1. Sorting
Damian Gordon

2. Sorting
Let’s remember our integer array from before:

3. Sorting 44 23 1 42 2 33 3 16 4 54 5 6 34 7 18
Age

4. Sorting 44 23 1 42 2 33 3 16 4 54 5 34 6 18 7
Age
How do we sort the data, in other words, get it into this order:

5. Sorting 44 23 1 42 2 33 3 16 4 54 5 6 34 7 18
Age
How do we sort the data, in other words, get it into this order: 16 18 1 23 2 33 3 34 4 42 5 6 44 7 54
Age

6. Sorting
As humans, we can sort the array just by inspection (just be looking at it), but if the array was 100,000 elements long it would be more of a challenge for us.

7. Sorting: Bubble Sort
The simplest algorithm for sort an array is called BUBBLE SORT.

8. Sorting: Bubble Sort
The simplest algorithm for sort an array is called BUBBLE SORT.
It works as follows:

9. Sorting: Bubble Sort
The simplest algorithm for sort an array is called BUBBLE SORT.
It works as follows for an array of size N:
Look at the first and second element
Are they in order?
If so, do nothing
If not, swap them around
Look at the second and third element
Do the same
Keep doing this until you get to the end of the array
Go back to the start again keep doing this whole process for N times.

10. Sorting: Bubble Sort Lets look at the swapping bit
if I wanted to swap two values, the following won’t work:
Age[0] <- Age[1];
Age[1] <- Age[0];
Why not?

11. Sorting: Bubble Sort
Lets assume Age[0]=44, and Age[1]=23, if we do the following:
Age[0] <- Age[1];
Age[1] <- Age[0];
What happens is:

12. Sorting: Bubble Sort
Lets assume Age[0]=44, and Age[1]=23, if we do the following:
Age[0] <- Age[1];
Age[1] <- Age[0];
What happens is: 23

13. Sorting: Bubble Sort
Lets assume Age[0]=44, and Age[1]=23, if we do the following:
Age[0] <- Age[1];
Age[1] <- Age[0];
What happens is: 23 23

14. Sorting: Bubble Sort
Lets assume Age[0]=44, and Age[1]=23, if we do the following:
Age[0] <- Age[1];
Age[1] <- Age[0];
What happens is: 23 23 23

15. Sorting: Bubble Sort
Lets assume Age[0]=44, and Age[1]=23, if we do the following:
Age[0] <- Age[1];
Age[1] <- Age[0];
What happens is: 23 23 23 23

16. NOT a Successful swap Sorting: Bubble Sort
Lets assume Age[0]=44, and Age[1]=23, if we do the following:
Age[0] <- Age[1];
Age[1] <- Age[0];
What happens is:
NOT a
Successful
swap 23 23 23 23

17. NOT a Successful swap Age[0]=23 Age[1]=23
Sorting: Bubble Sort
Lets assume Age[0]=44, and Age[1]=23, if we do the following:
Age[0] <- Age[1];
Age[1] <- Age[0];
What happens is:
NOT a
Successful
swap
Age[0]=23
Age[1]=23 23 23 23 23

18. Sorting: Bubble Sort
We need an extra variable to make this work:

19. Sorting: Bubble Sort We need an extra variable to make this work:
Lets call it Temp_Value.

20. Sorting: Bubble Sort We need an extra variable to make this work:
Lets call it Temp_Value.
Temp_Value <- Age[1];

21. Sorting: Bubble Sort We need an extra variable to make this work:
Lets call it Temp_Value.
Temp_Value <- Age[1];
Age[1] <- Age[0];

22. Sorting: Bubble Sort We need an extra variable to make this work:
Lets call it Temp_Value.
Temp_Value <- Age[1];
Age[1] <- Age[0];
Age[0] <- Temp_Value;

23. Sorting: Bubble Sort We need an extra variable to make this work:
Lets call it Temp_Value.
Temp_Value <- Age[1];
Age[1] <- Age[0];
Age[0] <- Temp_Value; 23

24. Sorting: Bubble Sort We need an extra variable to make this work:
Lets call it Temp_Value.
Temp_Value <- Age[1];
Age[1] <- Age[0];
Age[0] <- Temp_Value; 23 23

