{"id":15426,"date":"2023-04-02T12:37:33","date_gmt":"2023-04-02T09:07:33","guid":{"rendered":"https:\/\/nabfollower.com\/blog\/disjoint-set-union-heuristics-2e82\/"},"modified":"2023-04-02T12:37:33","modified_gmt":"2023-04-02T09:07:33","slug":"disjoint-set-union-heuristics-2e82","status":"publish","type":"post","link":"https:\/\/nabfollower.com\/blog\/disjoint-set-union-heuristics-2e82\/","title":{"rendered":"Disjoint Set Union \u0627\u06a9\u062a\u0634\u0627\u0641\u06cc &#8211; \u0627\u0646\u062c\u0645\u0646 DEV"},"content":{"rendered":"<div data-article-id=\"1423021\" id=\"article-body\">\n<p>DSU \u06cc\u06a9\u06cc \u0627\u0632 \u0638\u0631\u06cc\u0641 \u062a\u0631\u06cc\u0646 \u062f\u0631 \u0633\u0627\u062e\u062a\u0627\u0631 \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u067e\u06cc\u0627\u062f\u0647 \u0633\u0627\u0632\u06cc \u0627\u0633\u062a \u0648 \u0645\u0646 \u0628\u0627\u0631\u0647\u0627 \u062f\u0631 \u0632\u0646\u062f\u06af\u06cc \u0628\u0631\u0646\u0627\u0645\u0647 \u0646\u0648\u06cc\u0633\u06cc \u0631\u0642\u0627\u0628\u062a\u06cc \u062e\u0648\u062f \u0627\u0632 \u0622\u0646 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0631\u062f\u0647 \u0627\u0645.  \u0627\u06cc\u0646\u062a\u0631\u0646\u062a \u067e\u0631 \u0627\u0632 \u067e\u06cc\u0627\u062f\u0647 \u0633\u0627\u0632\u06cc \u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641 \u0628\u0631\u0627\u06cc \u0622\u0646 \u0627\u0633\u062a\u060c \u0627\u0645\u0627 \u0645\u062a\u0623\u0633\u0641\u0627\u0646\u0647 \u062a\u0642\u0631\u06cc\u0628\u0627\u064b \u0647\u06cc\u0686 \u0645\u0642\u0627\u0644\u0647 \u0627\u06cc \u0648\u062c\u0648\u062f \u0646\u062f\u0627\u0631\u062f \u06a9\u0647 \u0627\u062b\u0628\u0627\u062a \u062e\u0648\u0628\u06cc \u0628\u0631\u0627\u06cc \u06a9\u0627\u0631\u0627\u06cc\u06cc DSU \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u062f\u060c \u062f\u0631 \u0627\u06cc\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0628\u0647\u062a\u0631\u06cc\u0646 \u0646\u062d\u0648 \u0627\u06cc\u0646 \u0631\u0627\u0632 \u0631\u0627 \u06a9\u0634\u0641 \u062e\u0648\u0627\u0647\u0645 \u06a9\u0631\u062f. <\/p>\n<p>\u0633\u0627\u062e\u062a\u0627\u0631 \u062f\u0627\u062f\u0647 Trivial Disjoint Set Union \u0631\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646 \u0628\u0647 \u0631\u0648\u0634 \u0632\u06cc\u0631 \u067e\u06cc\u0627\u062f\u0647 \u0633\u0627\u0632\u06cc \u06a9\u0631\u062f<\/p>\n<div class=\"highlight js-code-highlight\">\n<pre class=\"highlight plaintext\"><code>class DSU \n{\n    private int[] parent;\n\n    void createSet(int vertex)\n    {\n        parent[vertex] = vertex;\n    } \n\n    bool isRepresentative(int vertex)\n    {\n        return parent[vertex] == vertex;\n    }\n\n    void findRepresentative(int vertex)\n    {\n        if (!isRepresentative(vertex))\n        {\n            return findRepresentative(parent[vertex]);\n        }\n\n        return vertex;\n    } \n\n\n    void mergeSets(int lhs, int rhs)\n    {\n        int rhsRepresentative = findRepresentative(rhs);\n        int lhsRepresentative = findRepresentative(lhs);\n\n        if (lhsRepresentative != rhsRepresentative)\n        {\n            parent[lhsRepresentative] = rhsRepresentative;\n        }\n    }\n}\n<\/code><\/pre>\n<div class=\"highlight__panel js-actions-panel\">\n<div class=\"highlight__panel-action js-fullscreen-code-action\">\n    <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"20px\" height=\"20px\" viewbox=\"0 0 24 24\" class=\"highlight-action crayons-icon highlight-action--fullscreen-on\"><title>\u0648\u0627\u0631\u062f \u062d\u0627\u0644\u062a \u062a\u0645\u0627\u0645 \u0635\u0641\u062d\u0647 \u0634\u0648\u06cc\u062f<\/title>\n    <path d=\"M16 3h6v6h-2V5h-4V3zM2 3h6v2H4v4H2V3zm18 16v-4h2v6h-6v-2h4zM4 19h4v2H2v-6h2v4z\"\/>\n<\/svg><\/p>\n<p>    <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"20px\" height=\"20px\" viewbox=\"0 0 24 24\" class=\"highlight-action crayons-icon highlight-action--fullscreen-off\"><title>\u0627\u0632 \u062d\u0627\u0644\u062a \u062a\u0645\u0627\u0645 \u0635\u0641\u062d\u0647 \u062e\u0627\u0631\u062c \u0634\u0648\u06cc\u062f<\/title>\n    <path d=\"M18 7h4v2h-6V3h2v4zM8 9H2V7h4V3h2v6zm10 8v4h-2v-6h6v2h-4zM8 15v6H6v-4H2v-2h6z\"\/>\n<\/svg><\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>\u0628\u06cc\u0627\u06cc\u06cc\u062f \u0628\u0627 \u062f\u0648 DSU \u0627\u06a9\u062a\u0634\u0627\u0641\u06cc \u0628\u06cc \u0627\u0647\u0645\u06cc\u062a \u0634\u0631\u0648\u0639 \u06a9\u0646\u06cc\u0645<\/p>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_84 counter-hierarchy ez-toc-counter-rtl ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">\u0641\u0647\u0631\u0633\u062a \u0645\u0637\u0627\u0644\u0628<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/nabfollower.com\/blog\/disjoint-set-union-heuristics-2e82\/#%D8%A7%DA%A9%D8%AA%D8%B4%D8%A7%D9%81%DB%8C_%D8%B1%D8%AA%D8%A8%D9%87_%D8%B9%D9%85%D9%82_%D8%AF%D8%B1%D8%AE%D8%AA\" >\u0627\u06a9\u062a\u0634\u0627\u0641\u06cc \u0631\u062a\u0628\u0647 \u0639\u0645\u0642 \u062f\u0631\u062e\u062a<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/nabfollower.com\/blog\/disjoint-set-union-heuristics-2e82\/#%D8%A7%DA%A9%D8%AA%D8%B4%D8%A7%D9%81%DB%8C_%D8%B1%D8%AA%D8%A8%D9%87_%D8%A8%D9%86%D8%AF%DB%8C_%D8%A7%D9%86%D8%AF%D8%A7%D8%B2%D9%87_%D8%AF%D8%B1%D8%AE%D8%AA\" >\u0627\u06a9\u062a\u0634\u0627\u0641\u06cc \u0631\u062a\u0628\u0647 \u0628\u0646\u062f\u06cc \u0627\u0646\u062f\u0627\u0632\u0647 \u062f\u0631\u062e\u062a<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/nabfollower.com\/blog\/disjoint-set-union-heuristics-2e82\/#%D8%A7%DA%A9%D8%AA%D8%B4%D8%A7%D9%81%DB%8C_%D9%81%D8%B4%D8%B1%D8%AF%D9%87_%D8%B3%D8%A7%D8%B2%DB%8C_%D9%85%D8%B3%DB%8C%D8%B1_%D8%AF%D8%B1%D8%AE%D8%AA%DB%8C\" >\u0627\u06a9\u062a\u0634\u0627\u0641\u06cc \u0641\u0634\u0631\u062f\u0647 \u0633\u0627\u0632\u06cc \u0645\u0633\u06cc\u0631 \u062f\u0631\u062e\u062a\u06cc<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/nabfollower.com\/blog\/disjoint-set-union-heuristics-2e82\/#%D8%AA%D8%B1%DA%A9%DB%8C%D8%A8_%D9%81%D8%B4%D8%B1%D8%AF%D9%87_%D8%B3%D8%A7%D8%B2%DB%8C_%D9%85%D8%B3%DB%8C%D8%B1_%D8%A8%D8%A7_%D8%A7%DA%A9%D8%AA%D8%B4%D8%A7%D9%81%DB%8C_%D8%B1%D8%AA%D8%A8%D9%87\" >\u062a\u0631\u06a9\u06cc\u0628 \u0641\u0634\u0631\u062f\u0647 \u0633\u0627\u0632\u06cc \u0645\u0633\u06cc\u0631 \u0628\u0627 \u0627\u06a9\u062a\u0634\u0627\u0641\u06cc \u0631\u062a\u0628\u0647<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/nabfollower.com\/blog\/disjoint-set-union-heuristics-2e82\/#%D8%AE%D9%84%D8%A7%D8%B5%D9%87\" >\u062e\u0644\u0627\u0635\u0647<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"%D8%A7%DA%A9%D8%AA%D8%B4%D8%A7%D9%81%DB%8C_%D8%B1%D8%AA%D8%A8%D9%87_%D8%B9%D9%85%D9%82_%D8%AF%D8%B1%D8%AE%D8%AA\"><\/span>\n<p>  \u0627\u06a9\u062a\u0634\u0627\u0641\u06cc \u0631\u062a\u0628\u0647 \u0639\u0645\u0642 \u062f\u0631\u062e\u062a<br \/>\n<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u0627\u06a9\u062a\u0634\u0627\u0641\u06cc \u0632\u06cc\u0631 \u0646\u0634\u0627\u0646 \u0645\u06cc \u062f\u0647\u062f \u06a9\u0647 \u0645\u0627 \u0628\u0627\u06cc\u062f \u06cc\u06a9 \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0631\u062e\u062a \u0628\u0627 \u0639\u0645\u0642 \u06a9\u0645\u062a\u0631 \u0631\u0627 \u0628\u0647 \u062f\u0631\u062e\u062a \u0645\u062c\u0645\u0648\u0639\u0647 \u0628\u0627 \u0639\u0645\u0642 \u0628\u06cc\u0634\u062a\u0631 \u0645\u062a\u0635\u0644 \u06a9\u0646\u06cc\u0645.<\/p>\n<div class=\"highlight js-code-highlight\">\n<pre class=\"highlight plaintext\"><code>void createSet(int vertex) \n{\n    parent[vertex] = vertex;\n    rank[vertex] = 1;\n}\n\nvoid mergeSets(int lhs, int rhs)\n{\n    int rhsRepresentative = findRepresentative(rhs);\n    int lhsRepresentative = findRepresentative(lhs);\n\n    if (rhsRepresentative != lhsRepresentative)\n    {\n        if (rank[lhsRepresentative] &lt; rank[rhsRepresentative]) \n        {\n            swap(lhsRepresentative, rhsRepresentative);\n        }\n\n        parent[rhsRepresentative] = lhsRepresentative;\n        if (depth[lhsRepresentative] == depth[rhsRepresentative]) \n        {\n            rank[lhsRepresentative] += 1;\n        }\n    }\n}\n<\/code><\/pre>\n<div class=\"highlight__panel js-actions-panel\">\n<div class=\"highlight__panel-action js-fullscreen-code-action\">\n    <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"20px\" height=\"20px\" viewbox=\"0 0 24 24\" class=\"highlight-action crayons-icon highlight-action--fullscreen-on\"><title>\u0648\u0627\u0631\u062f \u062d\u0627\u0644\u062a \u062a\u0645\u0627\u0645 \u0635\u0641\u062d\u0647 \u0634\u0648\u06cc\u062f<\/title>\n    <path d=\"M16 3h6v6h-2V5h-4V3zM2 3h6v2H4v4H2V3zm18 16v-4h2v6h-6v-2h4zM4 19h4v2H2v-6h2v4z\"\/>\n<\/svg><\/p>\n<p>    <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"20px\" height=\"20px\" viewbox=\"0 0 24 24\" class=\"highlight-action crayons-icon highlight-action--fullscreen-off\"><title>\u0627\u0632 \u062d\u0627\u0644\u062a \u062a\u0645\u0627\u0645 \u0635\u0641\u062d\u0647 \u062e\u0627\u0631\u062c \u0634\u0648\u06cc\u062f<\/title>\n    <path d=\"M18 7h4v2h-6V3h2v4zM8 9H2V7h4V3h2v6zm10 8v4h-2v-6h6v2h-4zM8 15v6H6v-4H2v-2h6z\"\/>\n<\/svg><\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>\u0628\u06cc\u0627\u06cc\u06cc\u062f \u0646\u0634\u0627\u0646 \u062f\u0647\u06cc\u0645 \u06a9\u0647 \u0627\u06cc\u0646 \u0627\u06a9\u062a\u0634\u0627\u0641\u06cc \u0628\u0647 \u06a9\u0627\u0647\u0634 \u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc findRepresentative \u0628\u0647 O(log(N)) \u06a9\u0645\u06a9 \u062e\u0648\u0627\u0647\u062f \u06a9\u0631\u062f. <\/p>\n<p>\u0645\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u0645 \u0627\u06cc\u0646 \u06a9\u0627\u0631 \u0631\u0627 \u0628\u0627 \u0627\u062b\u0628\u0627\u062a \u0627\u06cc\u0646\u06a9\u0647 \u0627\u06af\u0631 rank set-tree \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 K \u0628\u0627\u0634\u062f\u060c \u0627\u06cc\u0646 \u062f\u0631\u062e\u062a \u062d\u062f\u0627\u0642\u0644 \u062f\u0627\u0631\u0627\u06cc 2^K \u0631\u0626\u0648\u0633 \u0648 \u062f\u0627\u0631\u0627\u06cc \u0639\u0645\u0642 K \u0627\u0633\u062a. \u0627\u0632 \u0627\u0644\u0642\u0627\u0621 \u0631\u0648\u06cc K \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u062e\u0648\u0627\u0647\u06cc\u0645 \u06a9\u0631\u062f. <\/p>\n<p>\u0627\u06af\u0631 K = 1 \u0628\u0627\u0634\u062f\u060c \u0627\u0646\u062f\u0627\u0632\u0647 \u062f\u0631\u062e\u062a 1 \u0648 \u0639\u0645\u0642 \u0622\u0646 1 \u0627\u0633\u062a. <\/p>\n<p>\u0628\u06cc\u0627\u06cc\u06cc\u062f \u062f\u0631\u06a9 \u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u0686\u06af\u0648\u0646\u0647 \u06cc\u06a9 \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0631\u062e\u062a \u0628\u0627 \u0631\u062a\u0628\u0647 \u0628\u0631\u0627\u0628\u0631 K \u0628\u0647 \u062f\u0633\u062a \u0645\u06cc \u0622\u0648\u0631\u06cc\u0645. \u0627\u06af\u0631 \u062f\u0648 \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0631\u062e\u062a \u0627\u0632 \u0631\u062a\u0628\u0647 \u0647\u0627\u06cc K-1 \u06cc\u06a9\u0633\u0627\u0646 \u0631\u0627 \u0627\u062f\u063a\u0627\u0645 \u06a9\u0646\u06cc\u0645 \u0627\u06cc\u0646 \u0627\u062a\u0641\u0627\u0642 \u0645\u06cc \u0627\u0641\u062a\u062f.  \u0627\u0645\u0627 \u0645\u06cc \u062f\u0627\u0646\u06cc\u0645 \u06a9\u0647 \u0628\u0631\u0627\u06cc \u062f\u0631\u062e\u062a\u0627\u0646 \u0645\u062c\u0645\u0648\u0639\u0647 \u0628\u0627 \u0631\u062a\u0628\u0647 K-1\u060c \u0639\u0645\u0642 K-1 \u062f\u0627\u0631\u06cc\u0645\u060c \u0628\u0647 \u0627\u06cc\u0646 \u0645\u0639\u0646\u06cc \u0627\u0633\u062a \u06a9\u0647 \u06cc\u06a9 \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0631\u062e\u062a \u062c\u062f\u06cc\u062f \u0628\u0631\u0627\u06cc \u0631\u062a\u0628\u0647 K \u062d\u062f\u0627\u0642\u0644 \u0634\u0627\u0645\u0644 2 * 2^(K &#8211; 1) = 2^K \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f. \u0631\u0626\u0648\u0633 \u0648 \u062f\u0627\u0631\u0627\u06cc \u0639\u0645\u0642 \u062d\u062f\u0627\u06a9\u062b\u0631 K \u0647\u0633\u062a\u0646\u062f.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"%D8%A7%DA%A9%D8%AA%D8%B4%D8%A7%D9%81%DB%8C_%D8%B1%D8%AA%D8%A8%D9%87_%D8%A8%D9%86%D8%AF%DB%8C_%D8%A7%D9%86%D8%AF%D8%A7%D8%B2%D9%87_%D8%AF%D8%B1%D8%AE%D8%AA\"><\/span>\n<p>  \u0627\u06a9\u062a\u0634\u0627\u0641\u06cc \u0631\u062a\u0628\u0647 \u0628\u0646\u062f\u06cc \u0627\u0646\u062f\u0627\u0632\u0647 \u062f\u0631\u062e\u062a<br \/>\n<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u0627\u06a9\u062a\u0634\u0627\u0641\u06cc \u0645\u0634\u0627\u0628\u0647\u060c \u0627\u0645\u0627 \u067e\u06cc\u0634\u0646\u0647\u0627\u062f \u0645\u06cc\u200c\u06a9\u0646\u062f \u06a9\u0647 \u06cc\u06a9 \u0645\u062c\u0645\u0648\u0639\u0647 \u06a9\u0648\u0686\u06a9\u200c\u062a\u0631 \u0631\u0627 \u0628\u0647 \u062f\u0631\u062e\u062a \u0628\u0632\u0631\u06af\u200c\u062a\u0631 \u0645\u062a\u0635\u0644 \u06a9\u0646\u06cc\u062f.<\/p>\n<div class=\"highlight js-code-highlight\">\n<pre class=\"highlight plaintext\"><code>void createSet(int vertex) \n{\n    parent[vertex] = vertex;\n    size[vertex] = 1;\n}\n\nvoid mergeSets(int lhs, int rhs)\n{\n    int rhsRepresentative = findRepresentative(rhs);\n    int lhsRepresentative = findRepresentative(lhs);\n\n    if (rhsRepresentative != lhsRepresentative)\n    {\n        if (size[lhsRepresentative] &lt; size[rhsRepresentative]) \n        {\n            swap(lhsRepresentative, rhsRepresentative);\n        }\n\n        parent[rhsRepresentative] = lhsRepresentative;\n        size[lhsRepresentative] += size[rhsRepresentative];\n    }\n}\n<\/code><\/pre>\n<div class=\"highlight__panel js-actions-panel\">\n<div class=\"highlight__panel-action js-fullscreen-code-action\">\n    <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"20px\" height=\"20px\" viewbox=\"0 0 24 24\" class=\"highlight-action crayons-icon highlight-action--fullscreen-on\"><title>\u0648\u0627\u0631\u062f \u062d\u0627\u0644\u062a \u062a\u0645\u0627\u0645 \u0635\u0641\u062d\u0647 \u0634\u0648\u06cc\u062f<\/title>\n    <path d=\"M16 3h6v6h-2V5h-4V3zM2 3h6v2H4v4H2V3zm18 16v-4h2v6h-6v-2h4zM4 19h4v2H2v-6h2v4z\"\/>\n<\/svg><\/p>\n<p>    <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"20px\" height=\"20px\" viewbox=\"0 0 24 24\" class=\"highlight-action crayons-icon highlight-action--fullscreen-off\"><title>\u0627\u0632 \u062d\u0627\u0644\u062a \u062a\u0645\u0627\u0645 \u0635\u0641\u062d\u0647 \u062e\u0627\u0631\u062c \u0634\u0648\u06cc\u062f<\/title>\n    <path d=\"M18 7h4v2h-6V3h2v4zM8 9H2V7h4V3h2v6zm10 8v4h-2v-6h6v2h-4zM8 15v6H6v-4H2v-2h6z\"\/>\n<\/svg><\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>\u0628\u0647 \u0631\u0648\u0634\u06cc \u0645\u0634\u0627\u0628\u0647 \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u0645 \u062b\u0627\u0628\u062a \u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u0627\u06af\u0631 \u0627\u0646\u062f\u0627\u0632\u0647 \u062f\u0631\u062e\u062a \u0645\u062c\u0645\u0648\u0639\u0647 K \u0628\u0627\u0634\u062f\u060c \u0627\u0631\u062a\u0641\u0627\u0639 \u0622\u0646 log(K) \u0627\u0633\u062a.