Los conjuntos de polinomios se pueden representar por listas de listas de la misma longitud. Por ejemplo, los polinomios 3x\u00b2+5x+9, 10x\u00b3+9 y 8x\u00b3+5x\u00b2+x-1 se pueden representar por las listas [0,3,5,9], [10,0,0,9] y [8,5,1,-1].<\/p>\n
Definir la funci\u00f3n<\/p>\n
\n sumaPolinomios :: Num a => [[a]] -> [a]\n<\/pre>\ntal que (sumaPolinomios ps) es la suma de los polinomios ps. Por ejemplo,<\/p>\n
\n ghci> sumaPolinomios1 [[0,3,5,9],[10,0,0,9],[8,5,1,-1]]\n [18,8,6,17]\n ghci> sumaPolinomios6 (replicate 1000000 (replicate 3 1))\n [1000000,1000000,1000000]\n<\/pre>\nSoluciones<\/h4>\n\nimport Data.List (transpose)\nimport Data.Array ((!),accumArray,elems,listArray)\n\n-- 1\u00aa definici\u00f3n (por recursi\u00f3n):\nsumaPolinomios1 :: Num a => [[a]] -> [a]\nsumaPolinomios1 [] = []\nsumaPolinomios1 [xs] = xs\nsumaPolinomios1 (xs:ys:zss) = suma xs (sumaPolinomios1 (ys:zss))\n\n-- (suma xs ys) es la suma de los vectores xs e ys. Por ejemplo,\n-- suma [4,7,3] [1,2,5] == [5,9,8]\nsuma :: Num a => [a] -> [a] -> [a]\nsuma [] [] = []\nsuma (x:xs) (y:ys) = x+y : suma xs ys\n\n-- 2\u00aa definici\u00f3n (por recursi\u00f3n con zipWith): \nsumaPolinomios2 :: Num a => [[a]] -> [a]\nsumaPolinomios2 [] = []\nsumaPolinomios2 [xs] = xs\nsumaPolinomios2 (xs:xss) = zipWith (+) xs (sumaPolinomios2 xss)\n\n-- 3\u00aa definici\u00f3n (por plegado)\nsumaPolinomios3 :: Num a => [[a]] -> [a]\nsumaPolinomios3 = foldr1 (zipWith (+))\n\n-- 4\u00aa definici\u00f3n (por comprensi\u00f3n con transpose):\nsumaPolinomios4 :: Num a => [[a]] -> [a]\nsumaPolinomios4 xss = [sum xs | xs <- transpose xss]\n\n-- 5\u00aa definici\u00f3n (con map y transpose):\nsumaPolinomios5 :: Num a => [[a]] -> [a]\nsumaPolinomios5 = map sum . transpose \n\n-- 6\u00aa definici\u00f3n (con array)\nsumaPolinomios6 :: Num a => [[a]] -> [a]\nsumaPolinomios6 xss = [sum [p!(i,j) | i <- [1..m]] | j <- [1..n]] \n where m = length xss\n n = length (head xss)\n p = listArray ((1,1),(m,n)) (concat xss) \n\n-- 7\u00aa definici\u00f3n (con accumArray)\nsumaPolinomios7 :: Num a => [[a]] -> [a]\nsumaPolinomios7 xss = \n elems $ accumArray (+) 0 (1,n) (concat [zip [1..] xs | xs <- xss])\n where n = length (head xss)\n\n-- Comparaci\u00f3n de eficiencia\n-- ghci> sumaPolinomios1 (replicate 300000 (replicate 5 1))\n-- [300000,300000,300000,300000,300000]\n-- (3.94 secs, 354713532 bytes)\n-- \n-- ghci> sumaPolinomios2 (replicate 300000 (replicate 5 1))\n-- [300000,300000,300000,300000,300000]\n-- (2.08 secs, 185506908 bytes)\n-- \n-- ghci> sumaPolinomios3 (replicate 300000 (replicate 5 1))\n-- [300000,300000,300000,300000,300000]\n-- (1.48 secs, 167026728 bytes)\n-- \n-- ghci> sumaPolinomios4 (replicate 300000 (replicate 5 1))\n-- [300000,300000,300000,300000,300000]\n-- (1.08 secs, 148564752 bytes)\n-- \n-- ghci> sumaPolinomios5 (replicate 300000 (replicate 5 1))\n-- [300000,300000,300000,300000,300000]\n-- (1.02 secs, 148062764 bytes)\n-- \n-- ghci> sumaPolinomios6 (replicate 300000 (replicate 5 1))\n-- [300000,300000,300000,300000,300000]\n-- (3.17 secs, 463756028 bytes)\n-- \n-- ghci> sumaPolinomios7 (replicate 300000 (replicate 5 1))\n-- [300000,300000,300000,300000,300000]\n-- (1.50 secs, 291699548 bytes)\n<\/pre>\n","protected":false},"excerpt":{"rendered":"Los conjuntos de polinomios se pueden representar por listas de listas de la misma longitud. Por ejemplo, los polinomios 3x\u00b2+5x+9, 10x\u00b3+9 y 8x\u00b3+5x\u00b2+x-1 se pueden representar por las listas [0,3,5,9], [10,0,0,9] y [8,5,1,-1]. Definir la funci\u00f3n sumaPolinomios :: Num a => [[a]] -> [a] tal que (sumaPolinomios ps) es la suma de los polinomios ps….<\/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":[249,12,245,71,28,72,10,42,11,6,40,68,76],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/1128"}],"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=1128"}],"version-history":[{"count":4,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/1128\/revisions"}],"predecessor-version":[{"id":1167,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/1128\/revisions\/1167"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=1128"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=1128"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=1128"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}