Question

In python

Simply write the Euclid algorithm in a form that takes two numbers from input and prints the gcd. The code does not need to check for valid input. It must work for any pair of positive integers. Create a separate program that uses the python timeit module to provide test run-times for your code. Provide at-least 5 sample runs. Create a third file that implements another algorithm to find the gcd. Provide a program that uses the timeit module to provide sample run-times for this one as well.

Create a Microsoft word document that provides screen captures of running your two algorithms with your commentary of the results and your code. At the END of the document, include your code from your 4 python modules in TEXT format, NOT screen capture.

Answer 1

CODE 1

def eucledianGcd(a, b):

  if a == 0 :

    return b

  return eucledianGcd(b%a, a)

CODE 2)

import random

import time

for i in range(5):

a = random.randint(10, 200)

b = random.randint(10, 200)

start_time = time.time()

gcd = eucledianGcd(a, b)

end_time = time.time()

print("Run %d of Eucledian GCD took %s seconds " % (i+1, time.time() - start_time))

CODE 3)

def GCD(a,b):

  if (a == 0):

    return b

  if (b == 0):

    return a

  if (a == b):

    return a

  if (a > b):

    return GCD(a-b, b)

  return GCD(a, b-a)

CODE 4)

import random

import time

for i in range(5):

a = random.randint(10, 200)

b = random.randint(10, 200)

start_time = time.time()

gcd = GCD(a, b)

end_time = time.time()

print("Run %d of Normal GCD took %s seconds " % (i+1, time.time() - start_time))