Bubble sort is an algorithm that sorts a list of numbers by repeatedly swapping adjacent elements that are out of order. It works by comparing adjacent elements and swapping them if they are in the wrong order, "bubbling" the largest values to the end of the list over multiple iterations. The algorithm iterates through the list N-1 times, where N is the number of elements, to fully sort the list. It uses pairwise comparisons and swapping to move the largest remaining value to its correct place with each pass.

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.
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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
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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
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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
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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
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to_do
index
7
6
N 8
Swap
did_swap true

37. The First “Bubble Up”
331445 6 67 9823 42
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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