sum_of_multiples.py

"""
Sum of multiples.

l the limit
m the multiple
c the count the number of multiples (l / m)
s the sum of (mc + mc^2) / 2 for each multiple of m to l

for multiple multiples, subtract the sum of the multiples
that are common between the multiples

sum of multiples of 2 & 3 up to and including 20: 173

sum of 2's multiples: 2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 = 110
sum of 3's multiples: 3 + 6 + 9 + 12 + 15 + 18 = 63
sum of common multiples: 6 + 12 + 18 = 36

110 + 63 - 36 = 173
"""
import argparse
import math


def sum_of_one_set_of_multiples(multiples, limit=20, inclusive=False):
    """Sum of multiples."""
    total = 0

    for multiple in multiples:
        count = limit // multiple if inclusive else (limit - 1) // multiple
        low = multiple * count
        high = multiple * count ** 2
        total += (low + high) / 2

    return int(total)


def lcm(a, b):
    """Get the least common multiple of two numbers."""
    gcd = math.gcd(a, b)

    if gcd == 1:
        return a * b

    return a if gcd == b else b


def lcms(multiples, limit=20, inclusive=False):
    """Get a list of least common multiples."""
    lcms = list()
    limit_check = limit if inclusive else (limit - 1)

    for a in multiples:
        for b in reversed(multiples):
            if a == b:
                return lcms

            next_lcm = lcm(a, b)

            if next_lcm <= limit_check:
                lcms.append(next_lcm)


def sum_of_common_multiples(multiples, limit=20, inclusive=False):
    """Sum of the common multiples."""
    least_common_multiples = lcms(
        multiples, limit=limit, inclusive=inclusive
    )

    return sum_of_one_set_of_multiples(
        least_common_multiples, limit=limit, inclusive=inclusive
    )


def sum_of_multiples(multiples, limit=20, inclusive=False):
    """Get the sum of multiples."""
    total = sum_of_one_set_of_multiples(
        multiples, limit=limit, inclusive=inclusive
    )
    total_common = sum_of_common_multiples(
        multiples, limit=limit, inclusive=inclusive
    )

    return int(total - total_common)


def parse_args():
    """Parse input arguments."""
    parser = argparse.ArgumentParser(description="Sum of multiples")

    parser.add_argument(
        "-i", "--inclusive",
        action="store_true",
        help="The limiter should be inclusive"
    )
    parser.add_argument(
        "-l", "--limit",
        default=20,
        type=int,
        help="The limiter for multiples"
    )
    parser.add_argument(
        "multiples",
        type=int,
        nargs="+",
        help="A list of factors to sum multiples of"
    )

    return parser.parse_args()


if __name__ == "__main__":
    arguments = vars(parse_args())
    multiples = arguments.pop("multiples")

    print(sum_of_multiples(multiples, **arguments))