<\/p>\n<p>\u0627\u06af\u0631 K = 1 \u0628\u0627\u0634\u062f\u060c \u0648\u0627\u0636\u062d \u0627\u0633\u062a \u06a9\u0647 \u062f\u0631\u0633\u062a \u0627\u0633\u062a.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/nabfollower.com\/blog\/wp-content\/uploads\/2023\/04\/Disjoint-Set-Union-\u0627\u06a9\u062a\u0634\u0627\u0641\u06cc-\u0627\u0646\u062c\u0645\u0646-DEV.png\" alt=\"\u062a\u0648\u0636\u06cc\u062d\u0627\u062a \u062a\u0635\u0648\u06cc\u0631\" loading=\"lazy\" width=\"880\" height=\"174\" title=\"\"><\/p>\n<p>\u0628\u06cc\u0627\u06cc\u06cc\u062f \u0628\u0647 \u062f\u0648 \u062f\u0631\u062e\u062a Tree_k1 \u0628\u0627 \u0627\u0646\u062f\u0627\u0632\u0647 k1 \u0648 Tree_k2 \u0628\u0627 \u0627\u0646\u062f\u0627\u0632\u0647 k2 \u0646\u06af\u0627\u0647 \u06a9\u0646\u06cc\u0645.  \u0645\u06cc \u062a\u0648\u0627\u0646 \u06af\u0641\u062a \u06a9\u0647 Tree_k1 \u062f\u0627\u0631\u0627\u06cc log \u0627\u0631\u062a\u0641\u0627\u0639 (k1) \u0648 Tree_k2 \u062f\u0627\u0631\u0627\u06cc log \u0627\u0631\u062a\u0641\u0627\u0639 (k2) \u0627\u0633\u062a.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/nabfollower.com\/blog\/wp-content\/uploads\/2023\/04\/1680426452_183_Disjoint-Set-Union-\u0627\u06a9\u062a\u0634\u0627\u0641\u06cc-\u0627\u0646\u062c\u0645\u0646-DEV.png\" alt=\"\u062a\u0648\u0636\u06cc\u062d\u0627\u062a \u062a\u0635\u0648\u06cc\u0631\" loading=\"lazy\" width=\"880\" height=\"335\" title=\"\"><\/p>\n<p>\u0641\u0631\u0636 \u06a9\u0646\u06cc\u062f k1 >= k2\u060c \u0633\u067e\u0633 Tree_k2 \u0628\u0647 Tree_k1 \u0645\u062a\u0635\u0644 \u0645\u06cc \u0634\u0648\u062f \u0648 \u0627\u0631\u062a\u0641\u0627\u0639 \u062c\u062f\u06cc\u062f \u062f\u0631\u062e\u062a max(log(k1)\u060c log(k2) + 1 \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/nabfollower.com\/blog\/wp-content\/uploads\/2023\/04\/1680426452_893_Disjoint-Set-Union-\u0627\u06a9\u062a\u0634\u0627\u0641\u06cc-\u0627\u0646\u062c\u0645\u0646-DEV.png\" alt=\"\u062a\u0648\u0636\u06cc\u062d\u0627\u062a \u062a\u0635\u0648\u06cc\u0631\" loading=\"lazy\" width=\"880\" height=\"365\" title=\"\"><\/p>\n<p>\u0627\u06a9\u0646\u0648\u0646 \u0628\u0633\u06cc\u0627\u0631 \u0622\u0633\u0627\u0646 \u0627\u0633\u062a \u06a9\u0647 \u0646\u0634\u0627\u0646 \u062f\u0647\u06cc\u0645 \u0627\u0631\u062a\u0641\u0627\u0639 \u062c\u062f\u06cc\u062f h \u06a9\u0648\u0686\u06a9\u062a\u0631 \u0627\u0632 log (k1 + k2) \u0627\u0633\u062a.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/nabfollower.com\/blog\/wp-content\/uploads\/2023\/04\/1680426452_844_Disjoint-Set-Union-\u0627\u06a9\u062a\u0634\u0627\u0641\u06cc-\u0627\u0646\u062c\u0645\u0646-DEV.png\" alt=\"\u062a\u0648\u0636\u06cc\u062d\u0627\u062a \u062a\u0635\u0648\u06cc\u0631\" loading=\"lazy\" width=\"880\" height=\"197\" title=\"\"><\/p>\n<p>\u062d\u0627\u0644\u0627 \u0628\u06cc\u0627\u06cc\u06cc\u062f \u0646\u06af\u0627\u0647\u06cc \u0628\u0647 \u0627\u06a9\u062a\u0634\u0627\u0641\u06cc \u06a9\u0645\u06cc \u062c\u0627\u0644\u0628\u200c\u062a\u0631 \u0628\u06cc\u0646\u062f\u0627\u0632\u06cc\u0645 <\/p>\n<h2><span class=\"ez-toc-section\" id=\"%D8%A7%DA%A9%D8%AA%D8%B4%D8%A7%D9%81%DB%8C_%D9%81%D8%B4%D8%B1%D8%AF%D9%87_%D8%B3%D8%A7%D8%B2%DB%8C_%D9%85%D8%B3%DB%8C%D8%B1_%D8%AF%D8%B1%D8%AE%D8%AA%DB%8C\"><\/span>\n<p>  \u0627\u06a9\u062a\u0634\u0627\u0641\u06cc \u0641\u0634\u0631\u062f\u0647 \u0633\u0627\u0632\u06cc \u0645\u0633\u06cc\u0631 \u062f\u0631\u062e\u062a\u06cc<br \/>\n<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u0628\u06cc\u0627\u06cc\u06cc\u062f \u0628\u0647\u06cc\u0646\u0647 \u0633\u0627\u0632\u06cc \u0632\u06cc\u0631 \u062a\u0627\u0628\u0639 findRepresentative \u0631\u0627 \u062f\u0631 \u0646\u0638\u0631 \u0628\u06af\u06cc\u0631\u06cc\u0645<\/p>\n<div class=\"highlight js-code-highlight\">\n<pre class=\"highlight plaintext\"><code>public int findRepresentative(int vertex)\n{\n    if (!isRepresentative(vertex)) \n    {\n        parent[vertex] = findRepresentative(\n            parent[vertex]\n        );\n    }\n\n    return parent[vertex];\n}\n<\/code><\/pre>\n<div class=\"highlight__panel js-actions-panel\">\n<div class=\"highlight__panel-action js-fullscreen-code-action\">\n    <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"20px\" height=\"20px\" viewbox=\"0 0 24 24\" class=\"highlight-action crayons-icon highlight-action--fullscreen-on\"><title>\u0648\u0627\u0631\u062f \u062d\u0627\u0644\u062a \u062a\u0645\u0627\u0645 \u0635\u0641\u062d\u0647 \u0634\u0648\u06cc\u062f<\/title>\n    <path d=\"M16 3h6v6h-2V5h-4V3zM2 