Lösungen Aufgabe 13 2024

Code:
#!/usr/bin/env python3



points = set('ABCDEFGHIJKLMNOP')



edges = set(frozenset(ed) for ed in 'AB CD EF GH IJ KL MN OP AC BD EG FH IK JL MO NP AE BF CG DH IM JN KO LP AI BJ CK DL EM FN GO HP'.split())



squares = set(frozenset(sq) for sq in 'ABDC EFGH IJLK MNPO ACGE BDHF IKOM JLPN ABFE CDHG IJNM KLPO ABJI CDLK EFNM GHPO ACKI BDHF EGOM FHPN'.split())



cubes = set(frozenset(cu) for cu in 'ABCDEFGH IJKLMNOP ABIJEFMN CDKLGHOP ABCDIJKL EFGHMNOP BDFHJLNP ACEGIKMO'.split())



def increasing_subsets(st):

    def ssos(st, size):

        if size == 0:

            yield set()

        elif st:

            nst = st.copy()

            elem = nst.pop()

            for ss in ssos(nst, size):

                yield ss

            for ss in ssos(nst, size - 1):

                yield {elem} | ss

    for i in range(len(st) + 1):

        for ss in ssos(st, i):

            yield ss



def isconnected(st):

    if not st:

        return True

    openset = set(st)

    closedset = { openset.pop() }

    changed = True

    while changed:

        changed = False

        for po in openset.copy():

            for pc in closedset:

                if frozenset({po, pc}) in edges:

                    openset -= { po }

                    closedset |= { po }

                    changed = True

                    break;



    if openset:

        return False

    else:

        return True



# Now assume A has a Ruby and B doesn't

pointswithoutAB = points - {'A', 'B'}



for nonrubies in increasing_subsets(pointswithoutAB):

    nonrubies = nonrubies | { 'B' }

    rubies = points - nonrubies



    print(f'check {nonrubies=}')



    if not isconnected(nonrubies):

        continue



    if not isconnected(rubies):

        continue



    if not all(isconnected(nonrubies & sq) for sq in squares):

        continue



    if not all(isconnected(nonrubies & cu) for cu in cubes):

        continue



    if not all(isconnected(rubies & sq) for sq in squares):

        continue



    if not all(isconnected(rubies & cu) for cu in cubes):

        continue



    if not all(any(not isconnected((rubies - {r}) & sq) for sq in squares) for r in rubies):

        continue



    print(f'{nonrubies=}')

    break