{"id":4617,"date":"2019-01-23T06:00:53","date_gmt":"2019-01-23T04:00:53","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=4617"},"modified":"2019-01-30T10:06:41","modified_gmt":"2019-01-30T08:06:41","slug":"sucesion-triangular","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/sucesion-triangular\/","title":{"rendered":"Sucesi\u00f3n triangular"},"content":{"rendered":"<p>La sucesi\u00f3n triangular es la obtenida concatenando las listas [1], [1,2], [1,2,3], [1,2,3,4], &#8230;.  Sus primeros t\u00e9rminos son 1, 1, 2, 1, 2, 3, 1, 2, 3, 4, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 6, &#8230;<\/p>\n<p>Definir las funciones<\/p>\n<pre lang=\"text\"> \n   sucTriangular        :: [Integer]\n   terminoSucTriangular :: Int -> Integer\n   graficaSucTriangular :: Int -> IO ()\n<\/pre>\n<p>tales que<\/p>\n<ul>\n<li>sucTriangular es la lista de los t\u00e9rminos de la sucesi\u00f3n triangular. Por ejemplo,<\/li>\n<\/ul>\n<pre lang=\"text\">   \n     \u03bb> take 30 sucTriangular\n     [1,1,2,1,2,3,1,2,3,4,1,2,3,4,5,1,2,3,4,5,6,1,2,3,4,5,6,7,1,2]\n<\/pre>\n<ul>\n<li>(terminoSucTriangular n) es el t\u00e9rmino n-\u00e9simo de la sucesi\u00f3n triangular. Por ejemplo,<\/li>\n<\/ul>\n<pre lang=\"text\">\n     terminoSucTriangular 5       ==  3\n     terminoSucTriangular 10      ==  1\n     terminoSucTriangular 20      ==  6\n     terminoSucTriangular 100     ==  10\n     terminoSucTriangular 1001    ==  12\n     terminoSucTriangular (10^5)  ==  320\n<\/pre>\n<ul>\n<li>(graficaSucTriangular n) dibuja la gr\u00e1fica de los n primeros t\u00e9rminos de la sucesi\u00f3n triangular. Por ejemplo, (graficaSucTriangular 300) dibuja<\/li>\n<\/ul>\n<p><a href=\"https:\/\/i0.wp.com\/www.glc.us.es\/~jalonso\/exercitium\/wp-content\/uploads\/2019\/01\/Sucesion_triangular.png\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/i0.wp.com\/www.glc.us.es\/~jalonso\/exercitium\/wp-content\/uploads\/2019\/01\/Sucesion_triangular.png?resize=640%2C480\" alt=\"\" width=\"640\" height=\"480\" class=\"aligncenter size-full wp-image-4620\" srcset=\"https:\/\/i0.wp.com\/www.glc.us.es\/~jalonso\/exercitium\/wp-content\/uploads\/2019\/01\/Sucesion_triangular.png?w=640&amp;ssl=1 640w, https:\/\/i0.wp.com\/www.glc.us.es\/~jalonso\/exercitium\/wp-content\/uploads\/2019\/01\/Sucesion_triangular.png?resize=300%2C225&amp;ssl=1 300w\" sizes=\"(max-width: 640px) 100vw, 640px\" data-recalc-dims=\"1\" \/><\/a><\/p>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Data.List (inits)\nimport Test.QuickCheck\nimport Graphics.Gnuplot.Simple\n\n-- 1\u00aa definici\u00f3n de sucTriangular \n-- ==============================\n\nsucTriangular :: [Integer]\nsucTriangular =\n  concat [[1..n] | n <- [1..]]\n\n-- 2\u00aa definici\u00f3n de sucTriangular \n-- ==============================\n\nsucTriangular2 :: [Integer]\nsucTriangular2 =\n  [x | n <- [1..], x <- [1..n]]\n\n-- 3\u00aa definici\u00f3n de sucTriangular \n-- ==============================\n\nsucTriangular3 :: [Integer]\nsucTriangular3 =\n  concat (tail (inits [1..]))\n  \n-- 1\u00aa definici\u00f3n de terminoSucTriangular\n-- =====================================\n\nterminoSucTriangular :: Int -> Integer\nterminoSucTriangular k =\n  sucTriangular !! k\n\n-- 2\u00aa definici\u00f3n de terminoSucTriangular\n-- =====================================\n\nterminoSucTriangular2 :: Int -> Integer\nterminoSucTriangular2 k =\n  sucTriangular2 !! k\n\n-- 3\u00aa definici\u00f3n de terminoSucTriangular\n-- =====================================\n\nterminoSucTriangular3 :: Int -> Integer\nterminoSucTriangular3 k =\n  sucTriangular3 !! k\n\n-- Equivalencia de definiciones\n-- ============================\n\n-- La propiedad es\nprop_terminoTriangular :: Positive Int -> Bool\nprop_terminoTriangular (Positive n) =\n  terminoSucTriangular n == terminoSucTriangular2 n &&\n  terminoSucTriangular n == terminoSucTriangular3 n\n\n-- La comprobaci\u00f3n es\n--      \u03bb> quickCheck prop_terminoTriangular\n--      +++ OK, passed 100 tests.\n\n-- Comparaci\u00f3n de eficiencia\n-- =========================\n\n--    \u03bb> terminoSucTriangular (3*10^6)\n--    2425\n--    (2.07 secs, 384,707,936 bytes)\n--    \u03bb> terminoSucTriangular2 (3*10^6)\n--    2425\n--    (2.22 secs, 432,571,208 bytes)\n--    \u03bb> terminoSucTriangular3 (3*10^6)\n--    2425\n--    (0.69 secs, 311,259,504 bytes)\n\n-- Definici\u00f3n de graficaSucTriangular\n-- ==================================\n\ngraficaSucTriangular :: Int -> IO ()\ngraficaSucTriangular n =\n  plotList [ Key Nothing\n           , PNG \"Sucesion_triangular.png\"\n           ]\n           (take n sucTriangular)\n<\/pre>\n<h4>Pensamiento<\/h4>\n<blockquote><p>\nNadie debe asustarse de lo que piensa, aunque su pensar aparezca en pugna con las leyes m\u00e1s elementales de la l\u00f3gica. Porque todo ha de ser pensado por alguien, y el mayor desatino puede ser un punto de vista de lo real.<\/p>\n<p>Antonio Machado\n<\/p><\/blockquote>\n","protected":false},"excerpt":{"rendered":"<p>La sucesi\u00f3n triangular es la obtenida concatenando las listas [1], [1,2], [1,2,3], [1,2,3,4], &#8230;. Sus primeros t\u00e9rminos son 1, 1, 2, 1, 2, 3, 1, 2, 3, 4, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 6, &#8230; Definir las funciones sucTriangular :: [Integer] terminoSucTriangular :: Int -> Integer graficaSucTriangular :: Int ->&#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":[5],"tags":[8,12,376,309,47],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/4617"}],"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=4617"}],"version-history":[{"count":6,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/4617\/revisions"}],"predecessor-version":[{"id":4669,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/4617\/revisions\/4669"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=4617"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=4617"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=4617"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}