jevan-smith / GCD

Implementation of several algorithms related to computing the GCD(m, n) of two integers m and n.

Authors

Made by: Jevan, and Juan

Project Goals

1. Implement several algorithms related to computing the GCD(m, n) of two integers m and n.
2. Empirically determine the run-time complexity for different kinds of input (average-case / worst-case).
3. Write a short report summarizing the outcome of project in form of tables and scatter-plots.

Requirements

• Built using python 3.7
• matplotlib is required (Version 3.0.2)
• matplotlib.pyplot
• matplotlib.patches

Expected Outputs Below

❗ Note to use 'Scatter plot mode', matplotlib must be installed! Below is our programs output for 'User testing mode'

[1] Enter 'User testing mode'
[2] Enter 'Scatter plot mode'
[3] Exit
Option: 1

Mode: User testing
[1] Task 1
[2] Task 2
[3] Task 3
[4] Go Back
[5] Exit
Option: 1

Task 1: 
Enter positive value for 'n': 4
Average number of Modulo Divisions GCD is: 1.25
Average number of Divisions GCD is: 2.75

Mode: User testing
[1] Task 1
[2] Task 2
[3] Task 3
[4] Go Back
[5] Exit
Option: 2

Task 2: 
Enter positive value for 'k': 16
Fibonacci Sequence: [1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987]
Total number of Modulo Divisions is: 92
Fibonacci value of k: 987
Number of Modulo Divisions for the value of k: 14
Time Taken to output result: 0.0

Mode: User testing
[1] Task 1
[2] Task 2
[3] Task 3
[4] Go Back
[5] Exit
Option: 3

Task 3: 
Enter positive (m > 1) value for 'm': 15
Enter positive (n > 1) value for 'n': 9
Sieve's Algorithm based on 'm': [2, 3, 5, 7, 11, 13]
Sieve's Algorithm based on 'n': [2, 3, 5, 7]
Prime factors for 'm': [3, 5]
Prime factors for 'n': [3, 3]
Middle-school GCD(15,9) = 3 = 3