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Sorting

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kamea
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Sorting. Chapter 8. Chapter Objectives. To learn how to use the standard sorting methods in the Java API To learn how to implement the following sorting algorithms: selection sort bubble sort insertion sort Shell sort merge sort heapsort quicksort

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  1. Sorting Chapter 8

  2. Chapter Objectives • To learn how to use the standard sorting methods in the Java API • To learn how to implement the following sorting algorithms: • selection sort • bubble sort • insertion sort • Shell sort • merge sort • heapsort • quicksort • To understand the differences in performance of these algorithms, and which to use for small, medium, and large arrays

  3. Introduction • Sorting entails arranging data in order • Familiarity with sorting algorithms is an important programming skill • The study of sorting algorithms provides insight into • problem solving techniques such as divide and conquer • the analysis and comparison of algorithms which perform the same task

  4. Using Java Sorting Methods • The Java API provides a class Arrayswith several overloaded sort methods for different array types • The Collections class provides similar sorting methods for Lists • Sorting methods for arrays of primitive types are based on the quicksort algorithm • Sorting methods for arrays of objects and Lists are based on the merge sort algorithm • Both algorithms are O(n log n)

  5. Using Java Sorting Methods (cont.)

  6. Selection Sort Section 8.2

  7. Selection Sort • Selection sort is relatively easy to understand • It sorts an array by making several passes through the array, selecting a next smallest item in the array each time and placing it where it belongs in the array • While the sort algorithms are not limited to arrays, throughout this chapter we will sort arrays for simplicity • All items to be sorted must be Comparable objects, so, for example, any int values must be wrapped in Integer objects

  8. Trace of Selection Sort • n= number of elements in the array • for fill = 0 to n – 2 do • Set posMin to the subscript of a smallest item in the subarray starting at subscript fill • Exchange the item at posMin with the one at fill 0 1 2 3 4 35 65 30 60 20

  9. Trace of Selection Sort (cont.) • n= number of elements in the array • for fill = 0 to n – 2 do • Set posMin to the subscript of a smallest item in the subarray starting at subscript fill • Exchange the item at posMin with the one at fill 0 1 2 3 4 35 65 30 60 20 fill

  10. Trace of Selection Sort (cont.) • n= number of elements in the array • for fill = 0 to n – 2 do • Set posMin to the subscript of a smallest item in the subarray starting at subscript fill • Exchange the item at posMin with the one at fill 0 1 2 3 4 35 65 30 60 20 fill posMin

  11. Trace of Selection Sort (cont.) • n= number of elements in the array • for fill = 0 to n – 2 do • Set posMin to the subscript of a smallest item in the subarray starting at subscript fill • Exchange the item at posMin with the one at fill 0 1 2 3 4 20 65 30 60 35 fill posMin

  12. Trace of Selection Sort (cont.) • n= number of elements in the array • for fill = 0 to n – 2 do • Set posMin to the subscript of a smallest item in the subarray starting at subscript fill • Exchange the item at posMin with the one at fill 0 1 2 3 4 20 65 30 60 35 fill posMin

  13. Trace of Selection Sort (cont.) • n= number of elements in the array • for fill = 0 to n – 2 do • Set posMin to the subscript of a smallest item in the subarray starting at subscript fill • Exchange the item at posMin with the one at fill 0 1 2 3 4 20 65 30 60 35 fill posMin

  14. Trace of Selection Sort (cont.) • n= number of elements in the array • for fill = 0 to n – 2 do • Set posMin to the subscript of a smallest item in the subarray starting at subscript fill • Exchange the item at posMin with the one at fill 0 1 2 3 4 20 30 65 60 35 fill posMin

  15. Trace of Selection Sort (cont.) • n= number of elements in the array • for fill = 0 to n – 2 do • Set posMin to the subscript of a smallest item in the subarray starting at subscript fill • Exchange the item at posMin with the one at fill 0 1 2 3 4 20 30 65 60 35 fill posMin

  16. Trace of Selection Sort (cont.) • n= number of elements in the array • for fill = 0 to n – 2 do • Set posMin to the subscript of a smallest item in the subarray starting at subscript fill • Exchange the item at posMin with the one at fill 0 1 2 3 4 20 30 65 60 35 fill posMin

  17. Trace of Selection Sort (cont.) • n= number of elements in the array • for fill = 0 to n – 2 do • Set posMin to the subscript of a smallest item in the subarray starting at subscript fill • Exchange the item at posMin with the one at fill 0 1 2 3 4 20 30 35 60 65 fill posMin

  18. Trace of Selection Sort (cont.) • n= number of elements in the array • for fill = 0 to n – 2 do • Set posMin to the subscript of a smallest item in the subarray starting at subscript fill • Exchange the item at posMin with the one at fill 0 1 2 3 4 20 30 35 60 65 fill posMin

  19. Trace of Selection Sort (cont.) • n= number of elements in the array • for fill = 0 to n – 2 do • Set posMin to the subscript of a smallest item in the subarray starting at subscript fill • Exchange the item at posMin with the one at fill 0 1 2 3 4 20 30 35 60 65 fill posMin

