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Algorithms Lecture 4: Sorting Algorithms I

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Mohamed Loey

The document discusses three sorting algorithms: bubble sort, selection sort, and insertion sort. Bubble sort works by repeatedly swapping adjacent elements that are in the wrong order. Selection sort finds the minimum element and swaps it into the sorted portion of the array. Insertion sort inserts elements into the sorted portion of the array, swapping as needed to put the element in the correct position. Both selection sort and insertion sort have a time complexity of O(n^2) in the worst case.

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Analysis and Design of Algorithms Sorting Algorithms I
Analysis and Design of Algorithms Sorting Algorithms Bubble Sort Selection Sort Insertion Sort
Analysis and Design of Algorithms  Sorting Algorithm is an algorithm made up of a series of instructions that takes an array as input, and outputs a sorted array.  There are many sorting algorithms, such as:  Selection Sort, Bubble Sort, Insertion Sort, Merge Sort, Heap Sort, QuickSort, Radix Sort, Counting Sort, Bucket Sort, ShellSort, Comb Sort, Pigeonhole Sort, Cycle Sort
Analysis and Design of Algorithms Bubble Sort
Analysis and Design of Algorithms Bubble Sort is the simplest sorting algorithm that works by repeatedly swapping the adjacent elements if they are in wrong order.
Analysis and Design of Algorithms Algorithm:  Step1: Compare each pair of adjacent elements in the list  Step2: Swap two element if necessary  Step3: Repeat this process for all the elements until the entire array is sorted
Analysis and Design of Algorithms  Example 1 Assume the following Array: 5 1 4 2
Analysis and Design of Algorithms  First Iteration:  Compare 5 1 4 2  j  j+1
Analysis and Design of Algorithms  First Iteration:  Swap 1 5 4 2  j  j+1
Analysis and Design of Algorithms  First Iteration:  Compare 1 5 4 2  j  j+1
Analysis and Design of Algorithms  First Iteration:  Swap 1 4 5 2  j  j+1
Analysis and Design of Algorithms  First Iteration:  Compare 1 4 5 2  j  j+1
Analysis and Design of Algorithms  First Iteration:  Swap 1 4 2 5  j  j+1
Analysis and Design of Algorithms 1 4 2 5
Analysis and Design of Algorithms  Second Iteration:  Compare 1 4 2 5  j  j+1
Analysis and Design of Algorithms  Second Iteration:  Compare 1 4 2 5  j  j+1
Analysis and Design of Algorithms  Second Iteration:  Swap 1 2 4 5  j  j+1
Analysis and Design of Algorithms 1 2 4 5
Analysis and Design of Algorithms  Third Iteration:  Compare 1 2 4 5  j  j+1
Analysis and Design of Algorithms 1 2 4 5
Analysis and Design of Algorithms  Array is now sorted 1 2 3 4
Analysis and Design of Algorithms 5 4 2 1 3 4 5 2 1 3 4 2 5 1 3 4 2 1 5 3 4 2 1 3 5 4 2 1 3 5 2 4 1 3 5 2 1 4 3 5 2 1 3 4 5 2 1 3 4 5 1 2 3 4 5 1 2 3 4 5  Example 2:
Analysis and Design of Algorithms  What is the output of bubble sort after the 1st iteration given the following sequence of numbers: 13 2 9 4 18 45 37 63 a) 2 4 9 13 18 37 45 63 b) 2 9 4 13 18 37 45 63 c) 13 2 4 9 18 45 37 63 d) 2 4 9 13 18 45 37 63
Analysis and Design of Algorithms  What is the output of bubble sort after the 1st iteration given the following sequence of numbers: 13 2 9 4 18 45 37 63 a) 2 4 9 13 18 37 45 63 b) 2 9 4 13 18 37 45 63 c) 13 2 4 9 18 45 37 63 d) 2 4 9 13 18 45 37 63
Analysis and Design of Algorithms  Python Code
Analysis and Design of Algorithms
Analysis and Design of Algorithms  Time Complexity: O(n2) as there are two nested loops  Example of worst case 5 4 3 2 1
Analysis and Design of Algorithms Selection Sort
Analysis and Design of Algorithms The selection sort algorithm sorts an array by repeatedly finding the minimum element (considering ascending order) from unsorted part and putting it at the beginning.
