#Greatest Common Divisor First Method - Euclid's Algorithm - recurisive
def gcd1(a,b):
    if a == 0 and b != 0:
        return b
    if a != 0 and b == 0:
        return a
    #check if the numbers are positive integers, if not raise an error
    if a < 1 or b < 1:
        raise ValueError("Both numbers must be positive integers")
    return helper_gcd1(a,b)

def helper_gcd1(a,b):
    #Euclid's Algorithm: If one number is 0, the other number is the GCD. If not, divide the larger number by the smaller number, then divide the divisor by the remainder, repeat until the remainder
    if b == 0:
        return a
    if a == 0:
        return b
    if a > b:
        return helper_gcd1(a%b, b)
    else:
        return helper_gcd1(a, b%a)

#Greatest Common Divisor Second Method - Repeat Subtraction
def gcd2(a,b):
    #check if the numbers are positive integers, if not raise an error
    if a == 0 and b != 0:
        return b
    if a != 0 and b == 0:
        return a
    if a < 1 or b < 1:
        raise ValueError("Both numbers must be positive integers")
    #Euclid's Algorithm: If one
    while a != b:
        if a > b:
            a -= b
        else:
            b -= a
    return a

#Greatest Common Divisor Third Method - Euclid's Algorithm
def gcd3(a,b):
    #check if the numbers are positive integers, if not raise an error
    if a == 0 and b != 0:
        return b
    if a != 0 and b == 0:
        return a
    if a < 1 or b < 1:
        raise ValueError("Both numbers must be positive integers")
    #Euclid's Algorithm: Divide the larger number by the smaller number, then divide the divisor by the remainder, repeat until the remainder
    while b:
        a,b = b,a%b
    return a

#Time Function
import time
from tabulate import tabulate
def time_function(function):
    #input values for gcd
    input1 = [13, 18, 100, 252, 105, 625, 1000, 10000, 100000, 1000000, 3]
    input2 = [5, 24, 75, 147, 200, 500, 2100, 20000, 200000, 2000200, 0]
    #expected results for gcd
    expected = [1, 6, 25, 21, 5, 125, 100, 10000, 100000, 200,3]
    #results and times of running the gcd functions
    ret = []
    times = []
    for i in range(len(input1)):
        start = time.time() #start time
        ret.append(function(input1[i], input2[i]))  #run the function and append the result
        end = time.time()   #end time
        times.append(end-start) #calculate the time taken
    #print the results nicely
    labels2 = ["Expected", "Results", "Times"]
    table = [expected, ret, times]
    print(tabulate(table, showindex=labels2, tablefmt="fancy_grid"))


def main():
    time_function(gcd1)
    time_function(gcd2)
    time_function(gcd3)

if __name__ == "__main__":
    main()