25. Sorting: Bubble Sort We need an extra variable to make this work:
Lets call it Temp_Value.
Temp_Value <- Age[1];
Age[1] <- Age[0];
Age[0] <- Temp_Value; 23 23 44

26. Sorting: Bubble Sort We need an extra variable to make this work:
Lets call it Temp_Value.
Temp_Value <- Age[1];
Age[1] <- Age[0];
Age[0] <- Temp_Value; 23 23 44 44

27. Sorting: Bubble Sort We need an extra variable to make this work:
Lets call it Temp_Value.
Temp_Value <- Age[1];
Age[1] <- Age[0];
Age[0] <- Temp_Value; 23 23 44 44 23

28. Sorting: Bubble Sort We need an extra variable to make this work:
Lets call it Temp_Value.
Temp_Value <- Age[1];
Age[1] <- Age[0];
Age[0] <- Temp_Value; 23 23 44 44 23 23

29. Successful swap Sorting: Bubble Sort
We need an extra variable to make this work:
Lets call it Temp_Value.
Temp_Value <- Age[1];
Age[1] <- Age[0];
Age[0] <- Temp_Value; 23 23
Successful
swap 44 44 23 23

30. Age[0]=23 Age[1]=44 Successful swap
Sorting: Bubble Sort
We need an extra variable to make this work:
Lets call it Temp_Value.
Temp_Value <- Age[1];
Age[1] <- Age[0];
Age[0] <- Temp_Value; 23 23
Age[0]=23
Age[1]=44
Successful
swap 44 44 23 23

31. Sorting: Bubble Sort Let’s wrap an IF statement around this:
IF (Age[1] < Age[0])
THEN Temp_Value <- Age[1];
Age[1] <- Age[0];
Age[0] <- Temp_Value;
ENDIF;

32. Sorting: Bubble Sort And in general: IF (Age[N+1] < Age[N])
THEN Temp_Value <- Age[N+1];
Age[N+1] <- Age[N];
Age[N] <- Temp_Value;
ENDIF;

33. Sorting: Bubble Sort Let’s replace “N” with “Index”
IF (Age[Index+1] < Age[Index])
THEN Temp_Value <- Age[Index+1];
Age[Index+1] <- Age[Index];
Age[Index] <- Temp_Value;
ENDIF;

34. Sorting: Bubble Sort To get from one end of the array to another:
FOR Index IN 0 TO N-2
DO IF (Age[Index+1] < Age[Index])
THEN Temp_Value <- Age[Index+1];
Age[Index+1] <- Age[Index];
Age[Index] <- Temp_Value;
ENDIF;
ENDFOR;