Analysis and Design of Algorithms Algorithm:  Step1: Find the minimum value in the list  Step2: Swap it with the value in the current position  Step3: Repeat this process for all the elements until the entire array is sorted
Analysis and Design of Algorithms  Example 1 Assume the following Array: 8 12 5 9 2
Analysis and Design of Algorithms  Compare 8 12 5 9 2  i  j  min
Analysis and Design of Algorithms  Compare 8 12 5 9 2  i  j  min
Analysis and Design of Algorithms  Move 8 12 5 9 2  j  i  min
Analysis and Design of Algorithms  Compare 8 12 5 9 2  i  min  j
Analysis and Design of Algorithms  Compare 8 12 5 9 2  i  min  j
Analysis and Design of Algorithms  Move 8 12 5 9 2  i  j  min
Analysis and Design of Algorithms  Smallest 8 12 5 9 2  i  min
Analysis and Design of Algorithms  Swap 8 12 5 9 2  min  i
Analysis and Design of Algorithms  Sorted  Un Sorted 2 12 5 9 8  Sorted  Un Sorted
Analysis and Design of Algorithms  Compare 2 12 5 9 8  i  min  j  Sorted
Analysis and Design of Algorithms  Move 2 12 5 9 8  i  min  j  Sorted
Analysis and Design of Algorithms  Compare 2 12 5 9 8  Sorted  i  j  min
Analysis and Design of Algorithms  Compare 2 12 5 9 8  Sorted  i  j  min
Analysis and Design of Algorithms  Smallest 2 12 5 9 8  Sorted  i  min
Analysis and Design of Algorithms  Swap 2 12 5 9 8  Sorted  i  min
Analysis and Design of Algorithms  Sorted  Un Sorted 2 5 12 9 8  Sorted  Un Sorted
Analysis and Design of Algorithms  Compare 2 5 12 9 8  Sorted  i  j  min
Analysis and Design of Algorithms  Move 2 5 12 9 8  Sorted  i  j  min
Analysis and Design of Algorithms  Compare 2 5 12 9 8  Sorted  i  min  j
Analysis and Design of Algorithms  Move 2 5 12 9 8  Sorted  i  min  j
Analysis and Design of Algorithms  Smallest 2 5 12 9 8  Sorted  i  min
Analysis and Design of Algorithms  Swap 2 5 12 9 8  Sorted  i  min
Analysis and Design of Algorithms  Sorted  Un Sorted 2 5 8 9 12  Sorted  Un Sorted
Analysis and Design of Algorithms  Compare 2 5 8 9 12  Sorted  i  min  j
Analysis and Design of Algorithms  Sorted  Un Sorted 2 5 8 9 12  Sorted  Un Sorted
Analysis and Design of Algorithms  Sorted  Un Sorted 2 5 8 9 12  Sorted  i  min
Analysis and Design of Algorithms  Array is now sorted 2 5 8 9 12  Sorted
Analysis and Design of Algorithms 12 10 16 11 9 7 Example 2: 7 10 16 11 9 12 7 9 16 11 10 12 7 9 10 11 16 12 7 9 10 11 16 12 7 9 10 11 12 16 12 10 16 11 9 7
Analysis and Design of Algorithms  What is the output of selection sort after the 2nd iteration given the following sequence of numbers: 13 2 9 4 18 45 37 63 a) 2 4 9 13 18 37 45 63 b) 2 9 4 13 18 37 45 63 c) 13 2 4 9 18 45 37 63 d) 2 4 9 13 18 45 37 63
Analysis and Design of Algorithms  What is the output of selection sort after the 2nd iteration given the following sequence of numbers: 13 2 9 4 18 45 37 63 a) 2 4 9 13 18 37 45 63 b) 2 9 4 13 18 37 45 63 c) 13 2 4 9 18 45 37 63 d) 2 4 9 13 18 45 37 63
Analysis and Design of Algorithms  Python Code
Analysis and Design of Algorithms
Analysis and Design of Algorithms  Time Complexity: O(n2) as there are two nested loops  Example of worst case 2 3 4 5 1
Analysis and Design of Algorithms Insertion Sort
Analysis and Design of Algorithms Insertion sort is a simple sorting algorithm that works the way we sort playing cards in our hands.
