Eight sorting algorithms
1. Bubble sort
Sorting principle: Array elements are compared in pairs, their positions are exchanged, and the larger elements are placed later. Then after a round of comparison, the largest element will appear at the largest prime index.
/**
* @description 冒泡排序
* @author: PeiChen
* @version 1.0
*/
public class BubbleSort {
public static void main(String[] args) {
int[] arr = {
1, 24, 16, 8, 36, 5};
BubbleSort.bubbleSort(arr);
System.out.println(Arrays.toString(arr));
}
/**
* 排序原理：数组元素两两比较，交换位置，大元素往后放，那么经过一轮比较后，最大的元素，就会出现在最大素引处。
* @param array 待排序数组
*/
private static void bubbleSort(int[] array) {
for (int i = 0; i < array.length - 1; i++) {
for (int j = 0; j < array.length - 1 - i; j++) {
if (array[j] > array[j + 1]) {
int temp = array[j];
array[j] = array[j + 1];
array[j + 1] = temp;
}
}
}
}
}
Sort results:
[1, 5, 8, 16, 24, 36]
2. Selection sort
Sorting principle: start from the 0 index, compare with the following elements in turn, put the smaller elements forward, and after a round of comparison, the smallest element appears at the smallest index.
/**
* @description 选择排序
* @author: PeiChen
* @version 1.0
*/
public class SelectSort {
public static void main(String[] args) {
int[] arr = {
1, 24, 16, 8, 36, 5};
SelectSort.selectSort(arr);
System.out.println(Arrays.toString(arr));
}
/**
* 排序原理：从0索引处开始，依次和后面的元素进行比较，小的元素往前放,经过一轮比较后，最小的元素就出现在了最小索引处。
* @param array 待排序数组
*/
private static void selectSort(int[] array) {
for (int i = 0; i < array.length - 1; i++) {
for (int j = i + 1; j < array.length; j++) {
if (array[i] > array[j]) {
int temp = array[i];
array[i] = array[j];
array[j] = temp;
}
}
}
}
}
Sort results:
[1, 5, 8, 16, 24, 36]
3. Insertion sort
Direct insertion sorting: starting from index 1, insert the following elements into the previous ordered list in order to keep it in order.
/**
* @description 直接插入排序
* @author: PeiChen
* @version 1.0
*/
public class InsertSort {
public static void main(String[] args) {
int[] arr = {
1, 24, 16, 8, 36, 5};
insertSort(arr);
System.out.println(Arrays.toString(arr));
}
/**
* 直接插入排序：从 1 索引处开始，将后面的元素依次插入到之前的有序列表中使之仍保持有序。
* @param array 待排序数组
*/
private static void insertSort(int[] array) {
//控制循环的次数
for (int i = 1; i < array.length; i++) {
int j = i;
//升序排列直接插入，否则交换元素插入
while (j > 0 && array[j] < array[j - 1]) {
int temp = array[j];
array[j] = array[j - 1];
array[j - 1] = temp;
j--;
}
}
}
}
Sort results:
[1, 5, 8, 16, 24, 36]
4. Hill sort
Hill sorting: It is an optimization of direct insertion sorting. The core idea is to select a reasonable increment. After a round of sorting, the sequence will be roughly ordered, and then the increment will be continuously reduced to perform insertion sorting. Until the increment is 1, that is, the whole sorting ends.
/**
* @description 希尔排序
* @author: PeiChen
* @version 1.0
*/
public class ShellSort {
public static void main(String[] args) {
int[] arr = {
1, 24, 16, 8, 36, 5, 21, -2, 52};
shellSort(arr);
System.out.println(Arrays.toString(arr));
}
/**
* 希尔排序：它是对直接插入排序的一个优化，核心的思想就是合理的选取增量，经过一轮排序后,就会让序列大致有序，
* 然后再不断的缩小增量，进行插入排序，直到增量为 1 ，即整个排序结束。
* @param array 待排序数组
*/
private static void shellSort(int[] array) {
//根据克努特序列选取我们第一次的增量
int interval = 1;
while (interval <= array.length / 3) {
interval = interval * 3 + 1;
}
//控制增量步长
for (int step = interval; step > 0; step = (step - 1) / 3) {
//控制循环次数
for (int i = step; i < array.length; i++) {
//控制插入元素
for (int j = i; j >= step; j -= step) {
if (array[j] < array[j - step]) {
int temp = array[j];
array[j] = array[j - step];
array[j - step] = temp;
}
}
}
}
}
}
Sort results:
[-2, 1, 5, 8, 16, 21, 24, 36, 52]
5. Quick Sort
Divide and conquer: compare size, repartition
- Take a number from the array as the base number.