35. Sorting: Bubble Sort
Does this mean we have the array sorted?

36. Sorting: Bubble Sort
Does this mean we have the array sorted? No

37. Sorting: Bubble Sort 44 23 1 42 2 33 3 16 4 54 5 6 34 7 18
Age

38. Sorting: Bubble Sort 23 44 1 42 2 33 3 16 4 54 5 6 34 7 18
Age

39. Sorting: Bubble Sort 23 44 1 42 2 33 3 16 4 54 5 6 34 7 18
Age

40. Sorting: Bubble Sort 23 42 1 44 2 33 3 16 4 54 5 6 34 7 18
Age

41. Sorting: Bubble Sort 23 42 1 44 2 33 3 16 4 54 5 6 34 7 18
Age

42. Sorting: Bubble Sort 23 42 1 33 2 44 3 16 4 54 5 6 34 7 18
Age

43. Sorting: Bubble Sort 23 42 1 33 2 44 3 16 4 54 5 6 34 7 18
Age

44. Sorting: Bubble Sort 23 42 1 33 2 16 3 44 4 54 5 6 34 7 18
Age

45. Sorting: Bubble Sort 23 42 1 33 2 16 3 44 4 54 5 6 34 7 18
Age

46. Sorting: Bubble Sort 23 42 1 33 2 16 3 44 4 54 5 6 34 7 18
Age

47. Sorting: Bubble Sort 23 42 1 33 2 16 3 44 4 54 5 6 34 7 18
Age

48. Sorting: Bubble Sort 23 42 1 33 2 16 3 44 4 34 5 6 54 7 18
Age

49. Sorting: Bubble Sort 23 42 1 33 2 16 3 44 4 34 5 6 54 7 18
Age

50. Sorting: Bubble Sort 23 42 1 33 2 16 3 44 4 34 5 6 18 7 54
Age

51. Sorting: Bubble Sort 23 42 1 33 2 16 3 44 4 34 5 6 18 7 54
Age

52. Sorting: Bubble Sort Age 23 42 1 33 2 16 3 44 4 34 5 18 6 54 723 42 1 33 2 16 3 44 4 34 5 18 6 54 7
Age
So what happened?

53. Sorting: Bubble Sort Age 23 42 1 33 2 16 3 44 4 34 5 18 6 54 723 42 1 33 2 16 3 44 4 34 5 18 6 54 7
Age
So what happened?
We have moved the largest value (54) into the correct position.

54. Sorting: Bubble Sort
Let’s do it again:

55. Sorting: Bubble Sort 23 42 1 33 2 16 3 44 4 34 5 6 18 7 54
Age

56. Sorting: Bubble Sort 23 42 1 33 2 16 3 44 4 34 5 6 18 7 54
Age

57. Sorting: Bubble Sort 23 42 1 33 2 16 3 44 4 34 5 6 18 7 54
Age

58. Sorting: Bubble Sort 23 33 1 42 2 16 3 44 4 34 5 6 18 7 54
Age

59. Sorting: Bubble Sort 23 33 1 42 2 16 3 44 4 34 5 6 18 7 54
Age

60. Sorting: Bubble Sort 23 33 1 16 2 42 3 44 4 34 5 6 18 7 54
Age

61. Sorting: Bubble Sort 23 33 1 16 2 42 3 44 4 34 5 6 18 7 54
Age

62. Sorting: Bubble Sort 23 33 1 16 2 42 3 44 4 34 5 6 18 7 54
Age

63. Sorting: Bubble Sort 23 33 1 16 2 42 3 44 4 34 5 6 18 7 54
Age

64. Sorting: Bubble Sort 23 33 1 16 2 42 3 34 4 44 5 6 18 7 54
Age

65. Sorting: Bubble Sort 23 33 1 16 2 42 3 34 4 44 5 6 18 7 54
Age

66. Sorting: Bubble Sort 23 33 1 16 2 42 3 34 4 18 5 6 44 7 54
Age

67. Sorting: Bubble Sort 23 33 1 16 2 42 3 34 4 18 5 6 44 7 54
Age

68. Sorting: Bubble Sort Age 23 1 33 2 16 3 42 4 34 5 18 6 44 7 5423 1 33 2 16 3 42 4 34 5 18 6 44 7 54
Age
So what happened?

69. Sorting: Bubble Sort Age 23 1 33 2 16 3 42 4 34 5 18 6 44 7 5423 1 33 2 16 3 42 4 34 5 18 6 44 7 54
Age
So what happened?
We have moved the second largest value (44) into the correct position.

