{"id":54389,"date":"2019-12-25T00:00:00","date_gmt":"2019-12-24T21:00:00","guid":{"rendered":"https:\/\/prohoster.info\/blog\/blog_prohoster\/indeksiruemoe-binarnoe-derevo"},"modified":"2020-02-18T14:02:23","modified_gmt":"2020-02-18T11:02:23","slug":"indeksiruemoe-binarnoe-derevo","status":"publish","type":"post","link":"https:\/\/prohoster.info\/sk\/blog\/administrirovanie\/indeksiruemoe-binarnoe-derevo","title":{"rendered":"Indexovan\u00e9 bin\u00e1rne strom","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"<p><img decoding=\"async\" alt=\"Indexovan\u00e9 bin\u00e1rne strom\" src=\"\/wp-content\/uploads\/2019\/12\/8ceb987e007db02de04d29f33185e8ec.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>Dostal som \u00falohu tohto typu. Je potrebn\u00e9 implementova\u0165 kontajner na ukladanie d\u00e1t, ktor\u00fd zabezpe\u010duje nasleduj\u00facu funkcionalitu: <\/p>\n<p><\/p>\n<ul>\n<li>vlo\u017ei\u0165 nov\u00fd prvok<\/li>\n<li>odstr\u00e1ni\u0165 prvok pod\u013ea poradia<\/li>\n<li>z\u00edska\u0165 prvok pod\u013ea poradia<\/li>\n<li>d\u00e1ta s\u00fa uchov\u00e1van\u00e9 v zoradenom stave<\/li>\n<\/ul>\n<p><noindex><a rel=\"nofollow\" name=\"habracut\"><\/a><\/noindex><\/p>\n<p>D\u00e1ta sa neust\u00e1le prid\u00e1vaj\u00fa a odstra\u0148uj\u00fa, \u0161trukt\u00fara by mala zabezpe\u010di\u0165 r\u00fdchlu r\u00fdchlos\u0165 pr\u00e1ce. Najprv som sa sna\u017eil implementova\u0165 nie\u010do tak\u00e9 pomocou \u0161tandardn\u00fdch kontajnerov z <strong>std<\/strong>. Tento pr\u00edstup neuspel a pri\u0161lo pochopenie, \u017ee je potrebn\u00e9 implementova\u0165 nie\u010do samostatne. Jedin\u00e1 vec, ktor\u00e1 mi napadla, je pou\u017ei\u0165 bin\u00e1rny vyh\u013ead\u00e1vac\u00ed strom. Preto\u017ee vyhovuje po\u017eiadavk\u00e1m na r\u00fdchle vkladanie, odstra\u0148ovanie a uchov\u00e1vanie d\u00e1t v zoradenom stave. Ost\u00e1valo len vymyslie\u0165, ako indexova\u0165 v\u0161etky prvky a prepo\u010d\u00edtava\u0165 indexy, ke\u010f sa strom men\u00ed.<\/p>\n<p><\/p>\n<pre><code class=\"cpp\">struct node_s {    \n    data_t data;\n\n    uint64_t weight; \/\/ v\u00e1ha uzla\n\n    node_t *left;\n    node_t *right;\n\n    node_t *parent;\n};<\/code><\/pre>\n<p><\/p>\n<p>V \u010dl\u00e1nku bude viac obr\u00e1zkov a te\u00f3rie ako k\u00f3du. K\u00f3d si bude mo\u017en\u00e9 pozrie\u0165 prostredn\u00edctvom odkazu ni\u017e\u0161ie.<\/p>\n<p><\/p>\n<h2 id=\"ves\">Hmotnos\u0165<\/h2>\n<p><\/p>\n<p>Na tento \u00fa\u010del bol strom podroben\u00fd malej modifik\u00e1cii, pribudla dodato\u010dn\u00e1 inform\u00e1cia o <strong>v\u00e1he<\/strong> uzla. V\u00e1ha uzla je <strong>po\u010det potomkov tohto uzla<\/strong> + <strong>1<\/strong> (v\u00e1ha jedn\u00e9ho prvku).