- Partition: Put all the numbers greater than or equal to this number to its right, and all the numbers smaller than it to its left.
- Then repeat the second step for the left and right intervals until each interval has only one number.
/**
* @description 快速排序
* @author: PeiChen
* @version 1.0
*/
public class QuickSort {
public static void main(String[] args) {
int[] arr = {
1, 24, 16, 8, 36, 5, 21, -2, 52};
quickSort(arr,0,arr.length - 1);
System.out.println(Arrays.toString(arr));
}
private static void quickSort(int[] array, int start, int end) {
//找出分开左右分区的索引位置，然后分别对左右两区进行递归排序
if (start < end) {
int index = partition(array, start, end);
quickSort(array,start,index - 1);
quickSort(array,index + 1,end);
}
}
/**
* 1.将基准数挖出形成第一个坑
* 2.由后向前找比他小的数,找到后挖出此数填到前一个坑中
* 3.由前向后找比他大或等于的数,找到后也挖出此数填到前一个坑中
* 4.再重复执行2,3两步骤。
* @param array 待分区数组
* @param start 起始位置
* @param end 终止位置
* @return 分区的索引
*/
private static int partition(int[] array, int start, int end) {
int i = start;
int j = end;
//将基准数挖出形成第一个坑
int baseVal = array[i];
while (i < j) {
//由后向前找比较小的数，找到后挖出此数填到一个坑中
while (i < j && array[j] >= baseVal) {
j--;
}
if (i < j) {
array[i] = array[j];
i++;
}
//由前向后找比较大或等于的数，找到后也挖出此数填到前一个坑中
while (i < j && array[i] < baseVal) {
i++;
}
if (i < j) {
array[j] = array[i];
j--;
}
//把基准数填到最后一个坑中
array[i] = baseVal;
}
return i;
}
}
Sort results:
[-2, 1, 5, 8, 16, 21, 24, 36, 52]
6. Merge sort
Merge sort (Merge Sort) is a method of sorting using the idea of merging. Its principle is assuming that the initial sequence has N records, it can be regarded as N ordered subsequences, the length of each subsequence is 1, and then merged in pairs to obtain N/2 ordered sequences of length 2 or 1 The subsequences are merged two by two... Repeat until an ordered sequence of length N is obtained. This sorting method is called 2-way merge sorting.
/**
* @description 归并排序
* @author: PeiChen
* @version 1.0
*/
public class MergeSort {
public static void main(String[] args) {
int[] arr = {
1, 24, 16, 8, 36, 5, 21, -2, 52};
split(arr,0,arr.length - 1);
System.out.println(Arrays.toString(arr));
}
/**
* 拆分数组
* @param arr 原始数组
* @param startIndex 起始索引
* @param endIndex 结束索引
*/
private static void split(int[] arr, int startIndex, int endIndex) {
//寻找中间索引
int centerIndex = (startIndex + endIndex) / 2;
if (startIndex < endIndex) {
split(arr,startIndex,centerIndex);
split(arr,centerIndex + 1,endIndex);
merge(arr,startIndex,centerIndex,endIndex);
}
}
/**
* 归并数组
* @param arr 原始数组
* @param startIndex 起始索引
* @param centerIndex 中间索引
* @param endIndex 结束索引
*/
private static void merge(int[] arr, int startIndex, int centerIndex, int endIndex) {
int[] tempArr = new int[endIndex - startIndex + 1];
//定义左边数组的起始索引
int i = startIndex;
//定义右边数组的起始索引
int j = centerIndex + 1;
//临时数组的起始索引
int index = 0;
//比较两个数组中的元素大小，然后往临时数组里添加
while (i <= centerIndex && j <= endIndex) {
if (arr[i] <= arr[j]) {
tempArr[index] = arr[i];
i++;
} else {
tempArr[index] = arr[j];
j++;
}
index++;
}
//处理剩余元素
while (i <= centerIndex) {
tempArr[index] = arr[i];
i++;
index++;
}
while (j <= endIndex) {
tempArr[index] = arr[j];
j++;
index++;
}
//将临时数组的元素取到原始数组中
for (int k = 0; k < tempArr.length; k++) {
arr[startIndex + k] = tempArr[k];
}
}
}
Sort results:
[-2, 1, 5, 8, 16, 21, 24, 36, 52]
7. Radix sort
Cardinality sorting is different from the various types of sorting introduced before. The sorting methods introduced above are more or less achieved by using comparisons and moving records. The implementation of radix sorting does not need to compare keywords, but only needs to perform two operations of "assignment" and "collection" on keywords.