3h6v2H4v4H2V3zm18 16v-4h2v6h-6v-2h4zM4 19h4v2H2v-6h2v4z\"\/>\n<\/svg><\/p>\n<p>    <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"20px\" height=\"20px\" viewbox=\"0 0 24 24\" class=\"highlight-action crayons-icon highlight-action--fullscreen-off\"><title>\u0627\u0632 \u062d\u0627\u0644\u062a \u062a\u0645\u0627\u0645 \u0635\u0641\u062d\u0647 \u062e\u0627\u0631\u062c \u0634\u0648\u06cc\u062f<\/title>\n    <path d=\"M18 7h4v2h-6V3h2v4zM8 9H2V7h4V3h2v6zm10 8v4h-2v-6h6v2h-4zM8 15v6H6v-4H2v-2h6z\"\/>\n<\/svg><\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>\u062f\u0631 \u0627\u06cc\u0646 \u06a9\u062f \u0645\u0627 \u062a\u0645\u0627\u0645 \u0644\u0628\u0647 \u0647\u0627\u06cc \u06cc\u06a9 \u0645\u0633\u06cc\u0631 \u0631\u0627 \u062d\u0630\u0641 \u0645\u06cc \u06a9\u0646\u06cc\u0645 <code>vertex<\/code> \u0628\u0647 \u0631\u06cc\u0634\u0647 (\u0646\u0645\u0627\u06cc\u0646\u062f\u0647) \u0631\u0626\u0648\u0633 \u0627\u062a\u0635\u0627\u0644 \u062f\u0631\u062e\u062a \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0631 \u0645\u0633\u06cc\u0631 \u0628\u0647 \u0631\u06cc\u0634\u0647. <\/p>\n<p>\u0645\u0634\u0627\u0647\u062f\u0647 \u0627\u0648\u0644\u060c \u0627\u06cc\u0646\u06a9\u0647 \u0627\u06cc\u0646 \u0628\u0647 \u062a\u0646\u0647\u0627\u06cc\u06cc \u0645\u06cc \u062a\u0648\u0627\u0646\u062f \u062f\u0631\u062e\u062a\u06cc \u0628\u0627 \u0639\u0645\u0642 O(N) \u062a\u0648\u0644\u06cc\u062f \u06a9\u0646\u062f.  \u0628\u0631\u0627\u06cc \u0627\u06cc\u0646 \u06a9\u0627\u0631 \u0645\u0627 \u0647\u0645\u06cc\u0634\u0647 \u0631\u06cc\u0634\u0647 \u06cc\u06a9 set-tree \u0631\u0627 \u0628\u0647 \u06cc\u06a9 \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0631\u062e\u062a \u06cc\u06a9 \u0631\u0627\u0633 \u0645\u062a\u0635\u0644 \u0645\u06cc \u06a9\u0646\u06cc\u0645.  <\/p>\n<p><img decoding=\"async\" src=\"https:\/\/nabfollower.com\/blog\/wp-content\/uploads\/2023\/04\/1680426452_840_Disjoint-Set-Union-\u0627\u06a9\u062a\u0634\u0627\u0641\u06cc-\u0627\u0646\u062c\u0645\u0646-DEV.png\" alt=\"\u062a\u0648\u0636\u06cc\u062d\u0627\u062a \u062a\u0635\u0648\u06cc\u0631\" loading=\"lazy\" width=\"880\" height=\"376\" title=\"\"><\/p>\n<p>\u062f\u0631 \u062a\u0635\u0648\u06cc\u0631 \u0628\u0627\u0644\u0627 findRepresentative \u0647\u0645\u06cc\u0634\u0647 \u0628\u0631\u0627\u06cc \u0631\u06cc\u0634\u0647 set-tree \u0641\u0631\u0627\u062e\u0648\u0627\u0646\u06cc \u0645\u06cc \u0634\u0648\u062f\u060c \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0627\u06cc\u0646 \u0641\u0631\u0627\u062e\u0648\u0627\u0646\u06cc O(1) \u0627\u0633\u062a.<\/p>\n<p>\u0628\u06cc\u0627\u06cc\u06cc\u062f \u0645\u0648\u0631\u062f\u06cc \u0631\u0627 \u062f\u0631 \u0646\u0638\u0631 \u0628\u06af\u06cc\u0631\u06cc\u0645 \u06a9\u0647 findRepresentative \u0627\u0632 \u0631\u06cc\u0634\u0647 \u063a\u06cc\u0631 set-tree \u0641\u0631\u0627\u062e\u0648\u0627\u0646\u06cc \u0634\u0648\u062f \u0648 \u0628\u0641\u0647\u0645\u06cc\u0645 \u06a9\u0647 \u0686\u0631\u0627 \u0628\u0647 \u0637\u0648\u0631 \u0645\u062a\u0648\u0633\u0637 \u200b\u200b\u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc O(log N) \u062f\u0627\u0631\u062f.  \u0628\u0631\u0627\u06cc \u0627\u0646\u062c\u0627\u0645 \u0627\u06cc\u0646 \u06a9\u0627\u0631\u060c \u0627\u062c\u0627\u0632\u0647 \u0645\u06cc\u200c\u062f\u0647\u06cc\u0645 \u0628\u0627 \u0645\u0639\u0631\u0641\u06cc \u06cc\u06a9 \u062f\u0633\u062a\u0647 \u0628\u0631\u0627\u06cc \u0644\u0628\u0647\u200c\u0647\u0627\u06cc \u062f\u0631\u062e\u062a \u0645\u062c\u0645\u0648\u0639\u0647 \u0634\u0631\u0648\u0639 \u06a9\u0646\u06cc\u0645. <\/p>\n<p>\u062d\u0627\u0634\u06cc\u0647\u060c \u063a\u06cc\u0631\u0645\u062a\u0645\u0631\u06a9\u0632 <strong>(\u0627\u0644\u0641\u060c \u0628)<\/strong> \u062c\u0627\u06cc\u06cc \u06a9\u0647 <strong>\u0622<\/strong> \u067e\u062f\u0631 \u0648 \u0645\u0627\u062f\u0631 \u0627\u0633\u062a <strong>\u0628<\/strong> \u062f\u0633\u062a\u0647 \u0628\u0646\u062f\u06cc \u062f\u0627\u0631\u062f <strong>2^K<\/strong> \u0627\u06af\u0631 2^K <= \u0627\u0646\u062f\u0627\u0632\u0647(a) - \u0627\u0646\u062f\u0627\u0632\u0647(\u0628) <2^(K + 1). <\/p>\n<p>\u0628\u06cc\u0627\u06cc\u06cc\u062f \u0628\u0647 \u0645\u0633\u06cc\u0631\u06cc \u06a9\u0647 \u0647\u0646\u06af\u0627\u0645 \u062a\u0645\u0627\u0633 \u062d\u0630\u0641 \u0645\u06cc \u0634\u0648\u062f \u0646\u06af\u0627\u0647 \u06a9\u0646\u06cc\u0645 <code>findRepresentative(x)<\/code> (\u0628\u0627 \u0631\u0646\u06af \u0632\u0631\u062f \u0645\u0634\u062e\u0635 \u0634\u062f\u0647 \u0627\u0633\u062a)<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/nabfollower.com\/blog\/wp-content\/uploads\/2023\/04\/1680426452_112_Disjoint-Set-Union-\u0627\u06a9\u062a\u0634\u0627\u0641\u06cc-\u0627\u0646\u062c\u0645\u0646-DEV.png\" alt=\"\u062a\u0648\u0636\u06cc\u062d\u0627\u062a \u062a\u0635\u0648\u06cc\u0631\" loading=\"lazy\" width=\"880\" height=\"1107\" title=\"\"><\/p>\n<p>\u0627\u06af\u0631 \u0627\u06cc\u0646 \u0645\u0633\u06cc\u0631 \u062f\u0627\u0631\u0627\u06cc \u0644\u0628\u0647 \u0647\u0627\u06cc log(N) \u0628\u0627\u0634\u062f\u060c \u0645\u0627 \u0627\u0632 \u0622\u0646 \u0631\u0627\u0636\u06cc \u0647\u0633\u062a\u06cc\u0645 \u0632\u06cc\u0631\u0627 \u0645\u06cc \u062e\u0648\u0627\u0647\u06cc\u0645 \u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc O(log N) \u0631\u0627 \u0627\u062b\u0628\u0627\u062a \u06a9\u0646\u06cc\u0645. <\/p>\n<p>\u0641\u0631\u0636 \u06a9\u0646\u06cc\u062f \u0644\u0628\u0647 \u0647\u0627\u06cc \u0628\u06cc\u0634 \u0627\u0632 log(N) \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f.  \u062f\u0631 \u0627\u06cc\u0646 \u062d\u0627\u0644\u062a \u062d\u062f\u0627\u0642\u0644 \u062f\u0648 \u06cc\u0627\u0644 \u0628\u0627 \u0647\u0645\u0627\u0646 \u062f\u0633\u062a\u0647 K (<br \/>\u0627\u0635\u0644 \u06a9\u0628\u0648\u062a\u0631)<br \/><img decoding=\"async\" src=\"https:\/\/nabfollower.com\/blog\/wp-content\/uploads\/2023\/04\/1680426452_146_Disjoint-Set-Union-\u0627\u06a9\u062a\u0634\u0627\u0641\u06cc-\u0627\u0646\u062c\u0645\u0646-DEV.png\" alt=\"\u062a\u0648\u0636\u06cc\u062d\u0627\u062a \u062a\u0635\u0648\u06cc\u0631\" loading=\"lazy\" width=\"880\" height=\"1153\" title=\"\"><\/p>\n<p>\u0628\u06cc\u0627\u06cc\u06cc\u062f \u062a\u0639\u0631\u06cc\u0641 \u06a9\u0646\u06cc\u0645 <strong>\u0627\u0646\u062f\u0627\u0632\u0647 (a\/b)<\/strong> \u0628\u0647 \u0627\u0646\u062f\u0627\u0632\u0647 \u0627\u0646\u062f\u0627\u0632\u0647 \u062f\u0631\u062e\u062a \u0641\u0631\u0639\u06cc <strong>\u0622<\/strong> \u0628\u062f\u0648\u0646 \u062f\u0631\u062e\u062a \u0641\u0631\u0639\u06cc \u0627\u0632 <strong>\u0628<\/strong>.<\/p>\n<p>\u0645\u0627 \u0628\u0647 \u0631\u0627\u062d\u062a\u06cc \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u0645 \u0627\u0646\u062f\u0627\u0632\u0647 (u \/ v) >= 2^K + size(v) \u0648 size(a\/b) >= 2^K + size(b) \u0631\u0627 \u0628\u0628\u06cc\u0646\u06cc\u0645.  \u0627\u0645\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u0645 \u0628\u06cc\u0634\u062a\u0631 \u0628\u06af\u0648\u06cc\u06cc\u0645!  v \u062f\u0631 \u0632\u06cc\u0631 \u062f\u0631\u062e\u062a \u062e\u0648\u062f \u062d\u062f\u0627\u0642\u0644 \u0631\u0626\u0648\u0633 \u0627\u0646\u062f\u0627\u0632\u0647 (a \/ b) \u0631\u0627 \u0634\u0627\u0645\u0644 \u0645\u06cc \u0634\u0648\u062f\u060c \u0628\u0647 \u0627\u06cc\u0646 \u0645\u0639\u0646\u06cc \u06a9\u0647 \u0627\u0646\u062f\u0627\u0632\u0647 (u \/ v) >= \u0627\u0646\u062f\u0627\u0632\u0647 (a \/ b) + 2^K >= \u0627\u0646\u062f\u0627\u0632\u0647 (b) + 2^K + 2 ^ \u06a9.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/nabfollower.com\/blog\/wp-content\/uploads\/2023\/04\/1680426452_809_Disjoint-Set-Union-\u0627\u06a9\u062a\u0634\u0627\u0641\u06cc-\u0627\u0646\u062c\u0645\u0646-DEV.png\" alt=\"\u062a\u0648\u0636\u06cc\u062d\u0627\u062a \u062a\u0635\u0648\u06cc\u0631\" loading=\"lazy\" width=\"880\" height=\"972\" title=\"\"><\/p>\n<p>\u0628\u06cc\u0627\u06cc\u06cc\u062f \u0628\u0627 \u062f\u0642\u062a \u0628\u06cc\u0634\u062a\u0631\u06cc \u0628\u0647 \u0627\u0648\u0644\u06cc\u0646 \u0644\u0628\u0647 \u062f\u0633\u062a\u0647 2^K \u062f\u0631 \u0645\u0633\u06cc\u0631 \u0646\u06af\u0627\u0647 \u06a9\u0646\u06cc\u0645.  \u0628\u0627 \u0645\u0634\u0627\u0647\u062f\u0647 \u0628\u0627\u0644\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u0645 \u0628\u0641\u0647\u0645\u06cc\u0645 \u06a9\u0647 \u062f\u0633\u062a\u0647 \u06cc\u0627\u0644 (R, v) \u06a9\u0647 \u0628\u0647 \u062c\u0627\u06cc (u, v) \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0628\u062e\u0634\u06cc \u0627\u0632 \u0641\u0634\u0631\u062f\u0647 \u0633\u0627\u0632\u06cc \u0645\u0633\u06cc\u0631 \u0627\u0636\u0627\u0641\u0647 \u0645\u06cc \u06a9\u0646\u06cc\u0645 \u0686\u0647 \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f.  \u0627\u0646\u062f\u0627\u0632\u0647 \u062f\u0631\u062e\u062a \u0641\u0631\u0639\u06cc R \u062d\u062f\u0627\u0642\u0644 \u0627\u0646\u062f\u0627\u0632\u0647 (u \/ v) + \u0627\u0646\u062f\u0627\u0632\u0647 (v) \u0627\u0633\u062a \u06a9\u0647 \u0628\u06cc\u0634 \u0627\u0632 2^ (K + 1) + \u0627\u0646\u062f\u0627\u0632\u0647 (v) \u0627\u0633\u062a \u0648 \u0627\u0646\u062f\u0627\u0632\u0647 v \u0627\u0646\u062f\u0627\u0632\u0647 (v) \u0627\u0633\u062a\u060c \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u0627\u0646\u062f\u0627\u0632\u0647 ( R\/V) >= 2^(K + 1).  \u0627\u06cc\u0646 \u0628\u0647 \u0627\u06cc\u0646 \u0645\u0639\u0646\u06cc \u0627\u0633\u062a \u06a9\u0647 \u0627\u06af\u0631 \u062f\u0631 \u0645\u0633\u06cc\u0631\u06cc \u0627\u0632 \u0646\u0645\u0627\u06cc\u0646\u062f\u0647 (R) \u062a\u0627 \u0631\u0627\u0633 x \u0628\u06cc\u0634\u062a\u0631 \u0627\u0632 log(N) \u06cc\u0627\u0644 \u0648\u062c\u0648\u062f \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u062f\u060c \u062d\u062f\u0627\u0642\u0644 \u062f\u0631 \u0644\u0628\u0647 \u0628\u0627 \u062f\u0633\u062a\u0647 \u0627\u0641\u0632\u0627\u06cc\u0634 \u0648\u062c\u0648\u062f \u062e\u0648\u0627\u0647\u062f \u062f\u0627\u0634\u062a.  \u0627\u06cc\u0646 \u062f\u0633\u062a\u0647 \u0628\u0627 \u0627\u0646\u062f\u0627\u0632\u0647 \u062f\u0631\u062e\u062a \u0645\u062d\u062f\u0648\u062f \u0645\u06cc \u0634\u0648\u062f \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u0646\u0645\u06cc \u062a\u0648\u0627\u0646\u062f \u0628\u0647 \u0637\u0648\u0631 \u0646\u0627\u0645\u062d\u062f\u0648\u062f \u0631\u0634\u062f \u06a9\u0646\u062f. <\/p>\n<p><img decoding=\"async\" src=\"https:\/\/nabfollower.com\/blog\/wp-content\/uploads\/2023\/04\/1680426453_345_Disjoint-Set-Union-\u0627\u06a9\u062a\u0634\u0627\u0641\u06cc-\u0627\u0646\u062c\u0645\u0646-DEV.png\" alt=\"\u062a\u0648\u0636\u06cc\u062d\u0627\u062a \u062a\u0635\u0648\u06cc\u0631\" loading=\"lazy\" width=\"880\" height=\"1002\" title=\"\"><\/p>\n<p>\u0628\u06cc\u0627\u06cc\u06cc\u062f \u0646\u0634\u0627\u0646 \u062f\u0647\u06cc\u0645 \u06a9\u0647 \u0648\u0642\u062a\u06cc \u06cc\u06a9 \u06cc\u0627\u0644 \u0631\u0627 \u062f\u0631 \u0645\u0633\u06cc\u0631 \u0628\u0627 \u0644\u0628\u0647 \u0627\u06cc \u0628\u0647 \u0631\u06cc\u0634\u0647 \u062c\u0627\u06cc\u06af\u0632\u06cc\u0646 \u0645\u06cc \u06a9\u0646\u06cc\u0645\u060c \u062f\u0633\u062a\u0647 \u0622\u0646 \u06cc\u0627\u0644 \u0646\u0645\u06cc \u062a\u0648\u0627\u0646\u062f \u06a9\u0627\u0647\u0634 \u06cc\u0627\u0628\u062f.  \u0641\u0631\u0636 \u06a9\u0646\u06cc\u062f \u06a9\u0647 \u06cc\u0627\u0644 (u, v) \u0631\u0627 \u0628\u0627 \u06cc\u0627\u0644 (R, v) \u062c\u0627\u06cc\u06af\u0632\u06cc\u0646 \u0645\u06cc \u06a9\u0646\u06cc\u0645.  \u0627\u0632 \u0622\u0646\u062c\u0627\u06cc\u06cc \u06a9\u0647 R \u06cc\u06a9\u06cc \u0627\u0632 \u0627\u062c\u062f\u0627\u062f u \u0627\u0633\u062a\u060c \u062d\u062f\u0627\u0642\u0644 \u06cc\u06a9 \u0631\u0627\u0633 \u0628\u06cc\u0634\u062a\u0631 \u062f\u0631 \u0632\u06cc\u0631 \u062f\u0631\u062e\u062a \u062e\u0648\u062f \u062e\u0648\u0627\u0647\u062f \u062f\u0627\u0634\u062a\u060c \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u0627\u0646\u062f\u0627\u0632\u0647 (u, v) < size(R, v) + 1. <\/p>\n<p>\u0647\u0645\u0647 \u06cc\u0627\u0644\u200c\u0647\u0627\u06cc \u062f\u06cc\u06af\u0631 \u062f\u0633\u062a\u0647\u200c\u0628\u0646\u062f\u06cc \u062e\u0648\u062f \u0631\u0627 \u062a\u063a\u06cc\u06cc\u0631 \u0646\u0645\u06cc\u200c\u062f\u0647\u0646\u062f\u060c \u0632\u06cc\u0631\u0627 \u062c\u0627\u06cc\u06af\u0632\u06cc\u0646\u06cc \u06cc\u0627\u0644 \u0628\u0631 \u0622\u0646\u0647\u0627 \u062a\u0623\u062b\u06cc\u0631 \u0646\u0645\u06cc\u200c\u06af\u0630\u0627\u0631\u062f \u06cc\u0627 \u0627\u0646\u062f\u0627\u0632\u0647 \u0647\u0631 \u062f\u0648 \u0631\u0627\u0633 \u0622\u0646 \u06cc\u0627\u0644 \u0628\u0647 \u0647\u0645\u0627\u0646 \u062a\u0639\u062f\u0627\u062f \u06a9\u0627\u0647\u0634 \u0645\u06cc\u200c\u06cc\u0627\u0628\u062f. <\/p>\n<p>\u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u0628\u0627 \u062f\u0627\u0646\u0633\u062a\u0646 \u0627\u06cc\u0646\u06a9\u0647 \u062f\u0633\u062a\u0647 \u06cc\u0627\u0644\u200c\u0647\u0627 \u0641\u0642\u0637 \u062f\u0631 \u062d\u0627\u0644 \u0631\u0634\u062f \u0647\u0633\u062a\u0646\u062f \u0648 \u0645\u062d\u062f\u0648\u062f\u06cc\u062a \u062f\u0627\u0631\u0646\u062f\u060c \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u06af\u0641\u062a \u06a9\u0647 \u0628\u06cc\u0634\u062a\u0631 \u0627\u0632 (N &#8211; 1) * log(N) \u0646\u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f (\u0647\u0631 \u06cc\u0627\u0644 \u062f\u0631 \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0631\u062e\u062a \u0628\u0627 \u0627\u0646\u062f\u0627\u0632\u0647 N \u062d\u062f\u0627\u06a9\u062b\u0631 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u062f \u062f\u0633\u062a\u0647 \u062e\u0648\u062f \u0631\u0627 \u0627\u0641\u0632\u0627\u06cc\u0634 \u062f\u0647\u062f. \u0648\u0631\u0648\u062f \u0628\u0647 \u0633\u06cc\u0633\u062a\u0645 (N)).  \u0628\u0627 \u062a\u0631\u06a9\u06cc\u0628 \u0628\u0627 \u0633\u0646\u0627\u0631\u06cc\u0648\u06cc\u06cc \u06a9\u0647 \u0645\u0633\u06cc\u0631 \u0627\u0632 \u06cc\u06a9 \u0631\u0627\u0633 \u0628\u0647 \u0646\u0645\u0627\u06cc\u0646\u062f\u0647 \u06a9\u0645\u062a\u0631 \u06cc\u0627 \u0645\u0633\u0627\u0648\u06cc \u0628\u0627 log (N) \u0627\u0633\u062a\u060c \u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u06a9\u0644 \u0631\u0627 \u0628\u0631\u0627\u06cc \u0639\u0645\u0644\u06cc\u0627\u062a M \u0628\u0647 \u062f\u0633\u062a \u0622\u0648\u0631\u062f\u06cc\u0645 findRepresentative O((M + N)log(N)).