<\/p>\n<p><\/p>\n<p>Funkcia na z\u00edskanie v\u00e1hy uzla:<\/p>\n<p><\/p>\n<pre><code class=\"cpp\">uint64_t bntree::get_child_weight(node_t *node) {\n    if (node) {\n        return node-&gt;weight;\n    }\n\n    return 0;\n}<\/code><\/pre>\n<p><\/p>\n<p>U listu je v\u00e1ha samozrejme <strong>0<\/strong>.<\/p>\n<p><\/p>\n<p>\u010ealej prejdeme k n\u00e1zorn\u00e9mu zobrazeniu pr\u00edkladu tak\u00e9ho stromu. <strong>\u010ciernou<\/strong> farbou bude zobrazen\u00fd k\u013e\u00fa\u010d uzla (hodnota zobrazen\u00e1 nebude, preto\u017ee na tom nie je potreba), <strong>\u010dervenou<\/strong> \u2014 v\u00e1ha uzla, <strong>zelenou<\/strong> \u2014 index uzla.<\/p>\n<p><\/p>\n<p>Ke\u010f je strom pr\u00e1zdny, jeho v\u00e1ha je 0. Prid\u00e1me do\u0148 kore\u0148ov\u00fd prvok:<\/p>\n<p>\n<img decoding=\"async\" alt=\"Indexovan\u00e9 bin\u00e1rne strom\" src=\"\/wp-content\/uploads\/2019\/12\/2d4145039daee26582910556a40d2a5c.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>V\u00e1ha stromu sa st\u00e1va 1, v\u00e1ha kore\u0148ov\u00e9ho prvku 1. V\u00e1ha kore\u0148ov\u00e9ho prvku je v\u00e1hou stromu.<\/p>\n<p><\/p>\n<p>Prid\u00e1me e\u0161te nieko\u013eko prvkov:<\/p>\n<p>\n<img decoding=\"async\" alt=\"Indexovan\u00e9 bin\u00e1rne strom\" src=\"\/wp-content\/uploads\/2019\/12\/803cc4a65aa3d8a2fcb20fe325351cfa.jpg\" style=\"display:block;margin: 0 auto;\" \/><br \/>\n<img decoding=\"async\" alt=\"Indexovan\u00e9 bin\u00e1rne strom\" src=\"\/wp-content\/uploads\/2019\/12\/0aa12f41b822b4bb1e9fadb7564dc461.jpg\" style=\"display:block;margin: 0 auto;\" \/><br \/>\n<img decoding=\"async\" alt=\"Indexovan\u00e9 bin\u00e1rne strom\" src=\"\/wp-content\/uploads\/2019\/12\/8566df9404037e92f53b315bc3304016.jpg\" style=\"display:block;margin: 0 auto;\" \/><br \/>\n<img decoding=\"async\" alt=\"Indexovan\u00e9 bin\u00e1rne strom\" src=\"\/wp-content\/uploads\/2019\/12\/1847e6ddffdb28d0a6d9a4949ebb5f80.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>Pri ka\u017edom pridan\u00ed nov\u00e9ho prvku prech\u00e1dzame uzlami nadol a zvy\u0161ujeme po\u010d\u00edtadlo v\u00e1hy ka\u017ed\u00e9ho prech\u00e1dzan\u00e9ho uzla. Pri vytv\u00e1ran\u00ed nov\u00e9ho uzla mu nastav\u00edme v\u00e1hu <strong>1<\/strong>. Ak uzol s tak\u00fdmto k\u013e\u00fa\u010dom u\u017e existuje, prep\u00ed\u0161eme hodnotu a p\u00f4jdeme sp\u00e4\u0165 k kore\u0148u, pri\u010dom odcancelujeme zmeny v\u00e1h v\u0161etk\u00fdch uzlov, ktor\u00e9 sme pre\u0161li.<br \/>\nAk ide o odstr\u00e1nenie uzla, prech\u00e1dzame nadol a dekr\u00e9tujeme v\u00e1hy prech\u00e1dzaj\u00facich uzlov. <\/p>\n<p><\/p>\n<h2 id=\"indeksy\">Indexy<\/h2>\n<p><\/p>\n<p>Teraz prejdeme k tomu, ako indexova\u0165 uzly. Uzly zjavne neuchov\u00e1vaj\u00fa svoj index, ten sa po\u010d\u00edta na z\u00e1klade hmotnosti uzlov. Keby uchov\u00e1vali svoj index, trvalo by to <strong>O(n)<\/strong> \u010das, aby sa aktualizovali indexy v\u0161etk\u00fdch uzlov po ka\u017edej zmene stromu.