排序之希尔排序(shell sort)

前言

　　本篇博客是在伍迷兄的博客基础上进行的，其博客地址点击就可以进去，里面好博客很多，我的排序算法都来自于此；一些数据结构方面的概念我就不多阐述了，伍迷兄的博客中都有详细讲解，而我写这些博客只是记录自己学习过程，加入了一些自己的理解，同时也希望给别人提供帮助。

前提故事

　　骚年在上次与博主进行了直接插入排序的讨论后，找到了博主，说：“博主，对于直接插入排序，我有重大的发现”，博主想了想，就问：“什么发现？”，骚年：“我发现了如下两点”

　　　　1）当序列的个数比较少时，直接插入排序效率高；这个好理解，个数比较少，那么插入的次数也就少了，博主就说：“恩，这个发现不难，却也需要细心”。

　　　　2）如果序列本身就是基本有序，那么直接插入排序效率高；博主：“嗯？”，骚年解释道：“你看直接插入排序的核心代码：”

　　　　 for(int i=1; i<len; i++){
            for(int j=i-1; j>=0&&arr[j]>arr[j+1]; j--){
                swap(arr,j,j+1);
            }
        }

　　　　骚年接着道：“如果序列有序，那么j>=0&&arr[j]>arr[j+1]条件就是不满足的，插入操作就不会执行，效率自然就高了。”

　　　　博主：“然后了？”。

　　　　骚年：“那么我们是不是可以在这两点上做点事，来提高直接插入排序在普通序列上的效率了？”。

　　　　上述两个条件过于苛刻，现实中记录少或者基本有序都属于特殊情，有条件当然是好，条件不存在，我们创造条件，也是可以去做的；骚年与博主进行了研究与讨论，我们可以对序列进行分组，分割成若干个子序列，然后对每个子序列分别进行直接插入排序，当整个序列都基本有序时，注意只是基本有序时，再对全体记录进行一次直接插入排序。

　　　　此时一定有人开始疑惑了。这不对呀，比如我们现在有序列是{5,3,7,9,1,6,4,8,2}，现在将它分成三组，{5,3,7}， {9,1,6}，{4,8,2}，哪怕将它们各自排序排好了，变成{3,5,7}，{1,6,9}，{2,4,8}，再合并它们成 {3,5,7,1,6,9,2,4,8}，此时，这个序列还是杂乱无序，谈不上基本有序，要排序还是重来一遍直接插入有序，这样做有用吗？需要强调一下，所谓的基本有序，就是小的关键字基本在前面，大的基本在后面，不大不小的基本在中间，像{2,1,3,6,4,7,5,8,9}这样可以称为基本有序了。但像{3,5,7,1,6,9,2,4,8}这样的7在第三位，2在倒数第三位就谈不上基本有序。
那么问题就来了，我们分割待排序记录的目的是减少待排序记录的个数，并使整个序列向基本有序发展。而如上面这样分完组后，就各自排序的方法达不到我们的要求。因此，我们需要采取跳跃分割的策略：将相距某个“增量”的记录组成一个子序列，这样才能保证在子序列内分别进行直接插入排序后得到的结果是基本有序而不是局部有序。

基本思想

　　将整个序列按照相距某个“增量”进行拆分，然后逐个对子序列进行直接插入排序，使得得到的结果基本有序，最后对基本有序的序列进行一次直接插入排序，使得整个序列有序

代码实现

　　java实现

       /**
     * 希尔排序
     * @param arr 目标序列
     */
    public static void shellSort(int[] arr){
        int len = arr.length;
        for(int gap=len/2; gap>=1; gap=gap/2){                    //拆分整个序列，元素间距为gap(也就是增量)
            //对子序列进行直接插入排序
            for(int i=gap+1; i<len; i++){
                for(int j=i-gap; j>=0&&arr[j]>arr[j+gap]; j=j-gap){
                    swap(arr,j,j+gap);
                }
            }
        }
    }

执行过程模拟

　　1）程序开始执行，初始序列为{5,3,7,9,1,6,4,8,2}，如下图：

　　2）初始gap=len/2=4

　　　　2.1）i=gap=4，初始j=0；比较arr[j]与arr[j+gap],即arr[0]与arr[4],如下图：

　　　　　　j=j-gap=-4，跳出，i++，i=5

　　　　2.2）i=5，j=i-gap=1，arr[1]=3 < arr[5]=6,不交换数据，如下图：

　　　　aaarticlea/png;base64,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" alt="" />

　　　　　　j=j-gap=-3,跳出，i++,i=6

　　　　2.3)同理，当i=6，7时，序列如下图：

　　　　2.4）当i=8时，序列如下：

　　　　那么gap=4时，最终序列为

　　3）gap=gap/2=2

　　　　3.1)i=gap=2,j=i-gap=0,arr[0]=1 < arr[2]=4不交换，j=j-gap=-2，i++，此时序列为：

　　　　3.2）i=3，j=i-gap=1，arr[1]=3 < arr[3]=8,不交换，j=j-gap=-1，i++,此时序列为：

　　　　3.3）同理，i=4时：

　　　　3.4）i=5时：

aaarticlea/png;base64,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" alt="" />

　　　　3.5）i=6时：

　　　　3.6）i=7时：

　　　　3.7）i=8时：

　　4）gap=gap/2=1，此时

　　　　for(int gap=len/2; gap>=1; gap=gap/2){                    //拆分整个序列，元素间距为gap(也就是增量)
            //对子序列进行直接插入排序
            for(int i=gap; i<len; i++){
                for(int j=i-gap; j>=0&&arr[j]>arr[j+gap]; j=j-gap){
                    swap(arr,j,j+gap);
                }
            }

　　　　就是

            //对子序列进行直接插入排序
            for(int i=1; i<len; i++){
                for(int j=i-1; j>=0&&arr[j]>arr[j+1]; j=j-1){
                    swap(arr,j,j+1);
                }
            }

　　　　相信大家都发现了，上面代码就是我们的直接插入排序，那么具体的模拟过程我也就不再赘述了，不懂的可以去看排序之直接插入排序

　　至此，整个序列就有序了。

难解之处

　通过这段代码的剖析，相信大家有些明白，希尔排序的关键并不是随便的分组后各自排序，而是将相隔某个“增量”的记录组成一个子序列，实现跳跃式的移动，使得排序的效率提高。这里“增量”的选取就非常关键了，本例中是以gap=gap/2的方式选取增量的，可究竟应该选取什么样的增量才是最好，目前还是一个数学难题，迄今为止还没有人找到一种最好的增量序列。不过大量的研究表明，当增量序列为dlta[k]=2^t-k+1-1（0≤k≤t≤⌊log2(n+1)⌋）时，可以获得不错的效率。需要注意的是，增量序列的最后一个增量值必须等于1才行。　