{"id":6574,"date":"2022-02-01T05:00:24","date_gmt":"2022-02-01T03:00:24","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=6574"},"modified":"2022-02-23T15:05:13","modified_gmt":"2022-02-23T13:05:13","slug":"suma-de-una-fila-del-triangulo-de-los-impares","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/suma-de-una-fila-del-triangulo-de-los-impares\/","title":{"rendered":"Suma de una fila del tri\u00e1ngulo de los impares"},"content":{"rendered":"<p>Se condidera el siguiente tri\u00e1ngulo de n\u00fameros impares<\/p>\n<pre lang=\"text\">\n                1\n             3     5\n          7     9    11\n      13    15    17    19\n   21    23    25    27    29\n................................\n<\/pre>\n<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   sumaFilaTrianguloImpares :: Integer -> Integer\n<\/pre>\n<p>tal que (sumaFilaTrianguloImpares n) es la suma de la n-\u00e9sima fila del tri\u00e1ngulo de los n\u00fameros impares. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   sumaFilaTrianguloImpares 1  ==  1\n   sumaFilaTrianguloImpares 2  ==  8\n   length (show (sumaFilaTrianguloImpares (10^500)))    ==  1501\n   length (show (sumaFilaTrianguloImpares (10^5000)))   ==  15001\n   length (show (sumaFilaTrianguloImpares (10^50000)))  ==  150001\n<\/pre>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Test.QuickCheck\n\n-- 1\u00aa soluci\u00f3n\nsumaFilaTrianguloImpares1 :: Integer -> Integer\nsumaFilaTrianguloImpares1 n =\n  sum [n^2-n+1, n^2-n+3 .. n^2+n-1]\n\n-- 2\u00aa soluci\u00f3n\nsumaFilaTrianguloImpares2 :: Integer -> Integer\nsumaFilaTrianguloImpares2 = (^3)\n\n-- Equivalencia\n-- ============\n\n-- La propiedad es\nprop_sumaFilaTrianguloImpares :: Integer -> Property\nprop_sumaFilaTrianguloImpares n =\n  n > 0 ==> sumaFilaTrianguloImpares1 n == sumaFilaTrianguloImpares2 n\n\n-- La comprobaci\u00f3n es\n--    \u03bb> quickCheck prop_sumaFilaTrianguloImpares\n--    +++ OK, passed 100 tests.\n\n-- Comparaci\u00f3n de eficiencia\n-- =========================\n\n-- La comparaci\u00f3n es\n--    \u03bb> length (show (sumaFilaTrianguloImpares1 (10^7)))\n--    22\n--    (2.91 secs, 2,167,239,232 bytes)\n--    \u03bb> length (show (sumaFilaTrianguloImpares2 (10^7)))\n--    22\n--    (0.01 secs, 102,584 bytes)\n<\/pre>\n<p>El c\u00f3digo se encuentra en <a href=\"https:\/\/github.com\/jaalonso\/Exercitium\/blob\/main\/src\/Suma_de_fila_del_triangulo_de_los_impares.hs\">GitHub<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Se condidera el siguiente tri\u00e1ngulo de n\u00fameros impares 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 &#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230;.. Definir la funci\u00f3n sumaFilaTrianguloImpares :: Integer -> Integer tal que (sumaFilaTrianguloImpares n) es la suma de la n-\u00e9sima fila del tri\u00e1ngulo de los n\u00fameros impares. Por ejemplo, sumaFilaTrianguloImpares 1 == 1&#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":[2],"tags":[8],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/6574"}],"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=6574"}],"version-history":[{"count":3,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/6574\/revisions"}],"predecessor-version":[{"id":6684,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/6574\/revisions\/6684"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=6574"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=6574"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=6574"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}