1. Sorting Example Bubble Sort

2. Problem Definition
Sorting takes an unordered collection and makes it an ordered one.
Input: 77 42 35 12
101 5 5 12 35 42 77
101
Output:

3. One Idea: Bubble 1
Water
Air 2 3 1 2 3 1 2 3 1 3 2

4. "Bubbling Up" the Largest Element
Traverse a collection of elements
Move from the front to the end
“Bubble” the largest value to the end using pair-wise comparisons and swapping 77 42 35 12
101 5

5. "Bubbling Up" the Largest Element
Traverse a collection of elements
Move from the front to the end
“Bubble” the largest value to the end using pair-wise comparisons and swapping
Swap 42 77 77 42 35 12
101 5

6. "Bubbling Up" the Largest Element
Traverse a collection of elements
Move from the front to the end
“Bubble” the largest value to the end using pair-wise comparisons and swapping
Swap 35 77 42 77 35 12
101 5

7. "Bubbling Up" the Largest Element
Traverse a collection of elements
Move from the front to the end
“Bubble” the largest value to the end using pair-wise comparisons and swapping
Swap 12 77 42 35 77 12
101 5

8. "Bubbling Up" the Largest Element
Traverse a collection of elements
Move from the front to the end
“Bubble” the largest value to the end using pair-wise comparisons and swapping 42 35 12 77
101 5
No need to swap

9. "Bubbling Up" the Largest Element
Traverse a collection of elements
Move from the front to the end
“Bubble” the largest value to the end using pair-wise comparisons and swapping
Swap 5
101 42 35 12 77
101 5

10. "Bubbling Up" the Largest Element
Traverse a collection of elements
Move from the front to the end
“Bubble” the largest value to the end using pair-wise comparisons and swapping
101 42 35 12 77 5
Largest value correctly placed

11. The “Bubble Up” Algorithm
Bubble-Sort-step1( A ):
for k = 1 … (N – 1):
if A[k] > A[k+1]:
Swap( A, k, k+1 )
Swap( A, x, y ):
tmp = A[x]
A[x] = A[y]
A[y] = tmp
Python Code in

12. Need More Iterations
Notice that only the largest value is correctly placed
All other values are still out of order
So we need to repeat this process
101 42 35 12 77 5
Largest value correctly placed

13. Repeat “Bubble Up” How Many Times?
If we have N elements…
And if each time we bubble an element, we place it in its correct location…
Then we repeat the “bubble up” process N – 1 times.
This guarantees we’ll correctly place all N elements.

14. “Bubbling” All the Elements77 12 35 42 5
101
N - 1 5 42 12 35 77
101 42 5 35 12 77
101 42 35 5 12 77
101 42 35 12 5 77
101

15. The “Bubble Up” Algorithm
Bubble-Sort( A ):
for k = 1 … (N – 1):
if A[k] > A[k+1]:
Swap( A, k, k+1 )
Python Code in

16. The “Bubble Up” Algorithm
Bubble-Sort( A ):
for i = 1 … (N – 1):
for k = 1 … (N – 1):
if A[k] > A[k+1]:
Swap( A, k, k+1 )
Python Code in

17. The “Bubble Up” Algorithm
Bubble-Sort( A ):
for i = 1 … (N – 1):
for k = 1 … (N – 1):
if A[k] > A[k+1]:
Swap( A, k, k+1 )
To do N-1 iterations
To bubble a value
Inner loop
Outer loop
Python Code in

18. Reducing the Number of Comparisons12 35 42 77
101 5 77 12 35 42 5
101 5 42 12 35 77
101 42 5 35 12 77
101 42 35 5 12 77
101

19. Reducing the Number of Comparisons
Assume the array size  N
On the ith iteration, we only need to do N-i comparisons.
For example:
N = 6
i = 4 (4th iteration)
Thus, we have 2 comparisons to do 42 5 35 12 77
101

20. The “Bubble Up” Algorithm
Bubble-Sort( A ):
for i = 1 … (N – 1):
for k = 1 … (N – 1):
if A[k] > A[k+1]:
Swap( A, k, k+1 )
Python Code in

21. The “Bubble Up” Algorithm
Bubble-Sort( A ):
for i = 1 … (N – 1):
for k = 1 … (N – i):
if A[k] > A[k+1]:
Swap( A, k, k+1 )
Python Code in

