{"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\/hu\/blog\/administrirovanie\/indeksiruemoe-binarnoe-derevo","title":{"rendered":"Indexelhet\u0151 bin\u00e1ris fa","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"<p><img decoding=\"async\" alt=\"Indexelhet\u0151 bin\u00e1ris fa\" src=\"\/wp-content\/uploads\/2019\/12\/8ceb987e007db02de04d29f33185e8ec.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>Tal\u00e1ltam egy feladatot, amely a k\u00f6vetkez\u0151 jelleg\u0171. Meg kell val\u00f3s\u00edtanom egy adatot t\u00e1rol\u00f3 t\u00e1rol\u00f3t, amely biztos\u00edtja a k\u00f6vetkez\u0151 funkci\u00f3kat: <\/p>\n<p><\/p>\n<ul>\n<li>\u00faj elem besz\u00far\u00e1sa<\/li>\n<li>elem t\u00f6rl\u00e9se sorsz\u00e1m alapj\u00e1n<\/li>\n<li>elem lek\u00e9rdez\u00e9se sorsz\u00e1m alapj\u00e1n<\/li>\n<li>az adatok rendezett form\u00e1ban vannak t\u00e1rolva<\/li>\n<\/ul>\n<p><noindex><a rel=\"nofollow\" name=\"habracut\"><\/a><\/noindex><\/p>\n<p>Az adatok folyamatosan b\u0151v\u00fclnek \u00e9s t\u00f6rl\u0151dnek, a strukt\u00far\u00e1nak biztos\u00edtania kell a gyors m\u0171k\u00f6d\u00e9st. El\u0151sz\u00f6r megpr\u00f3b\u00e1ltam megval\u00f3s\u00edtani ezt a dolgot a <strong>std<\/strong>. Ez az \u00fat nem vezetett sikerre, \u00e9s bel\u00e1ttam, hogy valami \u00fajra van sz\u00fcks\u00e9g. Az egyetlen \u00f6tlet, ami eszembe jutott, az egy bin\u00e1ris keres\u0151fa haszn\u00e1lata volt. Mivel ez megfelel a gyors besz\u00far\u00e1s, t\u00f6rl\u00e9s \u00e9s az adatok rendezett form\u00e1ban val\u00f3 t\u00e1rol\u00e1s k\u00f6vetelm\u00e9nyeinek. Csak ki kellett tal\u00e1lni, hogyan indexelj\u00fck az \u00f6sszes elemet \u00e9s sz\u00e1m\u00edtsuk \u00fajra az indexeket, amikor a fa megv\u00e1ltozik.<\/p>\n<p><\/p>\n<pre><code class=\"cpp\">struct node_s {    \n    data_t data;\n\n    uint64_t weight; \/\/ a csom\u00f3pont s\u00falya\n\n    node_t *left;\n    node_t *right;\n\n    node_t *parent;\n};<\/code><\/pre>\n<p><\/p>\n<p>A cikkben t\u00f6bb k\u00e9p \u00e9s elm\u00e9let lesz, mint k\u00f3d. A k\u00f3dot az al\u00e1bbi linken lehet megtekinteni.<\/p>\n<p><\/p>\n<h2 id=\"ves\">T\u00f6meg<\/h2>\n<p><\/p>\n<p>Ehhez a f\u00e1hoz egy kis m\u00f3dos\u00edt\u00e1st v\u00e9geztem, tov\u00e1bbi inform\u00e1ci\u00f3t adtam hozz\u00e1 a <strong>s\u00falyr\u00f3l<\/strong> A csom\u00f3pont s\u00falya ez <strong>a csom\u00f3pont gyermekei sz\u00e1m\u00e1t jelenti<\/strong> + <strong>1<\/strong> (az egys\u00e9ges elem s\u00falya).<\/p>\n<p><\/p>\n<p>A csom\u00f3pont s\u00faly\u00e1nak lek\u00e9r\u00e9se:<\/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>A lev\u00e9l s\u00falya teh\u00e1t <strong>0<\/strong>.<\/p>\n<p><\/p>\n<p>T\u00e9rj\u00fcnk \u00e1t egy ilyen fa szeml\u00e9ltet\u0151 p\u00e9ld\u00e1j\u00e1ra. <strong>Fekete<\/strong> sz\u00ednnel a csom\u00f3pont kulcs\u00e1t \u00e1br\u00e1zoljuk (az \u00e9rt\u00e9ket nem mutatjuk meg, mivel erre nincs sz\u00fcks\u00e9g), <strong>piros<\/strong> \u2014 a csom\u00f3pont s\u00falya, <strong>z\u00f6ld<\/strong> \u2014 a csom\u00f3pont indexe.