m = 100 # integer to apply the conjecture on

n = m
while n != 1:
    print(n, end=", ")
    if n % 2 == 0:
        n = n // 2
    else:
        n = 3 * n + 1
print(1) # 1 was not printed
print(m, "is OK")

limit = 10
m = 1
while m <= limit:
    n = m
    while n != 1:
        if n % 2 == 0:
            n = n // 2
        else:
            n = 3 * n + 1
    print(m, "is OK")
    m += 1

for m in range(111, 98, -2):
    print(m, end=" ")

start, stop = 99, 110
for m in range(start, stop + 1):
    n = m
    while n != 1:
        if n % 2 == 0:
            n = n // 2
        else:
            n = 3 * n + 1
    print(m, "is OK")

mixed_list = [3, 5.14, "hello", True, [5], range]
print(mixed_list, type(mixed_list))

mixed_list[0]

mixed_list[2]

mixed_list[-1]

mixed_list[-2] == mixed_list[2]

mixed_list[1:3]

mixed_list[:2]

mixed_list[1:]

mixed_list[:-2]

mixed_list[:1]

mixed_list[7:8]

mixed_list[7]

mixed_list + [1, 2, 3]

mixed_list

mixed_list = mixed_list + [1, 2, 3]
mixed_list

numbers = [10, 3, 2, 56]
numbers

sum(numbers)

sum(['hello','world'])

len(numbers)

len(['hi','hello'])

print(sorted(numbers))
print(numbers)
print(numbers.sort())
print(numbers)

mixed_list

for item in mixed_list:
    if type(item) == str:
        print(item)

for i in range(len(mixed_list)):
    print(i)
    if type(mixed_list[i]) == str:
        print(mixed_list[i])

print(i)

i = 0 # important!
while i < len(mixed_list) and type(mixed_list[i]) != int:
    if type(mixed_list[i]) == str:
        print(mixed_list[i])
    i += 1

print(i)

[x ** 2 for x in range(1, 11)]

[x ** 0.5 for x in range(1, 21) if x % 2 == 1]

l = []
l += [1]
l

grades = [33, 55,45,87,88,95,34,76,87,56,45,98,87,89,45,67,45,67,76,73,33,87,12,100,77,89,92]

avg = sum(grades)/len(grades)
above = 0
for gr in grades:
    if gr > avg:
        above += 1
        
print(above, "grades are above the average", avg)

avg = sum(grades)/len(grades)
above = len([gr for gr in grades if gr > avg])
        
print(above, "grades are above the average", avg)

def max2(a,b):
    if a >= b:
        return a
    else:
        return b

def min2(a,b):
    if a <= b:
        return a
    else:
        return b
    
def max3(a,b,c):
    if a >= b and a >= c:
        return a
    elif b >= a and b >= c:
        return b
    else:
        return c

def max3v2(a,b,c):
    max_ab = max2(a,b)
    return max2(max_ab,c)

print(max2(5,10))
print(min2(5,10))
print(max3(5,10,10))
print(max3v2(5,10,10))

%timeit max3(100,45,67)
%timeit max3(45,67,100)
%timeit max3v2(100,45,67)
%timeit max3v2(45,67,100)

def is_perfect(n):
    '''
    is_perfect(integer) -> bool
    Return True iff n equals the sum of its divisors
    '''
    if n == sum(divisors(n)):
        return True
    else:
        return False

help(is_perfect)

def divisors(n):
    '''
    divisors(integer) -> list of integers
    Return the proper divisors of n (numbers less than n that divide evenly into n).
    '''
    return [div for div in range(1,n) if n % div == 0]

def is_perfect(n):
    '''
    is_perfect(integer) -> bool
    Return True iff n equals the sum of its divisors
    '''
    return n == sum(divisors(n))

print("perfect numbers in range(1,1000)\n")
print([n for n in range(1,1001) if is_perfect(n)])

def divisors2(n):
    divs = []
    for m in range(2,round(n * 0.5)):#1 and n**0.5 will be handled separately. why?
        if n % m == 0:
            divs += [m, n // m]
    divs += [1] # 1 surely divides n
    return divs

print(divisors(6))
print(divisors2(6))

%timeit -n 100 divisors(10**4)
%timeit -n 100 divisors2(10**4)