The document discusses three sorting algorithms - insertion sort, selection sort, and bubble sort. It provides descriptions of the sorting processes for each algorithm along with code examples and characteristics. Videos are also included to demonstrate how each algorithm works through animations of the sorting process.

1. CS261
DATA STRUCTURES & ALGORITHMS
(WEEK-7)
LECTURE-13 & 14
INTRODUCTION TO DATA STRUCTURES &
ALGORITHMS
Lecturer
Azka Aziz
Azka.a@scocs.edu.pk

2. Data structures & Algorithms
Lecture#13 Sorting

3. Lecture contents
Sorting
Insertion Sort
Selection Sort
Bubble Sort

4. Sorting
Arranging elements of a list / set in some particular order based
on some criteria
Purpose of Sorting
Bringing set/list elements in some ordered / sequence
Categorize elements
Group elements with similar characteristics
Making searching process very efficient
Making merging of sorted elements very efficient

5. Typical Sorting orders
Ascending Order
Arranging elements of a list starting from smallest value to largest value e.g. A
to Z, 0 to 9
Descending Order
Opposite to asceinding order. It arranges elements of a list starting from
largest value to smallest value e.g. Z to A, 9 to 0

6. Sorting Algorithms …….. Insertion Sort
Say an array (to be sorted) has N elements
We split array into two parts; first part contains sorted elements while
second part contains elements that are not sorted yet
Initially the sorted part contains only one element (as it is sorted obviously)
while second part contains N-1 elements
Sorted Elements Elements not sorted yet
3 4 6 22 98 35 34 18 11 65

7. Insertion sort process
Insertion sort is an iterative process
During every iteration one element (immediately next to sorted part) is taken
from unsorted part and is inserted into sorted part such a way that resultant
sorted part remains sorted with one more elements into it
Sorted Elements Elements not sorted yet
3 4 6 22 98 35 34 18 11 65
Sorted Elements Elements not sorted yet
3 4 6 22 98 35 34 18 11 65

8. Insertion sort process
We keep iterating until that part of list containing unsorted elements keeps
no element at all
At this point resultant list is sorted
6 4 3 22 98 35 34 18 11 65
4 6 3 22 98 35 34 18 11 65
3 4 6 11 18 22 34 35 65 98
3 4 6 22 98 35 34 18 11 65

9. Insertion sort … animation
animation url: https://en.wikipedia.org/wiki/File:Insertion-sort-example-300px.gif

10. Sorting Algorithms …….. Insertion Sort
Execute it on
board for sample
data:

11. Insertion Sort … C++ Code
int data[MAX]={10, 25, 90, 5, 61, 44, 82, 72, 38,
59};
int n = MAX-1, key, j, i;
for(i=1; i<MAX; i++){
key = data[i];
j = i-1;
while(j>=0 && data[j] > key){
data[j+1]=data[j]; j--;
}
data[j+1]=key;
}
for(i=0; i<MAX;i++){
std::cout<<data[i]<<",";
}
Execute it on board for
given data:

12. Insertion sort … characteristics
Simple algorithm
Efficient for small data set
Stable sort (does not swap identical elements)
Requires constant external memory (memory beyond data array)
For data already sorted / almost sorted array requires O(N) time
For reverse sorted array requires O(N2) time

13. Bubble sort
Say an array (to be sorted) has N elements
Starting from bottom of list (Nth element of data list) every element is
compared with its neighboring element (immediately above it) sequentially
After comparison whichever element is smaller, moves up and other moves
down (like lighter air bubbles in water)
When one complete round is over, smallest element is at the top of the list

14. Bubble sort
After one round is over, we start again from bottom of the list and repeat the
process
Now when N-1 rounds are over, all list elements are sorted

15. Bubble sort process … one complete round
12
43
71
20
3
36
24
12
43
71
20
3
24
36
12
43
71
20
3
24
36
12
43
71
3
20
24
36
12
43
3
71
20
24
36
12
3
43
71
20
24
36
3
12
43
71
20
24
36
At the end of complete round, only top element is guaranteed to be the
smallest (ascending sort)
We have to start over from bottom for another round to get second smallest
value at its right place

16. Bubble sort process … round 2
3
12
43
71
20
24
36
3
12
43
71
20
24
36
3
12
43
71
20
24
36
3
12
43
20
71
24
36
3
12
20
43
71
24
36
3
12
20
43
71
24
36

17. Bubble sort process … round 3
3
12
20
43
71
24
36
3
12
20
43
71
24
36
3
12
20
43
24
71
36
3
12
20
24
43
71
36
3
12
20
24
43
71
36

18. Bubble sort process … round 4
3
12
20
24
43
71
36
3
12
20
24
43
36
71
3
12
20
24
36
43
71
3
12
20
24
36
43
71

19. Bubble sort process … round 5
3
12
20
24
36
43
71
3
12
20
24
36
43
71
3
12
20
24
36
43
71

20. Bubble sort process … round 6
3
12
20
24
36
43
71
3
12
20
24
36
43
71
Final outcome:
Sorted Array

21. Bubble sort … algorithm

22. Bubble sort process … Source code
Code it yourself

23. Bubble sort … characteristics
Simple algorithm
Very popular algorithm (very inefficient though)
Easier to implement
Compares adjacent values only and swaps if necessary (if values are not in
order)
It is a slow sorting algorithm requiring O(N2) steps to sort an array of values

24. Data structures & Algorithms
Lecture#14 Sorting(continue)

25. Selection Sort … The process
1. We have N elements in the list
2. Find out the smallest value (ascending order) from the list and replace it
with 1st element in the list
3. Step 2 keeps the smallest value to its appropriate position while leaving the
unsorted list’s size to one less than actual size
4. We can keep repeating steps 2 & 3 until unsorted list size reduces to 1. At
that point, whole list is sorted

26. Selection sort process … Round 1

27. Selection sort process … Round 2

28. Selection sort process … Round 3

29. Selection sort process … Round 4

30. Selection sort process … Round 5

31. Selection sort process … Round 5

32. Selection sort process … Round 6

33. Selection sort process … Round 7

34. Selection sort process … Round 8

35. Sorting Algorithms …….. Selection Sort
Execute it on board for
sample data:

36. Selection sort sort process … Source code
Code it yourself

37. Selection sort … characteristics
Simple sorting technique
It is called Selection Sort as it repeatedly selects the smallest/largest in a sub-
array of unsorted elements
An item at moves only once
Method of choice for files containing very large records and small keys
It is a slow sorting algorithm requiring O(N2) steps to sort an array of values in
worst case

38. Sorting Algorithms ….. Videos
1. Selection Sort
https://www.youtube.com/watch?v=f8hXR_Hvybo
https://www.youtube.com/watch?v=lx9G71uLXIg
2. Insertion Sort
https://www.youtube.com/watch?v=DFG-XuyPYUQ
https://www.youtube.com/watch?v=TwGb6ohsvUU
3. Bubble Sort
https://www.youtube.com/watch?v=Ui97-_n5xjo
https://www.youtube.com/watch?v=Ui97-_n5xjo