Shell sort
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Shell sort is an improvement on insertion sort that aims to overcome insertion sort's inefficiency for average cases. It works by comparing elements separated by a distance to form multiple sublists, then applying insertion sort on each sublist to move elements towards their correct positions in a way that allows elements to take bigger steps. This reduces the number of comparisons needed compared to regular insertion sort.
Shell sort
- 1. Ver. 1.0 Shell Sort Shell sort algorithm: Insertion sort is an efficient algorithm only if the list is already partially sorted and results in an inefficient solution in an average case. To overcome this limitation, a computer scientist, D.L. Shell proposed an improvement over the insertion sort algorithm. The new algorithm was called shell sort after the name of its proposer. Sorting Data by Using Shell Sort
- 2. Ver. 1.0 Shell Sort Shell sort algorithm: Improves insertion sort by comparing the elements separated by a distance of several positions to form multiple sublists Applies insertion sort on each sublist to move the elements towards their correct positions Helps an element to take a bigger step towards its correct position, thereby reducing the number of comparisons Implementing Shell Sort Algorithm
- 3. Ver. 1.0 Shell Sort To understand the implementation of shell sort algorithm, consider an unsorted list of numbers stored in an array. Implementing Shell Sort Algorithm (Contd.) 210 43 70 104030 80arr 20 5 6 7 8 9 10 90 110 75 60 45
- 4. Ver. 1.0 Shell Sort To apply shell sort on this array, you need to: Select the distance by which the elements in a group will be separated to form multiple sublists. Apply insertion sort on each sublist to move the elements towards their correct positions. Implementing Shell Sort Algorithm (Contd.) 210 43 70 104030 80arr 20 5 6 7 8 9 10 90 110 75 60 45
- 5. Ver. 1.0 Shell Sort List 1 = Implementing Shell Sort Algorithm (Contd.) 210 43 arr 5 6 7 8 9 10 Increment = 3 Pass = 1 630 9 70 609010 741 10 30 4511080List 2 = 852 40 7520List 3 = 70 104030 80 20 90 110 75 60 45
- 6. Ver. 1.0 Shell Sort Implementing Shell Sort Algorithm (Contd.) 630 9 70 609010 741 10 30 4511080List 2 = 852 40 7520List 3 = Apply insertion sort to sort the three lists The lists are sorted 10 907060 30 1108045 20 7540 List 1 =
- 7. Ver. 1.0 Shell Sort Implementing Shell Sort Algorithm (Contd.) 210 43 10 602030 45arr 40 5 6 7 8 9 10 70 80 75 90 110 630 9 741 10 30List 2 = 852 75List 3 = 30 75 10 60 70 90 45 80 110 20 40 List 1 =
- 8. Ver. 1.0 Shell Sort Implementing Shell Sort Algorithm (Contd.) 210 43 10 602030 45arr 40 5 6 7 8 9 10 70 80 75 90 110 Increment = 2 Pass = 2List 1 = 420 6 10 704520 531 7 30 804060List 2 = 75 110 8 10 90 9
- 9. Ver. 1.0 Shell Sort Implementing Shell Sort Algorithm (Contd.) List 1 = 420 6 10 704520 531 7 30 804060List 2 = 75 110 8 10 90 9 Apply insertion sort on each sublist
- 10. Ver. 1.0 Shell Sort Implementing Shell Sort Algorithm (Contd.) List 1 = 420 6 10 704520 531 7 30 806040List 2 = 75 110 8 10 90 9 The lists are now sorted
- 11. Ver. 1.0 Shell Sort Implementing Shell Sort Algorithm (Contd.) List 1 = 420 6 10 704520 531 7 30 806040List 2 = 75 110 8 10 90 9 210 43 10 402030 45arr 60 5 6 7 8 9 10 70 80 75 90 110
- 12. Ver. 1.0 Shell Sort Implementing Shell Sort Algorithm (Contd.) 210 43 10 402030 45arr 60 5 6 7 8 9 10 70 80 75 90 110 Increment = 1 Pass = 3 Apply insertion sort to sort the list
- 13. Ver. 1.0 Shell Sort Implementing Shell Sort Algorithm (Contd.) 210 43 10 403020 45arr 60 5 6 7 8 9 10 70 75 80 90 110 Increment = 1 Pass = 3 The list is now sorted
- 14. Ver. 1.0 Shell Sort Which of the following sorting algorithms compares the elements separated by a distance of several positions to sort the data? The options are: 1. Insertion sort 2. Selection sort 3. Bubble sort 4. Shell sort Just a minute Answer: 4. Shell sort
- 15. Ver. 1.0 Shell Sort In this session, you learned that: Sorting is a process of arranging data in some pre-defined order of a key value. The order can be either ascending or descending. There are various sorting algorithms that are used to sort data. Some of them are: Bubble sort Selection sort Insertion sort Shell sort Merge sort Quick sort Heap sort Summary
- 16. Ver. 1.0 Shell Sort To select an appropriate algorithm, you need to consider the following: Execution time Storage space Programming effort Bubble sort and selection algorithms have a quadratic order of growth, and are therefore suitable for sorting small lists only. Insertion sort performs different number of comparisons depending on the initial ordering of elements. When the elements are already in the sorted order, insertion sort needs to make very few comparisons. Insertion sort is an efficient algorithm than bubble sort and selection sort if the list that needs to be sorted is nearly sorted. Summary (Contd.)
- 17. Ver. 1.0 Shell Sort Shell sort improves insertion sort by comparing the elements separated by a distance of several positions. This helps an element to take a bigger step towards its correct position, thereby reducing the number of comparisons. Summary (Contd.)
Editor's Notes
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- #15: In this slide you need to show the calculation to determine the sum of an arithmetic progression for bubble sort algorithm. Refer to student guide.