在满足条件之前，我该如何重复“ if”语句？

Question

I'm trying to make a python program that runs the Euclidian algorithm. This is my current code:

a = float(input())
b = float(input())
aplha = float(a/b)
omega = float(b/a)

import math
if a > b:
    print(str(a) + " = " + str(b) + " * " + str(math.floor(aplha)) + " + " + str(a%b)) 
elif b > a:
    print(str(b) + " = " + str(a) + " * " + str(math.floor(omega)) + " + " + str(b%a)) 
else:
    print("Both numbers have the same value. The greatest common denominator is 1.")

How do I make it so that the if and elif keeps repeating themselves until a%b = b%a = 0?

Answer 1

Here is one way to implement the Euclidean algorithm.

import math

a = float(input())
b = float(input())

# The greatest common denominator of a and b
def gcd(a,b):
    while (b != 0):
       t = b
       b = a % b
       a = t 
    return a

if (a > b):
    print(f'{a} = {b} * {math.floor(a/b)} + {a%b}')
else:
    print(f'{b} = {a} * {math.floor(b/a)} + {b%a}')


print(f'The greatest common denominator of {a} and {b} is {gcd(a,b)}')

if a==b it is not necessarily true that the GCD is one. Consider a = 150 and b = 150 as a counter example. The greatest common denominator of a and b is 150. gcd(a,b) = 150 .

Also a note on print(f'string{var}') . Print f-string is new in Python 3 and really helpful for printing the value of variables. The way it works is

>>> var = 5
>>> print(f'The value of var is {var}')
"The value of var is 5"