This document discusses various sorting algorithms like insertion sort, bubble sort, selection sort and quick sort. It provides pseudocode to implement insertion sort, bubble sort and selection sort. Insertion sort works by inserting elements in the sorted position of a list. Bubble sort works by exchanging adjacent elements to push larger elements to the end. Selection sort finds the minimum element and swaps it with the first unsorted element in each iteration. Quick sort is a highly efficient sorting algorithm that works by selecting a pivot element.

1. BIRLA VISHVAKARMA
MAHAVIDHYALAYA
Sorting in DATA STRUCTURE
Sr. No. Names Enrollment No.
1. Rudra Patel 140080116050
2. Rishab Shah 140080116054
3. Tushar Gonawala 140080116059
4. Rushang Patel 140080116064
PRESENTED TO: Prof. Vikram

2. SORTING
• Sorting is the process of ordering a list of elements in either ascending order or descending order.
• Sorting can be divided into two categories:
1. Internal Sorting: takes place in the main memory of the computer. It can take advantage of
the random access nature of the main memory. Element to be sorted is stored in an
integer array.
2. External Sorting: is carried on secondary memory. It becomes a necessity if the number of
elements to be sorted is too large to be fit in the main memory. Algorithm should always
take into account that movement of data between secondary storage and main storage is
best done by moving a block of contiguous element.

3. INSERTION SORT
• Insertion sort is based on the principle of inserting the element at its correct place in a previously
sorted list. It can be varied from 1 to n-1 to sort the entire array.
1st Iteration
0 5 1 9 2 6 4
2nd Iteration
0 1 5 9 2 6 4
3rd Iteration
0 1 5 9 2 6 4
4th Iteration
0 1 2 5 9 6 4
5th Iteration
0 1 2 5 6 9 4
6th Iteration
0 1 2 4 5 9 6
Sorted Unsorted
Sorted
Sorted
Sorted
Sorted
Sorted
Unsorted
Unsorted
Unsorted
Unsorted

4. ALGORITHM
void insertion_sort( int a[ ] , int n)
{
int I, j, temp;
for (i = 1 ; i < n ; i++)
{
temp = a[i];
for (j = i - 1 ; j >= 0 && a[j] > temp ; j--)
a[j + 1] = a[j];
a[j +1] = temp;
}
}

5. BUBBLE SORT
• Bubble sort is one of the simplest and the most popular sorting method. The basic idea behind
bubble sort is as a bubble rises up in water, the smallest element goes to the beginning. This
method is based on the successive selecting the smallest element through exchange of adjacent
element.
j = 0 5 6 2 8 1
j = 1 5 6 2 8 1
j = 2 5 2 6 8 1
j = 3 5 2 6 8 1
j = 0 5 2 6 1 8
j = 1 2 5 6 1 8
j = 2 2 5 6 1 8
j = 0 2 5 1 6 8
j = 1 2 5 1 6 8
j = 0 2 1 5 6 8
Sorted Array: 1 2 5 6 8
First Pass
i = 1
Second Pass
i = 2
Third Pass
i = 3
Fourth Pass
i = 1

6. ALGORITHM
void bubble_sort( int a[ ] , int n)
{
int I, j, temp;
for (i = 1 ; i < n ; i++)
for (j = i - 1 ; j <= n - i ; j++)
if(a[j] > a[j + 1])
{
temp = a[i];
a[j + 1] = a[j];
a[j] = temp;
}
}

7. SELECTION SORT
• Selection sort is a very simple sorting method. In the ith pass, we select the element with the
lowest value amongst a[i], a[i + 1],…,a[n – 1] and we swap it with a[i]. As a result, after i passes
first element will be in sorted order.
5 9 1 11 2 4 Original Array
1 9 5 11 2 4 After First Pass
1 2 5 11 9 4 After Second Pass
1 2 4 11 9 5 After Third Pass
1 2 4 5 9 11 After Fourth Pass
1 2 4 5 9 11 After Fifth Pass

8. ALGORITHM
void _sort( int a[ ] , int n)
{
int i, j, temp;
for (i = 0 ; i < n - 1 ; i++)
{
k = i;
for (j = i + 1 ; j < n ; j++)
if(a[j] < a[k])
k = j;
if ( k != i )
{
temp = a[i];
a[i] = a[k];
a[k] = temp;
}
}
}

9. Quick Sort
• Quick sort is the fastest internal sorting algorithm.
5 1 2 9 0 8 13
5 1 2 9 0 8 13
1 2 0
1 2 0
9 8 13
9 8 13
5
0
1
2 8
9
13
0 1 2 5 8 9 13

10. ALGORITHM
void _sort( int a[ ] , int n)
{
int i, j, temp;
for (i = 0 ; i < n - 1 ; i++)
{
k = i;
for (j = i + 1 ; j < n ; j++)
if(a[j] < a[k])
k = j;
if ( k != i )
{
temp = a[i];
a[i] = a[k];
a[k] = temp;
}
}
}