{"id":8547,"date":"2024-05-04T06:00:38","date_gmt":"2024-05-04T04:00:38","guid":{"rendered":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=8547"},"modified":"2024-05-09T14:36:29","modified_gmt":"2024-05-09T12:36:29","slug":"04-may-24","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/04-may-24\/","title":{"rendered":"Posiciones de las diagonales principales"},"content":{"rendered":"

Las posiciones de una matriz con 3 filas y 4 columnas son<\/p>\n

\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
La posiciones de sus 6 diagonales principales son<\/p>\n
\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
Definir la funci\u00f3n<\/p>\n
\n   posicionesDiagonalesPrincipales :: Int -> Int -> [[(Int, Int)]]\n<\/pre>\n
tal que posicionesdiagonalesprincipales m n<\/code> es la lista de las posiciones de las diagonales principales de una matriz con m<\/code> filas y n<\/code> columnas. Por ejemplo,<\/p>\n
\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
<\/p>\n
1. Soluciones en Haskell<\/h2>\n
\nimport Test.Hspec (Spec, describe, hspec, it, shouldBe)\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-- Verificaci\u00f3n\n-- ============\n\nverifica :: IO ()\nverifica = hspec spec\n\nspecG :: (Int -> Int -> [[(Int, Int)]]) -> Spec\nspecG posicionesDiagonalesPrincipales = do\n  it \"e1\" $\n    posicionesDiagonalesPrincipales 3 4 `shouldBe`\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  it \"e2\" $\n    posicionesDiagonalesPrincipales 4 4 `shouldBe`\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  it \"e3\" $\n    posicionesDiagonalesPrincipales 4 3 `shouldBe`\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\nspec :: Spec\nspec = do\n  describe \"def. 1\" $ specG posicionesDiagonalesPrincipales1\n  describe \"def. 2\" $ specG posicionesDiagonalesPrincipales2\n\n-- La verificaci\u00f3n es\n--    \u03bb> verifica\n--    6 examples, 0 failures\n\n-- Equivalencia de las definiciones\n-- ================================\n\n-- La propiedad es\nprop_posicionesDiagonalesPrincipales_equiv :: Positive Int -> Positive Int -> Bool\nprop_posicionesDiagonalesPrincipales_equiv (Positive m) (Positive n) =\n  posicionesDiagonalesPrincipales1 m n ==\n  posicionesDiagonalesPrincipales2 m n\n\n-- La comprobaci\u00f3n es\n--   \u03bb> quickCheck prop_posicionesDiagonalesPrincipales_equiv\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
2. Soluciones en Python<\/h2>\n
\nfrom timeit import Timer, default_timer\n\nfrom hypothesis import given\nfrom hypothesis import strategies as st\n\n# 1\u00aa soluci\u00f3n\n# ===========\n\ndef posicionesDiagonalesPrincipales1(m: int, n: int) -> list[list[tuple[int, int]]]:\n    def iniciales() -> list[tuple[int, int]]:\n        return [(i,1) for i in range(m,1,-1)] + [(1,j) for j in range(1, n+1)]\n    def extension(p: tuple[int, int]) -> list[tuple[int, int]]:\n        (i,j) = p\n        return [(i+k,j+k) for k in range(0, 1+min(m-i, n-j))]\n    return [extension(ij) for ij in iniciales()]\n\n# 2\u00aa soluci\u00f3n\n# ===========\n\ndef posicionesDiagonalesPrincipales2(m: int, n: int) -> list[list[tuple[int, int]]]:\n    return [list(zip(range(i,m+1), range(1,n+1))) for i in range(m,0,-1)] + \\\n           [list(zip(range(1,m+1), range(j,n+1))) for j in range(2,n+1)]\n\n# Verificaci\u00f3n\n# ============\n\ndef test_posicionesDiagonalesPrincipales() -> None:\n    for posicionesDiagonalesPrincipales in [posicionesDiagonalesPrincipales1,\n                                            posicionesDiagonalesPrincipales2]:\n        assert 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        assert 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        assert 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    print(\"Verificado\")\n\n# La verificaci\u00f3n es\n#    >>> test_posicionesDiagonalesPrincipales()\n#    Verificado\n\n# Equivalencia de las definiciones\n# ================================\n\n# La propiedad es\n@given(st.integers(min_value=1, max_value=100),\n       st.integers(min_value=1, max_value=100))\ndef test_posicionesDiagonalesPrincipales_equiv(m: int, n: int) -> None:\n    assert posicionesDiagonalesPrincipales1(m, n) == \\\n           posicionesDiagonalesPrincipales2(m, n)\n\n# La comprobaci\u00f3n es\n#    >>> test_posicionesDiagonalesPrincipales_equiv()\n#    >>>\n\n# Comparaci\u00f3n de eficiencia\n# =========================\n\ndef tiempo(e: str) -> None:\n    \"\"\"Tiempo (en segundos) de evaluar la expresi\u00f3n e.\"\"\"\n    t = Timer(e, \"\", default_timer, globals()).timeit(1)\n    print(f\"{t:0.2f} segundos\")\n\n# La comparaci\u00f3n es\n#    >>> tiempo('posicionesDiagonalesPrincipales1(10**4, 2*10**3)')\n#    3.32 segundos\n#    >>> tiempo('posicionesDiagonalesPrincipales2(10**4, 2*10**3)')\n#    2.16 segundos\n<\/pre>\n","protected":false},"excerpt":{"rendered":"
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…<\/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\/8547"}],"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=8547"}],"version-history":[{"count":1,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/8547\/revisions"}],"predecessor-version":[{"id":8548,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/8547\/revisions\/8548"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=8547"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=8547"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=8547"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}