Analysis and Design of Algorithms  Algorithm:  Step1: Compare each pair of adjacent elements in the list  Step2: Insert element into the sorted list, until it occupies correct position.  Step3: Swap two element if necessary  Step4: Repeat this process for all the elements until the entire array is sorted
Analysis and Design of Algorithms  Assume the following Array: 5 1 4 2
Analysis and Design of Algorithms  Compare  Store= 5 1 4 2  i  j  j+1 1
Analysis and Design of Algorithms  Move  Store= 5 4 2  i  j  j+1 1
Analysis and Design of Algorithms  Move  Store= 1 5 4 2  i  j+1
Analysis and Design of Algorithms  Compare  Store= 1 5 4 2  i  j 4  j+1
Analysis and Design of Algorithms  Move  Store= 1 5 2  i  j 4  j+1
Analysis and Design of Algorithms  Compare  Store= 1 5 2  i  j 4  j+1
Analysis and Design of Algorithms  Move  Store= 1 4 5 2  i  j  j+1
Analysis and Design of Algorithms  Compare  Store= 1 4 5 2  i  j 2  j+1
Analysis and Design of Algorithms  Move  Store= 1 4 5  i  j 2  j+1
Analysis and Design of Algorithms  Compare  Store= 1 4 5  i  j 2  j+1
Analysis and Design of Algorithms  Move  Store= 1 4 5  i  j 2  j+1
Analysis and Design of Algorithms  Compare  Store= 1 4 5  i  j 2  j+1
Analysis and Design of Algorithms  Compare  Store= 1 2 4 5  i  j  j+1
Analysis and Design of Algorithms  Array is now sorted 1 2 4 5
Analysis and Design of Algorithms 5 1 8 3 9 2  Example 2: 1 5 8 3 9 2 1 5 8 3 9 2 1 3 5 8 9 2 1 3 5 8 9 2 1 2 3 5 8 9 5 1 8 3 9 2
Analysis and Design of Algorithms  What is the output of insertion sort after the 1st iteration given the following sequence of numbers: 7 3 5 1 9 8 4 6 a) 3 7 5 1 9 8 4 6 b) 1 3 7 5 9 8 4 6 c) 3 4 1 5 6 8 7 9 d) 1 3 4 5 6 7 8 9
Analysis and Design of Algorithms  What is the output of insertion sort after the 1st iteration given the following sequence of numbers: 7 3 5 1 9 8 4 6 a) 3 7 5 1 9 8 4 6 b) 1 3 7 5 9 8 4 6 c) 3 4 1 5 6 8 7 9 d) 1 3 4 5 6 7 8 9
Analysis and Design of Algorithms  What is the output of insertion sort after the 2nd iteration given the following sequence of numbers: 7 3 5 1 9 8 4 6 a) 3 5 7 1 9 8 4 6 b) 1 3 7 5 9 8 4 6 c) 3 4 1 5 6 8 7 9 d) 1 3 4 5 6 7 8 9
Analysis and Design of Algorithms  What is the output of insertion sort after the 2nd iteration given the following sequence of numbers: 7 3 5 1 9 8 4 6 a) 3 5 7 1 9 8 4 6 b) 1 3 7 5 9 8 4 6 c) 3 4 1 5 6 8 7 9 d) 1 3 4 5 6 7 8 9
Analysis and Design of Algorithms  Python Code
Analysis and Design of Algorithms
Analysis and Design of Algorithms  Time Complexity: O(n2)  Example of worst case 5 4 3 2 1
Analysis and Design of Algorithms facebook.com/mloey mohamedloey@gmail.com twitter.com/mloey linkedin.com/in/mloey mloey@fci.bu.edu.eg mloey.github.io
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Algorithms Lecture 4: Sorting Algorithms I

  • 1. Analysis and Design of Algorithms Sorting Algorithms I
  • 2. Analysis and Design of Algorithms Sorting Algorithms Bubble Sort Selection Sort Insertion Sort
  • 3. Analysis and Design of Algorithms  Sorting Algorithm is an algorithm made up of a series of instructions that takes an array as input, and outputs a sorted array.  There are many sorting algorithms, such as:  Selection Sort, Bubble Sort, Insertion Sort, Merge Sort, Heap Sort, QuickSort, Radix Sort, Counting Sort, Bucket Sort, ShellSort, Comb Sort, Pigeonhole Sort, Cycle Sort
  • 4. Analysis and Design of Algorithms Bubble Sort
  • 5. Analysis and Design of Algorithms Bubble Sort is the simplest sorting algorithm that works by repeatedly swapping the adjacent elements if they are in wrong order.
