,56,99,53,12};
sorter.sort(input);
for(int i:input){
System.out.print(i);
System.out.print(" ");
}
}
}
5、歸并排序
- 原理圖
- 理解
將待排序的數(shù)列分成若干個(gè)長(zhǎng)度為1的子數(shù)列，然后將這些數(shù)列兩兩合并；得到若干個(gè)長(zhǎng)度為2的有序數(shù)列，再將這些數(shù)列兩兩合并；得到若干個(gè)長(zhǎng)度為4的有序數(shù)列，再將它們兩兩合并；直接合并成一個(gè)數(shù)列為止。
- Java Code
public class MergeSort {
private int[] array;
private int[] tempMergArr;
private int length;
public static void main(String a[]){
int[] inputArr = {45,23,11,89,77,98,4,28,65,43};
MyMergeSort mms = new MyMergeSort();
mms.sort(inputArr);
for(int i:inputArr){
System.out.print(i);
System.out.print(" ");
}
}
public void sort(int inputArr[]) {
this.array = inputArr;
this.length = inputArr.length;
this.tempMergArr = new int[length];
doMergeSort(0, length - 1);
}
private void doMergeSort(int lowerIndex, int higherIndex) {
if (lowerIndex < higherIndex) {
int middle = lowerIndex + (higherIndex - lowerIndex) / 2;
// Below step sorts the left side of the array
doMergeSort(lowerIndex, middle);
// Below step sorts the right side of the array
doMergeSort(middle + 1, higherIndex);
// Now merge both sides
mergeParts(lowerIndex, middle, higherIndex);
}
}
private void mergeParts(int lowerIndex, int middle, int higherIndex) {
for (int i = lowerIndex; i <= higherIndex; i++) {
tempMergArr[i] = array[i];
}
int i = lowerIndex;
int j = middle + 1;
int k = lowerIndex;
while (i <= middle && j <= higherIndex) {
if (tempMergArr[i] <= tempMergArr[j]) {
array[k] = tempMergArr[i];
i++;
} else {
array[k] = tempMergArr[j];
j++;
}
k++;
}
while (i <= middle) {
array[k] = tempMergArr[i];
k++;
i++;
}
}
}
常見(jiàn)排序算法復(fù)雜度
作者：taro_秋刀魚
