from functools import partial
from typing import Callable, Iterator, NamedTuple
from math import log


test_input = """
190: 10 19
3267: 81 40 27
83: 17 5
156: 15 6
7290: 6 8 6 15
161011: 16 10 13
192: 17 8 14
21037: 9 7 18 13
292: 11 6 16 20
""".strip()

test_solution_p1 = 3749
test_solution_p2 = 11387


def solve_p1(puzzle_input: str) -> int:
    equations = _parse_equations(puzzle_input)
    calibration_guard = partial(
        _is_calibrated,
        [
            int.__add__,
            int.__mul__,
        ],
    )
    return sum(equation.target for equation in filter(calibration_guard, equations))


def solve_p2(puzzle_input: str) -> int:
    equations = _parse_equations(puzzle_input)
    calibration_guard = partial(
        _is_calibrated,
        [
            int.__add__,
            int.__mul__,
            _concat_ints,
        ],
    )
    return sum(equation.target for equation in filter(calibration_guard, equations))


class Equation(NamedTuple):
    target: int
    factors: tuple[int, ...]


def _parse_equations(puzzle_input: str) -> Iterator[Equation]:
    for line in puzzle_input.split("\n"):
        if line:
            result_string, _, factors_string = line.partition(": ")
            yield Equation(
                int(result_string),
                tuple(map(int, factors_string.split(" "))),
            )


Operator = Callable[[int, int], int]


def _is_calibrated(operators: list[Operator], equation: Equation) -> bool:
    def _eval_permutations(factors: tuple[int, ...]) -> Iterator[int]:
        assert len(factors) > 0
        tail = factors[-1]
        if len(factors) == 1:
            yield tail
            return
        for head in _eval_permutations(factors[:-1]):
            if head > equation.target:
                continue
            for operator in operators:
                yield operator(head, tail)

    return any(
        result == equation.target for result in _eval_permutations(equation.factors)
    )


def _concat_ints(a: int, b: int) -> int:
    return 10 ** int(log(b, 10) + 1) * a + b