  • 6. Analysis and Design of Algorithms Algorithm:  Step1: Compare each pair of adjacent elements in the list  Step2: Swap two element if necessary  Step3: Repeat this process for all the elements until the entire array is sorted
  • 7. Analysis and Design of Algorithms  Example 1 Assume the following Array: 5 1 4 2
  • 8. Analysis and Design of Algorithms  First Iteration:  Compare 5 1 4 2  j  j+1
  • 9. Analysis and Design of Algorithms  First Iteration:  Swap 1 5 4 2  j  j+1
  • 10. Analysis and Design of Algorithms  First Iteration:  Compare 1 5 4 2  j  j+1
  • 11. Analysis and Design of Algorithms  First Iteration:  Swap 1 4 5 2  j  j+1
  • 12. Analysis and Design of Algorithms  First Iteration:  Compare 1 4 5 2  j  j+1
  • 13. Analysis and Design of Algorithms  First Iteration:  Swap 1 4 2 5  j  j+1
  • 14. Analysis and Design of Algorithms 1 4 2 5
  • 15. Analysis and Design of Algorithms  Second Iteration:  Compare 1 4 2 5  j  j+1
  • 16. Analysis and Design of Algorithms  Second Iteration:  Compare 1 4 2 5  j  j+1
  • 17. Analysis and Design of Algorithms  Second Iteration:  Swap 1 2 4 5  j  j+1
  • 18. Analysis and Design of Algorithms 1 2 4 5
  • 19. Analysis and Design of Algorithms  Third Iteration:  Compare 1 2 4 5  j  j+1
  • 20. Analysis and Design of Algorithms 1 2 4 5
  • 21. Analysis and Design of Algorithms  Array is now sorted 1 2 3 4
  • 22. Analysis and Design of Algorithms 5 4 2 1 3 4 5 2 1 3 4 2 5 1 3 4 2 1 5 3 4 2 1 3 5 4 2 1 3 5 2 4 1 3 5 2 1 4 3 5 2 1 3 4 5 2 1 3 4 5 1 2 3 4 5 1 2 3 4 5  Example 2:
  • 23. Analysis and Design of Algorithms  What is the output of bubble sort after the 1st iteration given the following sequence of numbers: 13 2 9 4 18 45 37 63 a) 2 4 9 13 18 37 45 63 b) 2 9 4 13 18 37 45 63 c) 13 2 4 9 18 45 37 63 d) 2 4 9 13 18 45 37 63
  • 24. Analysis and Design of Algorithms  What is the output of bubble sort after the 1st iteration given the following sequence of numbers: 13 2 9 4 18 45 37 63 a) 2 4 9 13 18 37 45 63 b) 2 9 4 13 18 37 45 63 c) 13 2 4 9 18 45 37 63 d) 2 4 9 13 18 45 37 63
  • 25. Analysis and Design of Algorithms  Python Code
  • 26. Analysis and Design of Algorithms
  • 27. Analysis and Design of Algorithms  Time Complexity: O(n2) as there are two nested loops  Example of worst case 5 4 3 2 1
  • 28. Analysis and Design of Algorithms Selection Sort
  • 29. Analysis and Design of Algorithms The selection sort algorithm sorts an array by repeatedly finding the minimum element (considering ascending order) from unsorted part and putting it at the beginning.