22. Code Demo

23. An Animated Example N 8 i 1 k 98 23 45 14 6 67 33 42

24. An Animated Example N 8 i 1 k 1 98 23 45 14 6 67 33 42

25. An Animated Example N 8 i 1 k 1 Swap 98 23 45 14 6 67 33 42

26. An Animated Example N 8 i 1 k 1 Swap 23 98 45 14 6 67 33 42

27. An Animated Example N 8 i 1 k 2 23 98 45 14 6 67 33 42

28. An Animated Example N 8 i 1 k 2 Swap 23 98 45 14 6 67 33 42

29. An Animated Example N 8 i 1 k 2 Swap 23 45 98 14 6 67 33 42

30. An Animated Example N 8 i 1 k 3 23 45 98 14 6 67 33 42

31. An Animated Example N 8 i 1 k 3 Swap 23 45 98 14 6 67 33 42

32. An Animated Example N 8 i 1 k 3 Swap 23 45 14 98 6 67 33 42

33. An Animated Example N 8 i 1 k 4 23 45 14 98 6 67 33 42

34. An Animated Example N 8 i 1 k 4 Swap 23 45 14 98 6 67 33 42

35. An Animated Example N 8 i 1 k 4 Swap 23 45 14 6 98 67 33 42

36. An Animated Example N 8 i 1 k 5 23 45 14 6 98 67 33 42

37. An Animated Example N 8 i 1 k 5 Swap 23 45 14 6 98 67 33 42

38. An Animated Example N 8 i 1 k 5 Swap 23 45 14 6 67 98 33 42

39. An Animated Example N 8 i 1 k 6 23 45 14 6 67 98 33 42

40. An Animated Example N 8 i 1 k 6 Swap 23 45 14 6 67 98 33 42

41. An Animated Example N 8 i 1 k 6 Swap 23 45 14 6 67 33 98 42

42. An Animated Example N 8 i 1 k 7 23 45 14 6 67 33 98 42

43. An Animated Example N 8 i 1 k 7 Swap 23 45 14 6 67 33 98 42

44. An Animated Example N 8 i 1 k 7 Swap 23 45 14 6 67 33 42 98

45. After First Pass of Outer LoopN 8 i 1
Finished first “Bubble Up” k 8 23 45 14 6 67 33 42 98

46. The Second “Bubble Up” N 8 i 2 k 1 23 45 14 6 67 33 42 98

47. The Second “Bubble Up” N 8 i 2 k 1 No Swap 23 45 14 6 67 33 42 98

48. The Second “Bubble Up” N 8 i 2 k 2 23 45 14 6 67 33 42 98

49. The Second “Bubble Up” N 8 i 2 k 2 Swap 23 45 14 6 67 33 42 98

50. The Second “Bubble Up” N 8 i 2 k 2 Swap 23 14 45 6 67 33 42 98

51. The Second “Bubble Up” N 8 i 2 k 3 23 14 45 6 67 33 42 98

52. The Second “Bubble Up” N 8 i 2 k 3 Swap 23 14 45 6 67 33 42 98

53. The Second “Bubble Up” N 8 i 2 k 3 Swap 23 14 6 45 67 33 42 98

54. The Second “Bubble Up” N 8 i 2 k 4 23 14 6 45 67 33 42 98

55. The Second “Bubble Up” N 8 i 2 k 4 No Swap 23 14 6 45 67 33 42 98

56. The Second “Bubble Up” N 8 i 2 k 5 23 14 6 45 67 33 42 98

57. The Second “Bubble Up” N 8 i 2 k 5 Swap 23 14 6 45 67 33 42 98

58. The Second “Bubble Up” N 8 i 2 k 5 Swap 23 14 6 45 33 67 42 98

59. The Second “Bubble Up” N 8 i 2 k 6 23 14 6 45 33 67 42 98

60. The Second “Bubble Up” N 8 i 2 k 6 Swap 23 14 6 45 33 67 42 98

61. The Second “Bubble Up” N 8 i 2 k 6 Swap 23 14 6 45 33 42 67 98

62. After Second Pass of Outer Loop8 i 2
Finished second “Bubble Up” k 7 23 14 6 45 33 42 67 98

63. The Third “Bubble Up” N 8 i 3 k 1 23 14 6 45 33 42 67 98

