小朋友学数据结构(9):希尔排序
(一)基本思想
希尔排序是把记录按下标的一定增量分组,对每组使用直接插入排序算法排序;随着增量逐渐减少,每组包含的关键词越来越多,当增量减至1时,整个文件恰被分成一组,算法便终止。
(二)例子
有一个数组,其原始数组为:
![](http://upload-images.jianshu.io/upload_images/6946981-6d36b509583f302c.png?imageMogr2/auto-orient/strip%7CimageView2/2/w/831/format/webp)
2-1.png
取初始增量gap = length / 2 = 5,这样就将整个数组分为5组(每组用相同的颜色表示)
![](http://upload-images.jianshu.io/upload_images/6946981-3fbc48a67af14e83.png?imageMogr2/auto-orient/strip%7CimageView2/2/w/875/format/webp)
2-2.png
将这5组的数据分别按由小到大的顺序排列,结果为
![](http://upload-images.jianshu.io/upload_images/6946981-c435a5e74c91c63d.png?imageMogr2/auto-orient/strip%7CimageView2/2/w/859/format/webp)
2-3.png
缩小增量gap = gap / 2 = 2,整个数组被分成两组
![](http://upload-images.jianshu.io/upload_images/6946981-687ac0832f5d3ed8.png?imageMogr2/auto-orient/strip%7CimageView2/2/w/845/format/webp)
2-4.png
将这两组的数据分别按由小到大的顺序排列,结果为
![](http://upload-images.jianshu.io/upload_images/6946981-d6b1ea7666a3af15.png?imageMogr2/auto-orient/strip%7CimageView2/2/w/822/format/webp)
2-5.png
再次缩小增量,整个数组被分为1组
![](http://upload-images.jianshu.io/upload_images/6946981-3bed101a709d4a54.png?imageMogr2/auto-orient/strip%7CimageView2/2/w/826/format/webp)
2-6.png
将这组数据按从小到大的顺序排序,最终结果为
![](http://upload-images.jianshu.io/upload_images/6946981-21c9c65cbc895d20.png?imageMogr2/auto-orient/strip%7CimageView2/2/w/826/format/webp)
2-7.png
(三)代码
1 C语言实现
#include<stdio.h>
void swap(int &a, int &b)
{
a ^= b;
b ^= a;
a ^= b;
}
void shellsort(int a[], int n)
{
int i, j, gap;
for (gap = n / 2; gap > 0; gap /= 2)
{
for (i = gap; i < n; i++)
{
for (j = i - gap; j >= 0 && a[j] > a[j + gap]; j -= gap)
{
swap(a[j], a[j + gap]);
}
}
}
}
int main()
{
int arr[] = {49, 38, 65, 97, 76, 13, 27, 48, 55, 4};
printf("Original array: ");
int i;
int len = sizeof(arr)/sizeof(int);
for(i = 0; i < len; i++)
{
printf("%d ", arr[i]);
}
printf("\n");
shellsort(arr, len);
printf("Sorted array: ");
for(i = 0; i < len; i++)
{
printf("%d ", arr[i]);
}
printf("\n");
return 0;
}
2 Java实现
import java.util.Arrays;
public class Sort {
public static void shellSort(int[] a) {
int i, j, gap;
int len = a.length;
for (gap = len / 2; gap > 0; gap /= 2) {
for (i = gap; i < len; i++) {
for (j = i - gap; j >= 0 && a[j] > a[j + gap]; j -= gap) {
// 交换两个数
a[j] ^= a[j + gap];
a[j + gap] ^= a[j];
a[j] ^= a[j + gap];
}
}
}
}
public static void main(String[] args) {
int[] arr = {49, 38, 65, 97, 76, 13, 27, 48, 55, 4};
System.out.println("Original array: " + Arrays.toString(arr));
shellSort(arr);
System.out.println("Sorted array: " + Arrays.toString(arr));
}
}
3 运行结果
Original array: [49, 38, 65, 97, 76, 13, 27, 48, 55, 4]
Sorted array: [4, 13, 27, 38, 48, 49, 55, 65, 76, 97]
![](https://images2018.cnblogs.com/blog/1252410/201809/1252410-20180907233957270-2082990930.png)