{"id":3741,"date":"2018-02-16T06:00:30","date_gmt":"2018-02-16T04:00:30","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=3741"},"modified":"2018-03-07T07:33:19","modified_gmt":"2018-03-07T05:33:19","slug":"vertices-de-un-cuadrado","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/vertices-de-un-cuadrado\/","title":{"rendered":"V\u00e9rtices de un cuadrado"},"content":{"rendered":"<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   esCuadrado :: (Num a, Ord a) => (a,a) -> (a,a) -> (a,a) -> (a,a) -> Bool\n<\/pre>\n<p>tal que (esCuadrado p q r s) se verifica si los puntos p, q, r y s son los v\u00e9rtices de un cuadrado. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   esCuadrado (0,0) (0,1) (1,1) (1,0)    == True\n   esCuadrado (0,0) (2,1) (3,-1) (1, -2) == True\n   esCuadrado (0,0) (1,1) (0,1) (1,0)    == True\n   esCuadrado (1,1) (1,1) (1,1) (1,1)    == True\n   esCuadrado (0,0) (0,2) (3,2) (3,0)    == False\n   esCuadrado (0,0) (3,4) (8,4) (5,0)    == False\n   esCuadrado (0,0) (0,0) (1,1) (0,0)    == False\n   esCuadrado (0,0) (0,0) (1,0) (0,1)    == False\n   esCuadrado (0,0) (1,0) (0,1) (-1,-1)  == False\n<\/pre>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Data.List (sort, tails)\n\nesCuadrado :: (Num a, Ord a) => (a,a) -> (a,a) -> (a,a) -> (a,a) -> Bool\nesCuadrado p q r s = and [a == b, b == c, c == d, e == f, a + b == e]\n  where [a,b,c,d,e,f] = sort (distancias p q r s)\n\n-- (distancias p q r s) es la lista de los cuadrados de las longitudes\n-- de los lados y de las diagonales del cuadril\u00e1tero cuyos v\u00e9rtices son\n-- los puntos p, q, r y s. Por ejemplo,\n--    distancias (0,0) (0,1) (1,1) (1,0)  ==  [1,2,1,1,2,1]\n--    distancias (0,0) (3,4) (8,4) (5,0)  ==  [25,80,25,25,20,25]\n--    distancias (0,0) (0,2) (3,2) (3,0)  ==  [4,13,9,9,13,4]\n--    distancias (0,0) (0,0) (1,1) (0,0)  ==  [0,2,0,2,0,2]\n--    distancias (0,0) (0,0) (1,0) (0,1)  ==  [0,1,1,1,1,2]\ndistancias :: Num a => (a,a) -> (a,a) -> (a,a) -> (a,a) -> [a]\ndistancias p q r s =\n  [l | (h:t) <- tails [p,q,r,s], l <- map (dist h) t]\n\n-- (dist p q) es el cuadrado de la distancia del punto p al q. Por\n-- ejemplo,\n--    dist (6,4) (3,8)  ==  25\ndist :: Num a => (a,a) -> (a,a) -> a\ndist (x1,y1) (x2,y2) = (x2-x1)^2 + (y2-y1)^2\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Definir la funci\u00f3n esCuadrado :: (Num a, Ord a) => (a,a) -> (a,a) -> (a,a) -> (a,a) -> Bool tal que (esCuadrado p q r s) se verifica si los puntos p, q, r y s son los v\u00e9rtices de un cuadrado. Por ejemplo, esCuadrado (0,0) (0,1) (1,1) (1,0) == True esCuadrado (0,0) (2,1) (3,-1)&#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":[7],"tags":[100,8,10,11,14,75],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/3741"}],"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=3741"}],"version-history":[{"count":2,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/3741\/revisions"}],"predecessor-version":[{"id":3845,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/3741\/revisions\/3845"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=3741"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=3741"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=3741"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}