from datetime import datetime


def is_happy(num, the_results=None, cache=None):
    if num in cache:
        return False
    the_total = 0
    for x in [int(y) for y in str(num)]:
        the_total += x ** 2
    if the_results is None:
            the_results = set()
    if the_total == 1:
        return True
    # Infinite loop detected
    elif the_total in the_results:
        cache.add(num)
        return False
    else:
        the_results.add(the_total)
        return is_happy(the_total, the_results, cache)
        
        
def run(the_number):
    the_ints = as_integer_array(the_number)
    pattern = []
    result = square_and_sum(the_ints)
    while result != 1 and result != the_number and result not in pattern:
        pattern.append(result)
        result = square_and_sum(as_integer_array(result))
    return result


def as_integer_array(the_number):
    return [int(x) for x in str(the_number)]


def square_and_sum(int_array):
    squared = [x * x for x in int_array]
    return sum(squared)


if __name__ == '__main__':
    count = 0
    cache = set()
    start_time = datetime.now()
    for x in range(0, 100000):
        if 1 == run(x):
            count += 1
    print('there are {} happy numbers'.format(count))
    print(datetime.now() - start_time)