1 using System;
2 using System.Collections.Generic;
3
4 namespace Com.Colobu.Algorithm.Insertion
5 {
6 /// <summary>
7 /// <b>Shell sort</b> is a sorting algorithm that is a generalization of insertion sort,
8 /// with two observations:
9 /// insertion sort is efficient if the input is "almost sorted"
10 /// insertion sort is typically inefficient because it moves values just one position at a time.
11 ///
12 /// 对有n个元素的可比较资料，先取一个小于n的整数d1作为第一个增量，
13 /// 把文件的全部记录分成d1个组。
14 /// 所有距离为d1的倍数的记录放在同一个组中。
15 /// 先在各组内进行直接插入排序；然后，取第二个增量d2<d1
16 /// 重复上述的分组和排序，直至所取的增量dt=1(dt<dt-1<…<d2<d1)，
17 /// 即所有记录放在同一组中进行直接插入排序为止。
18 /// 该方法实质上是一种分组插入方法。
19 ///
20 /// 平均时间复杂度:O(nlogn)
21 /// Stability:No
22 /// </summary>
23 public class ShellSortAlgorithm
24 {
25 public static void ShellSort<T>(IList<T> szArray) where T : IComparable
26 {
27 int i, j, k, gap;
28 T temp;
29
30 //gap sequence:a(n) = floor(fibonacci(n+1)^(1+sqrt(5)))
31 //the Fibonacci numbers (leaving out one of the starting 1's) to the power of twice the golden ratio
32 int[] gaps = { 1,5,13,43,113,297,815,1989,4711,11969,27901,84801,
33 213331,543749,1355339,3501671,8810089,21521774,
34 58548857,157840433,410151271,1131376761,2147483647 };
35
36 int n = szArray.Count;
37
38 //从素数序列中得到一个满足条件的最大的素数
39 for (k = 0; gaps[k] < n; k++) ;
40
41 while (--k >= 0)
42 {
43 gap = gaps[k]; //取增量
44
45 for (i = gap; i < n; i++) //按照此增量分组
46 {
47 temp = szArray[i];
48 j = i;
49 while (j >= gap && szArray[j - gap].CompareTo(temp) > 0) //将此组插入排序
50 {
51 szArray[j] = szArray[j - gap];
52 j = j - gap;
53 }
54 szArray[j] = temp;
55 }
56 }
57
58 }
59 }
60 }
61