{"id":6721,"date":"2022-03-04T06:00:51","date_gmt":"2022-03-04T04:00:51","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=6721"},"modified":"2022-04-15T12:04:08","modified_gmt":"2022-04-15T10:04:08","slug":"posiciones-de-las-diagonales-principales","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/posiciones-de-las-diagonales-principales\/","title":{"rendered":"Posiciones de las diagonales principales"},"content":{"rendered":"<p>Las posiciones de una matriz con 3 filas y 4 columnas son<\/p>\n<pre lang=\"text\">\n   (1,1) (1,2) (1,3) (1,4)\n   (2,1) (2,2) (2,3) (2,4)\n   (3,1) (3,2) (3,3) (3,4)\n<\/pre>\n<p>La posiciones de sus 6 diagonales principales son<\/p>\n<pre lang=\"text\">\n  [(3,1)]\n  [(2,1),(3,2)]\n  [(1,1),(2,2),(3,3)]\n  [(1,2),(2,3),(3,4)]\n  [(1,3),(2,4)]\n  [(1,4)]\n<\/pre>\n<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   posicionesDiagonalesPrincipales :: Int -> Int -> [[(Int, Int)]]\n<\/pre>\n<p>tal que (posicionesdiagonalesprincipales m n) es la lista de las posiciones de las diagonales principales de una matriz con m filas y n columnas. Por ejemplo,<\/p>\n<pre lang=\"text\">\n  \u03bb> mapM_ print (posicionesDiagonalesPrincipales 3 4)\n  [(3,1)]\n  [(2,1),(3,2)]\n  [(1,1),(2,2),(3,3)]\n  [(1,2),(2,3),(3,4)]\n  [(1,3),(2,4)]\n  [(1,4)]\n  \u03bb> mapM_ print (posicionesDiagonalesPrincipales 4 4)\n  [(4,1)]\n  [(3,1),(4,2)]\n  [(2,1),(3,2),(4,3)]\n  [(1,1),(2,2),(3,3),(4,4)]\n  [(1,2),(2,3),(3,4)]\n  [(1,3),(2,4)]\n  [(1,4)]\n  \u03bb> mapM_ print (posicionesDiagonalesPrincipales 4 3)\n  [(4,1)]\n  [(3,1),(4,2)]\n  [(2,1),(3,2),(4,3)]\n  [(1,1),(2,2),(3,3)]\n  [(1,2),(2,3)]\n  [(1,3)]\n<\/pre>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Test.QuickCheck\n\n-- 1\u00aa soluci\u00f3n\n-- ===========\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\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_posicionesDiagonalesPrincipales :: Positive Int -> Positive Int -> Bool\nprop_posicionesDiagonalesPrincipales (Positive m) (Positive n) =\n  posicionesDiagonalesPrincipales1 m n ==\n  posicionesDiagonalesPrincipales2 m n\n\n-- La comprobaci\u00f3n es\n--   \u03bb> quickCheck prop_posicionesDiagonalesPrincipales\n--   +++ OK, passed 100 tests.\n\n-- Comparaci\u00f3n de eficiencia\n-- =========================\n\n-- La comparaci\u00f3n es\n--   \u03bb> length (posicionesDiagonalesPrincipales1 (10^7) (10^6))\n--   10999999\n--   (6.14 secs, 3,984,469,440 bytes)\n--   \u03bb> length (posicionesDiagonalesPrincipales2 (10^7) (10^6))\n--   10999999\n--   (3.07 secs, 2,840,469,440 bytes)\n<\/pre>\n<p>El c\u00f3digo se encuentra en <a href=\"https:\/\/github.com\/jaalonso\/Exercitium\/blob\/main\/src\/Posiciones_diagonales_principales.hs\">GitHub<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Las posiciones de una matriz con 3 filas y 4 columnas son (1,1) (1,2) (1,3) (1,4) (2,1) (2,2) (2,3) (2,4) (3,1) (3,2) (3,3) (3,4) La posiciones de sus 6 diagonales principales son [(3,1)] [(2,1),(3,2)] [(1,1),(2,2),(3,3)] [(1,2),(2,3),(3,4)] [(1,3),(2,4)] [(1,4)] Definir la funci\u00f3n posicionesDiagonalesPrincipales :: Int -> Int -> [[(Int, Int)]] tal que (posicionesdiagonalesprincipales m n) es&#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":[8,42],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/6721"}],"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=6721"}],"version-history":[{"count":2,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/6721\/revisions"}],"predecessor-version":[{"id":6748,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/6721\/revisions\/6748"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=6721"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=6721"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=6721"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}