  20. Trace of Selection Sort (cont.) • n= number of elements in the array • for fill = 0 to n – 2 do • Set posMin to the subscript of a smallest item in the subarray starting at subscript fill • Exchange the item at posMin with the one at fill 0 1 2 3 4 20 30 35 60 65 fill posMin

  21. Trace of Selection Sort (cont.) • n= number of elements in the array • for fill = 0 to n – 2 do • Set posMin to the subscript of a smallest item in the subarray starting at subscript fill • Exchange the item at posMin with the one at fill 0 1 2 3 4 20 30 35 60 65

  22. Trace of Selection Sort Refinement • for fill = 0 to n – 2 do • Initialize posMin to fill • for next = fill + 1 to n – 1 do • if the item at next is less than the item at posMin • Reset posMin to next • Exchange the item at posMin with the one at fill 0 1 2 3 4 35 65 30 60 20

  23. Trace of Selection Sort Refinement (cont.) • for fill = 0 to n – 2 do • Initialize posMin to fill • for next = fill + 1 to n – 1 do • if the item at next is less than the item at posMin • Reset posMin to next • Exchange the item at posMin with the one at fill 0 1 2 3 4 35 65 30 60 20 fill

  24. Trace of Selection Sort Refinement (cont.) • for fill = 0 to n – 2 do • Initialize posMin to fill • for next = fill + 1 to n – 1 do • if the item at next is less than the item at posMin • Reset posMin to next • Exchange the item at posMin with the one at fill 0 1 2 3 4 35 65 30 60 20 fill posMin

  25. Trace of Selection Sort Refinement (cont.) • for fill = 0 to n – 2 do • Initialize posMin to fill • for next = fill + 1 to n – 1 do • if the item at next is less than the item at posMin • Reset posMin to next • Exchange the item at posMin with the one at fill 0 1 2 3 4 35 65 30 60 20 fill next posMin

  26. Trace of Selection Sort Refinement (cont.) • for fill = 0 to n – 2 do • Initialize posMin to fill • for next = fill + 1 to n – 1 do • if the item at next is less than the item at posMin • Reset posMin to next • Exchange the item at posMin with the one at fill 0 1 2 3 4 35 65 30 60 20 fill next posMin

  27. Trace of Selection Sort Refinement (cont.) • for fill = 0 to n – 2 do • Initialize posMin to fill • for next = fill + 1 to n – 1 do • if the item at next is less than the item at posMin • Reset posMin to next • Exchange the item at posMin with the one at fill 0 1 2 3 4 35 65 30 60 20 fill next posMin

  28. Trace of Selection Sort Refinement (cont.) • for fill = 0 to n – 2 do • Initialize posMin to fill • for next = fill + 1 to n – 1 do • if the item at next is less than the item at posMin • Reset posMin to next • Exchange the item at posMin with the one at fill 0 1 2 3 4 35 65 30 60 20 fill next posMin

  29. Trace of Selection Sort Refinement (cont.) • for fill = 0 to n – 2 do • Initialize posMin to fill • for next = fill + 1 to n – 1 do • if the item at next is less than the item at posMin • Reset posMin to next • Exchange the item at posMin with the one at fill 0 1 2 3 4 35 65 30 60 20 fill next posMin

  30. Trace of Selection Sort Refinement (cont.) • for fill = 0 to n – 2 do • Initialize posMin to fill • for next = fill + 1 to n – 1 do • if the item at next is less than the item at posMin • Reset posMin to next • Exchange the item at posMin with the one at fill 0 1 2 3 4 35 65 30 60 20 fill next posMin

  31. Trace of Selection Sort Refinement (cont.) • for fill = 0 to n – 2 do • Initialize posMin to fill • for next = fill + 1 to n – 1 do • if the item at next is less than the item at posMin • Reset posMin to next • Exchange the item at posMin with the one at fill 0 1 2 3 4 35 65 30 60 20 fill next posMin

  32. Trace of Selection Sort Refinement (cont.) • for fill = 0 to n – 2 do • Initialize posMin to fill • for next = fill + 1 to n – 1 do • if the item at next is less than the item at posMin • Reset posMin to next • Exchange the item at posMin with the one at fill 0 1 2 3 4 35 65 30 60 20 fill next posMin

  33. Trace of Selection Sort Refinement (cont.) • for fill = 0 to n – 2 do • Initialize posMin to fill • for next = fill + 1 to n – 1 do • if the item at next is less than the item at posMin • Reset posMin to next • Exchange the item at posMin with the one at fill 0 1 2 3 4 35 65 30 60 20 fill next posMin

  34. Trace of Selection Sort Refinement (cont.) • for fill = 0 to n – 2 do • Initialize posMin to fill • for next = fill + 1 to n – 1 do • if the item at next is less than the item at posMin • Reset posMin to next • Exchange the item at posMin with the one at fill 0 1 2 3 4 35 65 30 60 20 fill next posMin

  35. Trace of Selection Sort Refinement (cont.) • for fill = 0 to n – 2 do • Initialize posMin to fill • for next = fill + 1 to n – 1 do • if the item at next is less than the item at posMin • Reset posMin to next • Exchange the item at posMin with the one at fill 0 1 2 3 4 20 65 30 60 35 fill next posMin

