{"id":1497,"date":"2015-05-29T06:00:45","date_gmt":"2015-05-29T04:00:45","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=1497"},"modified":"2015-06-13T16:22:08","modified_gmt":"2015-06-13T14:22:08","slug":"matrices-latinas","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/matrices-latinas\/","title":{"rendered":"Matrices latinas"},"content":{"rendered":"<p>Una matriz latina de orden n es una matriz cuadrada de orden n tal que todos sus elementos son cero salvo los de su fila y columna central, si n es impar; o los de sus dos filas y columnas centrales, si n es par.<\/p>\n<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   latina :: Int -> Array (Int,Int) Int\n<\/pre>\n<p>tal que (latina n) es la siguiente matriz latina de orden n:<\/p>\n<ul>\n<li>Para n impar:<\/li>\n<\/ul>\n<pre lang=\"text\">\n     | 0  0... 0 1   0 ... 0   0|\n     | 0  0... 0 2   0 ... 0   0|\n     | 0  0... 0 3   0 ... 0   0|\n     | .........................|\n     | 1  2..............n-1   n|\n     | .........................|\n     | 0  0... 0 n-2 0 ... 0   0|\n     | 0  0... 0 n-1 0 ... 0   0|\n     | 0  0... 0 n   0 ... 0   0|\n<\/pre>\n<ul>\n<li>Para n par:<\/li>\n<\/ul>\n<pre lang=\"text\">\n     | 0  0... 0 1   n    0 ...   0   0|\n     | 0  0... 0 2   n-1  0 ...   0   0|\n     | 0  0... 0 3   n-2  0 ...   0   0|\n     | ................................|\n     | 1  2.....................n-1   n|\n     | n n-1 .................... 2   1|\n     | ................................|\n     | 0  0... 0 n-2  3   0 ...   0   0|\n     | 0  0... 0 n-1  2   0 ...   0   0|\n     | 0  0... 0 n    1   0 ...   0   0|\n<\/pre>\n<p>Por ejemplo,<\/p>\n<pre lang=\"text\">\n   ghci> elems (latina 5)\n   [0,0,1,0,0,\n    0,0,2,0,0,\n    1,2,3,4,5,\n    0,0,4,0,0,\n    0,0,5,0,0]\n   ghci> elems (latina 6)\n   [0,0,1,6,0,0,\n    0,0,2,5,0,0,\n    1,2,3,4,5,6,\n    6,5,4,3,2,1,\n    0,0,5,2,0,0,\n    0,0,6,1,0,0]\n<\/pre>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nlatina :: Int -> Array (Int,Int) Int\nlatina n | even n    = latinaPar n\n         | otherwise = latinaImpar n\n\n-- (latinaImpar n) es la matriz latina de orden n, siendo n un n\u00famero\n-- impar. Por ejemplo,\n--    ghci> elems (latinaImpar 5)\n--    [0,0,1,0,0,\n--     0,0,2,0,0,\n--     1,2,3,4,5,\n--     0,0,4,0,0,\n--     0,0,5,0,0]\nlatinaImpar :: Int -> Array (Int,Int) Int\nlatinaImpar n = \n    array ((1,1),(n,n)) [((i,j),f i j) | i <- [1..n], j <- [1..n]]\n    where c = 1 + (n `div` 2)\n          f i j | i == c    = j\n                | j == c    = i \n                | otherwise = 0 \n\n-- (latinaPar n) es la matriz latina de orden n, siendo n un n\u00famero\n-- par. Por ejemplo,\n--    ghci> elems (latinaPar 6)\n--    [0,0,1,6,0,0,\n--     0,0,2,5,0,0,\n--     1,2,3,4,5,6,\n--     6,5,4,3,2,1,\n--     0,0,5,2,0,0,\n--     0,0,6,1,0,0]\nlatinaPar :: Int -> Array (Int,Int) Int\nlatinaPar n = \n    array ((1,1),(n,n)) [((i,j),f i j) | i <- [1..n], j <- [1..n]]\n    where c = n `div` 2\n          f i j | i == c    = j\n                | i == c+1  = n-j+1\n                | j == c    = i\n                | j == c+1  = n-i+1\n                | otherwise = 0 \n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Una matriz latina de orden n es una matriz cuadrada de orden n tal que todos sus elementos son cero salvo los de su fila y columna central, si n es impar; o los de sus dos filas y columnas centrales, si n es par. Definir la funci\u00f3n latina :: Int -> Array (Int,Int) Int&#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":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/1497"}],"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=1497"}],"version-history":[{"count":2,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/1497\/revisions"}],"predecessor-version":[{"id":1559,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/1497\/revisions\/1559"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=1497"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=1497"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=1497"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}