{"id":1217,"date":"2015-03-20T06:00:09","date_gmt":"2015-03-20T04:00:09","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=1217"},"modified":"2015-05-01T08:58:36","modified_gmt":"2015-05-01T06:58:36","slug":"maximos-locales-de-una-matriz","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/maximos-locales-de-una-matriz\/","title":{"rendered":"M\u00e1ximos locales de una matriz"},"content":{"rendered":"<p>Un elemento de una matriz es un m\u00e1ximo local si es mayor que todos sus vecinos. Por ejemplo, en la matriz<\/p>\n<pre lang=\"text\">\n    [[1,0,0,8],\n     [0,2,0,3],\n     [0,0,0,5],\n     [3,5,7,6],\n     [1,2,3,4]]\n<\/pre>\n<p>los m\u00e1ximos locales son 8 (en la posici\u00f3n (1,4)), 2 (en la posici\u00f3n (2,2)) y 7 (en la posici\u00f3n (4,3)).<\/p>\n<p>Definimos el tipo de las matrices, mediante<\/p>\n<pre lang=\"text\">\n   type Matriz a = Array (Int,Int) Int\n<\/pre>\n<p>y el ejemplo anterior por<\/p>\n<pre lang=\"text\">\n   ej1 :: Matriz Int\n   ej1 = listArray ((1,1),(5,4)) (concat [[1,0,0,8],\n                                          [0,2,0,3],\n                                          [0,0,0,5],\n                                          [3,5,7,6],\n                                          [1,2,3,4]])\n<\/pre>\n<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   maximosLocales :: Matriz Int -> [((Int,Int),Int)]\n<\/pre>\n<p>tal que (maximosLocales p) es la lista de las posiciones en las que hay un m\u00e1ximo local, con el valor correspondiente. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   maximosLocales ej1 == [((1,4),8),((2,2),2),((4,3),7)]\n<\/pre>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Data.Array\n\ntype Matriz a = Array (Int,Int) a\n\nej1 :: Matriz Int\nej1 = listArray ((1,1),(5,4)) (concat [[1,0,0,8],\n                                       [0,2,0,3],\n                                       [0,0,0,5],\n                                       [3,5,7,6],\n                                       [1,2,3,4]])\n\nmaximosLocales :: Matriz Int -> [((Int,Int),Int)]\nmaximosLocales p = \n    [((i,j),p!(i,j)) | (i,j) <- indices p,\n               and [p!(a,b) < p!(i,j) | (a,b) <- vecinos (i,j)]] \n    where (_,(m,n)) = bounds p\n          vecinos (i,j) = [(a,b) | a <- [max 1 (i-1)..min m (i+1)],\n                                   b <- [max 1 (j-1)..min n (j+1)],\n                                   (a,b) \/= (i,j)]\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Un elemento de una matriz es un m\u00e1ximo local si es mayor que todos sus vecinos. Por ejemplo, en la matriz [[1,0,0,8], [0,2,0,3], [0,0,0,5], [3,5,7,6], [1,2,3,4]] los m\u00e1ximos locales son 8 (en la posici\u00f3n (1,4)), 2 (en la posici\u00f3n (2,2)) y 7 (en la posici\u00f3n (4,3)). Definimos el tipo de las matrices, mediante type Matriz&#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":[4],"tags":[100,43,8,82,42,83,84],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/1217"}],"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=1217"}],"version-history":[{"count":2,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/1217\/revisions"}],"predecessor-version":[{"id":1259,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/1217\/revisions\/1259"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=1217"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=1217"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=1217"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}