from typing import Any, List, Optional, overload, TypeVar
from itertools import product
from functools import cmp_to_key

from .posets_representation import MyFinitePoset

import act4e_interfaces as I

E = TypeVar("E")
X = TypeVar("X")

class SolFinitePosetMeasurement(I.FinitePosetMeasurement):
    def height(self, fp: I.FinitePoset[Any]) -> int:
        raise NotImplementedError()

    def width(self, fp: I.FinitePoset[Any]) -> int:
        raise NotImplementedError()


class SolFinitePosetConstructionOpposite(I.FinitePosetConstructionOpposite):
    def opposite(self, p: I.FinitePoset[X]) -> I.FinitePoset[X]:
        e = p.carrier().elements()
        values = []
        for a, b in product(e, e):
            if p.holds(a, b):
                # then the opposite holds(b, a)
                values.append((b, a))
        return MyFinitePoset(p.carrier(), values)


class SolFinitePosetSubsetProperties(I.FinitePosetSubsetProperties):
    def is_chain(self, fp: I.FinitePoset[X], s: List[X]) -> bool:
        try:
            def cmp(a, b):
                return fp._cmp(a, b)

            s_sorted = sorted(s, key=cmp_to_key(cmp))
        except RuntimeError as e:
            return False
        return True

    def is_antichain(self, fp: I.FinitePoset[X], s: List[X]) -> bool:
        # Comparison with itself should be ignored, since there is always a
        # relation to itself by antisymmetry
        not_the_same = lambda pair: not fp.carrier().equal(pair[0], pair[1])

        # Check that no elements are comparable
        for a, b in filter(not_the_same, product(s, s)):
            assert fp.carrier().contains(a) and fp.carrier().contains(b)
            if fp.holds(a, b):
                return False
        return True


class SolFinitePosetSubsetProperties2(I.FinitePosetSubsetProperties2):
    def is_lower_set(self, fp: I.FinitePoset[X], s: List[X]) -> bool:
        raise NotImplementedError()

    def is_upper_set(self, fp: I.FinitePoset[X], s: List[X]) -> bool:
        raise NotImplementedError()


class SolFinitePosetClosures(I.FinitePosetClosures):
    def upper_closure(self, fp: I.FinitePoset[X], s: List[X]) -> List[X]:
        raise NotImplementedError()

    def lower_closure(self, fp: I.FinitePoset[X], s: List[X]) -> List[X]:
        raise NotImplementedError()


class SolFinitePosetInfSup(I.FinitePosetInfSup):
    def lower_bounds(self, fp: I.FinitePoset[E], s: List[E]) -> List[E]:
        raise NotImplementedError()

    def upper_bounds(self, fp: I.FinitePoset[E], s: List[E]) -> List[E]:
        raise NotImplementedError()

    def infimum(self, fp: I.FinitePoset[E], s: List[E]) -> Optional[E]:
        raise NotImplementedError()

    def supremum(self, fp: I.FinitePoset[E], s: List[E]) -> Optional[E]:
        raise NotImplementedError()


class SolFinitePosetMinMax(I.FinitePosetMinMax):
    def minimal(self, fp: I.FinitePoset[E], S: List[E]) -> List[E]:
        raise NotImplementedError()

    def maximal(self, fp: I.FinitePoset[E], S: List[E]) -> List[E]:
        raise NotImplementedError()