{"id":5594,"date":"2020-02-25T05:30:13","date_gmt":"2020-02-25T03:30:13","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=5594"},"modified":"2020-03-03T07:44:29","modified_gmt":"2020-03-03T05:44:29","slug":"cliques-de-orden-k","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/cliques-de-orden-k\/","title":{"rendered":"Cliques de orden k"},"content":{"rendered":"<p>Nota: En este ejercicio usaremos las mismas notaciones que en el anterior importando el m\u00f3dulo <code>Cliques<\/code>.<\/p>\n<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   kCliques :: Eq a => Grafo a -> Int -> [[a]]\n<\/pre>\n<p>tal que (kCliques g k) es la lista de los cliques del grafo g de tama\u00f1o k. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   \u03bb> kCliques [(1,2),(2,3),(2,4),(2,5),(3,5),(4,5)] 3\n   [[2,3,5],[2,4,5]]\n   \u03bb> kCliques [(1,2),(2,3),(2,4),(2,5),(3,5),(4,5)] 2\n   [[1,2],[2,3],[2,4],[2,5],[3,5],[4,5]]\n   \u03bb> kCliques [(n,n+1) | n <- [1..100]] 3\n   []\n<\/pre>\n<p><strong>Nota<\/strong>: Escribir la soluci\u00f3n en el m\u00f3dulo <code>KCliques<\/code> para poderlo usar en los siguientes ejercicios.<\/p>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nmodule KCliques where\n\nimport Grafo\nimport Cliques\n\n-- 1\u00aa definici\u00f3n\nkCliques1 :: Eq a => Grafo a -> Int -> [[a]]\nkCliques1 g k =\n  [xs | xs <- cliques g\n      , length xs == k]\n\n-- 2\u00aa definici\u00f3n\nkCliques :: Eq a => Grafo a -> Int -> [[a]]\nkCliques g k =\n  [xs | xs <- kSubconjuntos (nodos g) k\n      , esClique g xs]\n\n-- (kSubconjuntos xs k) es la lista de los subconjuntos de xs con k\n-- elementos. Por ejemplo, \n--    ghci> kSubconjuntos \"bcde\" 2\n--    [\"bc\",\"bd\",\"be\",\"cd\",\"ce\",\"de\"]\n--    ghci> kSubconjuntos \"bcde\" 3\n--    [\"bcd\",\"bce\",\"bde\",\"cde\"]\n--    ghci> kSubconjuntos \"abcde\" 3\n--    [\"abc\",\"abd\",\"abe\",\"acd\",\"ace\",\"ade\",\"bcd\",\"bce\",\"bde\",\"cde\"]\nkSubconjuntos :: [a] -> Int -> [[a]]\nkSubconjuntos _ 0      = [[]]\nkSubconjuntos [] _     = []\nkSubconjuntos (x:xs) k = \n  [x:ys | ys <- kSubconjuntos xs (k-1)] ++ kSubconjuntos xs k  \n\n-- Comparaci\u00f3n de eficiencia\n-- =========================\n\n--    \u03bb> kCliques1 [(n,n+1) | n <- [1..20]] 3\n--    []\n--    (4.28 secs, 3,204,548,608 bytes)\n--    \u03bb> kCliques [(n,n+1) | n <- [1..20]] 3\n--    []\n--    (0.01 secs, 3,075,768 bytes)\n<\/pre>\n<h4>Otras soluciones<\/h4>\n<ul>\n<li>Se pueden escribir otras soluciones en los comentarios.\n<li>El c\u00f3digo se debe escribir entre una l\u00ednea con &#60;pre lang=\"haskell\"&#62; y otra con &#60;\/pre&#62;\n<\/ul>\n<h4>Pensamiento<\/h4>\n<blockquote><p>\n\"Es mejor resolver un problema de cinco maneras diferentes, que resolver cinco problemas de una sola manera.\" <\/p>\n<p><a href=\"https:\/\/en.wikipedia.org\/wiki\/George_P%C3%B3lya\">George P\u00f3lya<\/a>.\n<\/p><\/blockquote>\n","protected":false},"excerpt":{"rendered":"<p>Nota: En este ejercicio usaremos las mismas notaciones que en el anterior importando el m\u00f3dulo Cliques. Definir la funci\u00f3n kCliques :: Eq a => Grafo a -> Int -> [[a]] tal que (kCliques g k) es la lista de los cliques del grafo g de tama\u00f1o k. Por ejemplo, \u03bb> kCliques [(1,2),(2,3),(2,4),(2,5),(3,5),(4,5)] 3 [[2,3,5],[2,4,5]] \u03bb>&#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":[4],"tags":[8,28,6],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/5594"}],"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=5594"}],"version-history":[{"count":2,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/5594\/revisions"}],"predecessor-version":[{"id":5653,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/5594\/revisions\/5653"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=5594"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=5594"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=5594"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}