1. CS212: Data Structures and Algorithms
Sorting Algorithms

2. Outline Simple Sort Selection Sort Insertion Sort
Exchange (Bubble) Sort

3. Simple Sort – Algorithm
Get a list of unsorted numbers
Repeat steps 3 through 6 until the unsorted list is empty
Compare the unsorted numbers
Select the smallest unsorted number
Move this number to the sorted list
Store a maximum value in the place of the smallest number
Stop 3

4. Simple Sort
Unsorted Array
Sorted Array 4

5. Simple Sort
Unsorted Array
Sorted Array 5

6. Simple Sort
Unsorted Array
Sorted Array 6

7. Simple Sort
Unsorted Array
Sorted Array 7

8. Simple Sort
Unsorted Array
Sorted Array 8

9. Simple Sort
Unsorted Array
Sorted Array 9

10. Simple Sort
Unsorted Array
Sorted Array 10

11. Simple Sort
Unsorted Array
Sorted Array 11

12. Selection Sort
Find minimum element in the list and also the index of the minimum element.
Min_Index = 0
for (I = start; I <= end - 1; I++)
if (A[ Min_Index] > A[ I])
Min_Index = I; 12

13. Selection Sort Swap two elements of the list Swap(I, j) {
temp = A[ I ] ;
A[ I ] = A[ j ];
A[ j ] = temp; } 13

14. Selection Sort The complete algorithm is: for i ← 1 to n-1 do
min j ← i;
min x ← A[i]
for j ← i + 1 to n do
If A[j] < min x then
min j ← j
min x ← A[j]
A[min j] ← A [i]
A[i] ← min x 14

15. Selection Sort Unsorted Array
Swap first smallest i.e. 2 with first array
location i.e. 7 15

16. Selection Sort Unsorted Array Swap second smallest i.e. 3 with second
array location i.e. 8 16

17. Selection Sort Unsorted Array
Swap third smallest i.e 4 with third array
location i.e. 5 17

18. Selection Sort Unsorted Array Swap fourth smallest i.e. 5 with fourth
array location i.e. 7 18

19. Selection Sort Unsorted Array
Swap fifth smallest i.e. 6 with fifth array
location i.e. 7 19

20. Selection Sort Unsorted Array
Swap sixth smallest i.e. 7 with sixth array
location i.e. 7 20

21. Selection Sort
Sorted Array 21

22. Insertion Sort – Algorithm
Get a list of unsorted numbers
Set a marker for the sorted section after the first number in the list
Repeat steps 4 through 6 until the unsorted section is empty
Select the first unsorted number
Swap this number to the left until it arrives at the correct sorted position
Advance the marker to the right one position
Stop 22

23. Insertion Sort 23

24. Insertion Sort 24

25. Insertion Sort for i ← 2 to n do key ← A[i] j ← i – 1
for i ← 2 to n do
key ← A[i]
j ← i – 1
while j > 0 and A[j] > key do
A[j+1] ← A[j]
j ← j – 1
A[j+1] ← key 25

26. Insertion Sort ← j After while loop j = 1 so A[2] ← 108
Start sorting...
← j
i → 66
108 56 14 89 12 34
108 1 n
key
After while loop j = 1 so
A[2] ← 108 26

27. Insertion Sort ← j Enter while loop shift up 108 Continue sorting...66
108 56 14 89 12 34 56 1 n
key
Enter while loop
shift up 108 27

28. Insertion Sort ← j Shifting i → 66 108 56 14 89 12 34 56 1 n key 6628

29. Insertion Sort ← j Renter while loop shift up 66 Continue i → 66 10814 89 12 34 56 1 n
key
Renter while loop
shift up 66 29

30. Insertion Sort ← j Shifting i → 66 108 108 14 89 12 34 56 1 n key 6630

31. Insertion Sort ← j Exit while loop A[1] ← key Continue sorting... i →66 66
108 14 89 12 34 56 1 n
key
Exit while loop
A[1] ← key 31

32. Insertion Sort ← j Insert Key i → 66 66 108 14 89 12 34 56 1 n key 5632

33. Insertion Sort ← j Continue sorting... i → 56 66 108 14 89 12 34 14 1
key 33

34. Insertion Sort ← j Continue sorting... i → 14 56 66 108 89 12 34 89 1
key 34

35. Insertion Sort Continue sorting... 14 56 66 89 108 12 34 12 14 34 5635

36. Exchange (Bubble) Sort
for i ← n to 2 do
for j ← 1 to i – 1 do
if A[j] > A[j + 1] then
A[j] ↔ A[j + 1] 36

37. Exchange (Bubble) Sort
Start sorting...
← i
j → 66
108 56 14 89 12 34 1 n 37

38. Exchange (Bubble) Sort
Continue sorting...
j →
← i 66
108 56 14 89 12 34 1 n 66 56
108 14 89 12 34
So on .. 38

39. Exchange (Bubble) Sort
Continue sorting...
← i
j → 66 56 14 89 12
108 34 1 n 66 56 14 89 12 34
108 39

40. Exchange (Bubble) Sort
Continue sorting...
j →
← i 66 56 14 89 12 34
108 1 n 40