{"id":8178,"date":"2023-06-06T06:00:18","date_gmt":"2023-06-06T04:00:18","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=8178"},"modified":"2023-06-03T18:12:54","modified_gmt":"2023-06-03T16:12:54","slug":"06-jun-23","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/06-jun-23\/","title":{"rendered":"TAD de los grafos: Grado de un v\u00e9rtice"},"content":{"rendered":"<p>El <strong>grado<\/strong> de un v\u00e9rtice v de un grafo dirigido g, es el n\u00famero  aristas de g que contiene a v. Si g es no dirigido, el grado de un v\u00e9rtice v es el n\u00famero de aristas incidentes en v, teniendo en cuenta que los lazos se cuentan dos veces.<\/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   grado :: (Ix v,Num p) => Grafo v p -> v -> Int\n<\/pre>\n<p>tal que <code>grado g v<\/code> es el grado del v\u00e9rtice <code>v<\/code> en el grafo <code>g<\/code>. Por ejemplo,<\/p>\n<pre lang=\"text\">\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   g3 = creaGrafo' D  (1,3) [(1,2),(2,2),(3,1),(3,2)]\n   g4 = creaGrafo' D  (1,1) [(1,1)]\n   g5 = creaGrafo' ND (1,3) [(1,2),(1,3),(2,3),(3,3)]\n   g6 = creaGrafo' D  (1,3) [(1,2),(1,3),(2,3),(3,3)]\n   grado g1 5 ==  4\n   grado g2 5 ==  3\n   grado g2 1 ==  3\n   grado g3 2 ==  4\n   grado g3 1 ==  2\n   grado g3 3 ==  2\n   grado g4 1 ==  2\n   grado g6 3 ==  4\n   grado g6 3 ==  4\n<\/pre>\n<p>Comprobar con QuickCheck que en todo grafo, el n\u00famero de nodos de grado impar es par.<\/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_Grado_de_un_vertice where\n\nimport TAD.Grafo (Grafo, Orientacion (D, ND), dirigido, nodos, creaGrafo')\nimport Data.Ix (Ix)\nimport Grafo_Lazos_de_un_grafo (lazos)\nimport Grafo_Incidentes_de_un_vertice (incidentes)\nimport Grafo_Grados_positivos_y_negativos (gradoPos, gradoNeg)\nimport Test.Hspec (Spec, hspec, it, shouldBe)\n\ngrado :: (Ix v,Num p) => Grafo v p -> v -> Int\ngrado g v | dirigido g           = gradoNeg g v + gradoPos g v\n          | (v,v) `elem` lazos g = length (incidentes g v) + 1\n          | otherwise            = length (incidentes g v)\n\n-- La propiedad es\nprop_numNodosGradoImpar :: Grafo Int Int -> Bool\nprop_numNodosGradoImpar g =\n  even (length [v | v <- nodos g, odd (grado g v)])\n\n-- La comprobaci\u00f3n es\n--    \u03bb> quickCheck prop_numNodosGradoImpar\n--    +++ OK, passed 100 tests.\n\n-- Verificaci\u00f3n\n-- ============\n\nverifica :: IO ()\nverifica = hspec spec\n\nspec :: Spec\nspec = do\n  it \"e1\" $\n    grado g1 5 `shouldBe`  4\n  it \"e2\" $\n    grado g2 5 `shouldBe`  3\n  it \"e3\" $\n    grado g2 1 `shouldBe`  3\n  it \"e4\" $\n    grado g3 2 `shouldBe`  4\n  it \"e5\" $\n    grado g3 1 `shouldBe`  2\n  it \"e6\" $\n    grado g3 3 `shouldBe`  2\n  it \"e7\" $\n    grado g4 1 `shouldBe`  2\n  it \"e8\" $\n    grado g5 3 `shouldBe`  4\n  it \"e9\" $\n    grado g6 3 `shouldBe`  4\n  where\n    g1, g2, g3, g4, g5, g6 :: 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    g3 = creaGrafo' D  (1,3) [(1,2),(2,2),(3,1),(3,2)]\n    g4 = creaGrafo' D  (1,1) [(1,1)]\n    g5 = creaGrafo' ND (1,3) [(1,2),(1,3),(2,3),(3,3)]\n    g6 = creaGrafo' D  (1,3) [(1,2),(1,3),(2,3),(3,3)]\n\n-- La verificaci\u00f3n es\n--    \u03bb> verifica\n--\n--    e1\n--    e2\n--    e3\n--    e4\n--    e5\n--    e6\n--    e7\n--    e8\n--    e9\n--\n--    Finished in 0.0015 seconds\n--    9 examples, 0 failures\n<\/pre>\n<p><a name=\"python\"><\/a><br \/>\n<b>Soluciones en Python<\/b><\/p>\n<pre lang=\"python\">\nfrom hypothesis import given\n\nfrom src.Grafo_Grados_positivos_y_negativos import gradoNeg, gradoPos\nfrom src.Grafo_Incidentes_de_un_vertice import incidentes\nfrom src.Grafo_Lazos_de_un_grafo import lazos\nfrom src.TAD.Grafo import (Grafo, Orientacion, Vertice, creaGrafo_, dirigido,\n                           nodos)\nfrom src.TAD.GrafoGenerador import gen_grafo\n\n\ndef grado(g: Grafo, v: Vertice) -> int:\n    if dirigido(g):\n        return gradoNeg(g, v) + gradoPos(g, v)\n    if (v, v) in lazos(g):\n        return len(incidentes(g, v)) + 1\n    return len(incidentes(g, v))\n\n# La propiedad esp\n@given(gen_grafo())\ndef test_grado1(g):\n    assert len([v for v in nodos(g) if grado(g, v) % 2 == 1]) % 2 == 0\n\n# La comprobaci\u00f3n es\n#    src> poetry run pytest -q Grafo_Grado_de_un_vertice.py\n#    1 passed in 0.36s\n\n# Verificaci\u00f3n\n# ============\n\ndef test_grado() -> 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    g3 = creaGrafo_(Orientacion.D, (1,3),\n                    [(1,2),(2,2),(3,1),(3,2)])\n    g4 = creaGrafo_(Orientacion.D, (1,1),\n                    [(1,1)])\n    g5 = creaGrafo_(Orientacion.ND, (1,3),\n                    [(1,2),(1,3),(2,3),(3,3)])\n    g6 = creaGrafo_(Orientacion.D, (1,3),\n                    [(1,2),(1,3),(2,3),(3,3)])\n    assert grado(g1, 5) == 4\n    assert grado(g2, 5) == 3\n    assert grado(g2, 1) == 3\n    assert grado(g3, 2) == 4\n    assert grado(g3, 1) == 2\n    assert grado(g3, 3) == 2\n    assert grado(g4, 1) == 2\n    assert grado(g5, 3) == 4\n    assert grado(g6, 3) == 4\n    print(\"Verificado\")\n\n# La verificaci\u00f3n es\n#    >>> test_grado()\n#    Verificado\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>El grado de un v\u00e9rtice v de un grafo dirigido g, es el n\u00famero aristas de g que contiene a v. Si g es no dirigido, el grado de un v\u00e9rtice v es el n\u00famero de aristas incidentes en v, teniendo en cuenta que los lazos se cuentan dos veces. Usando el tipo abstracto de&#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\/8178"}],"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=8178"}],"version-history":[{"count":2,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/8178\/revisions"}],"predecessor-version":[{"id":8195,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/8178\/revisions\/8195"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=8178"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=8178"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=8178"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}