{"id":8176,"date":"2023-06-02T06:00:49","date_gmt":"2023-06-02T04:00:49","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=8176"},"modified":"2023-06-03T18:13:40","modified_gmt":"2023-06-03T16:13:40","slug":"02-jun-23","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/02-jun-23\/","title":{"rendered":"TAD de los grafos: Grado positivo y negativo de un v\u00e9rtice"},"content":{"rendered":"<p>El grado positivo de un v\u00e9rtice v de un grafo g es el n\u00famero de v\u00e9rtices de g adyacentes con v y su grado negativo es el n\u00famero de v\u00e9rtices de g incidentes con v.<\/p>\n<p>Usando el <a href=\"https:\/\/bit.ly\/45cQ3Fo\">tipo abstracto de datos de los grafos<\/a>, definir las funciones,<\/p>\n<pre lang=\"text\">\n   gradoPos :: (Ix v,Num p) => Grafo v p -> v -> Int\n   gradoNeg :: (Ix v,Num p) => Grafo v p -> v -> Int\n<\/pre>\n<p>tales que<br \/>\n+ <code>gradoPos g v<\/code> es el grado positivo del v\u00e9rtice <code>v<\/code> en el grafo <code>g<\/code>. Por ejemplo,<\/p>\n<pre lang=\"text\">\n     \u03bb> g1 = creaGrafo' ND (1,5) [(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)]\n     \u03bb> g2 = creaGrafo' D  (1,5) [(1,2),(1,3),(1,5),(2,4),(2,5),(4,3),(4,5)]\n     \u03bb> gradoPos g1 5\n     4\n     \u03bb> gradoPos g2 5\n     0\n     \u03bb> gradoPos g2 1\n     3\n<\/pre>\n<ul>\n<li><code>gradoNeg g v<\/code> es el grado negativo del v\u00e9rtice <code>v<\/code> en el grafo <code>g<\/code>. Por ejemplo,<\/li>\n<\/ul>\n<pre lang=\"text\">\n     \u03bb> gradoNeg g1 5\n     4\n     \u03bb> gradoNeg g2 5\n     3\n     \u03bb> gradoNeg g2 1\n     0\n<\/pre>\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_Grados_positivos_y_negativos where\n\nimport TAD.Grafo (Grafo, Orientacion (D, ND), adyacentes, creaGrafo')\nimport Data.Ix (Ix)\nimport Grafo_Incidentes_de_un_vertice (incidentes)\nimport Test.Hspec (Spec, hspec, it, shouldBe)\n\n-- 1\u00aa definici\u00f3n de gradoPos\ngradoPos :: (Ix v,Num p) => Grafo v p -> v -> Int\ngradoPos g v = length (adyacentes g v)\n\n-- 2\u00aa definici\u00f3n de gradoPos\ngradoPos2 :: (Ix v,Num p) => Grafo v p -> v -> Int\ngradoPos2 g = length . adyacentes g\n\n-- 1\u00aa definici\u00f3n de gradoNeg\ngradoNeg :: (Ix v,Num p) => Grafo v p -> v -> Int\ngradoNeg g v = length (incidentes g v)\n\n-- 2\u00aa definici\u00f3n de gradoNeg\ngradoNeg2 :: (Ix v,Num p) => Grafo v p -> v -> Int\ngradoNeg2 g = length . incidentes g\n\n-- Verificaci\u00f3n\n-- ============\n\nverifica :: IO ()\nverifica = hspec spec\n\nspec :: Spec\nspec = do\n  it \"e1\" $\n    gradoPos g1 5 `shouldBe` 4\n  it \"e2\" $\n    gradoPos g2 5 `shouldBe` 0\n  it \"e3\" $\n    gradoPos g2 1 `shouldBe` 3\n  it \"e4\" $\n    gradoNeg g1 5 `shouldBe` 4\n  it \"e5\" $\n    gradoNeg g2 5 `shouldBe` 3\n  it \"e6\" $\n    gradoNeg g2 1 `shouldBe` 0\n  it \"e7\" $\n    gradoPos2 g1 5 `shouldBe` 4\n  it \"e8\" $\n    gradoPos2 g2 5 `shouldBe` 0\n  it \"e9\" $\n    gradoPos2 g2 1 `shouldBe` 3\n  it \"e10\" $\n    gradoNeg2 g1 5 `shouldBe` 4\n  it \"e11\" $\n    gradoNeg2 g2 5 `shouldBe` 3\n  it \"e12\" $\n    gradoNeg2 g2 1 `shouldBe` 0\n  where\n    g1, g2 :: Grafo Int Int\n    g1 = creaGrafo' ND (1,5) [(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)]\n    g2 = creaGrafo' D  (1,5) [(1,2),(1,3),(1,5),(2,4),(2,5),(4,3),(4,5)]\n\n-- La verificaci\u00f3n es\n--    \u03bb> verifica\n--\n--    def. 1\n--      e1\n--      e2\n--      e3\n--      e4\n--      e5\n--      e6\n--    def. 2\n--      e1\n--      e2\n--      e3\n--      e4\n--      e5\n--      e6\n--\n--    Finished in 0.0013 seconds\n--    12 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_Incidentes_de_un_vertice import incidentes\nfrom src.TAD.Grafo import Grafo, Orientacion, Vertice, adyacentes, creaGrafo_\n\n\ndef gradoPos(g: Grafo, v: Vertice) -> int:\n    return len(adyacentes(g, v))\n\ndef gradoNeg(g: Grafo, v: Vertice) -> int:\n    return len(incidentes(g, v))\n\n# Verificaci\u00f3n\n# ============\n\ndef test_GradoPosNeg() -> None:\n    g1 = creaGrafo_(Orientacion.ND, (1,5),\n                    [(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)])\n    g2 = creaGrafo_(Orientacion.D, (1,5),\n                    [(1,2),(1,3),(1,5),(2,4),(2,5),(4,3),(4,5)])\n    assert gradoPos(g1, 5) == 4\n    assert gradoPos(g2, 5) == 0\n    assert gradoPos(g2, 1) == 3\n    assert gradoNeg(g1, 5) == 4\n    assert gradoNeg(g2, 5) == 3\n    assert gradoNeg(g2, 1) == 0\n    print(\"Verificado\")\n\n# La verificaci\u00f3n es\n#    >>> test_GradoPosNeg()\n#    Verificado\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>El grado positivo de un v\u00e9rtice v de un grafo g es el n\u00famero de v\u00e9rtices de g adyacentes con v y su grado negativo es el n\u00famero de v\u00e9rtices de g incidentes con v. Usando el tipo abstracto de datos de los grafos, definir las funciones, gradoPos :: (Ix v,Num p) => Grafo v&#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\/8176"}],"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=8176"}],"version-history":[{"count":2,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/8176\/revisions"}],"predecessor-version":[{"id":8197,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/8176\/revisions\/8197"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=8176"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=8176"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=8176"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}