sorting algorithm graphical method

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This document describes and compares several common sorting algorithms, including bubble sort, selection sort, and insertion sort. It provides pseudocode examples to illustrate how each algorithm works and analyzes their time complexities. Specifically, it shows the steps to sort sample data using each algorithm through multiple iterations and compares their performance, with bubble, selection, and insertion sorts having O(n2) time and others like merge and quicksort having O(n log n) time.

SORTING ALGORITHM GRAPHICAL
METHOD
Made by-
Shantanu
BCA-V sem.
Guided by
Mr. Sanjeev Kumar Singh

INTRODUCTION
• Sorting of an array is the process of arranging the data present is an
array in a particular manner either by ascending or descending order.
• A sorting algorithm is an algorithm that puts elements of a list in a
certain order.
• The most used orders are numerical order and lexicographical order.

WHAT DOES SORTS DO?
I am taking an example:-
Take: [6,24,10,76,35,0,37]
Make the above pattern into this:[0,6,10,24,35,37,76]

OBJECTIVE
The main objective of my project is to graphically show sorting
algorithm by arranging the records in ascending order.
The language used in my project is .NET .

BASIC FLOW DIAGRAM
USER
SELECTION
OF SORTING
ALGORITHM
SORTED ARRAY
OUTPUT BY
GRAPHICAL
REPRESENTATION

SORTING METHODS
The popular sorting methods are:
• Bubble sort
• Selection sort
• Insertion sort
• Merge sort
• Quick sort

HOW FAST CAN WE SORT?
• Selection Sort, Bubble Sort, Insertion Sort :
O(n2)
• Heap Sort, Merge sort :
O(n log n)
• Quicksort :
• Average: O(n log n)
• Best: O(n log n) or O(n)

BUBBLE SORT
• Bubble Sort works by comparing each element of the list with the
element next to it and swapping them if required. With each pass, the
largest of the list is "bubbled" to the end of the list whereas the
smaller values sink to the bottom.

ILLUSTRATION OF BUBBLE SORT
Consider the following array of four items:
Now I will sort this array using bubble sort:
FIRST ITERATION :
1st pass:
90 45 70 15
90 45 70 15
45 90 70 15

2nd pass:
3rd pass:
SECOND ITERATION :
1st pass:
2nd pass:
45 70 90 15
45 70 15 90
45 70 15 90
45 70 15 90
45 15 70 90

THIRD ITERATION :
1st pass:
45 15 70 90
15 45 70 90
As seen from the above illustration , that for four elements, we need
three iterations . It means that if there are n elements then there will
be n-1 iterations.

$IMPLIMENTATION IN C void BubbleSort(int a[], int array_size) { int i, j, temp; for (i = 0; i < (array_size - 1); ++i) { for (j = 0; j < array_size - 1 - i; ++j ) { if (a[j] > a[j+1]) { temp = a[j+1]; a[j+1] = a[j]; a[j] = temp; } } } }$

SELECTION SORT
• The idea of Selection Sort is rather simple. It basically determines the
minimum (or maximum) of the list and swaps it with the element at
the index where its supposed to be. The process is repeated such that
the nth minimum (or maximum) element is swapped with the
element at the (n-1)th index of the list.

ILLUSTRATION OF SELECTION SORT
Consider the following array of four items:
Now I will sort this array using selection sort:
1st pass:
2nd pass:
3rd pass:
90 45 70 15
15 90 45 70
15 45 90 70
15 45 70 90

IMPLIMENTATION IN C
for(i=0;i<=10;i++)
{
for(j=i+1;j<=10;j++)
{
if(a[i]>a[j])
{
t=a[i];
a[i]=a[j];
a[j]=t;
}
}
}

INSERTION SORT
The Insertion Sort algorithm is a commonly used algorithm. In this type
of sorting algorithm , the array is divided into two parts : the sorted
and unsorted array. The very first element of the array is treated as
sorted array and the rest of array is treated as the unsorted array . For
sorting, first of all the first element of the unsorted array is inserted in
the sorted array. After that the second element is inserted . The
process continues till the last element of the unsorted array is inserted
in the sorted array

ILLUSTRATION OF INSERTION SORT
Consider the following array of four items:
90 45 70 15
90
45
70
15
Sorted Array
Unsorted Array

After 1st iteration:
45
90
70
15
After 2nd iteration:
Sorted Array
Unsorted Array
45
70
90
15
Sorted Array
Unsorted Array

After 3rd iteration:
15
45
70
90
Sorted Array
From the above illustration , we see that for an array of four elements ,
we need to process the array three times to get the sorted array. It
means that if there are n elements then there will be n-1 iterations.

