{"id":3409,"date":"2022-08-28T20:55:29","date_gmt":"2022-08-28T17:55:29","guid":{"rendered":"https:\/\/demensdeum.com\/blog\/?p=3409"},"modified":"2024-12-16T22:32:16","modified_gmt":"2024-12-16T19:32:16","slug":"tree-sort","status":"publish","type":"post","link":"https:\/\/demensdeum.com\/blog\/pt\/2022\/08\/28\/tree-sort\/","title":{"rendered":"Tipo de \u00e1rvore"},"content":{"rendered":"<p>Classifica\u00e7\u00e3o em \u00e1rvore \u2013 classifica\u00e7\u00e3o usando uma \u00e1rvore de pesquisa bin\u00e1ria. Complexidade de tempo &#8211; O(n\u00b2). Nessa \u00e1rvore, cada n\u00f3 da esquerda tem n\u00fameros menores que o n\u00f3, \u00e0 direita h\u00e1 mais que o n\u00f3, ao vir da raiz e imprimir os valores da esquerda para a direita, obtemos uma lista ordenada de n\u00fameros . Surpreendente, certo?<\/p>\n<p>Considere o diagrama de \u00e1rvore de pesquisa bin\u00e1ria:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/demensdeum.com\/blog\/wp-content\/uploads\/2022\/08\/tree.png\" alt=\"\" class=\"alignnone size-full wp-image-3410\" width=\"474\" height=\"393\" srcset=\"https:\/\/demensdeum.com\/blog\/wp-content\/uploads\/2022\/08\/tree.png 474w, https:\/\/demensdeum.com\/blog\/wp-content\/uploads\/2022\/08\/tree-300x249.png 300w\" sizes=\"auto, (max-width: 474px) 100vw, 474px\" \/><\/p>\n<p><span class=\"mw-mmv-title\" original-title=\"\"><a href=\"https:\/\/commons.wikimedia.org\/wiki\/User:Dcoetzee\" target=\"_blank\" rel=\" noopener\">Derrick Coetzee<\/a> (dom\u00ednio p\u00fablico)<\/span><\/p>\n<p>Tente ler manualmente os n\u00fameros come\u00e7ando pelo pen\u00faltimo n\u00f3 esquerdo do canto inferior esquerdo, para cada n\u00f3 \u00e0 esquerda &#8211; um n\u00f3 &#8211; \u00e0 direita.<\/p>\n<p>Ficar\u00e1 assim:<\/p>\n<ol>\n<li>Pen\u00faltimo n\u00f3 no canto inferior esquerdo &#8211; 3.<\/li>\n<li>Tem um ramo esquerdo &#8211; 1.<\/li>\n<li>Pegue este n\u00famero (1)<\/li>\n<li>Em seguida, pegamos o v\u00e9rtice 3 (1, 3)<\/li>\n<li>\u00c0 direita est\u00e1 o ramo 6, mas cont\u00e9m ramos. Portanto, lemos da mesma maneira.<\/li>\n<li>Ramo esquerdo do n\u00f3 6 n\u00famero 4 (1, 3, 4)<\/li>\n<li>O pr\u00f3prio n\u00f3 \u00e9 6 (1, 3, 4, 6)<\/li>\n<li>Direita 7 (1, 3, 4, 6, 7)<\/li>\n<li>V\u00e1 at\u00e9 o n\u00f3 raiz &#8211; 8 (1,3, 4,6, 7, 8)<\/li>\n<li>Imprimimos tudo \u00e0 direita por analogia<\/li>\n<li>Obtemos a lista final &#8211; 1, 3, 4, 6, 7, 8, 10, 13, 14<\/li>\n<\/ol>\n<p>Para implementar o algoritmo em c\u00f3digo, voc\u00ea precisar\u00e1 de duas fun\u00e7\u00f5es:<\/p>\n<ol>\n<li>Montando uma \u00e1rvore de pesquisa bin\u00e1ria<\/li>\n<li>Imprimindo a \u00e1rvore de pesquisa bin\u00e1ria na ordem correta<\/li>\n<\/ol>\n<p>A \u00e1rvore bin\u00e1ria de busca \u00e9 montada da mesma forma que \u00e9 lida, um n\u00famero \u00e9 anexado a cada n\u00f3 \u00e0 esquerda ou \u00e0 direita, dependendo se \u00e9 menor ou maior.<\/p>\n<p>Exemplo em Lua:<\/p>\n<div class=\"hcb_wrap\">\n<div class=\"hcb_wrap\">\n<pre class=\"prism line-numbers lang-unknown\" data-lang=\"unknown\"><code>\nfunction Node:new(value, lhs, rhs)\n    output = {}\n    setmetatable(output, self)\n    self.