## Sorting an Array Using Shellsort

In this guide, we will sort the array using Shell’s algorithm – Shellsort. The algorithm works like this.

The array is divided into groups, each of which consists of two elements. The distance between pairs of elements is d=n/2, where n is the number of array elements. The elements of the pair are compared to each other and if needed, reversed. Then groups merge in pairs. Each new group has 4 elements, and distance between elements is d=d/2. Sorting is performed in the middle of the group, and then the groups are merged. The process continues as long as the distance between items becomes 1. At this point, the array is sorted by the method of insertion. The number of comparisons is 0.5*n3/2.

The solution in C++ looks like this:

#include<iostream.h> #include<conio.h> #include<iomanip.h> int v[20], n; int m_comp=0, m_move=0 void input() { cout<<"Enter number of elements (n<20)"<<endl; cin>>n; cout<<"Enter array"<<endl; for(int i=0;i<n;i++) cin>>v[i]; } void output() { for(int i=0;i<n;i++) cout<<setw(5)<<v[i]<<" "; cout<<endl; } void sort() { for(int k=n/2;k>0;k/=2) for(int i=k;i<n;i++) { m_comp++; for(int j=i-k;j>=0&&v[j]>v[j+k];j-=k) { int temp=v[j]; v[j]=v[j+k]; v[j+k]=temp; m_move++; output(); } } } void main() { cout<<"Sorting by Shell"<<endl; input(); cout<<"Array before sort"<<endl; output(); sort(); cout<<"Array after sort"<<endl; output(); cout<<"m_comp="<<m_comp<<" m_move="<<m_move<<endl; getch(); }

And the work of the program can be illustrated using this table:

Original array: a_input= {20,-5, 8, 7, 0, 3, -1, 4};

№ of iteration | Distance between the compared groups of elements | Groups of elements | Result of the iteration |

i=1 | d=n/2=8/2=4 | {{20,-5, 8, 7} {0, 3,-1, 4}} | {{0,-5,-1, 4} {20,3,8, 7}} |

i=2 | d=d/2=4/2=2 | {{0,-5} {-1,4} {20,3} {8,7}}{{-1,-5} {0,4} {20,3} {8,7}}{{-1, -5} {0, 3} {20,4} {8,7}} | {{-1,-5}{0,3}{8,4}{20,7}} |

i=3 | d=d/2=2/2=1 | {{-1} {-5} {0} {3} {8} {4} {20} {7}}{{-5} {-1} {0} {3} {4} {8} {7} {20}} | {-5,-1, 0, 3, 4, 7, 8, 20} |

End |

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