{"id":7362,"date":"2022-09-14T06:00:30","date_gmt":"2022-09-14T04:00:30","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=7362"},"modified":"2022-12-14T14:31:36","modified_gmt":"2022-12-14T12:31:36","slug":"interseccion-de-intervalos-cerrados","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/interseccion-de-intervalos-cerrados\/","title":{"rendered":"Intersecci\u00f3n de intervalos cerrados"},"content":{"rendered":"

Los intervalos cerrados se pueden representar mediante una lista de dos n\u00fameros (el primero es el extremo inferior del intervalo y el segundo el superior).<\/p>\n

Definir la funci\u00f3n<\/p>\n

\n   interseccion :: Ord a => [a] -> [a] -> [a]\n<\/pre>\n
tal que (interseccion i1 i2)<\/code> es la intersecci\u00f3n de los intervalos i1<\/code> e i2<\/code>. Por ejemplo,<\/p>\n
\n   interseccion [] [3,5]     ==  []\n   interseccion [3,5] []     ==  []\n   interseccion [2,4] [6,9]  ==  []\n   interseccion [2,6] [6,9]  ==  [6,6]\n   interseccion [2,6] [0,9]  ==  [2,6]\n   interseccion [2,6] [0,4]  ==  [2,4]\n   interseccion [4,6] [0,4]  ==  [4,4]\n   interseccion [5,6] [0,4]  ==  []\n<\/pre>\n
Comprobar con QuickCheck que la intersecci\u00f3n de intervalos es conmutativa.<\/p>\n
Soluciones<\/b><\/p>\n
A continuaci\u00f3n se muestran las soluciones en Haskell<\/a> y las soluciones en Python<\/a>.<\/p>\n
<\/a>
\nSoluciones en Haskell<\/b><\/p>\n
\nimport Test.QuickCheck\n\ninterseccion :: Ord a => [a] -> [a] -> [a]\ninterseccion [] _ = []\ninterseccion _ [] = []\ninterseccion [a1,b1] [a2,b2]\n    | a <= b    = [a,b]\n    | otherwise = []\n    where a = max a1 a2\n          b = min b1 b2\n\n-- La propiedad es\nprop_interseccion :: Int -> Int -> Int -> Int -> Property\nprop_interseccion a1 b1 a2 b2 =\n  a1 <= b1 && a2 <= b2 ==>\n  interseccion [a1,b1] [a2,b2] == interseccion [a2,b2] [a1,b1]\n\n-- La comprobaci\u00f3n es\n--    \u03bb> quickCheck prop_interseccion\n--    +++ OK, passed 100 tests; 263 discarded.\n<\/pre>\n
El c\u00f3digo se encuentra en GitHub<\/a>.<\/p>\n
<\/a>
\nSoluciones en Python<\/b><\/p>\n
\nfrom hypothesis import given, assume, strategies as st\n\nRectangulo = list[float]\n\ndef interseccion(i1: Rectangulo,\n                 i2: Rectangulo) -> Rectangulo:\n    if i1 and i2:\n        [a1, b1] = i1\n        [a2, b2] = i2\n        a = max(a1, a2)\n        b = min(b1, b2)\n        if a <= b:\n            return [a, b]\n        return []\n    return []\n\n# La propiedad es\n@given(st.floats(), st.floats(), st.floats(), st.floats())\ndef test_prop_raices(a1, b1, a2, b2):\n    assume(a1 <= b1 and a2 <= b2)\n    assert interseccion([a1, b1], [a2, b2]) == interseccion([a2, b2], [a1, b1])\n\n# La comprobaci\u00f3n es\n#    src> poetry run pytest -q interseccion_de_intervalos_cerrados.py\n#    1 passed in 0.64s\n<\/pre>\n
El c\u00f3digo se encuentra en GitHub<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"
Los intervalos cerrados se pueden representar mediante una lista de dos n\u00fameros (el primero es el extremo inferior del intervalo y el segundo el superior). Definir la funci\u00f3n interseccion :: Ord a => [a] -> [a] -> [a] tal que (interseccion i1 i2) es la intersecci\u00f3n de los intervalos i1 e i2. Por ejemplo, interseccion…<\/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":[581],"tags":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7362"}],"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=7362"}],"version-history":[{"count":2,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7362\/revisions"}],"predecessor-version":[{"id":7692,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7362\/revisions\/7692"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=7362"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=7362"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=7362"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}