<\/p>\n<p><\/p>\n<p>Amikor a fa \u00fcres, akkor a s\u00falya 0. Adjunk hozz\u00e1 egy gy\u00f6k\u00e9r elemet:<\/p>\n<p>\n<img decoding=\"async\" alt=\"Indexelhet\u0151 bin\u00e1ris fa\" src=\"\/wp-content\/uploads\/2019\/12\/2d4145039daee26582910556a40d2a5c.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>A fa s\u00falya 1-re n\u0151, a gy\u00f6k\u00e9r elem s\u00falya 1. A gy\u00f6k\u00e9r elem s\u00falya a fa s\u00faly\u00e1t is jelenti.<\/p>\n<p><\/p>\n<p>Adjunk hozz\u00e1 m\u00e9g n\u00e9h\u00e1ny elemet:<\/p>\n<p>\n<img decoding=\"async\" alt=\"Indexelhet\u0151 bin\u00e1ris fa\" src=\"\/wp-content\/uploads\/2019\/12\/803cc4a65aa3d8a2fcb20fe325351cfa.jpg\" style=\"display:block;margin: 0 auto;\" \/><br \/>\n<img decoding=\"async\" alt=\"Indexelhet\u0151 bin\u00e1ris fa\" src=\"\/wp-content\/uploads\/2019\/12\/0aa12f41b822b4bb1e9fadb7564dc461.jpg\" style=\"display:block;margin: 0 auto;\" \/><br \/>\n<img decoding=\"async\" alt=\"Indexelhet\u0151 bin\u00e1ris fa\" src=\"\/wp-content\/uploads\/2019\/12\/8566df9404037e92f53b315bc3304016.jpg\" style=\"display:block;margin: 0 auto;\" \/><br \/>\n<img decoding=\"async\" alt=\"Indexelhet\u0151 bin\u00e1ris fa\" src=\"\/wp-content\/uploads\/2019\/12\/1847e6ddffdb28d0a6d9a4949ebb5f80.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>Minden alkalommal, amikor egy \u00faj elemet adunk hozz\u00e1, a csom\u00f3pontokon lefel\u00e9 haladunk \u00e9s n\u00f6velj\u00fck a s\u00faly sz\u00e1ml\u00e1l\u00f3j\u00e1t minden \u00e1thaladott csom\u00f3pont eset\u00e9ben. Amikor \u00faj csom\u00f3pontot hozunk l\u00e9tre, a s\u00faly\u00e1t <strong>1<\/strong>\u00e1ll\u00edtjuk be. Ha olyan csom\u00f3pont l\u00e9tezik m\u00e1r ezzel a kulccsal, akkor fel\u00fcl\u00edrjuk az \u00e9rt\u00e9ket \u00e9s visszafel\u00e9 megy\u00fcnk a gy\u00f6k\u00e9r fel\u00e9, visszavonva a s\u00falyok m\u00f3dos\u00edt\u00e1s\u00e1t minden \u00e1thaladott csom\u00f3pontban.<br \/>\nHa csom\u00f3pontot t\u00f6rl\u00fcnk, akkor lefel\u00e9 haladunk \u00e9s cs\u00f6kkentj\u00fck az \u00e1thaladott csom\u00f3pontok s\u00faly\u00e1t. <\/p>\n<p><\/p>\n<h2 id=\"indeksy\">Indexek<\/h2>\n<p><\/p>\n<p>Most m\u00e1r \u00e1tt\u00e9rhet\u00fcnk arra, hogyan indexelj\u00fck a csom\u00f3pontokat. A csom\u00f3pontok egy\u00e9rtelm\u0171en nem t\u00e1rolj\u00e1k az index\u00fcket, azt a csom\u00f3pontok s\u00faly\u00e1nak alapj\u00e1n sz\u00e1m\u00edtj\u00e1k ki. Ha t\u00e1roln\u00e1k az index\u00fcket, akkor az \u00f6sszes csom\u00f3pont index\u00e9nek friss\u00edt\u00e9se minden fa m\u00f3dos\u00edt\u00e1sa ut\u00e1n sok id\u0151t venne ig\u00e9nybe. <strong>O(n)<\/strong> a f\u00e1k m\u00f3dos\u00edt\u00e1sa ut\u00e1n.<br \/>\nN\u00e9zz\u00fck meg a szeml\u00e9letes \u00e1br\u00e1zol\u00e1st. A f\u00e1nk \u00fcres, adjunk hozz\u00e1 egy csom\u00f3pontot:<\/p>\n<p>\n<img decoding=\"async\" alt=\"Indexelhet\u0151 bin\u00e1ris fa\" src=\"\/wp-content\/uploads\/2019\/12\/8a3b176f318cd077b1cf50ddf232e0da.