La lista de las diagonales principales de la matriz<\/p>\n
\n 1 2 3 4\n 5 6 7 8\n 9 10 11 12\n<\/pre>\nes<\/p>\n
\n [[9],[5,10],[1,6,11],[2,7,12],[3,8],[4]]\n<\/pre>\nDefinir la funci\u00f3n<\/p>\n
\n diagonalesPrincipales :: Array (Int,Int) a -> [[a]]\n<\/pre>\ntal que diagonalesPrincipales p<\/code> es la lista de las diagonales principales de p<\/code>. Por ejemplo,<\/p>\n\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<\/p>\n
1. Soluciones en Haskell<\/h2>\n\nimport Data.Array (Array, (!), bounds, listArray)\nimport Test.Hspec (Spec, describe, hspec, it, shouldBe)\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-- Verificaci\u00f3n\n-- ============\n\nverifica :: IO ()\nverifica = hspec spec\n\nspecG :: (Array (Int,Int) Int -> [[Int]]) -> Spec\nspecG diagonalesPrincipales = do\n it \"e1\" $\n diagonalesPrincipales (listArray ((1,1),(3,4)) [1..12]) `shouldBe`\n [[9],[5,10],[1,6,11],[2,7,12],[3,8],[4]]\n\nspec :: Spec\nspec = do\n describe \"def. 1\" $ specG diagonalesPrincipales1\n describe \"def. 2\" $ specG diagonalesPrincipales2\n\n-- La verificaci\u00f3n es\n-- \u03bb> verifica\n-- 2 examples, 0 failures\n\n-- Equivalencia de las definiciones\n-- ================================\n\n-- La propiedad es\nprop_diagonalesPrincipales2 :: Positive Int -> Positive Int -> Bool\nprop_diagonalesPrincipales2 (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_diagonalesPrincipales2\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>\n2. Soluciones en Python<\/h2>\n\nfrom typing import TypeVar\n\nfrom src.Posiciones_diagonales_principales import (\n posicionesDiagonalesPrincipales1, posicionesDiagonalesPrincipales2)\n\nA = TypeVar('A')\n\n# 1\u00aa soluci\u00f3n\n# ===========\n\nmatriz = list[list[A]]\n\ndef diagonalesPrincipales1(p: matriz[A]) -> list[list[A]]:\n m = len(p)\n n = len(p[0])\n return [[p[i-1][j-1] for (i,j) in ijs]\n for ijs in posicionesDiagonalesPrincipales1(m, n)]\n\n# 2\u00aa soluci\u00f3n\n# ===========\n\ndef diagonalesPrincipales2(p: matriz[A]) -> list[list[A]]:\n m = len(p)\n n = len(p[0])\n return [[p[i-1][j-1] for (i,j) in ijs]\n for ijs in posicionesDiagonalesPrincipales2(m, n)]\n\n# Verificaci\u00f3n\n# ============\n\ndef test_diagonalesPrincipales() -> None:\n for diagonalesPrincipales in [diagonalesPrincipales1,\n diagonalesPrincipales2]:\n assert diagonalesPrincipales([[ 1, 2, 3, 4],\n [ 5, 6, 7, 8],\n [ 9,10,11,12]]) == \\\n [[9],[5,10],[1,6,11],[2,7,12],[3,8],[4]]\n print(\"Verificado\")\n\n# La verificaci\u00f3n es\n# >>> test_diagonalesPrincipales()\n# Verificado\n<\/pre>\n","protected":false},"excerpt":{"rendered":"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]]<\/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":"default","_kad_post_title":"default","_kad_post_layout":"default","_kad_post_sidebar_id":"","_kad_post_content_style":"default","_kad_post_vertical_padding":"default","_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":[581],"tags":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/8549"}],"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=8549"}],"version-history":[{"count":1,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/8549\/revisions"}],"predecessor-version":[{"id":8550,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/8549\/revisions\/8550"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=8549"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=8549"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=8549"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}