Internal Sorting: Shellsort: Sorting by Insertion

Shellsort:希尔排序

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Animation

Shellsort with gaps 23, 10, 4, 1 in action.

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The step-by-step process of replacing pairs of items during the shell sorting algorithm.

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Complexity

Class Sorting algorithm Data structure Array Worst case performance O(n2) Best case performance O(nlog2n) Average case performance depends on gap sequence Worst case space complexity О(n) total, O(1) auxiliary

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Algorithm D

Algorithm D (Shellsort).Records R1,...,RN are rearranged in place; after
sorting is complete, their keys will be in order, K1<=...<=KN.Anauxiliary
sequence of increments ht−1,ht−2,...,h0 is used to control the sorting process,
where h0=1;proper choice of these increments can significantly decrease the
sorting time. This algorithm reduces to Algorithm S when t=1.
D1. [Loop on s.] Performstep D2 for s=t−1,t−2,...,0; then terminate the
algorithm.
D2. [Loop on j.] Set h←hs, and perform steps D3 through D6 for h
(We will use a straight insertion method to sort elements that are h positions
apart, so that Ki<=Ki+h for 1<=i<=N−h. Steps D3 through D6 are
essentially the same as steps S2 through S5, respectively, in Algorithm S.)
D3. [Set up i,K,R.]Set i←j−h,K←Kj,R←Rj.
D4. [Compare K:Ki.] If K>=Ki, go to step D6.
D5. [Move Ri, decrease i.] Set Ri+h←Ri, then i←i−h. If i>0, go back to
step D4.
D6. [R into Ri+h.] Set Ri+h←R. |

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Data table

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Java program

In this program, R1,…,RN weresimplified to K1,…,KN.

/** * Created with IntelliJ IDEA. * User: 1O1O * Date: 11/23/13 * Time: 10:01 PM * :)~ * Shellsort:Sorting by Insertion:Internal Sorting */public class Main {    public static void main(String[] args) {        int N = 16;        int[] K = new int[17];        /*Prepare the data*/        K[1] = 503;        K[2] = 87;        K[3] = 512;        K[4] = 61;        K[5] = 908;        K[6] = 170;        K[7] = 897;        K[8] = 275;        K[9] = 653;        K[10] = 426;        K[11] = 154;        K[12] = 509;        K[13] = 612;        K[14] = 677;        K[15] = 765;        K[16] = 703;        /*Output unsorted Ks*/        System.out.println("Unsorted Ks:");        for(int i=1; i<=N; i++){            System.out.println(i+":"+K[i]);        }        System.out.println();        /*Kernel of the Algorithm!*/        for(int h=N/2; h>=1; h/=2){            for(int j=h+1; j<=N; j+=h){                int Key = K[j];                int i = j-h;                while (i > 0){                    if(Key >= K[i]){                        K[i+h] = Key;                        break;                    }else {                        K[i+h] = K[i];                        i-=h;                    }                }                if(i <= 0){                    K[i+h] = Key;                }            }        }        /*Output sorted Ks*/        System.out.println("Sorted Ks:");        for(int i=1; i<=N; i++){            System.out.println(i+":"+K[i]);        }    }}

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Outputs

UnsortedKs:1:5032:873:5124:615:9086:1707:8978:2759:65310:42611:15412:50913:61214:67715:76516:703SortedKs:1:612:873:1544:1705:2756:4267:5038:5099:51210:61211:65312:67713:70314:76515:89716:908

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Reference

<< The art of computer programming: Sorting and Searching >> VOLUME 3, DONALD E. KNUTH
https://en.wikipedia.org/wiki/Shellsort