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>Az els\u0151 csom\u00f3pont indexe <strong>0<\/strong>, \u00e9s most k\u00e9t eset lehets\u00e9ges. Az els\u0151 esetben a gy\u00f6k\u00e9r elem indexe megv\u00e1ltozik, a m\u00e1sodik esetben nem v\u00e1ltozik meg.<\/p>\n<p>\n<img decoding=\"async\" alt=\"Indexelhet\u0151 bin\u00e1ris fa\" src=\"\/wp-content\/uploads\/2019\/12\/cb863be8f42385d3bbb2f46700a8cff3.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>A gy\u00f6k\u00e9r bal als\u00f3 f\u00e1ja 1 s\u00falyt k\u00e9pvisel.<\/p>\n<p><\/p>\n<p>M\u00e1sodik eset:<\/p>\n<p>\n<img decoding=\"async\" alt=\"Indexelhet\u0151 bin\u00e1ris fa\" src=\"\/wp-content\/uploads\/2019\/12\/35eec59a81fc8b056c7e91daa3ee508e.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>A gy\u00f6k\u00e9r indexe nem v\u00e1ltozott, mivel a bal als\u00f3 fa s\u00falya 0 maradt.<\/p>\n<p><\/p>\n<p>A csom\u00f3pont index\u00e9nek kisz\u00e1m\u00edt\u00e1sa a bal als\u00f3 fa s\u00faly\u00e1nak \u00f6sszege + a sz\u00fcl\u0151t\u0151l kapott sz\u00e1m. Mi ez a sz\u00e1m? Ez az indexek sz\u00e1ml\u00e1l\u00f3ja, kezdetben 0, mivel a gy\u00f6k\u00e9rnek nincs sz\u00fcl\u0151je. Innent\u0151l f\u00fcgg, hogy balra vagy jobbra l\u00e9p\u00fcnk. Ha balra, akkor a sz\u00e1ml\u00e1l\u00f3hoz nem adunk semmit. Ha jobbra l\u00e9p\u00fcnk, akkor hozz\u00e1adjuk az aktu\u00e1lis csom\u00f3pont index\u00e9t. <strong>0<\/strong>P\u00e9ld\u00e1ul, hogyan sz\u00e1m\u00edthatjuk ki a 8-as kulcs\u00fa elem index\u00e9t (a gy\u00f6k\u00e9r jobb gyermeke). Ez a \"gy\u00f6k\u00e9r index\" + a \"bal als\u00f3 fa s\u00falya a 8-as kulcs\u00fa csom\u00f3pontban\" + \"1\" == 3 + 2 + 1 ==<\/p>\n<p>\n<img decoding=\"async\" alt=\"Indexelhet\u0151 bin\u00e1ris fa\" src=\"\/wp-content\/uploads\/2019\/12\/d328174370ef52c646d8689cce977302.jpg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>P\u00e9ld\u00e1ul, hogyan sz\u00e1m\u00edtj\u00e1k ki a 8-as kulccsal rendelkez\u0151 elem index\u00e9t (a gy\u00f6k\u00e9r jobb gyereke). Ez a &#171;Gy\u00f6k\u00e9r indexe&#187; + &#171;a 8-as kulccsal rendelkez\u0151 csom\u00f3pont bal almennyezet\u00e9nek s\u00falya&#187; + &#171;1&#187; == 3 + 2 + 1 == <strong>6<\/strong><br \/>\nA 6-os kulccsal rendelkez\u0151 elem indexe a k\u00f6vetkez\u0151k\u00e9ppen alakul: &#171;Gy\u00f6k\u00e9r indexe&#187; + 1 == 3 + 1 == <strong>4<\/strong><\/p>\n<p><\/p>\n<p>O(log n) <strong>, mivel a megfelel\u0151 elem megtal\u00e1l\u00e1s\u00e1hoz el\u0151sz\u00f6r a gy\u00f6k\u00e9rt\u0151l kell indulnunk e csom\u00f3ponthoz.<\/strong>M\u00e9lys\u00e9g<\/p>\n<p><\/p>\n<h2 id=\"glubina\">A s\u00faly alapj\u00e1n a fa m\u00e9lys\u00e9ge is meghat\u00e1rozhat\u00f3. Ez sz\u00fcks\u00e9ges a kiegyens\u00falyoz\u00e1shoz.<\/h2>\n<p><\/p>\n<p>Ehhez a jelenlegi csom\u00f3pont s\u00faly\u00e1t az els\u0151 2-es hatv\u00e1nyra kell kerek\u00edteni, amely nagyobb vagy egyenl\u0151 a megfelel\u0151 s\u00falyn\u00e1l, \u00e9s a logaritmus\u00e1t kell venni. \u00cdgy kapjuk meg a fa m\u00e9lys\u00e9g\u00e9t, felt\u00e9ve, hogy az kiegyens\u00falyozott. A fa kiegyens\u00falyoz\u00e1sa \u00faj elem besz\u00far\u00e1sa ut\u00e1n t\u00f6rt\u00e9nik. A f\u00e1k kiegyens\u00falyoz\u00e1s\u00e1nak elm\u00e9let\u00e9t nem r\u00e9szletezem. A forr\u00e1sk\u00f3dokban megtal\u00e1lhat\u00f3k a kiegyens\u00falyoz\u00f3 f\u00fcggv\u00e9nyek.