  • 30. Analysis and Design of Algorithms Algorithm:  Step1: Find the minimum value in the list  Step2: Swap it with the value in the current position  Step3: Repeat this process for all the elements until the entire array is sorted
  • 31. Analysis and Design of Algorithms  Example 1 Assume the following Array: 8 12 5 9 2
  • 32. Analysis and Design of Algorithms  Compare 8 12 5 9 2  i  j  min
  • 33. Analysis and Design of Algorithms  Compare 8 12 5 9 2  i  j  min
  • 34. Analysis and Design of Algorithms  Move 8 12 5 9 2  j  i  min
  • 35. Analysis and Design of Algorithms  Compare 8 12 5 9 2  i  min  j
  • 36. Analysis and Design of Algorithms  Compare 8 12 5 9 2  i  min  j
  • 37. Analysis and Design of Algorithms  Move 8 12 5 9 2  i  j  min
  • 38. Analysis and Design of Algorithms  Smallest 8 12 5 9 2  i  min
  • 39. Analysis and Design of Algorithms  Swap 8 12 5 9 2  min  i
  • 40. Analysis and Design of Algorithms  Sorted  Un Sorted 2 12 5 9 8  Sorted  Un Sorted
  • 41. Analysis and Design of Algorithms  Compare 2 12 5 9 8  i  min  j  Sorted
  • 42. Analysis and Design of Algorithms  Move 2 12 5 9 8  i  min  j  Sorted
  • 43. Analysis and Design of Algorithms  Compare 2 12 5 9 8  Sorted  i  j  min
  • 44. Analysis and Design of Algorithms  Compare 2 12 5 9 8  Sorted  i  j  min
  • 45. Analysis and Design of Algorithms  Smallest 2 12 5 9 8  Sorted  i  min
  • 46. Analysis and Design of Algorithms  Swap 2 12 5 9 8  Sorted  i  min
  • 47. Analysis and Design of Algorithms  Sorted  Un Sorted 2 5 12 9 8  Sorted  Un Sorted
  • 48. Analysis and Design of Algorithms  Compare 2 5 12 9 8  Sorted  i  j  min
  • 49. Analysis and Design of Algorithms  Move 2 5 12 9 8  Sorted  i  j  min
  • 50. Analysis and Design of Algorithms  Compare 2 5 12 9 8  Sorted  i  min  j
  • 51. Analysis and Design of Algorithms  Move 2 5 12 9 8  Sorted  i  min  j
  • 52. Analysis and Design of Algorithms  Smallest 2 5 12 9 8  Sorted  i  min
  • 53. Analysis and Design of Algorithms  Swap 2 5 12 9 8  Sorted  i  min
  • 54. Analysis and Design of Algorithms  Sorted  Un Sorted 2 5 8 9 12  Sorted  Un Sorted
  • 55. Analysis and Design of Algorithms  Compare 2 5 8 9 12  Sorted  i  min  j
  • 56. Analysis and Design of Algorithms  Sorted  Un Sorted 2 5 8 9 12  Sorted  Un Sorted
  • 57. Analysis and Design of Algorithms  Sorted  Un Sorted 2 5 8 9 12  Sorted  i  min
  • 58. Analysis and Design of Algorithms  Array is now sorted 2 5 8 9 12  Sorted
  • 59. Analysis and Design of Algorithms 12 10 16 11 9 7 Example 2: 7 10 16 11 9 12 7 9 16 11 10 12 7 9 10 11 16 12 7 9 10 11 16 12 7 9 10 11 12 16 12 10 16 11 9 7
  • 60. Analysis and Design of Algorithms  What is the output of selection sort after the 2nd iteration given the following sequence of numbers: 13 2 9 4 18 45 37 63 a) 2 4 9 13 18 37 45 63 b) 2 9 4 13 18 37 45 63 c) 13 2 4 9 18 45 37 63 d) 2 4 9 13 18 45 37 63
  • 61. Analysis and Design of Algorithms  What is the output of selection sort after the 2nd iteration given the following sequence of numbers: 13 2 9 4 18 45 37 63 a) 2 4 9 13 18 37 45 63 b) 2 9 4 13 18 37 45 63 c) 13 2 4 9 18 45 37 63 d) 2 4 9 13 18 45 37 63
  • 62. Analysis and Design of Algorithms  Python Code
  • 63. Analysis and Design of Algorithms
  • 64. Analysis and Design of Algorithms  Time Complexity: O(n2) as there are two nested loops  Example of worst case 2 3 4 5 1
  • 65. Analysis and Design of Algorithms Insertion Sort
  • 66. Analysis and Design of Algorithms Insertion sort is a simple sorting algorithm that works the way we sort playing cards in our hands.
