{"id":8188,"date":"2023-06-09T06:00:59","date_gmt":"2023-06-09T04:00:59","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=8188"},"modified":"2023-06-03T18:12:06","modified_gmt":"2023-06-03T16:12:06","slug":"09-jun-23","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/09-jun-23\/","title":{"rendered":"TAD de los grafos: Grafos k-regulares"},"content":{"rendered":"<p>Un <a href=\"https:\/\/bit.ly\/3C16Uxn\">grafo k-regular<\/a> es un grafo con todos sus v\u00e9rtices son de grado k.<\/p>\n<p>Usando el <a href=\"https:\/\/bit.ly\/45cQ3Fo\">tipo abstracto de datos de los grafos<\/a>, definir la funci\u00f3n,<\/p>\n<pre lang=\"text\">\n   regularidad :: (Ix v,Num p) => Grafo v p -> Maybe Int\n<\/pre>\n<p>tal que (regularidad g) es la regularidad de g. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   regularidad (creaGrafo' ND (1,2) [(1,2),(2,3)]) == Just 1\n   regularidad (creaGrafo' D (1,2) [(1,2),(2,3)])  == Nothing\n   regularidad (completo 4)                        == Just 3\n   regularidad (completo 5)                        == Just 4\n   regularidad (grafoCiclo 4)                      == Just 2\n   regularidad (grafoCiclo 5)                      == Just 2\n<\/pre>\n<p>Comprobar que el grafo completo de orden n es (n-1)-regular (para n de 1 a 20) y el grafo ciclo de orden n es 2-regular (para n de 3 a 20).<\/p>\n<p><b>Soluciones<\/b><\/p>\n<p>A continuaci\u00f3n se muestran las <a href=\"#haskell\">soluciones en Haskell<\/a> y las <a href=\"#python\">soluciones en Python<\/a>.<\/p>\n<p><a name=\"haskell\"><\/a><br \/>\n<b>Soluciones en Haskell<\/b><\/p>\n<pre lang=\"haskell\">\nmodule Grafo_Grafos_k_regulares where\n\nimport TAD.Grafo (Grafo, Orientacion (D, ND), nodos, creaGrafo')\nimport Data.Ix (Ix)\nimport Grafo_Grado_de_un_vertice (grado)\nimport Grafo_Grafos_regulares (regular)\nimport Grafo_Grafos_completos (completo)\nimport Grafo_Grafos_ciclos (grafoCiclo)\nimport Test.Hspec (Spec, hspec, it, shouldBe)\n\nregularidad :: (Ix v,Num p) => Grafo v p -> Maybe Int\nregularidad g\n  | regular g = Just (grado g (head (nodos g)))\n  | otherwise = Nothing\n\n-- La propiedad de k-regularidad de los grafos completos es\nprop_completoRegular :: Int -> Bool\nprop_completoRegular n =\n  regularidad (completo n) == Just (n-1)\n\n-- La comprobaci\u00f3n es\n--    \u03bb> and [prop_completoRegular n | n <- [1..20]]\n--    True\n\n-- La propiedad de k-regularidad de los grafos ciclos es\nprop_cicloRegular :: Int -> Bool\nprop_cicloRegular n =\n  regularidad (grafoCiclo n) == Just 2\n\n-- La comprobaci\u00f3n es\n--    \u03bb> and [prop_cicloRegular n | n <- [3..20]]\n--    True\n\n-- Verificaci\u00f3n\n-- ============\n\nverifica :: IO ()\nverifica = hspec spec\n\nspec :: Spec\nspec = do\n  it \"e1\" $\n    regularidad g1             `shouldBe` Just 1\n  it \"e2\" $\n    regularidad g2             `shouldBe` Nothing\n  it \"e3\" $\n    regularidad (completo 4)   `shouldBe` Just 3\n  it \"e4\" $\n    regularidad (completo 5)   `shouldBe` Just 4\n  it \"e5\" $\n    regularidad (grafoCiclo 4) `shouldBe` Just 2\n  it \"e6\" $\n    regularidad (grafoCiclo 5) `shouldBe` Just 2\n  where\n    g1, g2 :: Grafo Int Int\n    g1 = creaGrafo' ND (1,2) [(1,2),(2,3)]\n    g2 = creaGrafo' D (1,2) [(1,2),(2,3)]\n\n-- La verificaci\u00f3n es\n--    \u03bb> verifica\n--\n--    e1\n--    e2\n--    e3\n--    e4\n--    e5\n--    e6\n--\n--    Finished in 0.0027 seconds\n--    6 examples, 0 failures\n<\/pre>\n<p><a name=\"python\"><\/a><br \/>\n<b>Soluciones en Python<\/b><\/p>\n<pre lang=\"python\">\nfrom typing import Optional\n\nfrom src.Grafo_Grado_de_un_vertice import grado\nfrom src.Grafo_Grafos_ciclos import grafoCiclo\nfrom src.Grafo_Grafos_completos import completo\nfrom src.Grafo_Grafos_regulares import regular\nfrom src.TAD.Grafo import Grafo, Orientacion, creaGrafo_, nodos\n\n\ndef regularidad(g: Grafo) -> Optional[int]:\n    if regular(g):\n        return grado(g, nodos(g)[0])\n    return None\n\n# La propiedad de k-regularidad de los grafos completos es\ndef prop_completoRegular(n: int) -> bool:\n    return regularidad(completo(n)) == n - 1\n\n# La comprobaci\u00f3n es\n#    >>> all(prop_completoRegular(n) for n in range(1, 21))\n#    True\n\n# La propiedad de k-regularidad de los grafos ciclos es\ndef prop_cicloRegular(n: int) -> bool:\n    return regularidad(grafoCiclo(n)) == 2\n\n# La comprobaci\u00f3n es\n#    >>> all(prop_cicloRegular(n) for n in range(3, 21))\n#    True\n\n# Verificaci\u00f3n\n# ============\n\ndef test_k_regularidad() -> None:\n    g1 = creaGrafo_(Orientacion.ND, (1,2), [(1,2),(2,3)])\n    g2 = creaGrafo_(Orientacion.D, (1,2), [(1,2),(2,3)])\n    assert regularidad(g1) == 1\n    assert regularidad(g2) is None\n    assert regularidad(completo(4)) == 3\n    assert regularidad(completo(5)) == 4\n    assert regularidad(grafoCiclo(4)) == 2\n    assert regularidad(grafoCiclo(5)) == 2\n    print(\"Verificado\")\n\n# La verificaci\u00f3n es\n#    >>> test_k_regularidad()\n#    Verificado\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Un grafo k-regular es un grafo con todos sus v\u00e9rtices son de grado k. Usando el tipo abstracto de datos de los grafos, definir la funci\u00f3n, regularidad :: (Ix v,Num p) => Grafo v p -> Maybe Int tal que (regularidad g) es la regularidad de g. Por ejemplo, regularidad (creaGrafo&#8217; ND (1,2) [(1,2),(2,3)]) ==&#8230;<\/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":[453],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/8188"}],"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=8188"}],"version-history":[{"count":2,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/8188\/revisions"}],"predecessor-version":[{"id":8193,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/8188\/revisions\/8193"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=8188"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=8188"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=8188"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}