<br \/>\nPrejdime k n\u00e1zorn\u00e9mu zn\u00e1zorneniu. Na\u0161e stromy s\u00fa pr\u00e1zdne, pridajme do neho prv\u00fd uzol:<\/p>\n<p>\n<img decoding=\"async\" alt=\"Indexovan\u00e9 bin\u00e1rne strom\" src=\"\/wp-content\/uploads\/2019\/12\/8a3b176f318cd077b1cf50ddf232e0da.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>Prv\u00fd uzol m\u00e1 index <strong>0<\/strong>, a teraz s\u00fa mo\u017en\u00e9 dva pr\u00edpady. V prvom pr\u00edpade sa index kore\u0148ov\u00e9ho prvku zmen\u00ed, v druhom nie.<\/p>\n<p>\n<img decoding=\"async\" alt=\"Indexovan\u00e9 bin\u00e1rne strom\" src=\"\/wp-content\/uploads\/2019\/12\/cb863be8f42385d3bbb2f46700a8cff3.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>Kore\u0148ov\u00e9 \u013eav\u00e9 podstrom m\u00e1 hmotnos\u0165 1.<\/p>\n<p><\/p>\n<p>Druh\u00fd pr\u00edpad:<\/p>\n<p>\n<img decoding=\"async\" alt=\"Indexovan\u00e9 bin\u00e1rne strom\" src=\"\/wp-content\/uploads\/2019\/12\/35eec59a81fc8b056c7e91daa3ee508e.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>Index kore\u0148a sa nezmenil, preto\u017ee hmotnos\u0165 jeho \u013eav\u00e9ho podstromu zostala 0.<\/p>\n<p><\/p>\n<p>Index uzla sa po\u010d\u00edta ako hmotnos\u0165 jeho \u013eav\u00e9ho podstromu + \u010d\u00edslo od rodi\u010da. \u010co to \u010d\u00edslo je?, Je to \u010d\u00edta\u010d indexov, p\u00f4vodne je to <strong>0<\/strong>, preto\u017ee kore\u0148 nem\u00e1 rodi\u010da. \u010ealej z\u00e1vis\u00ed od toho, kam sa dost\u00e1vame, k \u013eav\u00e9mu alebo prav\u00e9mu die\u0165a\u0165u. Ak k \u013eav\u00e9mu, \u010d\u00edta\u010d sa nezvy\u0161uje. Ak k prav\u00e9mu, pripo\u010d\u00edtavame index aktu\u00e1lneho uzla.<\/p>\n<p>\n<img decoding=\"async\" alt=\"Indexovan\u00e9 bin\u00e1rne strom\" src=\"\/wp-content\/uploads\/2019\/12\/d328174370ef52c646d8689cce977302.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>Napr\u00edklad, ako sa vypo\u010d\u00edtava index prvku s k\u013e\u00fa\u010dom 8 (prav\u00fd potomok kore\u0148a). To je \u201eIndex kore\u0148a\u201c + \u201ev\u00e1ha \u013eav\u00e9ho podstromu uzla s k\u013e\u00fa\u010dom 8\u201c + \u201e1\u201c == 3 + 2 + 1 == <strong>6<\/strong><br \/>\nIndex prvku s k\u013e\u00fa\u010dom 6 bude \u201eIndex kore\u0148a\u201c + 1 == 3 + 1 = <strong>4<\/strong><\/p>\n<p><\/p>\n<p>Preto aby sme z\u00edskali, odstr\u00e1nili prvok pod\u013ea indexu, potrebujeme \u010das <strong>O(log n)<\/strong>, preto\u017ee aby sme z\u00edskali po\u017eadovan\u00fd prvok, mus\u00edme ho najprv n\u00e1js\u0165 (dosta\u0165 sa z kore\u0148a k tomuto prvku).<\/p>\n<p><\/p>\n<h2 id=\"glubina\">H\u013abka<\/h2>\n<p><\/p>\n<p>Na z\u00e1klade hmotnosti sa tie\u017e d\u00e1 vypo\u010d\u00edta\u0165 h\u013abka stromu. Potrebn\u00e1 na vyv\u00e1\u017eenie.