{"id":8207,"date":"2023-06-14T06:00:51","date_gmt":"2023-06-14T04:00:51","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=8207"},"modified":"2023-06-05T13:38:54","modified_gmt":"2023-06-05T11:38:54","slug":"14-jun-23","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/14-jun-23\/","title":{"rendered":"TAD de los grafos: Recorrido en profundidad"},"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   recorridoEnProfundidad :: (Num p, Eq p, Ix v) => v -> Grafo v p -> [v]\n<\/pre>\n<p>tal que <code>recorridoEnProfundidad i g<\/code> es el recorrido en profundidad del grafo <code>g<\/code> desde el v\u00e9rtice <code>i<\/code>. Por ejemplo, en el grafo<\/p>\n<pre lang=\"text\">\n   +---> 2 <---+\n   |           |\n   |           |\n   1 --> 3 --> 6 --> 5\n   |                 |\n   |                 |\n   +---> 4 <---------+\n<\/pre>\n<p>definido por<\/p>\n<pre lang=\"text\">\n   grafo1 :: Grafo Int Int\n   grafo1 = creaGrafo' D (1,6) [(1,2),(1,3),(1,4),(3,6),(5,4),(6,2),(6,5)]\n<\/pre>\n<p>entonces<\/p>\n<pre lang=\"text\">\n   recorridoEnProfundidad 1 grafo1  ==  [1,2,3,6,5,4]\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_Recorrido_en_profundidad where\nimport TAD.Grafo (Grafo, Orientacion (D, ND), adyacentes,\n                  creaGrafo')\nimport Data.Ix (Ix)\nimport Test.Hspec (Spec, hspec, it, shouldBe)\n\ngrafo1 :: Grafo Int Int\ngrafo1 = creaGrafo' D (1,6) [(1,2),(1,3),(1,4),(3,6),(5,4),(6,2),(6,5)]\n\n-- 1\u00aa soluci\u00f3n\n-- ===========\n\nrecorridoEnProfundidad1 :: (Num p, Eq p, Ix v) => v -> Grafo v p -> [v]\nrecorridoEnProfundidad1 i g = rp [i] []\n  where\n    rp [] vis    = vis\n    rp (c:cs) vis\n        | c `elem` vis = rp cs vis\n        | otherwise    = rp (adyacentes g c ++ cs) (vis ++ [c])\n\n-- Traza del c\u00e1lculo de (recorridoEnProfundidad1 1 grafo1)\n--    recorridoEnProfundidad1 1 grafo1\n--    = rp [1]     []\n--    = rp [2,3,4] [1]\n--    = rp [3,4]   [1,2]\n--    = rp [6,4]   [1,2,3]\n--    = rp [2,5,4] [1,2,3,6]\n--    = rp [5,4]   [1,2,3,6]\n--    = rp [4,4]   [1,2,3,6,5]\n--    = rp [4]     [1,2,3,6,5,4]\n--    = rp []      [1,2,3,6,5,4]\n--    = [1,2,3,6,5,4]\n\n-- 2\u00aa soluci\u00f3n\n-- ===========\n\nrecorridoEnProfundidad :: (Num p, Eq p, Ix v) => v -> Grafo v p -> [v]\nrecorridoEnProfundidad i g = reverse (rp [i] [])\n  where\n    rp [] vis     = vis\n    rp (c:cs) vis\n        | c `elem` vis = rp cs vis\n        | otherwise    = rp (adyacentes g c ++ cs) (c:vis)\n\n-- Traza del c\u00e1lculo de (recorridoEnProfundidad 1 grafo1)\n--    RecorridoEnProfundidad 1 grafo1\n--    = reverse (rp [1]     [])\n--    = reverse (rp [2,3,4] [1])\n--    = reverse (rp [3,4]   [2,1])\n--    = reverse (rp [6,4]   [3,2,1])\n--    = reverse (rp [2,5,4] [6,3,2,1])\n--    = reverse (rp [5,4]   [6,3,2,1])\n--    = reverse (rp [4,4]   [5,6,3,2,1])\n--    = reverse (rp [4]     [4,5,6,3,2,1])\n--    = reverse (rp []      [4,5,6,3,2,1])\n--    = reverse [4,5,6,3,2,1]\n--    = [1,2,3,6,5,4]\n\n-- Verificaci\u00f3n\n-- ============\n\nverifica :: IO ()\nverifica = hspec spec\n\nspec :: Spec\nspec = do\n  it \"e1\" $\n    recorridoEnProfundidad1 1 grafo1 `shouldBe` [1,2,3,6,5,4]\n  it \"e2\" $\n    recorridoEnProfundidad 1 grafo1 `shouldBe` [1,2,3,6,5,4]\n  it \"e3\" $\n    recorridoEnProfundidad1 1 grafo2 `shouldBe` [1,2,6,3,5,4]\n  it \"e4\" $\n    recorridoEnProfundidad 1 grafo2 `shouldBe` [1,2,6,3,5,4]\n  where\n    grafo2 :: Grafo Int Int\n    grafo2 = creaGrafo' ND (1,6) [(1,2),(1,3),(1,4),(3,6),(5,4),(6,2),(6,5)]\n\n-- La verificaci\u00f3n es\n--    \u03bb> verifica\n--\n--    e1\n--    e2\n--    e3\n--    e4\n--\n--    Finished in 0.0022 seconds\n--    4 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.TAD.Grafo import Grafo, Orientacion, Vertice, adyacentes, creaGrafo_\n\ngrafo1: Grafo = creaGrafo_(Orientacion.D,\n                           (1,6),\n                           [(1,2),(1,3),(1,4),(3,6),(5,4),(6,2),(6,5)])\n\n# 1\u00aa soluci\u00f3n\n# ===========\n\ndef recorridoEnProfundidad1(i: Vertice, g: Grafo) -> list[Vertice]:\n    def rp(cs: list[Vertice], vis: list[Vertice]) -> list[Vertice]:\n        if not cs:\n            return vis\n        d, *ds = cs\n        if d in vis:\n            return rp(ds, vis)\n        return rp(adyacentes(g, d) + ds, vis + [d])\n    return rp([i], [])\n\n# Traza del c\u00e1lculo de recorridoEnProfundidad1(1, grafo1)\n#    recorridoEnProfundidad1(1, grafo1)\n#    = rp([1],     [])\n#    = rp([2,3,4], [1])\n#    = rp([3,4],   [1,2])\n#    = rp([6,4],   [1,2,3])\n#    = rp([2,5,4], [1,2,3,6])\n#    = rp([5,4],   [1,2,3,6])\n#    = rp([4,4],   [1,2,3,6,5])\n#    = rp([4],     [1,2,3,6,5,4])\n#    = rp([],      [1,2,3,6,5,4])\n#    = [1,2,3,6,5,4]\n\n# 2\u00aa soluci\u00f3n\n# ===========\n\ndef recorridoEnProfundidad(i: Vertice, g: Grafo) -> list[Vertice]:\n    def rp(cs: list[Vertice], vis: list[Vertice]) -> list[Vertice]:\n        if not cs:\n            return vis\n        d, *ds = cs\n        if d in vis:\n            return rp(ds, vis)\n        return rp(adyacentes(g, d) + ds, [d] + vis)\n    return list(reversed(rp([i], [])))\n\n# Traza del c\u00e1lculo de (recorridoEnProfundidad(1, grafo1)\n#    recorridoEnProfundidad(1, grafo1)\n#    = reverse(rp([1],     []))\n#    = reverse(rp([2,3,4], [1]))\n#    = reverse(rp([3,4],   [2,1]))\n#    = reverse(rp([6,4],   [3,2,1]))\n#    = reverse(rp([2,5,4], [6,3,2,1]))\n#    = reverse(rp([5,4],   [6,3,2,1]))\n#    = reverse(rp([4,4],   [5,6,3,2,1]))\n#    = reverse(rp([4],     [4,5,6,3,2,1]))\n#    = reverse(rp([],      [4,5,6,3,2,1]))\n#    = reverse([4,5,6,3,2,1])\n#    = [1,2,3,6,5,4]\n\n# Verificaci\u00f3n\n# ============\n\ndef test_recorridoEnProfundidad() -> None:\n    grafo2 = creaGrafo_(Orientacion.ND,\n                        (1,6),\n                        [(1,2),(1,3),(1,4),(3,6),(5,4),(6,2),(6,5)])\n    assert recorridoEnProfundidad1(1, grafo1) == [1,2,3,6,5,4]\n    assert recorridoEnProfundidad1(1, grafo2) == [1,2,6,3,5,4]\n    assert recorridoEnProfundidad(1, grafo1) == [1,2,3,6,5,4]\n    assert recorridoEnProfundidad(1, grafo2) == [1,2,6,3,5,4]\n    print(\"Verificado\")\n\n# La verificaci\u00f3n es\n#    >>> test_recorridoEnProfundidad()\n#    Verificado\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Usando el tipo abstracto de datos de los grafos, definir la funci\u00f3n, recorridoEnProfundidad :: (Num p, Eq p, Ix v) => v -> Grafo v p -> [v] tal que recorridoEnProfundidad i g es el recorrido en profundidad del grafo g desde el v\u00e9rtice i. Por ejemplo, en el grafo +&#8212;> 2 3 &#8211;> 6&#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\/8207"}],"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=8207"}],"version-history":[{"count":1,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/8207\/revisions"}],"predecessor-version":[{"id":8208,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/8207\/revisions\/8208"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=8207"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=8207"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=8207"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}