465659705-15-DSA-PPT-Sorting-Techniques-I.pdf

Ice Breaker (5 mins)
2
If you were stranded on a desert island,
what three items would you want to have
with you?

Concepts
● Sorting Techniques
○ Internal Sorting
■ Bubble Sort
■ Selection Sort
■ Insertion Sort
○ External Sorting
4

Questions for this session
We will answer the following questions in this session-
● How can we sort elements in a 1-D array?
5

Sorting Techniques
6
● Internal Sorting Techniques
○ Bubble Sort
○ Selection Sort
○ Insertion Sort
○ Quick Sort
○ Radix Sort
● External Sorting Techniques
○ Merge Sort

Bubble Sort
7
● Used for sorting small set of numbers
● Compares all the elements one by one and
sorts them based on their values
● n-1 iterations/ passes are required for
sorting n numbers

Algorithm/Pseudocode: Bubble Sort
8
Algorithm Bubble_Sort ( A, n) where A is a 1-D array of n elements to be sorted
for (i = 0 ; i < ( n - 1 ); i++)
{
for (j = 0 ; j < (n - i - 1); j++)
{
if (a[j] > a[j+1])
{
Swap a[j] and a[j+1]
}
}
}

C Program: Bubble Sort
9
#include <stdio.h>
void bubble_sort(int[], int);
int main() {
int a[100], n, i;
printf("Enter the number of elementsn");
scanf("%d", &n);
printf("Enter the elementsn");
for (i = 0; i < n; i++)
scanf("%d", &a[i]);
bubble_sort(a, n);
printf("Sorted list in ascending order:n");
for ( i = 0 ; i < n ; i++ )
printf("%dn", a[i]);
return 0; }
void bubble_sort(int a[], int n)
{
int i, j, t;
for (i = 0 ; i < ( n - 1 ); i++)
{
for (j = 0 ; j < (n - i - 1); j++)
{
if (a[j] > a[j+1])
{
t = a[j];
a[j] = a[j+1];
a[j+1] = t;
} } } }

Time Complexity of Bubble Sort-
● Best Case Complexity- O(n2
)
● Average Case Complexity- O(n2
)
● Worst Case Complexity- O(n2
)
Advantages-
● It is popular and easy to implement
● It sorts the numbers without using additional temporary storage
Disadvantage-
● This approach does not work for lists having large number of elements
Complexity, Advantages and Disadvantage: Bubble Sort
10

Insertion Sort
11
● Simple sorting algorithm
● Sorts the elements by shifting them one at a
time
● n-1 iterations/passes
● Sorting starts with the second element as the key
● Key compared with elements before it
● Key is then put in its appropriate location

Algorithm/Pseudocode: Insertion Sort
12
Algorithm Insertion_Sort ( A, n) where A is a 1-D array of n elements to be sorted
for (int i = 1 ; i <= n - 1; i++)
{
int j = i, t;
while ( j > 0)
{
if(arr[j] < arr[j-1])
{
Swap arr[j] and arr[j-1]
}
j--;
}
}

Identify the solution: Insertion Sort (5 mins)
13
Can you quickly write the C program for
implementing Insertion Sort algorithm?

Solution: Insertion Sort: C Program
14
#include <stdio.h>
void insertion_sort(int[], int);
int main() {
int a[100], n, i;
scanf("%d", &n);
for (i = 0; i < n; i++)
scanf("%d", &a[i]);
insertion_sort(a, n);
for ( i = 0 ; i < n ; i++ )
return 0; }
void insertion_sort(int a[], int n)
{
for (int i = 1 ; i <= n - 1; i++)
{
int j = i, t;
while ( j > 0)
{
if(arr[j] < arr[j-1])
{
t = arr[j];
arr[j] = arr[j-1];
arr[j-1] = t;
}
j--; } } }

Time Complexity of Bubble Sort-
● Best Case Complexity- O(n)
)
)
Advantages-
● This algorithm has the simplest implementation
● It is stable and does not change the relative ordering of elements with equal values
● It is more eﬃcient compared to Bubble and Selection Sort
Disadvantages-
● This algorithm works well for smaller data sets but is not suitable for larger data sets
● It requires additional memory space for sorting the elements
Complexity, Advantages and Disadvantages: Insertion Sort
15

InClass Activity: Selection Sort
Instructions:
Activity Type- Exploration
Students can divide themselves into groups of 2
Time Allotted for this activity is 20 minutes
Question:
Develop and Analyze the algorithm/ C program for implementing Selection Sort technique
16

Solution: Selection Sort
● Simple sorting technique
● Uses n-1 iterations/passes for sorting n elements
● Works as follows-
○ 1st iteration- Replaces smallest array element with the
element in 0th position/ index
○ 2nd iteration- Replaces second smallest array element
with the element in 1st index/ position and so on
○ This continues till all elements are sorted
17

Solution: Algorithm of Selection Sort
Algorithm Selection_Sort ( A, n) where A is a 1-D array of n elements to be sorted
for (int i = 0 ; i < ( n - 1 ) ; i++ )
{
temp = i;
for (j = i + 1 ; j < n ; j++ )
{
if ( arr[temp] > arr[j] )
temp = j;
}
if ( temp != i )
{
Swap a[i] and a[temp]
}
}
18

void selection_sort(int a[], int n) {
int temp,t,j;
for (int i = 0 ; i < ( n - 1 ) ; i++ ) {
temp = i;
for (j = i + 1 ; j < n ; j++ ) {
if ( arr[temp] > arr[j] )
temp = j;
}
if ( temp != i ) {
t = arr[i];
arr[i] = arr[temp];
arr[temp] = t;
} } }
Solution: C Program for Selection Sort
19
#include <stdio.h>
void selection_sort(int[], int);
int main() {
int a[100], n, i;
scanf("%d", &n);
for (i = 0; i < n; i++)
scanf("%d", &a[i]);
selection_sort(a, n);
for ( i = 0 ; i < n ; i++ )
return 0; }

Time Complexity of Selection Sort-
● Best Case Complexity- O(n2
)
)
)
Advantages-
● It is popular and easy to implement
● It sorts the numbers without using additional temporary storage
Disadvantage-
● This approach does not work for lists having large number of elements
Solution: Complexity, Advantages and Disadvantage of Selection Sort
20

Learning Outcomes
In this session, you have learnt to:
1. Deﬁne the basic concepts of sorting the array elements
2. Explain the algorithms for internal sorting techniques
3. Design and implement the appropriate sorting technique for developing solutions to real-world
problems and applications in C
4. Students will be able to analyze the complexity of sorting algorithms
5. Students will be able to sort a list of elements by deciding and choosing the appropriate sorting
algorithm
Go through the following learning resources on the platform
● Sorting Techniques-I
21

Q & A
If you have more questions, please post them in the community on
the platform.
22

What Next?
In the next session the following concepts will be covered
● Sorting Techniques
○ Quick Sort
○ Merge Sort
○ Radix Sort
Go through the following learning resources on the platform
• Sorting Techniques-II
23

465659705-15-DSA-PPT-Sorting-Techniques-I.pdf

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