{"id":2122,"date":"2016-02-16T06:00:30","date_gmt":"2016-02-16T04:00:30","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=2122"},"modified":"2016-02-23T06:52:38","modified_gmt":"2016-02-23T04:52:38","slug":"diagonales-de-matrices-como-listas","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/diagonales-de-matrices-como-listas\/","title":{"rendered":"Diagonales de matrices como listas"},"content":{"rendered":"<p>Las matrices se pueden representar como listas de listas de la misma longitud, donde cada uno de sus elementos representa una fila de la matriz.<\/p>\n<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   diagonal :: [[a]] -> [a]\n<\/pre>\n<p>tal que (diagonal xss) es la diagonal de la matriz xss. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   diagonal [[3,5,2],[4,7,1],[6,9,0]]           ==  [3,7,0]\n   diagonal [[3,5],[4,7],[6,9]]                 ==  [3,7]\n   diagonal [[3,5,2],[4,7,1]]                   ==  [3,7]\n   sum (diagonal (replicate 20000 [1..20000]))  ==  200010000\n<\/pre>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Data.Array  ((!), listArray)\nimport Data.Matrix (fromLists, getDiag)\nimport Data.Vector (toList)\n\n-- 1\u00aa definici\u00f3n (por recursi\u00f3n):\ndiagonal1 :: [[a]] -> [a]\ndiagonal1 ((x:_):xss) = x : diagonal1 [tail xs | xs <- xss]\ndiagonal1 _           = []\n\n-- 2\u00aa definici\u00f3n (por comprensi\u00f3n):\ndiagonal2 :: [[a]] -> [a]\ndiagonal2 xss = [xs!!k | (xs,k) <- zip xss [0..n]]\n    where n = length (head xss) - 1\n\n-- 3\u00aa definici\u00f3n (con Data.Matrix)\ndiagonal3 :: [[a]] -> [a]\ndiagonal3 = toList . getDiag . fromLists\n\n-- 4\u00aa definici\u00f3n (con Data.Array)\ndiagonal4 :: [[a]] -> [a]\ndiagonal4 xss = [p!(i,i) | i <- [1..k]] \n    where m = length xss\n          n = length (head xss)\n          k = min m n\n          p = listArray ((1,1),(m,n)) (concat xss)\n\n-- Comparaci\u00f3n de eficiencia\n--    \u03bb> let n = 3000 in sum (diagonal1 (replicate n [1..n]))\n--    4501500\n--    (2.08 secs, 754,089,992 bytes)\n--    \u03bb> let n = 3000 in sum (diagonal2 (replicate n [1..n]))\n--    4501500\n--    (0.06 secs, 0 bytes)\n--    \u03bb> let n = 3000 in sum (diagonal3 (replicate n [1..n]))\n--    4501500\n--    (1.22 secs, 1,040,787,360 bytes)\n--    \u03bb> let n = 3000 in sum (diagonal4 (replicate n [1..n]))\n--    4501500\n--    (0.96 secs, 624,463,632 bytes)\n<\/pre>\n<h4>Soluci\u00f3n con Maxima<\/h4>\n<pre lang=\"maxima\">\ndiagonal (xss) := block ([A],\n  A : apply (matrix, xss),\n  [m,n] : matrix_size (A),\n  k : min (m,n),\n  makelist (A[i,i],i,k))$\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Las matrices se pueden representar como listas de listas de la misma longitud, donde cada uno de sus elementos representa una fila de la matriz. Definir la funci\u00f3n diagonal :: [[a]] -> [a] tal que (diagonal xss) es la diagonal de la matriz xss. Por ejemplo, diagonal [[3,5,2],[4,7,1],[6,9,0]] == [3,7,0] diagonal [[3,5],[4,7],[6,9]] == [3,7] diagonal&#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":[160,96,325,71,28,72,42,84,6,45,260,76],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2122"}],"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=2122"}],"version-history":[{"count":6,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2122\/revisions"}],"predecessor-version":[{"id":2162,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2122\/revisions\/2162"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=2122"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=2122"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=2122"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}