<br \/>\nA s\u00faly m\u00e9lys\u00e9gg\u00e9 alak\u00edt\u00e1s\u00e1nak k\u00f3dja.<\/p>\n<p><\/p>\n<p>\u00daj elem besz\u00far\u00e1sa<\/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\">\u00d6sszegz\u00e9s<\/h2>\n<p><\/p>\n<ul>\n<li>sorozatsz\u00e1m alapj\u00e1n t\u00f6rt\u00e9nik <strong>, mivel a megfelel\u0151 elem megtal\u00e1l\u00e1s\u00e1hoz el\u0151sz\u00f6r a gy\u00f6k\u00e9rt\u0151l kell indulnunk e csom\u00f3ponthoz.<\/strong><\/li>\n<li>elem t\u00f6rl\u00e9se a sorrendi sz\u00e1m alapj\u00e1n <strong>, mivel a megfelel\u0151 elem megtal\u00e1l\u00e1s\u00e1hoz el\u0151sz\u00f6r a gy\u00f6k\u00e9rt\u0151l kell indulnunk e csom\u00f3ponthoz.<\/strong><\/li>\n<li>sorozatsz\u00e1m alapj\u00e1n t\u00f6rt\u00e9nik <strong>, mivel a megfelel\u0151 elem megtal\u00e1l\u00e1s\u00e1hoz el\u0151sz\u00f6r a gy\u00f6k\u00e9rt\u0151l kell indulnunk e csom\u00f3ponthoz.<\/strong><\/li>\n<\/ul>\n<p><\/p>\n<p>Sebess\u00e9ggel <strong>, mivel a megfelel\u0151 elem megtal\u00e1l\u00e1s\u00e1hoz el\u0151sz\u00f6r a gy\u00f6k\u00e9rt\u0151l kell indulnunk e csom\u00f3ponthoz.<\/strong> fizet\u00fcnk az\u00e9rt, hogy minden adat rendezett form\u00e1ban legyen t\u00e1rolva. <\/p>\n<p><\/p>\n<p>Nem tudom, hol lehet egy ilyen strukt\u00far\u00e1ra sz\u00fcks\u00e9g. Csak egy feladat, hogy m\u00e9g egyszer \u00e1tgondoljam, hogyan m\u0171k\u00f6dnek a f\u00e1k. K\u00f6sz\u00f6n\u00f6m a figyelmet.<\/p>\n<p><\/p>\n<h2 id=\"ssylki\">Hivatkoz\u00e1sok<\/h2>\n<p><\/p>\n<ul>\n<li><noindex><a rel=\"nofollow\" href=\"https:\/\/github.com\/dvjdjvu\/bntree\">A fa forr\u00e1sk\u00f3dja<\/a><\/noindex><\/li>\n<\/ul>\n<p><\/p>\n<p>A projekt tesztadatokat tartalmaz a teljes\u00edtm\u00e9ny ellen\u0151rz\u00e9s\u00e9hez. A fa felt\u00f6lt\u00e9se <strong>1000000<\/strong> elemekkel t\u00f6rt\u00e9nik. Ezut\u00e1n folyamatban van az elemek elt\u00e1vol\u00edt\u00e1sa, besz\u00far\u00e1sa \u00e9s megnyer\u00e9se. <strong>1000000<\/strong> alkalommal. Azaz <strong>3000000<\/strong> m\u0171veletek. Az eredm\u00e9ny meglehet\u0151sen j\u00f3nak bizonyult ~ 8 m\u00e1sodperc.<\/p>\n<p>Forr\u00e1s: <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 [&hellip;]<\/p>\n","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[688],"tags":[],"class_list":["post-54389","post","type-post","status-publish","format-standard","hentry","category-administrirovanie"],"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO 5.0.3 - aioseo.com -->\n\t<meta name=\"description\" content=\"\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.\" \/>\n\t<meta name=\"robots\" content=\"max-image-preview:large\" \/>\n\t<meta name=\"author\" content=\"Yuri Gagarin\"\/>\n\t<link rel=\"canonical\" href=\"https:\/\/prohoster.info\/hu\/blog\/administrirovanie\/indeksiruemoe-binarnoe-derevo\" \/>\n\t\t<meta name=\"generator\" content=\"All 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