{"id":7786,"date":"2023-01-17T06:00:11","date_gmt":"2023-01-17T04:00:11","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=7786"},"modified":"2022-12-31T10:35:07","modified_gmt":"2022-12-31T08:35:07","slug":"17-ene-23","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/17-ene-23\/","title":{"rendered":"M\u00e1ximos valores de una expresi\u00f3n aritm\u00e9tica"},"content":{"rendered":"

Las expresiones aritm\u00e9ticas generales se pueden definir usando el siguiente tipo de datos<\/p>\n

\n   data Expr = C Int\n             | X\n             | S Expr Expr\n             | R Expr Expr\n             | P Expr Expr\n             | E Expr Int\n     deriving (Eq, Show)\n<\/pre>\n
Por ejemplo, la expresi\u00f3n<\/p>\n
\n   3*x - (x+2)^7\n<\/pre>\n
se puede definir por<\/p>\n
\n   R (P (C 3) X) (E (S X (C 2)) 7)\n<\/pre>\n
Definir la funci\u00f3n<\/p>\n
\n   maximo :: Expr -> [Int] -> (Int,[Int])\n<\/pre>\n
tal que maximo e xs<\/code> es el par formado por el m\u00e1ximo valor de la expresi\u00f3n e<\/code> para los puntos de xs<\/code> y en qu\u00e9 puntos alcanza el m\u00e1ximo. Por ejemplo,<\/p>\n
\n   \u03bb> maximo (E (S (C 10) (P (R (C 1) X) X)) 2) [-3..3]\n   (100,[0,1])\n<\/pre>\n
Soluciones<\/b><\/p>\n
A continuaci\u00f3n se muestran las soluciones en Haskell<\/a> y las soluciones en Python<\/a>.<\/p>\n
<\/a>
\nSoluciones en Haskell<\/b><\/p>\n
\ndata Expr = C Int\n          | X\n          | S Expr Expr\n          | R Expr Expr\n          | P Expr Expr\n          | E Expr Int\n  deriving (Eq, Show)\n\nmaximo :: Expr -> [Int] -> (Int,[Int])\nmaximo e ns = (m,[n | n <- ns, valor e n == m])\n  where m = maximum [valor e n | n <- ns]\n\nvalor :: Expr -> Int -> Int\nvalor (C x) _     = x\nvalor X     n     = n\nvalor (S e1 e2) n = valor e1 n + valor e2 n\nvalor (R e1 e2) n = valor e1 n - valor e2 n\nvalor (P e1 e2) n = valor e1 n * valor e2 n\nvalor (E e1 m1) n = valor e1 n ^ m1\n<\/pre>\n
<\/a>
\nSoluciones en Python<\/b><\/p>\n
\nfrom dataclasses import dataclass\n\n\n@dataclass\nclass Expr:\n    pass\n\n@dataclass\nclass C(Expr):\n    x: int\n\n@dataclass\nclass X(Expr):\n    pass\n\n@dataclass\nclass S(Expr):\n    x: Expr\n    y: Expr\n\n@dataclass\nclass R(Expr):\n    x: Expr\n    y: Expr\n\n@dataclass\nclass P(Expr):\n    x: Expr\n    y: Expr\n\n@dataclass\nclass E(Expr):\n    x: Expr\n    y: int\n\ndef valor(e: Expr, n: int) -> int:\n    match e:\n        case C(a):\n            return a\n        case X():\n            return n\n        case S(e1, e2):\n            return valor(e1, n) + valor(e2, n)\n        case R(e1, e2):\n            return valor(e1, n) - valor(e2, n)\n        case P(e1, e2):\n            return valor(e1, n) * valor(e2, n)\n        case E(e1, m):\n            return valor(e1, n) ** m\n    assert False\n\ndef maximo(e: Expr, ns: list[int]) -> tuple[int, list[int]]:\n    m = max((valor(e, n) for n in ns))\n    return (m, [n for n in ns if valor(e, n) == m])\n<\/pre>\n","protected":false},"excerpt":{"rendered":"
Las expresiones aritm\u00e9ticas generales se pueden definir usando el siguiente tipo de datos data Expr = C Int | X | S Expr Expr | R Expr Expr | P Expr Expr | E Expr Int deriving (Eq, Show) Por ejemplo, la expresi\u00f3n 3*x – (x+2)^7 se puede definir por R (P (C 3) X)…<\/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":[581],"tags":[582],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7786"}],"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=7786"}],"version-history":[{"count":1,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7786\/revisions"}],"predecessor-version":[{"id":7787,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7786\/revisions\/7787"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=7786"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=7786"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=7786"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}