<br \/>\nNa to treba hmotnos\u0165 aktu\u00e1lneho uzla zaokr\u00fahli\u0165 na prv\u00e9 \u010d\u00edslo v mocnine 2, ktor\u00e9 je v\u00e4\u010d\u0161ie alebo rovn\u00e9 danej hmotnosti, a z\u00edska\u0165 od neho bin\u00e1rny logaritmus. Takto z\u00edskame h\u013abku stromu, za predpokladu, \u017ee je vyv\u00e1\u017een\u00fd. Strom sa vyv\u00e1\u017ei po vlo\u017een\u00ed nov\u00e9ho prvku. Te\u00f3riu o tom, ako vyva\u017eova\u0165 stromy nebudem uv\u00e1dza\u0165. V p\u00f4vodn\u00fdch k\u00f3doch je uveden\u00e1 funkcia na vyv\u00e1\u017eenie.<\/p>\n<p><\/p>\n<p>K\u00f3d na prevod hmotnosti na h\u013abku.<\/p>\n<p><\/p>\n<pre><code class=\"cpp\">\/*\n * \u0412\u043e\u0437\u0432\u0440\u0430\u0449\u0430\u0435\u0442 \u043f\u0435\u0440\u0432\u043e\u0435 \u0447\u0438\u0441\u043b\u043e \u0432 \u0441\u0442\u0435\u043f\u0435\u043d\u0438 2, \u043a\u043e\u0442\u043e\u0440\u043e\u0435 \u0431\u043e\u043b\u044c\u0448\u0435 \u0438\u043b\u0438 \u0440\u043e\u0432\u043d\u043e x\n *\/\nuint64_t bntree::cpl2(uint64_t x) {\n    x = x - 1;\n    x = x | (x &gt;&gt; 1);\n    x = x | (x &gt;&gt; 2);\n    x = x | (x &gt;&gt; 4);\n    x = x | (x &gt;&gt; 8);\n    x = x | (x &gt;&gt; 16);\n    x = x | (x &gt;&gt; 32);\n\n    return x + 1;\n}\n\n\/*\n * \u0414\u0432\u043e\u0438\u0447\u043d\u044b\u0439 \u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c \u043e\u0442 \u0447\u0438\u0441\u043b\u0430\n *\/\nlong bntree::ilog2(long d) {\n    int result;\n    std::frexp(d, &amp;result);\n    return result - 1;\n}\n\n\/*\n * \u0412\u0435\u0441 \u043a \u0433\u043b\u0443\u0431\u0438\u043d\u0435\n *\/\nuint64_t bntree::weight_to_depth(node_t *p) {\n    if (p == NULL) {\n        return 0;\n    }\n\n    if (p-&gt;weight == 1) {\n        return 1;\n    } else if (p-&gt;weight == 2) {\n        return 2;\n    }\n\n    return this-&gt;ilog2(this-&gt;cpl2(p-&gt;weight));\n}<\/code><\/pre>\n<p><\/p>\n<h2 id=\"itogi\">Zhrnutie<\/h2>\n<p><\/p>\n<ul>\n<li>vlo\u017eenie nov\u00e9ho prvku sa uskuto\u010d\u0148uje za <strong>O(log n)<\/strong><\/li>\n<li>odstr\u00e1nenie prvku pod\u013ea poradov\u00e9ho \u010d\u00edsla sa uskuto\u010d\u0148uje za <strong>O(log n)<\/strong><\/li>\n<li>z\u00edskanie prvku pod\u013ea poradov\u00e9ho \u010d\u00edsla sa uskuto\u010d\u0148uje za <strong>O(log n)<\/strong><\/li>\n<\/ul>\n<p><\/p>\n<p>R\u00fdchlos\u0165 <strong>O(log n)<\/strong> plat\u00edme za to, \u017ee v\u0161etky \u00fadaje s\u00fa ulo\u017een\u00e9 v usporiadanom tvare. <\/p>\n<p><\/p>\n<p>Neviem, kde by sa tak\u00e1to \u0161trukt\u00fara mohla uplatni\u0165. Iba \u00faloha, aby som sa znova dostal do problematiky fungovania stromov. \u010eakujem za pozornos\u0165.<\/p>\n<p><\/p>\n<h2 id=\"ssylki\">Odkazy<\/h2>\n<p><\/p>\n<ul>\n<li><noindex><a rel=\"nofollow\" href=\"https:\/\/github.com\/dvjdjvu\/bntree\">Zdrojov\u00fd k\u00f3d stromu<\/a><\/noindex><\/li>\n<\/ul>\n<p><\/p>\n<p>Projekt obsahuje testovacie \u00fadaje na kontrolu r\u00fdchlosti v\u00fdkonu. Strom sa vypl\u0148uje <strong>1000000<\/strong> prvkov. A doch\u00e1dza k postupn\u00e9mu odstra\u0148ovaniu, vkladaniu a z\u00edskavaniu prvkov <strong>1000000<\/strong> raz. \u010ci\u017ee <strong>3000000<\/strong> oper\u00e1ci\u00ed. V\u00fdsledok sa uk\u00e1zal ako celkom dobr\u00fd ~ 8 sek\u00fand.