__index = self  \n    output.value = value\n    output.lhs = lhs\n    output.rhs = rhs\n    output.counter = 1\n    return output  \nend\n\nfunction Node:Increment()\n    self.counter = self.counter + 1\nend\n\nfunction Node:Insert(value)\n    if self.lhs ~= nil and self.lhs.value > value then\n        self.lhs:Insert(value)\n        return\n    end\n\n    if self.rhs ~= nil and self.rhs.value < value then\n        self.rhs:Insert(value)\n        return\n    end\n\n    if self.value == value then\n        self:Increment()\n        return\n    elseif self.value > value then\n        if self.lhs == nil then\n            self.lhs = Node:new(value, nil, nil)\n        else\n            self.lhs:Insert(value)\n        end\n        return\n    else\n        if self.rhs == nil then\n            self.rhs = Node:new(value, nil, nil)\n        else\n            self.rhs:Insert(value)\n        end\n        return\n    end\nend\n\nfunction Node:InOrder(output)\n    if self.lhs ~= nil then\n       output = self.lhs:InOrder(output)\n    end\n    output = self:printSelf(output)\n    if self.rhs ~= nil then\n        output = self.rhs:InOrder(output)\n    end\n    return output\nend\n\nfunction Node:printSelf(output)\n    for i=0,self.counter-1 do\n        output = output .. tostring(self.value) .. \" \"\n    end\n    return output\nend\n\nfunction PrintArray(numbers)\n    output = \"\"\n    for i=0,#numbers do\n        output = output .. tostring(numbers[i]) .. \" \"\n    end    \n    print(output)\nend\n\nfunction Treesort(numbers)\n    rootNode = Node:new(numbers[0], nil, nil)\n    for i=1,#numbers do\n        rootNode:Insert(numbers[i])\n    end\n    print(rootNode:InOrder(\"\"))\nend\n\n\nnumbersCount = 10\nmaxNumber = 9\n\nnumbers = {}\n\nfor i=0,numbersCount-1 do\n    numbers[i] = math.random(0, maxNumber)\nend\n\nPrintArray(numbers)\nTreesort(numbers)<\/code><\/pre>\n<\/div>\n<p>\u0412\u0430\u0436\u043d\u044b\u0439 \u043d\u044e\u0430\u043d\u0441 \u0447\u0442\u043e \u0434\u043b\u044f \u0447\u0438\u0441\u0435\u043b \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u0440\u0430\u0432\u043d\u044b \u0432\u0435\u0440\u0448\u0438\u043d\u0435 \u043f\u0440\u0438\u0434\u0443\u043c\u0430\u043d\u043e \u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u043e \u0438\u043d\u0442\u0435\u0440\u0435\u0441\u043d\u044b\u0445 \u043c\u0435\u0445\u0430\u043d\u0438\u0437\u043c\u043e\u0432 \u043f\u043e\u0434\u0446\u0435\u043f\u043b\u0435\u043d\u0438\u044f \u043a \u043d\u043e\u0434\u0435, \u044f \u0436\u0435 \u043f\u0440\u043e\u0441\u0442\u043e \u0434\u043e\u0431\u0430\u0432\u0438\u043b \u0441\u0447\u0435\u0442\u0447\u0438\u043a \u043a \u043a\u043b\u0430\u0441\u0441\u0443 \u0432\u0435\u0440\u0448\u0438\u043d\u044b, \u043f\u0440\u0438 \u0440\u0430\u0441\u043f\u0435\u0447\u0430\u0442\u043a\u0435 \u0447\u0438\u0441\u043b\u0430 \u0432\u043e\u0437\u0432\u0440\u0430\u0449\u0430\u044e\u0442\u0441\u044f \u043f\u043e \u0441\u0447\u0435\u0442\u0447\u0438\u043a\u0443.<\/p>\n<h3>\u0421\u0441\u044b\u043b\u043a\u0438<\/h3>\n<p><a href=\"https:\/\/gitlab.com\/demensdeum\/algorithms\/-\/tree\/master\/sortAlgorithms\/treesort\" target=\"_blank\" rel=\"noopener\">https:\/\/gitlab.com\/demensdeum\/algorithms\/-\/tree\/master\/sortAlgorithms\/treesort<\/a><\/p>\n<h3>\u0418\u0441\u0442\u043e\u0447\u043d\u0438\u043a\u0438<\/h3>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=nNg_digu7tQ\" target=\"_blank\" rel=\"noopener\">TreeSort Algorithm Explained and Implemented with Examples in Java | Sorting Algorithms | Geekific &#8211; YouTube<\/a><\/p>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=3rez7Qnw84M\" target=\"_blank\" rel=\"noopener\">Tree sort &#8211; YouTube<\/a><\/p>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=12omz-VAyRk\" target=\"_blank\" rel=\"noopener\">Convert