{"id":3821,"date":"2018-03-02T06:00:52","date_gmt":"2018-03-02T04:00:52","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=3821"},"modified":"2018-03-14T07:52:53","modified_gmt":"2018-03-14T05:52:53","slug":"matrices-centro-simetricas","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/matrices-centro-simetricas\/","title":{"rendered":"Matrices centro sim\u00e9tricas"},"content":{"rendered":"<p>Una <a href=\"http:\/\/bit.ly\/2ER8X85\">matriz centro sim\u00e9trica<\/a> es una matriz cuadrada que es sim\u00e9trica respecto de su centro. Por ejemplo, de las siguientes matrices, las dos primeras son sim\u00e9tricas y las otras no lo son<\/p>\n<pre lang=\"text\">\n   (1 2)   (1 2 3)   (1 2 3)   (1 2 3)    \n   (2 1)   (4 5 4)   (4 5 4)   (4 5 4)\n           (3 2 1)   (3 2 2)\n<\/pre>\n<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   esCentroSimetrica :: Eq t => Array (Int,Int) t -> Bool\n<\/pre>\n<p>tal que (esCentroSimetrica a) se verifica si la matriz a es centro sim\u00e9trica. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   \u03bb> esCentroSimetrica (listArray ((1,1),(2,2)) [1,2, 2,1])\n   True\n   \u03bb> esCentroSimetrica (listArray ((1,1),(3,3)) [1,2,3, 4,5,4, 3,2,1])\n   True\n   \u03bb> esCentroSimetrica (listArray ((1,1),(3,3)) [1,2,3, 4,5,4, 3,2,2])\n   False\n   \u03bb> esCentroSimetrica (listArray ((1,1),(2,3)) [1,2,3, 4,5,4])\n   False\n<\/pre>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Data.Array \n\nesCentroSimetrica :: Eq t => Array (Int,Int) t -> Bool\nesCentroSimetrica a =\n  n == m && and [a!(i,j) == a!(n-i+1,n-j+1) | i <- [1..n], j <- [i..n]] \n  where (_,(n,m)) = bounds a\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Una matriz centro sim\u00e9trica es una matriz cuadrada que es sim\u00e9trica respecto de su centro. Por ejemplo, de las siguientes matrices, las dos primeras son sim\u00e9tricas y las otras no lo son (1 2) (1 2 3) (1 2 3) (1 2 3) (2 1) (4 5 4) (4 5 4) (4 5 4) (3&#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":[5],"tags":[43,72,42],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/3821"}],"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=3821"}],"version-history":[{"count":2,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/3821\/revisions"}],"predecessor-version":[{"id":3854,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/3821\/revisions\/3854"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=3821"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=3821"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=3821"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}