{"id":8186,"date":"2023-06-08T06:00:04","date_gmt":"2023-06-08T04:00:04","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=8186"},"modified":"2023-06-03T18:12:24","modified_gmt":"2023-06-03T16:12:24","slug":"08-jun-23","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/08-jun-23\/","title":{"rendered":"TAD de los grafos: Grafos regulares"},"content":{"rendered":"<p>Un <a href=\"https:\/\/bit.ly\/3C16Uxn\">grafo regular<\/a> es un grafo en el que todos sus v\u00e9rtices tienen el mismo grado.<\/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   regular :: (Ix v,Num p) => Grafo v p -> Bool\n<\/pre>\n<p>tal que (regular g) se verifica si el grafo g es regular. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   \u03bb> regular (creaGrafo' D (1,3) [(1,2),(2,3),(3,1)])\n   True\n   \u03bb> regular (creaGrafo' ND (1,3) [(1,2),(2,3)])\n   False\n   \u03bb> regular (completo 4)\n   True\n<\/pre>\n<p>Comprobar que los grafos completos son regulares.<\/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_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_completos (completo)\nimport Test.Hspec (Spec, hspec, it, shouldBe)\n\nregular :: (Ix v,Num p) => Grafo v p -> Bool\nregular g = and [grado g v == k | v <- vs]\n  where vs = nodos g\n        k  = grado g (head vs)\n\n-- La propiedad de la regularidad de todos los grafos completos de orden\n-- entre m y n es\nprop_CompletoRegular :: Int -> Int -> Bool\nprop_CompletoRegular m n =\n  and [regular (completo x) | x <- [m..n]]\n\n-- La comprobaci\u00f3n es\n--    \u03bb> prop_CompletoRegular 1 30\n--    True\n\n-- Verificaci\u00f3n\n-- ============\n\nverifica :: IO ()\nverifica = hspec spec\n\nspec :: Spec\nspec = do\n  it \"e1\" $\n    regular g1 `shouldBe` True\n  it \"e2\" $\n    regular g2 `shouldBe` False\n  it \"e3\" $\n    regular (completo 4) `shouldBe` True\n  where\n    g1, g2 :: Grafo Int Int\n    g1 = creaGrafo' D (1,3) [(1,2),(2,3),(3,1)]\n    g2 = creaGrafo' ND (1,3) [(1,2),(2,3)]\n\n-- La verificaci\u00f3n es\n--    \u03bb> verifica\n--\n--    e1\n--    e2\n--    e3\n--\n--    Finished in 0.0006 seconds\n--    3 examples, 0 failures\n<\/pre>\n<p><a name=\"python\"><\/a><br \/>\n<b>Soluciones en Python<\/b><\/p>\n<pre lang=\"python\">\nfrom src.Grafo_Grado_de_un_vertice import grado\nfrom src.Grafo_Grafos_completos import completo\nfrom src.TAD.Grafo import Grafo, Orientacion, creaGrafo_, nodos\n\n\ndef regular(g: Grafo) -> bool:\n    vs = nodos(g)\n    k = grado(g, vs[0])\n    return all(grado(g, v) == k for v in vs)\n\n# La propiedad de la regularidad de todos los grafos completos de orden\n# entre m y n es\ndef prop_CompletoRegular(m: int, n: int) -> bool:\n    return all(regular(completo(x)) for x in range(m, n + 1))\n\n# La comprobaci\u00f3n es\n#    >>> prop_CompletoRegular(1, 30)\n#    True\n\n# Verificaci\u00f3n\n# ============\n\ndef test_regular() -> None:\n    g1 = creaGrafo_(Orientacion.D, (1,3), [(1,2),(2,3),(3,1)])\n    g2 = creaGrafo_(Orientacion.ND, (1,3), [(1,2),(2,3)])\n    assert regular(g1)\n    assert not regular(g2)\n    assert regular(completo(4))\n    print(\"Verificado\")\n\n# La verificaci\u00f3n es\n#    >>> test_regular()\n#    Verificado\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Un grafo regular es un grafo en el que todos sus v\u00e9rtices tienen el mismo grado. Usando el tipo abstracto de datos de los grafos, definir la funci\u00f3n, regular :: (Ix v,Num p) => Grafo v p -> Bool tal que (regular g) se verifica si el grafo g es regular. Por ejemplo, \u03bb> regular&#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\/8186"}],"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=8186"}],"version-history":[{"count":2,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/8186\/revisions"}],"predecessor-version":[{"id":8194,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/8186\/revisions\/8194"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=8186"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=8186"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=8186"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}