Bubble Sort Complete Description with algorithm, coding and step by step dry run.

1. Bubble Sort
Prepared By:
Rao Muhammad Salman
MCS
The Islamia University BahawalPur(Pakistan)

2. Sorting
• Sorting takes an unordered collection and
makes it an ordered one.
1 2 3 4 5 6 7 8
674523 14 6 3398 42
1 2 3 4 5 6 7 8
452314 33 42 676 98

3. "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
1 2 3 4 5 6 7 8
674523 14 6 3398 42

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
Swap
1 2 3 4 5 6 7 8
674598 14 6 3323 42
Value swapped

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
1 2 3 4 5 6 7 8
679845 14 6 3323 42
Value swapped

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
1 2 3 4 5 6 7 8
671445 98 6 3323 42
Value swapped

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
Value swapped
Swap
1 2 3 4 5 6 7 8
671445 6 98 3323 42

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
Swap
1 2 3 4 5 6 7 8
981445 6 67 3323 42
Value swapped

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
1 2 3 4 5 6 7 8
331445 6 67 9823 42
Value swapped

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
Swap
1 2 3 4 5 6 7 8
331445 6 67 4223 98
Value swapped

11. "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
Largest value correctly placed
1 2 3 4 5 6 7 8
331445 6 67 4223 98

12. The “Bubble Up” Algorithm
index <- 1
last_compare_at <- n – 1
loopouter
exitif(index > last_compare_at)
Loopinner
to_do<-0
exitif(to_do > index)
if(A[to_do] > A[to_do + 1]) then
Swap(A[to_do], A[to_do + 1])
endif
to_do<- to_do + 1
endloopinner
index <- index - 1
endloopouter

13. No, Swap isn’t built in.
Procedure Swap(a, b isoftype in/out Num)
temp isoftype Num
temp <- a
a <- b
b <- temp
endprocedure // Swap

14. Bubble Sort Code
void bubble_sort( int data[ ], int size)
{
int outer, inner,temp;
for(outer = size-1; outer =>0; --outer)
{
for(inner = 0; inner < outer;++inner)
if(data[inner] > data[inner+1])
{
temp = data[inner];
data[inner] = data[inner+1];
data[inner+1] = temp;
}
}
}

15. Items of Interest
• Notice that only the largest value is
correctly placed
• All other values are still out of order
• So we need to repeat this process
Largest value correctly placed
1 2 3 4 5 6 7 8
331445 6 67 4223 98

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

17. Dry Run

18. 674523 14 6 3398 42
1 2 3 4 5 6 7 8
to_do
index
7
N 8 did_swap true
The First “Bubble Up”

19. 674523 14 6 3398 42
1 2 3 4 5 6 7 8
to_do
index
7
1
N 8 did_swap false
The First “Bubble Up”