70. Sorting: Bubble Sort
Let’s do it again:

71. Sorting: Bubble Sort 23 33 1 16 2 42 3 34 4 18 5 6 44 7 54
Age

72. Sorting: Bubble Sort 23 33 1 16 2 42 3 34 4 18 5 6 44 7 54
Age

73. Sorting: Bubble Sort 23 33 1 16 2 42 3 34 4 18 5 6 44 7 54
Age

74. Sorting: Bubble Sort 23 16 1 33 2 42 3 34 4 18 5 6 44 7 54
Age

75. Sorting: Bubble Sort 23 16 1 33 2 42 3 34 4 18 5 6 44 7 54
Age

76. Sorting: Bubble Sort 23 16 1 33 2 42 3 34 4 18 5 6 44 7 54
Age

77. Sorting: Bubble Sort 23 16 1 33 2 42 3 34 4 18 5 6 44 7 54
Age

78. Sorting: Bubble Sort 23 16 1 33 2 42 3 34 4 18 5 6 44 7 54
Age

79. Sorting: Bubble Sort 23 16 1 33 2 34 3 42 4 18 5 6 44 7 54
Age

80. Sorting: Bubble Sort 23 16 1 33 2 34 3 42 4 18 5 6 44 7 54
Age

81. Sorting: Bubble Sort 23 16 1 33 2 34 3 18 4 42 5 6 44 7 54
Age

82. Sorting: Bubble Sort 23 16 1 33 2 34 3 18 4 42 5 6 44 7 54
Age

83. Sorting: Bubble Sort 23 16 1 33 2 34 3 18 4 42 5 6 44 7 54
Age

84. Sorting: Bubble Sort 23 16 1 33 2 34 3 18 4 42 5 6 44 7 54
Age

85. Sorting: Bubble Sort Age 23 16 1 33 2 34 3 18 4 42 5 44 6 54 723 16 1 33 2 34 3 18 4 42 5 44 6 54 7
Age
So what happened?
We have moved the third largest value (42) into the correct position.

86. Sorting: Bubble Sort
Let’s do it again:

87. Sorting: Bubble Sort 23 16 1 33 2 34 3 18 4 42 5 6 44 7 54
Age

88. Sorting: Bubble Sort 16 23 1 33 2 34 3 18 4 42 5 6 44 7 54
Age

89. Sorting: Bubble Sort 16 23 1 33 2 34 3 18 4 42 5 6 44 7 54
Age

90. Sorting: Bubble Sort 16 23 1 33 2 34 3 18 4 42 5 6 44 7 54
Age

91. Sorting: Bubble Sort 16 23 1 33 2 34 3 18 4 42 5 6 44 7 54
Age

92. Sorting: Bubble Sort 16 23 1 33 2 34 3 18 4 42 5 6 44 7 54
Age

93. Sorting: Bubble Sort 16 23 1 33 2 34 3 18 4 42 5 6 44 7 54
Age

94. Sorting: Bubble Sort 16 23 1 33 2 18 3 34 4 42 5 6 44 7 54
Age

95. Sorting: Bubble Sort 16 23 1 33 2 18 3 34 4 42 5 6 44 7 54
Age

96. Sorting: Bubble Sort 16 23 1 33 2 18 3 34 4 42 5 6 44 7 54
Age

97. Sorting: Bubble Sort 16 23 1 33 2 18 3 34 4 42 5 6 44 7 54
Age

98. Sorting: Bubble Sort 16 23 1 33 2 18 3 34 4 42 5 6 44 7 54
Age

99. Sorting: Bubble Sort 16 23 1 33 2 18 3 34 4 42 5 6 44 7 54
Age

100. Sorting: Bubble Sort Age 16 23 1 33 2 18 3 34 4 42 5 44 6 54 716 23 1 33 2 18 3 34 4 42 5 44 6 54 7
Age
So what happened?

101. Sorting: Bubble Sort Age 16 23 1 33 2 18 3 34 4 42 5 44 6 54 716 23 1 33 2 18 3 34 4 42 5 44 6 54 7
Age
So what happened?
We have moved the fourth largest value (34) into the correct position.