64. The Third “Bubble Up” N 8 i 3 k 1 Swap 23 14 6 45 33 42 67 98

65. The Third “Bubble Up” N 8 i 3 k 1 Swap 14 23 6 45 33 42 67 98

66. The Third “Bubble Up” N 8 i 3 k 2 14 23 6 45 33 42 67 98

67. The Third “Bubble Up” N 8 i 3 k 2 Swap 14 23 6 45 33 42 67 98

68. The Third “Bubble Up” N 8 i 3 k 2 Swap 14 6 23 45 33 42 67 98

69. The Third “Bubble Up” N 8 i 3 k 3 14 6 23 45 33 42 67 98

70. The Third “Bubble Up” N 8 i 3 k 3 No Swap 14 6 23 45 33 42 67 98

71. The Third “Bubble Up” N 8 i 3 k 4 14 6 23 45 33 42 67 98

72. The Third “Bubble Up” N 8 i 3 k 4 Swap 14 6 23 45 33 42 67 98

73. The Third “Bubble Up” N 8 i 3 k 4 Swap 14 6 23 33 45 42 67 98

74. The Third “Bubble Up” N 8 i 3 k 5 14 6 23 33 45 42 67 98

75. The Third “Bubble Up” N 8 i 3 k 5 Swap 14 6 23 33 45 42 67 98

76. The Third “Bubble Up” N 8 i 3 k 5 Swap 14 6 23 33 42 45 67 98

77. After Third Pass of Outer LoopN 8 i 3
Finished third “Bubble Up” k 6 14 6 23 33 42 45 67 98

78. The Fourth “Bubble Up” N 8 i 4 k 1 14 6 23 33 42 45 67 98

79. The Fourth “Bubble Up” N 8 i 4 k 1 Swap 14 6 23 33 42 45 67 98

80. The Fourth “Bubble Up” N 8 i 4 k 1 Swap 6 14 23 33 42 45 67 98

81. The Fourth “Bubble Up” N 8 i 4 k 2 6 14 23 33 42 45 67 98

82. The Fourth “Bubble Up” N 8 i 4 k 2 No Swap 6 14 23 33 42 45 67 98

83. The Fourth “Bubble Up” N 8 i 4 k 3 6 14 23 33 42 45 67 98

84. The Fourth “Bubble Up” N 8 i 4 k 3 No Swap 6 14 23 33 42 45 67 98

85. The Fourth “Bubble Up” N 8 i 4 k 4 6 14 23 33 42 45 67 98

86. The Fourth “Bubble Up” N 8 i 4 k 4 No Swap 6 14 23 33 42 45 67 98

87. After Fourth Pass of Outer LoopN 8 i 4
Finished fourth “Bubble Up” k 5 6 14 23 33 42 45 67 98

88. The Fifth “Bubble Up” N 8 i 5 k 1 6 14 23 33 42 45 67 98

89. The Fifth “Bubble Up” N 8 i 5 k 1 No Swap 6 14 23 33 42 45 67 98

90. The Fifth “Bubble Up” N 8 i 5 k 2 6 14 23 33 42 45 67 98

91. The Fifth “Bubble Up” N 8 i 5 k 2 No Swap 6 14 23 33 42 45 67 98

92. The Fifth “Bubble Up” N 8 i 5 k 3 6 14 23 33 42 45 67 98

93. The Fifth “Bubble Up” N 8 i 5 k 3 No Swap 6 14 23 33 42 45 67 98

94. After Fifth Pass of Outer LoopN 8 i 5
Finished fifth “Bubble Up” k 4 6 14 23 33 42 45 67 98

95. N 8 i 5 k 4 6 14 23 33 42 45 67 98

96. Summary
“Bubble Up” algorithm will move largest value to its correct location (to the right)
Repeat “Bubble Up” until all elements are correctly placed:
Maximum of N-1 times
Can finish early if no swapping occurs
We reduce the number of elements we compare each time one is correctly placed

97. Truth in CS Act Bubble sort will do the job, but not efficientlyLB
Truth in CS Act
Bubble sort will do the job, but not efficiently
There are more efficient algorithms for sorting

98. Sorting Algorithms
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