20. The First “Bubble Up”
674523 14 6 3398 42
1 2 3 4 5 6 7 8
to_do
index
7
1
N 8
Swap
did_swap false

21. The First “Bubble Up”
674598 14 6 3323 42
1 2 3 4 5 6 7 8
to_do
index
7
1
N 8
Swap
did_swap true

22. The First “Bubble Up”
674598 14 6 3323 42
1 2 3 4 5 6 7 8
to_do
index
7
2
N 8 did_swap true

23. The First “Bubble Up”
674598 14 6 3323 42
1 2 3 4 5 6 7 8
to_do
index
7
2
N 8
Swap
did_swap true

24. The First “Bubble Up”
679845 14 6 3323 42
1 2 3 4 5 6 7 8
to_do
index
7
2
N 8
Swap
did_swap true

25. The First “Bubble Up”
679845 14 6 3323 42
1 2 3 4 5 6 7 8
to_do
index
7
3
N 8 did_swap true

26. The First “Bubble Up”
679845 14 6 3323 42
1 2 3 4 5 6 7 8
to_do
index
7
3
N 8
Swap
did_swap true

27. The First “Bubble Up”
671445 98 6 3323 42
1 2 3 4 5 6 7 8
to_do
index
7
3
N 8
Swap
did_swap true

28. The First “Bubble Up”
671445 98 6 3323 42
1 2 3 4 5 6 7 8
to_do
index
7
4
N 8 did_swap true

29. The First “Bubble Up”
671445 98 6 3323 42
1 2 3 4 5 6 7 8
to_do
index
7
4
N 8
Swap
did_swap true

30. The First “Bubble Up”
671445 6 98 3323 42
1 2 3 4 5 6 7 8
to_do
index
7
4
N 8
Swap
did_swap true

31. The First “Bubble Up”
671445 6 98 3323 42
1 2 3 4 5 6 7 8
to_do
index
7
5
N 8 did_swap true

32. The First “Bubble Up”
671445 6 98 3323 42
1 2 3 4 5 6 7 8
to_do
index
7
5
N 8
Swap
did_swap true

33. The First “Bubble Up”
981445 6 67 3323 42
1 2 3 4 5 6 7 8
to_do
index
7
5
N 8
Swap
did_swap true

34. The First “Bubble Up”
981445 6 67 3323 42
1 2 3 4 5 6 7 8
to_do
index
7
6
N 8 did_swap true

35. The First “Bubble Up”
981445 6 67 3323 42
1 2 3 4 5 6 7 8
to_do
index
7
6
N 8
Swap
did_swap true

36. The First “Bubble Up”
331445 6 67 9823 42
1 2 3 4 5 6 7 8
to_do
index
7
6
N 8
Swap
did_swap true

37. The First “Bubble Up”
331445 6 67 9823 42
1 2 3 4 5 6 7 8
to_do
index
7
7
N 8 did_swap true

38. The First “Bubble Up”
331445 6 67 9823 42
1 2 3 4 5 6 7 8
to_do
index
7
7
N 8
Swap
did_swap true

39. The First “Bubble Up”
331445 6 67 4223 98
1 2 3 4 5 6 7 8
to_do
index
7
7
N 8 did_swap true
Finished 1st “Bubble Up”
No Swap

40. The Second “Bubble Up”
331445 6 67 4223 98
1 2 3 4 5 6 7 8
to_do
index
6
1
N 8 did_swap false

41. The Second “Bubble Up”
331445 6 67 4223 98
1 2 3 4 5 6 7 8
to_do
index
6
1
N 8 did_swap false
No Swap

42. The Second “Bubble Up”
331445 6 67 4223 98
1 2 3 4 5 6 7 8
to_do
index
6
2
N 8 did_swap false

43. The Second “Bubble Up”
331445 6 67 4223 98
1 2 3 4 5 6 7 8
to_do
index
6
2
N 8 did_swap false
Swap

44. The Second “Bubble Up”
334514 6 67 4223 98
1 2 3 4 5 6 7 8
to_do
index
6
2
N 8 did_swap true
Swap

45. The Second “Bubble Up”
334514 6 67 4223 98
1 2 3 4 5 6 7 8
to_do
index
6
3
N 8 did_swap true

46. The Second “Bubble Up”
334514 6 67 4223 98
1 2 3 4 5 6 7 8
to_do
index
6
3
N 8 did_swap true
Swap

47. The Second “Bubble Up”
33614 45 67 4223 98
1 2 3 4 5 6 7 8
to_do
index
6
3
N 8 did_swap true
Swap

48. The Second “Bubble Up”
33614 45 67 4223 98
1 2 3 4 5 6 7 8
to_do
index
6
4
N 8 did_swap true

49. The Second “Bubble Up”
33614 45 67 4223 98
1 2 3 4 5 6 7 8
to_do
index
6
4
N 8 did_swap true
No Swap

50. The Second “Bubble Up”
33614 45 67 4223 98
1 2 3 4 5 6 7 8
to_do
index
6
5
N 8 did_swap true

51. The Second “Bubble Up”
33614 45 67 4223 98
1 2 3 4 5 6 7 8
to_do
index
6
5
N 8 did_swap true
Swap

52. The Second “Bubble Up”
67614 45 33 4223 98
1 2 3 4 5 6 7 8
to_do
index
6
5
N 8 did_swap true
Swap

53. The Second “Bubble Up”
67614 45 33 4223 98
1 2 3 4 5 6 7 8
to_do
index
6
6
N 8 did_swap true

54. The Second “Bubble Up”
42614 45 33 6723 98
1 2 3 4 5 6 7 8
to_do
index
6
6
N 8 did_swap true
Swap

55. The Second “Bubble Up”
42614 45 33 6723 98
1 2 3 4 5 6 7 8
to_do
index
6
6
N 8 did_swap true
Swap
Finished 2nd “Bubble Up”

