{"id":2524,"date":"2016-11-02T06:00:03","date_gmt":"2016-11-02T04:00:03","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=2524"},"modified":"2016-11-09T07:08:53","modified_gmt":"2016-11-09T05:08:53","slug":"triangulos_geometricos","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/triangulos_geometricos\/","title":{"rendered":"Tri\u00e1ngulos geom\u00e9tricos"},"content":{"rendered":"

Un tri\u00e1ngulo geom\u00e9trico es un tri\u00e1ngulo de lados enteros, representados por la terna (a,b,c) tal que a \u2264 b \u2264 c y est\u00e1n en progresi\u00f3n geom\u00e9trica, es decir, b^2 = a*c. Por ejemplo, un tri\u00e1ngulo de lados a = 144, b = 156 y c = 169.<\/p>\n

Definir la funci\u00f3n<\/p>\n

\n   numeroTG :: Integer -> Int\n<\/pre>\n
tal que (numeroTG n) es el n\u00famero de tri\u00e1ngulos geom\u00e9tricos de per\u00edmetro menor o igual que n. Por ejemplo<\/p>\n
\n    numeroTG 10  == 3\n    numeroTG 100 == 42\n    numeroTG 200 == 91\n<\/pre>\n
Nota<\/strong>: Los tri\u00e1ngulos geom\u00e9tricos de per\u00edmetro menor o igual que 20 son<\/p>\n
\n   [(1,1,1),(2,2,2),(3,3,3),(4,4,4),(5,5,5),(6,6,6),(4,6,9)]\n<\/pre>\n
Se observa que (1,2,4) aunque cumple que 1+2+4 <= 20 y 2^2 = 1*4 no pertenece a la lista ya que 1+2 > 4 y, por tanto, no hay ning\u00fan tri\u00e1ngulo cuyos lados midan 1, 2 y 4.<\/p>\n
Soluciones<\/h4>\n
\n-- 1\u00aa definici\u00f3n:\nnumeroTG :: Integer -> Int\nnumeroTG n = \n    length [(a,b,c) | c <- [1..n]\n                    , b <- [1..c]\n                    , a <- [1..b]\n                    , a+b > c\n                    , a+b+c <= n\n                    , b^2 == a*c\n                    ]\n\n-- 2\u00aa definici\u00f3n:\nnumeroTG2 :: Integer -> Int\nnumeroTG2 n = \n    length [(a,b,c) | c <- [1..n]\n                    , b <- [1..c]\n                    , b^2 `rem` c == 0\n                    , let a = b^2 `div` c\n                    , a+b > c\n                    , a+b+c <= n\n                    ]\n\n-- Comparaci\u00f3n de eficiencia:\n--    \u03bb> numeroTG 300\n--    143\n--    (2.40 secs, 1,496,824,720 bytes)\n--    \u03bb> numeroTG2 300\n--    143\n--    (0.05 secs, 40,908,568 bytes)\n<\/pre>\n
Referencia<\/h4>\n
El ejercicio est\u00e1 basado en el problema 370<\/a> del proyecto Euler.<\/p>\n","protected":false},"excerpt":{"rendered":"
Un tri\u00e1ngulo geom\u00e9trico es un tri\u00e1ngulo de lados enteros, representados por la terna (a,b,c) tal que a \u2264 b \u2264 c y est\u00e1n en progresi\u00f3n geom\u00e9trica, es decir, b^2 = a*c. Por ejemplo, un tri\u00e1ngulo de lados a = 144, b = 156 y c = 169. Definir la funci\u00f3n numeroTG :: Integer -> Int…<\/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":[8,30,28,31],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2524"}],"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=2524"}],"version-history":[{"count":10,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2524\/revisions"}],"predecessor-version":[{"id":2553,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2524\/revisions\/2553"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=2524"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=2524"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=2524"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}