Sorted Array to Binary Search Tree (LeetCode 108. Algorithm Explained) &#8211; YouTube<\/a><\/p>\n<p><a href=\"https:\/\/rosettacode.org\/wiki\/Sorting_algorithms\/Tree_sort_on_a_linked_list\" target=\"_blank\" rel=\"noopener\">Sorting algorithms\/Tree sort on a linked list &#8211; Rosetta Code<\/a><\/p>\n<p><a href=\"https:\/\/www.geeksforgeeks.org\/tree-sort\/\" target=\"_blank\" rel=\"noopener\">Tree Sort &#8211; GeeksforGeeks<\/a><\/p>\n<p><a href=\"https:\/\/en.wikipedia.org\/wiki\/Tree_sort\" target=\"_blank\" rel=\"noopener\">Tree sort &#8211; Wikipedia<\/a><\/p>\n<p><a href=\"https:\/\/www.geeksforgeeks.org\/how-to-handle-duplicates-in-binary-search-tree\/\" target=\"_blank\" rel=\"noopener\">How to handle duplicates in Binary Search Tree? &#8211; GeeksforGeeks<\/a><\/p>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=n2MLjGeK7qA\" target=\"_blank\" rel=\"noopener\">Tree Sort | GeeksforGeeks &#8211; YouTube<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Classifica\u00e7\u00e3o em \u00e1rvore \u2013 classifica\u00e7\u00e3o usando uma \u00e1rvore de pesquisa bin\u00e1ria. Complexidade de tempo &#8211; O(n\u00b2). Nessa \u00e1rvore, cada n\u00f3 da esquerda tem n\u00fameros menores que o n\u00f3, \u00e0 direita h\u00e1 mais que o n\u00f3, ao vir da raiz e imprimir os valores da esquerda para a direita, obtemos uma lista ordenada de n\u00fameros .<a class=\"more-link\" href=\"https:\/\/demensdeum.com\/blog\/pt\/2022\/08\/28\/tree-sort\/\">Continue reading <span class=\"screen-reader-text\">&#8220;Tipo de \u00e1rvore&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[61,52],"tags":[131,190,207],"class_list":["post-3409","post","type-post","status-publish","format-standard","hentry","category-techie","category-tutorials","tag-algorithms","tag-sorting","tag-tree-sort","entry"],"translation":{"provider":"WPGlobus","version":"3.0.2","language":"pt","enabled_languages":["en","ru","zh","de","fr","ja","pt","hi"],"languages":{"en":{"title":true,"content":true,"excerpt":false},"ru":{"title":true,"content":true,"excerpt":false},"zh":{"title":true,"content":true,"excerpt":false},"de":{"title":true,"content":true,"excerpt":false},"fr":{"title":true,"content":true,"excerpt":false},"ja":{"title":true,"content":true,"excerpt":false},"pt":{"title":true,"content":true,"excerpt":false},"hi":{"title":false,"content":false,"excerpt":false}}},"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/demensdeum.com\/blog\/pt\/wp-json\/wp\/v2\/posts\/3409","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/demensdeum.com\/blog\/pt\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/demensdeum.com\/blog\/pt\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/demensdeum.com\/blog\/pt\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/demensdeum.com\/blog\/pt\/wp-json\/wp\/v2\/comments?post=3409"}],"version-history":[{"count":7,"href":"https:\/\/demensdeum.com\/blog\/pt\/wp-json\/wp\/v2\/posts\/3409\/revisions"}],"predecessor-version":[{"id":3870,"href":"https:\/\/demensdeum.com\/blog\/pt\/wp-json\/wp\/v2\/posts\/3409\/revisions\/3870"}],"wp:attachment":[{"href":"https:\/\/demensdeum.com\/blog\/pt\/wp-json\/wp\/v2\/media?parent=3409"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/demensdeum.com\/blog\/pt\/wp-json\/wp\/v2\/categories?post=3409"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/demensdeum.com\/blog\/pt\/wp-json\/wp\/v2\/tags?post=3409"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}