{"id":6723,"date":"2022-03-07T06:00:31","date_gmt":"2022-03-07T04:00:31","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=6723"},"modified":"2022-04-15T12:03:52","modified_gmt":"2022-04-15T10:03:52","slug":"diagonales-principales-de-una-matriz","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/diagonales-principales-de-una-matriz\/","title":{"rendered":"Diagonales principales de una matriz"},"content":{"rendered":"<p>La lista de las diagonales principales de la matriz<\/p>\n<pre lang=\"text\">\n   1  2  3  4\n   5  6  7  8\n   9 10 11 12\n<\/pre>\n<p>es<\/p>\n<pre lang=\"text\">\n   [[9],[5,10],[1,6,11],[2,7,12],[3,8],[4]]\n<\/pre>\n<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   diagonalesPrincipales :: Array (Int,Int) a -> [[a]]\n<\/pre>\n<p>tal que (diagonalesPrincipales p) es la lista de las diagonales principales de p. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   \u03bb> diagonalesPrincipales (listArray ((1,1),(3,4)) [1..12])\n   [[9],[5,10],[1,6,11],[2,7,12],[3,8],[4]]\n<\/pre>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Data.Array (Array, (!), bounds, listArray)\nimport Test.QuickCheck\n\n-- 1\u00aa soluci\u00f3n\n-- ===========\n\ndiagonalesPrincipales1 :: Array (Int,Int) a -> [[a]]\ndiagonalesPrincipales1 p =\n  [[p ! ij | ij <- ijs] | ijs <- posicionesDiagonalesPrincipales1 m n]\n  where (_,(m,n)) = bounds p\n\nposicionesDiagonalesPrincipales1 :: Int -> Int -> [[(Int, Int)]]\nposicionesDiagonalesPrincipales1 m n =\n  [extension ij | ij <- iniciales]\n  where iniciales = [(i,1) | i <- [m,m-1..2]] ++ [(1,j) | j <- [1..n]]\n        extension (i,j) = [(i+k,j+k) | k <- [0..min (m-i) (n-j)]]\n\n-- 2\u00aa soluci\u00f3n\n-- ===========\n\ndiagonalesPrincipales2 :: Array (Int,Int) a -> [[a]]\ndiagonalesPrincipales2 p =\n  [[p ! ij | ij <- ijs] | ijs <- posicionesDiagonalesPrincipales2 m n]\n  where (_,(m,n)) = bounds p\n\nposicionesDiagonalesPrincipales2 :: Int -> Int -> [[(Int, Int)]]\nposicionesDiagonalesPrincipales2 m n =\n  [zip [i..m] [1..n] | i <- [m,m-1..1]] ++\n  [zip [1..m] [j..n] | j <- [2..n]]\n\n-- Equivalencia de las definiciones\n-- ================================\n\n-- La propiedad es\nprop_diagonalesPrincipales :: Positive Int -> Positive Int -> Bool\nprop_diagonalesPrincipales (Positive m) (Positive n) =\n  diagonalesPrincipales1 p == diagonalesPrincipales2 p\n  where p = listArray ((1,1),(m,n)) [1..]\n\n-- La comprobaci\u00f3n es\n--    \u03bb> quickCheck prop_diagonalesPrincipales\n--    +++ OK, passed 100 tests.\n\n-- Comparaci\u00f3n de eficiencia\n-- =========================\n\n-- La comparaci\u00f3n es\n--    \u03bb> length (diagonalesPrincipales1 (listArray ((1,1),(10^4,10^4)) [1..]))\n--    19999\n--    (6.90 secs, 8,010,369,224 bytes)\n--    \u03bb> length (diagonalesPrincipales2 (listArray ((1,1),(10^4,10^4)) [1..]))\n--    19999\n--    (6.78 secs, 8,008,289,224 bytes)\n<\/pre>\n<p>El c\u00f3digo se encuentra en <a href=\"https:\/\/github.com\/jaalonso\/Exercitium\/blob\/main\/src\/Diagonales_principales.hs\">GitHub<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>La lista de las diagonales principales de la matriz 1 2 3 4 5 6 7 8 9 10 11 12 es [[9],[5,10],[1,6,11],[2,7,12],[3,8],[4]] Definir la funci\u00f3n diagonalesPrincipales :: Array (Int,Int) a -> [[a]] tal que (diagonalesPrincipales p) es la lista de las diagonales principales de p. Por ejemplo, \u03bb> diagonalesPrincipales (listArray ((1,1),(3,4)) [1..12]) [[9],[5,10],[1,6,11],[2,7,12],[3,8],[4]] Soluciones&#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":[8,507,42],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/6723"}],"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=6723"}],"version-history":[{"count":2,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/6723\/revisions"}],"predecessor-version":[{"id":6770,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/6723\/revisions\/6770"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=6723"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=6723"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=6723"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}