/**
* @description 基数排序(桶排序)(此案例只适用于非负数，负数再加一个判断即可)
* @author: PeiChen
* @version 1.0
*/
public class BaseSort {
public static void main(String[] args) {
int[] arr = {
1, 24, 16, 8, 36, 28, 5, 21, 2, 52, 666, 127, 520, 68};
baseSort(arr);
System.out.println(Arrays.toString(arr));
}
/**
* 基数排序：先分配再收集
* @param arr 待排序数组
*/
private static void baseSort(int[] arr) {
//定义二维数组，放10个桶
int[][] tempArr = new int[10][arr.length];
//定义统计数组
int[] counts = new int[10];
//计算最大数的位数
int maxLength = getMaxLength(arr);
//循环次数
for (int i = 0, k = 1; i < maxLength; i++, k*= 10) {
//分配
for (int value : arr) {
//获取每位上的数字
int everyNum = value / k % 10;
//放到对应的桶内，并且对每个桶中的元素计数
tempArr[everyNum][counts[everyNum]++] = value;
}
//收集
int index = 0;
for (int m = 0; m < counts.length; m++) {
if (counts[m] != 0) {
for (int n = 0; n < counts[m]; n++) {
//从桶中取出元素放入原数组
arr[index++] = tempArr[m][n];
}
//清空上一次统计的个数
counts[m] = 0;
}
}
}
}
private static int getMaxLength(int[] arr) {
int max = arr[0];
for (int num : arr) {
if (num > max) {
max = num;
}
}
return String.valueOf(max).length();
}
}
Sort results:
[1, 2, 5, 8, 16, 21, 24, 28, 36, 52, 68, 127, 520, 666]
8. Heap sort
Heap sort is a sorting algorithm designed using the data structure of the heap, and heap sort is a selection sort.
The basic idea of heap sorting:
- Construct the sequence to be sorted into a large top heap. At this time, the maximum value of the entire sequence is the root node at the top of the heap.
- Swap it with the end element, and the end is the maximum value.
- Then reconstruct the remaining n-1 elements into a heap, so that the second smallest value of n elements will be obtained.
- So repeated execution, you can get an ordered sequence.
/**
* @description 堆排序
* @author: PeiChen
* @version 1.0
*/
public class HeapSort {
public static void main(String[] args) {
int[] arr = {
1, 24, 16, 8, 36, 28, 5, 21, 2, 52, 666, 127, 520, 68};
//开始调整的位置
int startIndex = (arr.length - 1) / 2;
//循环调整大顶堆
for (int i = startIndex; i >= 0; i--) {
toBigHeap(arr,arr.length,i);
}
//循环把根元素与最后一个元素进行交换
for (int i = arr.length - 1; i > 0; i--) {
int temp = arr[0];
arr[0] = arr[i];
arr[i] = temp;
//调整完之后继续把剩余元素调整为大顶堆
toBigHeap(arr,i,0);
}
System.out.println(Arrays.toString(arr));
}
/**
* 把一个数组转换成大顶堆
* @param arr 原始数组
* @param size 调整的元素个数
* @param index 开始调整的位置
*/
private static void toBigHeap(int[] arr, int size, int index) {
//获取左右子节点的索引
int leftNodeIndex = index * 2 + 1;
int rightNodeIndex = index * 2 + 2;
//查找最大节点所对应的索引
int maxIndex = index;
if (leftNodeIndex < size && arr[leftNodeIndex] > arr[maxIndex]) {
maxIndex = leftNodeIndex;
}
if (rightNodeIndex < size && arr[rightNodeIndex] > arr[maxIndex]) {
maxIndex = rightNodeIndex;
}
//如果最大元素不是当前元素，则需调换位置
if (maxIndex != index) {
int temp = arr[maxIndex];
arr[maxIndex] = arr[index];
arr[index] = temp;
//交换完位置以后很有可能会破坏原先大顶堆结构，所以还需重新调换
toBigHeap(arr,size,maxIndex);
}
}
}
Sort results:
[1, 2, 5, 8, 16, 21, 24, 28, 36, 52, 68, 127, 520, 666]