{"id":8173,"date":"2023-06-01T06:00:20","date_gmt":"2023-06-01T04:00:20","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=8173"},"modified":"2023-06-03T18:13:58","modified_gmt":"2023-06-03T16:13:58","slug":"01-jun-23","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/01-jun-23\/","title":{"rendered":"TAD de los grafos: N\u00famero de aristas de un grafo"},"content":{"rendered":"<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   nAristas :: (Ix v,Num p) => Grafo v p ->  Int\n<\/pre>\n<p>tal que <code>nAristas g<\/code> es el n\u00famero de aristas del grafo <code>g<\/code>. Si g es no dirigido, las aristas de <code>v1<\/code> a <code>v2<\/code> y de <code>v2<\/code> a <code>v1<\/code> s\u00f3lo se cuentan una vez. 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> g3 = creaGrafo' ND (1,3) [(1,2),(1,3),(2,3),(3,3)]\n   \u03bb> g4 = creaGrafo' ND (1,4) [(1,1),(1,2),(3,3)]\n   \u03bb> nAristas g1\n   8\n   \u03bb> nAristas g2\n   7\n   \u03bb> nAristas g3\n   4\n   \u03bb> nAristas g4\n   3\n   \u03bb> nAristas (completo 4)\n   6\n   \u03bb> nAristas (completo 5)\n   10\n<\/pre>\n<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   prop_nAristasCompleto :: Int -> Bool\n<\/pre>\n<p>tal que <code>prop_nAristasCompleto n<\/code> se verifica si el n\u00famero de aristas del grafo completo de orden <code>n<\/code> es <code>n*(n-1)\/2<\/code> y, usando la funci\u00f3n, comprobar que la propiedad se cumple para <code>n<\/code> de 1 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_Numero_de_aristas_de_un_grafo where\n\nimport TAD.Grafo (Grafo, Orientacion (D, ND), dirigido, aristas, creaGrafo')\nimport Data.Ix (Ix)\nimport Grafo_Lazos_de_un_grafo (nLazos)\nimport Grafo_Grafos_completos (completo)\nimport Test.Hspec (Spec, hspec, it, shouldBe, describe)\n\n-- 1\u00aa soluci\u00f3n\n-- ===========\n\nnAristas :: (Ix v,Num p) => Grafo v p ->  Int\nnAristas g | dirigido g = length (aristas g)\n           | otherwise  = (length (aristas g) + nLazos g) `div` 2\n\n-- 2\u00aa soluci\u00f3n\n-- ===========\n\nnAristas2 :: (Ix v,Num p) => Grafo v p ->  Int\nnAristas2 g | dirigido g = length (aristas g)\n            | otherwise  = length [(x,y) | ((x,y),_) <- aristas g, x <= y]\n\n-- Propiedad\n-- =========\n\nprop_nAristasCompleto :: Int -> Bool\nprop_nAristasCompleto n =\n  nAristas (completo n) == n*(n-1) `div` 2\n\n-- La comprobaci\u00f3n es\n--    \u03bb> and [prop_nAristasCompleto n | n <- [1..20]]\n--    True\n\n-- Verificaci\u00f3n\n-- ============\n\nverifica :: IO ()\nverifica = hspec spec\n\nspec :: Spec\nspec = do\n  describe \"def. 1\" $ specG nAristas\n  describe \"def. 2\" $ specG nAristas2\n\nspecG :: (Grafo Int Int -> Int) -> Spec\nspecG nAristas' = do\n  it \"e1\" $\n    nAristas' g1 `shouldBe` 8\n  it \"e2\" $\n    nAristas' g2 `shouldBe` 7\n  it \"e3\" $\n    nAristas' g3 `shouldBe` 4\n  it \"e4\" $\n    nAristas' g4 `shouldBe` 3\n  it \"e5\" $\n    nAristas' (completo 4) `shouldBe` 6\n  it \"e6\" $\n    nAristas' (completo 5) `shouldBe` 10\n  where\n    g1, g2, g3, g4 :: 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' ND (1,3) [(1,2),(1,3),(2,3),(3,3)]\n    g4 = creaGrafo' ND (1,4) [(1,1),(1,2),(3,3)]\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_Grafos_completos import completo\nfrom src.Grafo_Lazos_de_un_grafo import nLazos\nfrom src.TAD.Grafo import Grafo, Orientacion, aristas, creaGrafo_, dirigido\n\n# 1\u00aa soluci\u00f3n\n# ===========\n\ndef nAristas(g: Grafo) -> int:\n    if dirigido(g):\n        return len(aristas(g))\n    return (len(aristas(g)) + nLazos(g)) \/\/ 2\n\n# 2\u00aa soluci\u00f3n\n# ===========\n\ndef nAristas2(g: Grafo) -> int:\n    if dirigido(g):\n        return len(aristas(g))\n    return len([(x, y) for ((x,y),_) in aristas(g) if x <= y])\n\n# Propiedad\n# =========\n\ndef prop_nAristasCompleto(n: int) -> bool:\n    return nAristas(completo(n)) == n*(n-1) \/\/ 2\n\n# La comprobaci\u00f3n es\n#    >>> all(prop_nAristasCompleto(n) for n in range(1, 21))\n#    True\n\n# Verificaci\u00f3n\n# ============\n\ndef test_nAristas() -> 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.ND, (1,3), [(1,2),(1,3),(2,3),(3,3)])\n    g4 = creaGrafo_(Orientacion.ND, (1,4), [(1,1),(1,2),(3,3)])\n    for nAristas_ in [nAristas, nAristas2]:\n        assert nAristas_(g1) == 8\n        assert nAristas_(g2) == 7\n        assert nAristas_(g3) == 4\n        assert nAristas_(g4) == 3\n        assert nAristas_(completo(4)) == 6\n        assert nAristas_(completo(5)) == 10\n    print(\"Verificado\")\n\n# La verificaci\u00f3n es\n#    >>> test_nAristas()\n#    Verificado\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Usando el tipo abstracto de datos de los grafos, definir la funci\u00f3n, nAristas :: (Ix v,Num p) => Grafo v p -> Int tal que nAristas g es el n\u00famero de aristas del grafo g. Si g es no dirigido, las aristas de v1 a v2 y de v2 a v1 s\u00f3lo se cuentan una&#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\/8173"}],"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=8173"}],"version-history":[{"count":2,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/8173\/revisions"}],"predecessor-version":[{"id":8198,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/8173\/revisions\/8198"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=8173"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=8173"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=8173"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}