$IMPLIMENTATION IN C void insertionSort(int a[], int array_size) { int i, j, index; for (i = 1; i < array_size; ++i) { index = a[i]; for (j = i; j > 0 && a[j-1] > index; j--) { a[j] = a[j-1]; } a[j] = index; } }$

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1. SORTING ALGORITHM GRAPHICAL METHOD Made by- Shantanu BCA-V sem. Guided by Mr. Sanjeev Kumar Singh

2. INTRODUCTION • Sorting of an array is the process of arranging the data present is an array in a particular manner either by ascending or descending order. • A sorting algorithm is an algorithm that puts elements of a list in a certain order. • The most used orders are numerical order and lexicographical order.

3. WHAT DOES SORTS DO? I am taking an example:- Take: [6,24,10,76,35,0,37] Make the above pattern into this:[0,6,10,24,35,37,76]

4. OBJECTIVE The main objective of my project is to graphically show sorting algorithm by arranging the records in ascending order. The language used in my project is .NET .

5. BASIC FLOW DIAGRAM USER SELECTION OF SORTING ALGORITHM SORTED ARRAY OUTPUT BY GRAPHICAL REPRESENTATION

6. SORTING METHODS The popular sorting methods are: • Bubble sort • Selection sort • Insertion sort • Merge sort • Quick sort

7. HOW FAST CAN WE SORT? • Selection Sort, Bubble Sort, Insertion Sort : O(n2) • Heap Sort, Merge sort : O(n log n) • Quicksort : • Average: O(n log n) • Best: O(n log n) or O(n)

8. BUBBLE SORT • Bubble Sort works by comparing each element of the list with the element next to it and swapping them if required. With each pass, the largest of the list is "bubbled" to the end of the list whereas the smaller values sink to the bottom.

9. ILLUSTRATION OF BUBBLE SORT Consider the following array of four items: Now I will sort this array using bubble sort: FIRST ITERATION : 1st pass: 90 45 70 15 90 45 70 15 45 90 70 15

10. 2nd pass: 3rd pass: SECOND ITERATION : 1st pass: 2nd pass: 45 70 90 15 45 70 15 90 45 70 15 90 45 70 15 90 45 15 70 90

11. THIRD ITERATION : 1st pass: 45 15 70 90 15 45 70 90 As seen from the above illustration , that for four elements, we need three iterations . It means that if there are n elements then there will be n-1 iterations.

12. IMPLIMENTATION IN C void BubbleSort(int a[], int array_size) { int i, j, temp; for (i = 0; i < (array_size - 1); ++i) { for (j = 0; j < array_size - 1 - i; ++j ) { if (a[j] > a[j+1]) { temp = a[j+1]; a[j+1] = a[j]; a[j] = temp; } } } }

13. SELECTION SORT • The idea of Selection Sort is rather simple. It basically determines the minimum (or maximum) of the list and swaps it with the element at the index where its supposed to be. The process is repeated such that the nth minimum (or maximum) element is swapped with the element at the (n-1)th index of the list.

14. ILLUSTRATION OF SELECTION SORT Consider the following array of four items: Now I will sort this array using selection sort: 1st pass: 2nd pass: 3rd pass: 90 45 70 15 15 90 45 70 15 45 90 70 15 45 70 90

15. IMPLIMENTATION IN C for(i=0;i<=10;i++) { for(j=i+1;j<=10;j++) { if(a[i]>a[j]) { t=a[i]; a[i]=a[j]; a[j]=t; } } }

16. INSERTION SORT The Insertion Sort algorithm is a commonly used algorithm. In this type of sorting algorithm , the array is divided into two parts : the sorted and unsorted array. The very first element of the array is treated as sorted array and the rest of array is treated as the unsorted array . For sorting, first of all the first element of the unsorted array is inserted in the sorted array. After that the second element is inserted . The process continues till the last element of the unsorted array is inserted in the sorted array

17. ILLUSTRATION OF INSERTION SORT Consider the following array of four items: 90 45 70 15 90 45 70 15 Sorted Array Unsorted Array

18. After 1st iteration: 45 90 70 15 After 2nd iteration: Sorted Array Unsorted Array 45 70 90 15 Sorted Array Unsorted Array

19. After 3rd iteration: 15 45 70 90 Sorted Array From the above illustration , we see that for an array of four elements , we need to process the array three times to get the sorted array. It means that if there are n elements then there will be n-1 iterations.

20. IMPLIMENTATION IN C void insertionSort(int a[], int array_size) { int i, j, index; for (i = 1; i < array_size; ++i) { index = a[i]; for (j = i; j > 0 && a[j-1] > index; j--) { a[j] = a[j-1]; } a[j] = index; } }

21. THANK YOU

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