56. The Third “Bubble Up”
42614 45 33 6723 98
1 2 3 4 5 6 7 8
to_do
index
5
1
N 8 did_swap false

57. The Third “Bubble Up”
42614 45 33 6723 98
1 2 3 4 5 6 7 8
to_do
index
5
1
N 8 did_swap false
Swap

58. The Third “Bubble Up”
42623 45 33 6714 98
1 2 3 4 5 6 7 8
to_do
index
5
1
N 8 did_swap true
Swap

59. The Third “Bubble Up”
42623 45 33 6714 98
1 2 3 4 5 6 7 8
to_do
index
5
2
N 8 did_swap true

60. The Third “Bubble Up”
42623 45 33 6714 98
1 2 3 4 5 6 7 8
to_do
index
5
2
N 8 did_swap true
Swap

61. The Third “Bubble Up”
42236 45 33 6714 98
1 2 3 4 5 6 7 8
to_do
index
5
2
N 8 did_swap true
Swap

62. The Third “Bubble Up”
42236 45 33 6714 98
1 2 3 4 5 6 7 8
to_do
index
5
3
N 8 did_swap true

63. The Third “Bubble Up”
42236 45 33 6714 98
1 2 3 4 5 6 7 8
to_do
index
5
3
N 8 did_swap true
No Swap

64. The Third “Bubble Up”
42236 45 33 6714 98
1 2 3 4 5 6 7 8
to_do
index
5
4
N 8 did_swap true

65. The Third “Bubble Up”
42236 45 33 6714 98
1 2 3 4 5 6 7 8
to_do
index
5
4
N 8 did_swap true
Swap

66. The Third “Bubble Up”
42236 33 45 6714 98
1 2 3 4 5 6 7 8
to_do
index
5
4
N 8 did_swap true
Swap

67. The Third “Bubble Up”
42236 33 45 6714 98
1 2 3 4 5 6 7 8
to_do
index
5
5
N 8 did_swap true

68. The Third “Bubble Up”
42236 33 45 6714 98
1 2 3 4 5 6 7 8
to_do
index
5
5
N 8 did_swap true
Swap

69. The Third “Bubble Up”
45236 33 42 6714 98
1 2 3 4 5 6 7 8
to_do
index
5
5
N 8 did_swap true
Swap
Finished 3rd “Bubble Up”

70. The Fourth “Bubble Up”
45236 33 42 6714 98
1 2 3 4 5 6 7 8
to_do
index
4
1
N 8 did_swap false

71. The Fourth “Bubble Up”
45236 33 42 6714 98
1 2 3 4 5 6 7 8
to_do
index
4
1
N 8 did_swap false
Swap

72. The Fourth “Bubble Up”
452314 33 42 676 98
1 2 3 4 5 6 7 8
to_do
index
4
1
N 8 did_swap true
Swap

73. The Fourth “Bubble Up”
452314 33 42 676 98
1 2 3 4 5 6 7 8
to_do
index
4
2
N 8 did_swap true

74. The Fourth “Bubble Up”
452314 33 42 676 98
1 2 3 4 5 6 7 8
to_do
index
4
2
N 8 did_swap true
No Swap

75. The Fourth “Bubble Up”
452314 33 42 676 98
1 2 3 4 5 6 7 8
to_do
index
4
3
N 8 did_swap true

76. The Fourth “Bubble Up”
452314 33 42 676 98
1 2 3 4 5 6 7 8
to_do
index
4
3
N 8 did_swap true
No Swap

77. The Fourth “Bubble Up”
452314 33 42 676 98
1 2 3 4 5 6 7 8
to_do
index
4
4
N 8 did_swap true

78. The Fourth “Bubble Up”
452314 33 42 676 98
1 2 3 4 5 6 7 8
to_do
index
4
4
N 8 did_swap true
No Swap
Finished 4th “Bubble Up”

79. The Fifth “Bubble Up”
452314 33 42 676 98
1 2 3 4 5 6 7 8
to_do
index
3
1
N 8 did_swap false

80. The Fifth “Bubble Up”
452314 33 42 676 98
1 2 3 4 5 6 7 8
to_do
index
3
1
N 8 did_swap false
No Swap

81. The Fifth “Bubble Up”
452314 33 42 676 98
1 2 3 4 5 6 7 8
to_do
index
3
2
N 8 did_swap false

82. The Fifth “Bubble Up”
452314 33 42 676 98
1 2 3 4 5 6 7 8
to_do
index
3
2
N 8 did_swap false
No Swap

83. The Fifth “Bubble Up”
452314 33 42 676 98
1 2 3 4 5 6 7 8
to_do
index
3
3
N 8 did_swap false

84. The Fifth “Bubble Up”
452314 33 42 676 98
1 2 3 4 5 6 7 8
to_do
index
3
3
N 8 did_swap false
No Swap
Finished 5th “Bubble Up”

85. The Sixth “Bubble Up”
452314 33 42 676 98
1 2 3 4 5 6 7 8
to_do
index
2
1
N 8 did_swap false

86. The Sixth “Bubble Up”
452314 33 42 676 98
1 2 3 4 5 6 7 8
to_do
index
2
1
N 8 did_swap false
No Swap

87. The Sixth “Bubble Up”
452314 33 42 676 98
1 2 3 4 5 6 7 8
to_do
index
2
2
N 8 did_swap false

88. The Sixth “Bubble Up”
452314 33 42 676 98
1 2 3 4 5 6 7 8
to_do
index
2
2
N 8 did_swap false
No Swap
Finished 6th “Bubble Up”

89. The Seventh “Bubble Up”
452314 33 42 676 98
1 2 3 4 5 6 7 8
to_do
index
1
1
N 8 did_swap false

90. The Seventh “Bubble Up”
452314 33 42 676 98
1 2 3 4 5 6 7 8
to_do
index
1
1
N 8 did_swap false
No Swap
Finished 7th “Bubble Up”

91. Sorted Elements
452314 33 42 676 98
1 2 3 4 5 6 7 8

92. 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