Advent of Code 2024 day 13 part 2

from fractions import Fraction
from sys import argv


def parse_number(line, index):
    '''Parse the number starting at line[index] and the first index after
       it.'''
    acc = ''
    while index < len(line) and line[index].isdigit():
        acc += line[index]
        index += 1

    return int(acc), index


def parse_coords(line):
    '''Parse the X and Y coordinates of a button or prize.'''

    # find X then skip past 1 character
    index = line.find('X') + 2

    # parse the X value then skip 4 characters
    x, index = parse_number(line, index)
    index += 4

    # parse Y and return
    y, _ = parse_number(line, index)

    return x, y


def parse_machine(src):
    '''Parse the button and prize coordinates of a machine.'''
    return tuple(parse_coords(line) for line in src.split('\n') if line != '')


def parse(src):
    '''Parse each machine in the input.'''
    return [parse_machine(lines) for lines in src.split('\n\n')]


def solve(a1, a2, b1, b2, c1, c2):
    '''Solve a two-variable system of linear equations.'''

    # use special case of Cramer's rule:
    # https://en.wikipedia.org/wiki/Cramer's_rule#Explicit_formulas_for_small_systems
    denom = a1 * b2 - a2 * b1
    if denom == 0:
        return None, None

    # No floating-point inaccuracy issues with Fraction!
    x = Fraction(b2 * c1 - b1 * c2, denom)
    y = Fraction(a1 * c2 - c1 * a2, denom)
    return x, y


def in_range(n):
    '''Check if n is a valid number of presses'''
    return n is not None and n.is_integer() and n >= 0


def cost(a, b, prize):
    '''Calculate the token cost of winning the prize for this machine.

       A machine with no solution has a 'cost' of 0.'''
    prize = (prize[0] + 10000000000000, prize[1] + 10000000000000)
    a_presses, b_presses = solve(*a, *b, *prize)
    if in_range(a_presses) and in_range(b_presses):
        return 3 * a_presses + b_presses
    else:
        return 0


def main(machines):
    '''Calculate the total cost of winning each possible machine.'''
    return sum(cost(*machine) for machine in machines)


if __name__ == '__main__':
    # pass the path to the puzzle input as the first argument
    print(main(parse(open(argv[1]).read())))