102. Sorting: Bubble Sort
Let’s do it again:

103. Sorting: Bubble Sort 16 23 1 33 2 18 3 34 4 42 5 6 44 7 54
Age

104. Sorting: Bubble Sort 16 23 1 33 2 18 3 34 4 42 5 6 44 7 54
Age

105. Sorting: Bubble Sort 16 23 1 33 2 18 3 34 4 42 5 6 44 7 54
Age

106. Sorting: Bubble Sort 16 23 1 33 2 18 3 34 4 42 5 6 44 7 54
Age

107. Sorting: Bubble Sort 16 23 1 33 2 18 3 34 4 42 5 6 44 7 54
Age

108. Sorting: Bubble Sort 16 23 1 18 2 33 3 34 4 42 5 6 44 7 54
Age

109. Sorting: Bubble Sort 16 23 1 18 2 33 3 34 4 42 5 6 44 7 54
Age

110. Sorting: Bubble Sort 16 23 1 18 2 33 3 34 4 42 5 6 44 7 54
Age

111. Sorting: Bubble Sort 16 23 1 18 2 33 3 34 4 42 5 6 44 7 54
Age

112. Sorting: Bubble Sort 16 23 1 18 2 33 3 34 4 42 5 6 44 7 54
Age

113. Sorting: Bubble Sort 16 23 1 18 2 33 3 34 4 42 5 6 44 7 54
Age

114. Sorting: Bubble Sort 16 23 1 18 2 33 3 34 4 42 5 6 44 7 54
Age

115. Sorting: Bubble Sort 16 23 1 18 2 33 3 34 4 42 5 6 44 7 54
Age

116. Sorting: Bubble Sort Age 16 23 1 18 2 33 3 34 4 42 5 44 6 54 716 23 1 18 2 33 3 34 4 42 5 44 6 54 7
Age
So what happened?
We have moved the fifth largest value (33) into the correct position.

117. Sorting: Bubble Sort
Let’s do it again:

118. Sorting: Bubble Sort 16 23 1 18 2 33 3 34 4 42 5 6 44 7 54
Age

119. Sorting: Bubble Sort 16 23 1 18 2 33 3 34 4 42 5 6 44 7 54
Age

120. Sorting: Bubble Sort 16 23 1 18 2 33 3 34 4 42 5 6 44 7 54
Age

121. Sorting: Bubble Sort 16 18 1 23 2 33 3 34 4 42 5 6 44 7 54
Age

122. Sorting: Bubble Sort 16 18 1 23 2 33 3 34 4 42 5 6 44 7 54
Age

123. Sorting: Bubble Sort 16 18 1 23 2 33 3 34 4 42 5 6 44 7 54
Age

124. Sorting: Bubble Sort 16 18 1 23 2 33 3 34 4 42 5 6 44 7 54
Age

125. Sorting: Bubble Sort 16 18 1 23 2 33 3 34 4 42 5 6 44 7 54
Age

126. Sorting: Bubble Sort 16 18 1 23 2 33 3 34 4 42 5 6 44 7 54
Age

127. Sorting: Bubble Sort 16 18 1 23 2 33 3 34 4 42 5 6 44 7 54
Age

128. Sorting: Bubble Sort 16 18 1 23 2 33 3 34 4 42 5 6 44 7 54
Age

129. Sorting: Bubble Sort 16 18 1 23 2 33 3 34 4 42 5 6 44 7 54
Age

130. Sorting: Bubble Sort 16 18 1 23 2 33 3 34 4 42 5 6 44 7 54
Age

131. Sorting: Bubble Sort Age 16 18 1 23 2 33 3 34 4 42 5 44 6 54 716 18 1 23 2 33 3 34 4 42 5 44 6 54 7
Age
So what happened?

132. Sorting: Bubble Sort Age 16 18 1 23 2 33 3 34 4 42 5 44 6 54 716 18 1 23 2 33 3 34 4 42 5 44 6 54 7
Age
So what happened?
We have moved the sixth largest value (23) into the correct position.

133. Sorting: Bubble Sort
Let’s do it again:

134. Sorting: Bubble Sort
Let’s do it again:
Let’s not bother!

135. Sorting: Bubble Sort
Let’s do it again:
Let’s not bother!
It’s sorted!

136. Sorting: Bubble Sort 16 18 1 23 2 33 3 34 4 42 5 6 44 7 54
Age

137. Sorting: Bubble Sort
So we need two loops:

138. Sorting: Bubble Sort So we need two loops: FOR Outer-Index IN 0 TO N-1
DO FOR Index IN 0 TO N-2
DO IF (Age[Index+1] < Age[Index])
THEN Temp_Value <- Age[Index+1];
Age[Index+1] <- Age[Index];
Age[Index] <- Temp_Value;
ENDIF;
ENDFOR;

139. Sorting: Bubble Sort
PROGRAM BubbleSort: Integer Age[8] <- {44,23,42,33,16,54,34,18}; FOR Outer-Index IN 0 TO N-1 DO FOR Index IN 0 TO N-2 DO IF (Age[Index+1] < Age[Index]) THEN Temp_Value <- Age[Index+1]; Age[Index+1] <- Age[Index]; Age[Index] <- Temp_Value; ENDIF; ENDFOR; END.

140. Sorting: Bubble Sort

141. etc.