  36. Trace of Selection Sort Refinement (cont.) • for fill = 0 to n – 2 do • Initialize posMin to fill • for next = fill + 1 to n – 1 do • if the item at next is less than the item at posMin • Reset posMin to next • Exchange the item at posMin with the one at fill 0 1 2 3 4 20 65 30 60 35 fill next posMin

  37. Trace of Selection Sort Refinement (cont.) • for fill = 0 to n – 2 do • Initialize posMin to fill • for next = fill + 1 to n – 1 do • if the item at next is less than the item at posMin • Reset posMin to next • Exchange the item at posMin with the one at fill 0 1 2 3 4 20 65 30 60 35 fill next posMin

  38. Trace of Selection Sort Refinement (cont.) • for fill = 0 to n – 2 do • Initialize posMin to fill • for next = fill + 1 to n – 1 do • if the item at next is less than the item at posMin • Reset posMin to next • Exchange the item at posMin with the one at fill 0 1 2 3 4 20 65 30 60 35 fill next posMin

  39. Trace of Selection Sort Refinement (cont.) • for fill = 0 to n – 2 do • Initialize posMin to fill • for next = fill + 1 to n – 1 do • if the item at next is less than the item at posMin • Reset posMin to next • Exchange the item at posMin with the one at fill 0 1 2 3 4 20 65 30 60 35 fill next posMin

  40. Trace of Selection Sort Refinement (cont.) • for fill = 0 to n – 2 do • Initialize posMin to fill • for next = fill + 1 to n – 1 do • if the item at next is less than the item at posMin • Reset posMin to next • Exchange the item at posMin with the one at fill 0 1 2 3 4 20 65 30 60 35 fill next posMin

  41. Trace of Selection Sort Refinement (cont.) • for fill = 0 to n – 2 do • Initialize posMin to fill • for next = fill + 1 to n – 1 do • if the item at next is less than the item at posMin • Reset posMin to next • Exchange the item at posMin with the one at fill 0 1 2 3 4 20 65 30 60 35 fill next posMin

  42. Trace of Selection Sort Refinement (cont.) • for fill = 0 to n – 2 do • Initialize posMin to fill • for next = fill + 1 to n – 1 do • if the item at next is less than the item at posMin • Reset posMin to next • Exchange the item at posMin with the one at fill 0 1 2 3 4 20 65 30 60 35 fill next posMin

  43. Trace of Selection Sort Refinement (cont.) • for fill = 0 to n – 2 do • Initialize posMin to fill • for next = fill + 1 to n – 1 do • if the item at next is less than the item at posMin • Reset posMin to next • Exchange the item at posMin with the one at fill 0 1 2 3 4 20 65 30 60 35 fill next posMin

  44. Trace of Selection Sort Refinement (cont.) • for fill = 0 to n – 2 do • Initialize posMin to fill • for next = fill + 1 to n – 1 do • if the item at next is less than the item at posMin • Reset posMin to next • Exchange the item at posMin with the one at fill 0 1 2 3 4 20 65 30 60 35 fill next posMin

  45. Trace of Selection Sort Refinement (cont.) • for fill = 0 to n – 2 do • Initialize posMin to fill • for next = fill + 1 to n – 1 do • if the item at next is less than the item at posMin • Reset posMin to next • Exchange the item at posMin with the one at fill 0 1 2 3 4 20 30 65 60 35 fill next posMin

  46. Trace of Selection Sort Refinement (cont.) • for fill = 0 to n – 2 do • Initialize posMin to fill • for next = fill + 1 to n – 1 do • if the item at next is less than the item at posMin • Reset posMin to next • Exchange the item at posMin with the one at fill 0 1 2 3 4 20 30 65 60 35 fill next posMin

  47. Trace of Selection Sort Refinement (cont.) • for fill = 0 to n – 2 do • Initialize posMin to fill • for next = fill + 1 to n – 1 do • if the item at next is less than the item at posMin • Reset posMin to next • Exchange the item at posMin with the one at fill 0 1 2 3 4 20 30 65 60 35 fill next posMin

  48. Trace of Selection Sort Refinement (cont.) • for fill = 0 to n – 2 do • Initialize posMin to fill • for next = fill + 1 to n – 1 do • if the item at next is less than the item at posMin • Reset posMin to next • Exchange the item at posMin with the one at fill 0 1 2 3 4 20 30 65 60 35 fill next posMin

  49. Trace of Selection Sort Refinement (cont.) • for fill = 0 to n – 2 do • Initialize posMin to fill • for next = fill + 1 to n – 1 do • if the item at next is less than the item at posMin • Reset posMin to next • Exchange the item at posMin with the one at fill 0 1 2 3 4 20 30 65 60 35 fill next posMin

  50. Trace of Selection Sort Refinement (cont.) • for fill = 0 to n – 2 do • Initialize posMin to fill • for next = fill + 1 to n – 1 do • if the item at next is less than the item at posMin • Reset posMin to next • Exchange the item at posMin with the one at fill 0 1 2 3 4 20 30 65 60 35 fill next posMin