{"id":7775,"date":"2023-01-10T06:00:31","date_gmt":"2023-01-10T04:00:31","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=7775"},"modified":"2022-12-30T12:02:30","modified_gmt":"2022-12-30T10:02:30","slug":"10-ene-23","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/10-ene-23\/","title":{"rendered":"N\u00famero de variables de una expresi\u00f3n aritm\u00e9tica"},"content":{"rendered":"<p>Las expresiones aritm\u00e9ticas construidas con una variable (denotada por <code>X<\/code>), los n\u00fameros enteros y las operaciones de sumar y multiplicar se pueden representar mediante el tipo de datos Expr definido por<\/p>\n<pre lang=\"text\">\n   data Expr = X\n             | C Int\n             | S Expr Expr\n             | P Expr Expr\n<\/pre>\n<p>Por ejemplo, la expresi\u00f3n <code>X\u00b7(13+X)<\/code> se representa por<\/p>\n<pre lang=\"text\">\n   P X (S (C 13) X)\n<\/pre>\n<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   numVars :: Expr -> Int\n<\/pre>\n<p>tal que <code>numVars e<\/code> es el n\u00famero de variables en la expresi\u00f3n <code>e<\/code>. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   numVars (C 3)               ==  0\n   numVars X                   ==  1\n   numVars (P X (S (C 13) X))  ==  2\n<\/pre>\n<p><b>Soluciones<\/b><\/p>\n<p>A continuaci\u00f3n se muestran las <a href=\"#haskell\">soluciones en Haskell<\/a> y las <a href=\"#python\">soluciones en Python<\/a>.<\/p>\n<p><a name=\"haskell\"><\/a><br \/>\n<b>Soluciones en Haskell<\/b><\/p>\n<pre lang=\"haskell\">\ndata Expr = X\n          | C Int\n          | S Expr Expr\n          | P Expr Expr\n\nnumVars :: Expr -> Int\nnumVars X       = 1\nnumVars (C _)   = 0\nnumVars (S a b) = numVars a + numVars b\nnumVars (P a b) = numVars a + numVars b\n<\/pre>\n<p><a name=\"python\"><\/a><br \/>\n<b>Soluciones en Python<\/b><\/p>\n<pre lang=\"python\">\nfrom dataclasses import dataclass\n\n\n@dataclass\nclass Expr:\n    pass\n\n@dataclass\nclass X(Expr):\n    pass\n\n@dataclass\nclass C(Expr):\n    x: int\n\n@dataclass\nclass S(Expr):\n    x: Expr\n    y: Expr\n\n@dataclass\nclass P(Expr):\n    x: Expr\n    y: Expr\n\ndef numVars(e: Expr) -> int:\n    match e:\n        case X():\n            return 1\n        case C(_):\n            return 0\n        case S(e1, e2):\n            return numVars(e1) + numVars(e2)\n        case P(e1, e2):\n            return numVars(e1) + numVars(e2)\n    assert False\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Las expresiones aritm\u00e9ticas construidas con una variable (denotada por X), los n\u00fameros enteros y las operaciones de sumar y multiplicar se pueden representar mediante el tipo de datos Expr definido por data Expr = X | C Int | S Expr Expr | P Expr Expr Por ejemplo, la expresi\u00f3n X\u00b7(13+X) se representa por P&#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":[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\/7775"}],"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=7775"}],"version-history":[{"count":1,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7775\/revisions"}],"predecessor-version":[{"id":7776,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7775\/revisions\/7776"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=7775"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=7775"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=7775"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}