{"id":496,"date":"2014-07-18T07:00:13","date_gmt":"2014-07-18T05:00:13","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=496"},"modified":"2015-05-01T09:01:28","modified_gmt":"2015-05-01T07:01:28","slug":"matriz-permutacion","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/matriz-permutacion\/","title":{"rendered":"Matriz permutaci\u00f3n"},"content":{"rendered":"

Introducci\u00f3n<\/h3>\n

Una matriz permutaci\u00f3n<\/a> es una matriz cuadrada con todos sus elementos iguales a 0, excepto uno cualquiera por cada fila y columna, el cual debe ser igual a 1.<\/p>\n

Ejercicio<\/h3>\n
\n-- En este ejercicio se usar\u00e1 el tipo de las matrices definido por\n--    type Matriz a = Array (Int,Int) a\n-- y los siguientes ejemplos de matrices\n--    q1, q2, q3 :: Matriz Int\n--    q1 = array ((1,1),(2,2)) [((1,1),1),((1,2),0),((2,1),0),((2,2),1)]\n--    q2 = array ((1,1),(2,2)) [((1,1),0),((1,2),1),((2,1),0),((2,2),1)]\n--    q3 = array ((1,1),(2,2)) [((1,1),3),((1,2),0),((2,1),0),((2,2),1)]\n--\n-- Definir la funci\u00f3n\n--    esMatrizPermutacion :: Num a => Matriz a -> Bool\n-- tal que (esMatrizPermutacion p) se verifica si p es una matriz\n-- permutaci\u00f3n. Por ejemplo.\n--    1esMatrizPermutacion q1  ==  True\n--    esMatrizPermutacion q2  ==  False\n--    esMatrizPermutacion q3  ==  False\n<\/pre>\n
Soluciones<\/h4>\n
\nimport Data.Array\n\ntype Matriz a = Array (Int,Int) a\n\nq1, q2, q3 :: Matriz Int\nq1 = array ((1,1),(2,2)) [((1,1),1),((1,2),0),((2,1),0),((2,2),1)]\nq2 = array ((1,1),(2,2)) [((1,1),0),((1,2),1),((2,1),0),((2,2),1)]\nq3 = array ((1,1),(2,2)) [((1,1),3),((1,2),0),((2,1),0),((2,2),1)]\n\nesMatrizPermutacion :: (Num a, Eq a) => Matriz a -> Bool\nesMatrizPermutacion p = \n    and [esListaUnitaria [p!(i,j) | i <- [1..n]] | j <- [1..n]] &&\n    and [esListaUnitaria [p!(i,j) | j <- [1..n]] | i <- [1..n]] \n    where (_,(n,_)) = bounds p\n\n-- (esListaUnitaria xs) se verifica si xs tiene un 1 y los restantes\n-- elementos son 0. Por ejemplo,\n--    esListaUnitaria [0,1,0,0]  ==  True\n--    esListaUnitaria [0,1,0,1]  ==  False\n--    esListaUnitaria [0,2,0,0]  ==  False\nesListaUnitaria :: (Num a, Eq a) => [a] -> Bool\nesListaUnitaria xs = [x | x <- xs, x \/= 0] == [1]\n<\/pre>\n","protected":false},"excerpt":{"rendered":"
Introducci\u00f3n Una matriz permutaci\u00f3n es una matriz cuadrada con todos sus elementos iguales a 0, excepto uno cualquiera por cada fila y columna, el cual debe ser igual a 1. Ejercicio — En este ejercicio se usar\u00e1 el tipo de las matrices definido por — type Matriz a = Array (Int,Int) a — y los…<\/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":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/496"}],"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=496"}],"version-history":[{"count":3,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/496\/revisions"}],"predecessor-version":[{"id":659,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/496\/revisions\/659"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=496"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=496"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=496"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}