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Chapter 7: Sorting (Insertion Sort, Shellsort)

Chapter 7: Sorting (Insertion Sort, Shellsort). CE 221 Data Structures and Algorithms. T ext : Read Weiss, § 7 . 1 – 7 . 4. Preliminaries. Main memory sorting algorithms All algorithms are Interchangeable; an array containing the N elements will be passed.

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Chapter 7: Sorting (Insertion Sort, Shellsort)

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  1. Chapter 7: Sorting(Insertion Sort, Shellsort) CE 221 Data Structures and Algorithms Text: Read Weiss, § 7.1 – 7.4 Izmir University of Economics

  2. Preliminaries • Main memory sorting algorithms • All algorithms are Interchangeable; an array containing the N elements will be passed. • “<“, “>” (comparison) and “=“ (assignment) are the only operations allowed on the input data : comparison-based sorting Izmir University of Economics

  3. Contents Selection Sort Insertion Sort Shell Sort

  4. CE 221 Selection Sort

  5. Selection Sort Given the input in array a[N] below, compare a[i] to a[min].

  6. Selection Sort

  7. Selection Sort

  8. Selection Sort

  9. Selection Sort

  10. Selection Sort

  11. Selection Sort

  12. Selection Sort

  13. Selection Sort

  14. Selection Sort

  15. Selection Sort

  16. Selection Sort

  17. Selection Sort

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  20. Selection Sort

  21. Selection Sort

  22. Selection Sort

  23. Selection Sort

  24. Time Analysis of Selection Sort Comparisons: Exchanges: N

  25. CE 221 Insertion Sort

  26. Insertion Sort

  27. Insertion Sort

  28. Insertion Sort

  29. Insertion Sort

  30. Insertion Sort

  31. Insertion Sort

  32. Insertion Sort

  33. Insertion Sort

  34. Insertion Sort

  35. Insertion Sort

  36. Insertion Sort

  37. Insertion Sort

  38. Insertion Sort

  39. Time Analysis Number of comparisions: Number of excahnges:

  40. Effective Algorithms Shell Sort

  41. Shell Sort Move entries more than one position at a time by h–sorting the array • Start at L and look at every 4th element and sort it • Start at E and look at every 4th ekement and sort it • Start at E and look at every 4th ekement and sort it • Start at A and look at every 4th ekement and sort it

  42. Decreasing sequence of values of h

  43. Example

  44. Example: S O R T E X A M P L E Result: A E E L M O P R S T X

  45. Implementation

  46. Time Analysis

  47. Shell Sort vs Insertion Sort • Insertion sort compares every single item with all the rest elements of the list in order to find its place, • Shell sort compares items that lie far apart. This makes smaller elements to move faster to the front of the list.

  48. Yes !!!

  49. Insertion Sort Analysis • One of the simplest sorting algorithms • Consists of N-1 passes. • for pass p = 1 to N-1 (0 thru p-1 already known to be sorted) • elements in position 0 trough p(p+1 elements)are sorted by moving the element left until a smaller element is encountered. Izmir University of Economics

  50. Insertion Sort - Algorithm N*N iterations, hence, time complexity = O(N2) in the worst case.This bound is tight (input in the reverse order). Number of element comparisons in the inner loop is p, summing up over all p = (1+2)+(1+3)+...+N-1 = Θ(N2). If the input is sorted O(N). Izmir University of Economics

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