<\/p>\n<h2><span class=\"ez-toc-section\" id=\"%D8%AA%D8%B1%DA%A9%DB%8C%D8%A8_%D9%81%D8%B4%D8%B1%D8%AF%D9%87_%D8%B3%D8%A7%D8%B2%DB%8C_%D9%85%D8%B3%DB%8C%D8%B1_%D8%A8%D8%A7_%D8%A7%DA%A9%D8%AA%D8%B4%D8%A7%D9%81%DB%8C_%D8%B1%D8%AA%D8%A8%D9%87\"><\/span>\n<p>  \u062a\u0631\u06a9\u06cc\u0628 \u0641\u0634\u0631\u062f\u0647 \u0633\u0627\u0632\u06cc \u0645\u0633\u06cc\u0631 \u0628\u0627 \u0627\u06a9\u062a\u0634\u0627\u0641\u06cc \u0631\u062a\u0628\u0647<br \/>\n<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u0627\u062b\u0628\u0627\u062a \u0627\u06cc\u0646 \u0627\u0645\u0631 \u0646\u0633\u0628\u062a\u0627\u064b \u067e\u06cc\u0686\u06cc\u062f\u0647 \u0627\u0633\u062a\u060c \u0627\u0645\u0627 \u0645\u0646 \u0645\u0639\u062a\u0642\u062f\u0645 \u0644\u0627\u0632\u0645 \u0628\u0647 \u0630\u06a9\u0631 \u0627\u0633\u062a \u06a9\u0647 \u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0627\u06cc\u0646 \u0627\u06a9\u062a\u0634\u0627\u0641\u06cc\u060c \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0631\u0627 \u0628\u0647 O(ackermann(n)) \u0633\u0631\u0639\u062a \u0645\u06cc \u0628\u062e\u0634\u062f\u060c \u06a9\u0647 \u062f\u0631 \u0622\u0646 \u0622\u06a9\u0631\u0645\u0646 \u062a\u0627\u0628\u0639 \u0622\u06a9\u0631\u0645\u0646 \u0645\u0639\u06a9\u0648\u0633 \u0627\u0633\u062a \u06a9\u0647 \u0631\u0634\u062f \u0628\u0633\u06cc\u0627\u0631 \u06a9\u0646\u062f\u06cc \u062f\u0627\u0631\u062f (\u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0645\u062b\u0627\u0644 \u0628\u0631\u0627\u06cc n <= 10). ^500\u060c ackermann(n) < 4).<\/p>\n<h2><span class=\"ez-toc-section\" id=\"%D8%AE%D9%84%D8%A7%D8%B5%D9%87\"><\/span>\n<p>  \u062e\u0644\u0627\u0635\u0647<br \/>\n<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u062f\u0631 \u0627\u06cc\u0646 \u0645\u0642\u0627\u0644\u0647 \u0646\u06af\u0627\u0647\u06cc \u0628\u0647 \u06cc\u06a9 \u0633\u0627\u062e\u062a\u0627\u0631 \u062f\u0627\u062f\u0647 \u062c\u0630\u0627\u0628 DSU \u0627\u0646\u062f\u0627\u062e\u062a\u06cc\u0645 \u0648 \u0631\u0627\u06cc\u062c\u200c\u062a\u0631\u06cc\u0646 \u0627\u06a9\u062a\u0634\u0627\u0641\u06cc\u200c\u0647\u0627\u06cc \u0645\u0648\u0631\u062f \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u062f\u0631 \u0622\u0646 \u0631\u0627 \u062b\u0627\u0628\u062a \u06a9\u0631\u062f\u06cc\u0645 \u0648 \u06cc\u06a9 \u0627\u06a9\u062a\u0634\u0627\u0641\u06cc \u0628\u0633\u06cc\u0627\u0631 \u06a9\u0627\u0631\u0622\u0645\u062f \u0631\u0627 \u0630\u06a9\u0631 \u06a9\u0631\u062f\u06cc\u0645 \u06a9\u0647 \u062f\u0648 \u0645\u0648\u0631\u062f \u0627\u0632 \u0622\u0646\u0647\u0627 \u0631\u0627 \u062a\u0631\u06a9\u06cc\u0628 \u0645\u06cc\u200c\u06a9\u0646\u062f.<\/p>\n<\/p><\/div>\n","protected":false},"excerpt":{"rendered":"<p>DSU \u06cc\u06a9\u06cc \u0627\u0632 \u0638\u0631\u06cc\u0641 \u062a\u0631\u06cc\u0646 \u062f\u0631 \u0633\u0627\u062e\u062a\u0627\u0631 \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u067e\u06cc\u0627\u062f\u0647 \u0633\u0627\u0632\u06cc \u0627\u0633\u062a \u0648 \u0645\u0646 \u0628\u0627\u0631\u0647\u0627 \u062f\u0631 \u0632\u0646\u062f\u06af\u06cc \u0628\u0631\u0646\u0627\u0645\u0647 \u0646\u0648\u06cc\u0633\u06cc \u0631\u0642\u0627\u0628\u062a\u06cc \u062e\u0648\u062f \u0627\u0632 \u0622\u0646 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0631\u062f\u0647 \u0627\u0645. \u0627\u06cc\u0646\u062a\u0631\u0646\u062a \u067e\u0631 \u0627\u0632 \u067e\u06cc\u0627\u062f\u0647 \u0633\u0627\u0632\u06cc \u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641 \u0628\u0631\u0627\u06cc \u0622\u0646 \u0627\u0633\u062a\u060c \u0627\u0645\u0627 \u0645\u062a\u0623\u0633\u0641\u0627\u0646\u0647 \u062a\u0642\u0631\u06cc\u0628\u0627\u064b \u0647\u06cc\u0686 \u0645\u0642\u0627\u0644\u0647 \u0627\u06cc \u0648\u062c\u0648\u062f \u0646\u062f\u0627\u0631\u062f \u06a9\u0647 \u0627\u062b\u0628\u0627\u062a \u062e\u0648\u0628\u06cc \u0628\u0631\u0627\u06cc \u06a9\u0627\u0631\u0627\u06cc\u06cc DSU \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u062f\u060c \u062f\u0631 \u0627\u06cc\u0646 \u0645\u0642\u0627\u0644\u0647 &hellip;<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"","fifu_image_alt":"","footnotes":""},"categories":[339],"tags":[],"class_list":["post-15426","post","type-post","status-publish","format-standard","hentry","category-dev"],"_links":{"self":[{"href":"https:\/\/nabfollower.com\/blog\/wp-json\/wp\/v2\/posts\/15426","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/nabfollower.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/nabfollower.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/nabfollower.com\/blog\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/nabfollower.com\/blog\/wp-json\/wp\/v2\/comments?post=15426"}],"version-history":[{"count":0,"href":"https:\/\/nabfollower.com\/blog\/wp-json\/wp\/v2\/posts\/15426\/revisions"}],"wp:attachment":[{"href":"https:\/\/nabfollower.com\/blog\/wp-json\/wp\/v2\/media?parent=15426"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/nabfollower.com\/blog\/wp-json\/wp\/v2\/categories?post=15426"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/nabfollower.com\/blog\/wp-json\/wp\/v2\/tags?post=15426"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}