  • 67. Analysis and Design of Algorithms  Algorithm:  Step1: Compare each pair of adjacent elements in the list  Step2: Insert element into the sorted list, until it occupies correct position.  Step3: Swap two element if necessary  Step4: Repeat this process for all the elements until the entire array is sorted
  • 68. Analysis and Design of Algorithms  Assume the following Array: 5 1 4 2
  • 69. Analysis and Design of Algorithms  Compare  Store= 5 1 4 2  i  j  j+1 1
  • 70. Analysis and Design of Algorithms  Move  Store= 5 4 2  i  j  j+1 1
  • 71. Analysis and Design of Algorithms  Move  Store= 1 5 4 2  i  j+1
  • 72. Analysis and Design of Algorithms  Compare  Store= 1 5 4 2  i  j 4  j+1
  • 73. Analysis and Design of Algorithms  Move  Store= 1 5 2  i  j 4  j+1
  • 74. Analysis and Design of Algorithms  Compare  Store= 1 5 2  i  j 4  j+1
  • 75. Analysis and Design of Algorithms  Move  Store= 1 4 5 2  i  j  j+1
  • 76. Analysis and Design of Algorithms  Compare  Store= 1 4 5 2  i  j 2  j+1
  • 77. Analysis and Design of Algorithms  Move  Store= 1 4 5  i  j 2  j+1
  • 78. Analysis and Design of Algorithms  Compare  Store= 1 4 5  i  j 2  j+1
  • 79. Analysis and Design of Algorithms  Move  Store= 1 4 5  i  j 2  j+1
  • 80. Analysis and Design of Algorithms  Compare  Store= 1 4 5  i  j 2  j+1
  • 81. Analysis and Design of Algorithms  Compare  Store= 1 2 4 5  i  j  j+1
  • 82. Analysis and Design of Algorithms  Array is now sorted 1 2 4 5
  • 83. Analysis and Design of Algorithms 5 1 8 3 9 2  Example 2: 1 5 8 3 9 2 1 5 8 3 9 2 1 3 5 8 9 2 1 3 5 8 9 2 1 2 3 5 8 9 5 1 8 3 9 2
  • 84. Analysis and Design of Algorithms  What is the output of insertion sort after the 1st iteration given the following sequence of numbers: 7 3 5 1 9 8 4 6 a) 3 7 5 1 9 8 4 6 b) 1 3 7 5 9 8 4 6 c) 3 4 1 5 6 8 7 9 d) 1 3 4 5 6 7 8 9
  • 85. Analysis and Design of Algorithms  What is the output of insertion sort after the 1st iteration given the following sequence of numbers: 7 3 5 1 9 8 4 6 a) 3 7 5 1 9 8 4 6 b) 1 3 7 5 9 8 4 6 c) 3 4 1 5 6 8 7 9 d) 1 3 4 5 6 7 8 9
  • 86. Analysis and Design of Algorithms  What is the output of insertion sort after the 2nd iteration given the following sequence of numbers: 7 3 5 1 9 8 4 6 a) 3 5 7 1 9 8 4 6 b) 1 3 7 5 9 8 4 6 c) 3 4 1 5 6 8 7 9 d) 1 3 4 5 6 7 8 9
  • 87. Analysis and Design of Algorithms  What is the output of insertion sort after the 2nd iteration given the following sequence of numbers: 7 3 5 1 9 8 4 6 a) 3 5 7 1 9 8 4 6 b) 1 3 7 5 9 8 4 6 c) 3 4 1 5 6 8 7 9 d) 1 3 4 5 6 7 8 9
  • 88. Analysis and Design of Algorithms  Python Code
  • 89. Analysis and Design of Algorithms
  • 90. Analysis and Design of Algorithms  Time Complexity: O(n2)  Example of worst case 5 4 3 2 1
  • 91. Analysis and Design of Algorithms facebook.com/mloey mohamedloey@gmail.com twitter.com/mloey linkedin.com/in/mloey mloey@fci.bu.edu.eg mloey.github.io
  • 92. Analysis and Design of Algorithms www.YourCompany.com © 2020 Companyname PowerPoint Business Theme. All Rights Reserved. THANKS FOR YOUR TIME