<\/p>\n<p>Zdroj: <a content=\"nofollow\" rel=\"nofollow\" href=\"https:\/\/habr.com\/ru\/post\/481372\/\">habr.com<\/a><\/p>","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"excerpt":{"rendered":"<p>\u041f\u043e\u043f\u0430\u043b\u0430\u0441\u044c \u043c\u043d\u0435 \u0437\u0430\u0434\u0430\u0447\u0430 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0433\u043e \u0432\u0438\u0434\u0430. \u041d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u0440\u0435\u0430\u043b\u0438\u0437\u043e\u0432\u0430\u0442\u044c \u043a\u043e\u043d\u0442\u0435\u0439\u043d\u0435\u0440 \u0445\u0440\u0430\u043d\u0435\u043d\u0438\u044f \u0434\u0430\u043d\u043d\u044b\u0445 \u043e\u0431\u0435\u0441\u043f\u0435\u0447\u0438\u0432\u0430\u044e\u0449\u0438\u0439 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u043e\u043d\u0430\u043b: \u0432\u0441\u0442\u0430\u0432\u0438\u0442\u044c \u043d\u043e\u0432\u044b\u0439 \u044d\u043b\u0435\u043c\u0435\u043d\u0442 \u0443\u0434\u0430\u043b\u0438\u0442\u044c \u044d\u043b\u0435\u043c\u0435\u043d\u0442 \u043f\u043e \u043f\u043e\u0440\u044f\u0434\u043a\u043e\u0432\u043e\u043c\u0443 \u043d\u043e\u043c\u0435\u0440\u0443 \u043f\u043e\u043b\u0443\u0447\u0438\u0442\u044c \u044d\u043b\u0435\u043c\u0435\u043d\u0442 \u043f\u043e \u043f\u043e\u0440\u044f\u0434\u043a\u043e\u0432\u043e\u043c\u0443 \u043d\u043e\u043c\u0435\u0440\u0443 \u0434\u0430\u043d\u043d\u044b\u0435 \u0445\u0440\u0430\u043d\u044f\u0442\u0441\u044f \u0432 \u0441\u043e\u0440\u0442\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u043e\u043c \u0432\u0438\u0434\u0435 \u0414\u0430\u043d\u043d\u044b\u0435 \u043f\u043e\u0441\u0442\u043e\u044f\u043d\u043d\u043e \u0434\u043e\u0431\u0430\u0432\u043b\u044f\u044e\u0442\u0441\u044f \u0438 \u0443\u0434\u0430\u043b\u044f\u044e\u0442\u0441\u044f, \u0441\u0442\u0440\u0443\u043a\u0442\u0443\u0440\u0430 \u0434\u043e\u043b\u0436\u043d\u0430 \u043e\u0431\u0435\u0441\u043f\u0435\u0447\u0438\u0432\u0430\u0442\u044c \u0431\u044b\u0441\u0442\u0440\u0443\u044e \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u044c \u0440\u0430\u0431\u043e\u0442\u044b. \u0421\u043d\u0430\u0447\u0430\u043b\u0430 \u043f\u044b\u0442\u0430\u043b\u0441\u044f \u0440\u0435\u0430\u043b\u0438\u0437\u043e\u0432\u0430\u0442\u044c \u0442\u0430\u043a\u0443\u044e \u0432\u0435\u0449\u044c \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f \u0441\u0442\u0430\u043d\u0434\u0430\u0440\u0442\u043d\u044b\u0435 \u043a\u043e\u043d\u0442\u0435\u0439\u043d\u0435\u0440\u044b \u0438\u0437 std. \u042d\u0442\u043e\u0442 \u043f\u0443\u0442\u044c \u043d\u0435 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