Soluciones en Python<\/b><\/p>\n\nfrom __future__ import annotations\n\nfrom abc import abstractmethod\nfrom copy import deepcopy\nfrom functools import reduce\nfrom typing import Protocol, TypeVar\n\nfrom hypothesis import given\n\nfrom src.TAD.conjunto import (Conj, conjuntoAleatorio, elimina, esVacio,\n inserta, menor, vacio)\nfrom src.TAD_Transformaciones_conjuntos_listas import (conjuntoAlista,\n listaAconjunto)\nfrom src.TAD_Union_de_dos_conjuntos import union\n\n\nclass Comparable(Protocol):\n @abstractmethod\n def __lt__(self: A, otro: A) -> bool:\n pass\n\nA = TypeVar('A', bound=Comparable)\nB = TypeVar('B', bound=Comparable)\n\n# 1\u00aa soluci\u00f3n\n# ===========\n\n# (agrega x c) es el conjunto de los pares de x con los elementos de\n# c. Por ejemplo,\n# >>> agrega(2, inserta(9, inserta(4, inserta(3, vacio()))))\n# {(2, 3), (2, 4), (2, 9)}\ndef agrega(x: A, c: Conj[B]) -> Conj[tuple[A, B]]:\n if esVacio(c):\n return vacio()\n mc = menor(c)\n rc = elimina(mc, c)\n return inserta((x, mc), agrega(x, rc))\n\ndef productoC(c1: Conj[A], c2: Conj[B]) -> Conj[tuple[A, B]]:\n if esVacio(c1):\n return vacio()\n mc1 = menor(c1)\n rc1 = elimina(mc1, c1)\n return union(agrega(mc1, c2), productoC(rc1, c2))\n\n# La funci\u00f3n union est\u00e1 definida en el ejercicio\n# \"Uni\u00f3n de dos conjuntos\" que se encuentra en\n# https:\/\/bit.ly\/3Y1jBl8\n\n# 2\u00aa soluci\u00f3n\n# ===========\n\ndef productoC2(c1: Conj[A], c2: Conj[B]) -> Conj[tuple[A, B]]:\n xs = conjuntoAlista(c1)\n ys = conjuntoAlista(c2)\n return reduce(lambda bs, a: inserta(a, bs), [(x,y) for x in xs for y in ys], vacio())\n\n# 3\u00aa soluci\u00f3n\n# ===========\n\ndef productoC3(c1: Conj[A], c2: Conj[B]) -> Conj[tuple[A, B]]:\n xs = conjuntoAlista(c1)\n ys = conjuntoAlista(c2)\n return listaAconjunto([(x,y) for x in xs for y in ys])\n\n# 4\u00aa soluci\u00f3n\n# ===========\n\ndef agrega4Aux(x: A, c: Conj[B]) -> Conj[tuple[A, B]]:\n r: Conj[tuple[A, B]] = vacio()\n while not esVacio(c):\n mc = menor(c)\n c = elimina(mc, c)\n r = inserta((x, mc), r)\n return r\n\ndef agrega4(x: A, c: Conj[B]) -> Conj[tuple[A, B]]:\n _c = deepcopy(c)\n return agrega4Aux(x, _c)\n\ndef productoC4(c1: Conj[A], c2: Conj[B]) -> Conj[tuple[A, B]]:\n r: Conj[tuple[A, B]] = vacio()\n while not esVacio(c1):\n mc1 = menor(c1)\n c1 = elimina(mc1, c1)\n r = union(agrega4(mc1, c2), r)\n return r\n\n# 5\u00aa soluci\u00f3n\n# ===========\n\ndef agrega5Aux(x: A, c: Conj[B]) -> Conj[tuple[A, B]]:\n r: Conj[tuple[A, B]] = Conj()\n while not c.esVacio():\n mc = c.menor()\n c.elimina(mc)\n r.inserta((x, mc))\n return r\n\ndef agrega5(x: A, c: Conj[B]) -> Conj[tuple[A, B]]:\n _c = deepcopy(c)\n return agrega5Aux(x, _c)\n\ndef productoC5(c1: Conj[A], c2: Conj[B]) -> Conj[tuple[A, B]]:\n r: Conj[tuple[A, B]] = Conj()\n while not c1.esVacio():\n mc1 = c1.menor()\n c1.elimina(mc1)\n r = union(agrega5(mc1, c2), r)\n return r\n\n# Comprobaci\u00f3n de equivalencia\n# ============================\n\n# La propiedad es\n@given(c1=conjuntoAleatorio(), c2=conjuntoAleatorio())\ndef test_productoC(c1: Conj[int], c2: Conj[int]) -> None:\n r = productoC(c1, c2)\n assert productoC2(c1, c2) == r\n assert productoC3(c1, c2) == r\n assert productoC4(c1, c2) == r\n\n# La comprobaci\u00f3n de las propiedades es\n# > poetry run pytest -q TAD_Producto_cartesiano.py\n# 1 passed in 0.35s\n<\/pre>\n","protected":false},"excerpt":{"rendered":"Utilizando el tipo abstracto de datos de los conjuntos (https:\/\/bit.ly\/3HbB7fo) definir la funci\u00f3n productoC :: (Ord a, Ord b) => Conj a -> Conj b -> Conj (a,b) tal que productoC c1 c2 es el producto cartesiano de los conjuntos c1 y c2. Por ejemplo, \u03bb> ej1 = inserta 2 (inserta 5 vacio) \u03bb> ej2…<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_kad_post_transparent":"","_kad_post_title":"","_kad_post_layout":"","_kad_post_sidebar_id":"","_kad_post_content_style":"","_kad_post_vertical_padding":"","_kad_post_feature":"","_kad_post_feature_position":"","_kad_post_header":false,"_kad_post_footer":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"footnotes":"","_jetpack_memberships_contains_paid_content":false},"categories":[581],"tags":[331,585],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7994"}],"collection":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/comments?post=7994"}],"version-history":[{"count":2,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7994\/revisions"}],"predecessor-version":[{"id":7996,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7994\/revisions\/7996"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=7994"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=7994"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=7994"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}