{"id":6227,"date":"2021-03-30T06:00:15","date_gmt":"2021-03-30T04:00:15","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=6227"},"modified":"2021-04-06T09:02:21","modified_gmt":"2021-04-06T07:02:21","slug":"menor-prefijo-con-suma-positiva","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/menor-prefijo-con-suma-positiva\/","title":{"rendered":"Menor prefijo con suma positiva"},"content":{"rendered":"<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   menorPrefijoSumaPositiva1 :: [[Int]] -> Maybe [[Int]]\n<\/pre>\n<p>tal que (menorPrefijoSumaPositiva1 xss) es justamente el menor prejijo de xss tal que la suma de lsas sumas de sus elementos es positivo y es Nothing si tal prefijo no existe. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   menorPrefijoSumaPositiva [[1],[-3],[2,4]]     == Just [[1]]\n   menorPrefijoSumaPositiva [[-2,1],[-3],[2,4]]  == Just [[-2,1],[-3],[2,4]]\n   menorPrefijoSumaPositiva [[-2,1],[3],[2,4]]   == Just [[-2,1],[3]]\n   menorPrefijoSumaPositiva [[-2,1],[-3],[2,-4]] == Nothing\n   menorPrefijoSumaPositiva [[-k..k] | k <- [1..5000]]              == Nothing\n   fmap length (menorPrefijoSumaPositiva [[-3000..k] | k <- [0..]]) == Just 5198\n<\/pre>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Data.List (inits)\nimport Data.Maybe (listToMaybe)\nimport Test.QuickCheck\n\n-- 1\u00aa soluci\u00f3n\n-- ===========\n\nmenorPrefijoSumaPositiva1 :: [[Int]] -> Maybe [[Int]]\nmenorPrefijoSumaPositiva1 xss =\n  listToMaybe [xs | xs <- tail (inits xss),\n                    sum (concat xs) > 0]\n\n-- 2\u00aa soluci\u00f3n\n-- ===========\n\nmenorPrefijoSumaPositiva2 :: [[Int]] -> Maybe [[Int]]\nmenorPrefijoSumaPositiva2 xss = aux [] xss\n  where aux yss _  | sum (concat yss) > 0 = Just (reverse yss)\n        aux _   []                        = Nothing\n        aux yss (zs:zss)                  = aux (zs : yss) zss\n\n-- 3\u00aa soluci\u00f3n\n-- ===========\n\nmenorPrefijoSumaPositiva3 :: [[Int]] -> Maybe [[Int]]\nmenorPrefijoSumaPositiva3 xss =\n  aux (0,[]) (zip (map sum xss) xss)\n  where aux (s,yss) _  | s > 0   = Just (reverse yss)\n        aux _ []                 = Nothing\n        aux (s,yss) ((t,zs):zss) = aux (s+t,zs:yss) zss\n\n-- Comprobaci\u00f3n de equivalencia\n-- ============================\n\n-- La propiedad es\nprop_equivalencia :: [[Int]] -> Bool\nprop_equivalencia xss =\n  all (== (menorPrefijoSumaPositiva1 xss))\n      [ menorPrefijoSumaPositiva2 xss,\n        menorPrefijoSumaPositiva3 xss ]\n\n-- La comprobaci\u00f3n es\n--    \u03bb> quickCheck prop_equivalencia\n--    +++ OK, passed 100 tests.\n\n-- Comparaci\u00f3n de eficiencia\n-- =========================\n--\n-- La comparaci\u00f3n es\n--    \u03bb> fmap length (menorPrefijoSumaPositiva1 [[-200..k] | k <- [0..]])\n--    Just 348\n--    (2.40 secs, 2,801,967,392 bytes)\n--    \u03bb> fmap length (menorPrefijoSumaPositiva2 [[-200..k] | k <- [0..]])\n--    Just 348\n--    (2.46 secs, 2,800,717,720 bytes)\n--    \u03bb> fmap length (menorPrefijoSumaPositiva3 [[-200..k] | k <- [0..]])\n--    Just 348\n--    (0.01 secs, 18,128,464 bytes)\n\n--    \u03bb> menorPrefijoSumaPositiva1 [[-k..k] | k <- [1..500]]\n--    Nothing\n--    (6.39 secs, 6,127,124,136 bytes)\n--    \u03bb> menorPrefijoSumaPositiva2 [[-k..k] | k <- [1..500]]\n--    Nothing\n--    (6.47 secs, 6,124,201,288 bytes)\n--    \u03bb> menorPrefijoSumaPositiva3 [[-k..k] | k <- [1..500]]\n--    Nothing\n--    (0.03 secs, 37,944,760 bytes)\n<\/pre>\n<h4>Nuevas soluciones<\/h4>\n<ul>\n<li>En los comentarios se pueden escribir nuevas soluciones.\n<li>El c\u00f3digo se debe escribir entre una l\u00ednea con &#60;pre lang=&quot;haskell&quot;&#62; y otra con &#60;\/pre&#62;\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Definir la funci\u00f3n menorPrefijoSumaPositiva1 :: [[Int]] -> Maybe [[Int]] tal que (menorPrefijoSumaPositiva1 xss) es justamente el menor prejijo de xss tal que la suma de lsas sumas de sus elementos es positivo y es Nothing si tal prefijo no existe. Por ejemplo, menorPrefijoSumaPositiva [[1],[-3],[2,4]] == Just [[1]] menorPrefijoSumaPositiva [[-2,1],[-3],[2,4]] == Just [[-2,1],[-3],[2,4]] menorPrefijoSumaPositiva [[-2,1],[3],[2,4]] ==&#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":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/6227"}],"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=6227"}],"version-history":[{"count":2,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/6227\/revisions"}],"predecessor-version":[{"id":6260,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/6227\/revisions\/6260"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=6227"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=6227"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=6227"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}