{"id":254,"date":"2018-04-18T13:44:37","date_gmt":"2018-04-18T12:44:37","guid":{"rendered":"http:\/\/ens-info.irem.univ-mrs.fr\/?p=254"},"modified":"2018-04-18T13:45:31","modified_gmt":"2018-04-18T12:45:31","slug":"deux-documents-sur-la-recursivite","status":"publish","type":"post","link":"https:\/\/ens-info.irem.univ-mrs.fr\/?p=254","title":{"rendered":"Deux documents sur la r\u00e9cursivit\u00e9"},"content":{"rendered":"<p>Deux papiers de Fernand Didier (IREM d\u2019Aix-Marseille) sur la r\u00e9cursivit\u00e9, qui pr\u00e9sentent cette notion \u00e0 travers des exemples diff\u00e9rents de ceux que l&rsquo;on a l&rsquo;habitude de pr\u00e9senter (Tours de hano\u00ef, quick sort, &#8230;).<\/p>\n<h2>La r\u00e9cursivit\u00e9 comme un outil pour \u00e9num\u00e9rer l&rsquo;arbre de tous les choix possibles.<\/h2>\n<p><a href=\"https:\/\/ens-info.irem.univ-mrs.fr\/wp-content\/uploads\/La-r\u00e9cursivit\u00e9-comme-outil-Fernand-Didier-2014.pdf\">La r\u00e9cursivit\u00e9 comme outil (Fernand Didier, 2014)<\/a><\/p>\n<p>Ce document illustre cette utilisation de la r\u00e9cursivit\u00e9 sur plusieurs exemples et contient aussi les programmes Python correspondants:<\/p>\n<ul>\n<li>Enum\u00e9ration de tous les n-uplet.<\/li>\n<li>Enum\u00e9ration des permutations sur un ensemble fini donn\u00e9.<\/li>\n<li>Placement de huit reines sur un \u00e9chiquier.<\/li>\n<li>Cavalier d&rsquo;Euler.<\/li>\n<li>Jeu du Sudoku.<\/li>\n<\/ul>\n<h2>R\u00e9cursivit\u00e9 et r\u00e9currence<\/h2>\n<p><a href=\"https:\/\/ens-info.irem.univ-mrs.fr\/wp-content\/uploads\/R\u00e9cursivit\u00e9-et-r\u00e9currence-Fernand-Didier-2015.pdf\">R\u00e9cursivit\u00e9 et r\u00e9currence (Fernand Didier, 2015)<\/a><\/p>\n<p>Ce document illustre le lien entre r\u00e9cursivit\u00e9 et r\u00e9currence \u00e0 travers plusieurs exemples issus du programme de math\u00e9matiques du Lyc\u00e9e.<\/p>\n<p>Il montre aussi comment \u00e9num\u00e9ration et d\u00e9nombrement sont fortement li\u00e9s.<\/p>\n<ul>\n<li>Enum\u00e9ration et d\u00e9nombrement des parties d&rsquo;un ensemble.<\/li>\n<li>Enum\u00e9ration et d\u00e9nombrement des combinaisons.<\/li>\n<li>Enum\u00e9ration et d\u00e9nombrement des bijections.<\/li>\n<li>Enum\u00e9ration et d\u00e9nombrement des surjections.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Deux papiers de Fernand Didier (IREM d\u2019Aix-Marseille) sur la r\u00e9cursivit\u00e9, qui pr\u00e9sentent cette notion \u00e0 travers des exemples diff\u00e9rents de ceux que l&rsquo;on a l&rsquo;habitude de pr\u00e9senter (Tours de hano\u00ef, quick sort, &#8230;). La r\u00e9cursivit\u00e9 comme un outil pour \u00e9num\u00e9rer l&rsquo;arbre de tous les choix possibles. La r\u00e9cursivit\u00e9 comme outil (Fernand Didier, 2014) Ce document&hellip;&nbsp;<a href=\"https:\/\/ens-info.irem.univ-mrs.fr\/?p=254\" rel=\"bookmark\">Lire la suite &raquo;<span class=\"screen-reader-text\">Deux documents sur la r\u00e9cursivit\u00e9<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"neve_meta_sidebar":"","neve_meta_container":"","neve_meta_enable_content_width":"","neve_meta_content_width":0,"neve_meta_title_alignment":"","neve_meta_author_avatar":"","neve_post_elements_order":"","neve_meta_disable_header":"","neve_meta_disable_footer":"","neve_meta_disable_title":""},"categories":[18,22,23],"tags":[],"_links":{"self":[{"href":"https:\/\/ens-info.irem.univ-mrs.fr\/index.php?rest_route=\/wp\/v2\/posts\/254"}],"collection":[{"href":"https:\/\/ens-info.irem.univ-mrs.fr\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ens-info.irem.univ-mrs.fr\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ens-info.irem.univ-mrs.fr\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ens-info.irem.univ-mrs.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=254"}],"version-history":[{"count":2,"href":"https:\/\/ens-info.irem.univ-mrs.fr\/index.php?rest_route=\/wp\/v2\/posts\/254\/revisions"}],"predecessor-version":[{"id":260,"href":"https:\/\/ens-info.irem.univ-mrs.fr\/index.php?rest_route=\/wp\/v2\/posts\/254\/revisions\/260"}],"wp:attachment":[{"href":"https:\/\/ens-info.irem.univ-mrs.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=254"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ens-info.irem.univ-mrs.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=254"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ens-info.irem.univ-mrs.fr\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=254"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}