{"id":353210,"date":"2021-02-23T01:48:47","date_gmt":"2021-02-22T17:48:47","guid":{"rendered":"http:\/\/4563.org\/?p=353210"},"modified":"2021-02-23T01:48:47","modified_gmt":"2021-02-22T17:48:47","slug":"%e5%a6%82%e4%bd%95%e6%a3%80%e6%b5%8b%e7%a4%be%e4%ba%a4%e7%bd%91%e7%bb%9c%e4%b8%ad%e4%b8%a4%e4%b8%aa%e4%ba%ba%e6%98%af%e5%90%a6%e6%98%af%e6%9c%8b%e5%8f%8b%e5%85%b3%e7%b3%bb%ef%bc%88union-find-%e7%ae%97","status":"publish","type":"post","link":"http:\/\/4563.org\/?p=353210","title":{"rendered":"\u5982\u4f55\u68c0\u6d4b\u793e\u4ea4\u7f51\u7edc\u4e2d\u4e24\u4e2a\u4eba\u662f\u5426\u662f\u670b\u53cb\u5173\u7cfb\uff08union-find \u7b97\u6cd5\uff09"},"content":{"rendered":"<div>\n<div>\n<div>\n<h1>                  \u5982\u4f55\u68c0\u6d4b\u793e\u4ea4\u7f51\u7edc\u4e2d\u4e24\u4e2a\u4eba\u662f\u5426\u662f\u670b\u53cb\u5173\u7cfb\uff08union-find \u7b97\u6cd5\uff09               <\/h1>\n<p> <\/p>\n<div>\n<div> <span>\u8cc7\u6df1\u5927\u4f6c : HuaAn9527 <\/span>  <span><i><\/i> 0<\/span> <\/div>\n<div> <\/div>\n<\/p><\/div>\n<\/p><\/div>\n<\/p><\/div>\n<div isfirst=\"1\"> <\/p>\n<blockquote>\n<p>\u672c\u6587\u5df2\u88ab Github \u4ed3\u5e93\u6536\u5f55 https:\/\/github.com\/silently9527\/JavaCore<\/p>\n<p>\u7a0b\u5e8f\u5458\u5e38\u7528\u7684 IDEA \u63d2\u4ef6\uff1ahttps:\/\/github.com\/silently9527\/ToolsetIdeaPlugin<\/p>\n<p>\u5b8c\u5168\u5f00\u6e90\u7684\u6dd8\u5ba2\u9879\u76ee\uff1ahttps:\/\/github.com\/silently9527\/mall-coupons-server<\/p>\n<\/blockquote>\n<h2>\u524d\u8a00<\/h2>\n<p>\u6625\u8282\u653e\u5047\u4f1a\u4e86\u8001\u5bb6\uff0c\u505c\u66f4\u4e86\u5f88\u591a\u5929\uff0c\u8fd9\u662f\u5e74\u540e\u8fde\u591c\u809d\u51fa\u6765\u7684\u7b2c\u4e00\u7bc7\u6587\u7ae0\uff0c\u5148\u6765\u804a\u804a\u6625\u8282\u653e\u5047\u671f\u95f4\u53d1\u751f\u7684\u4e8b\uff0c\u8fd9\u6b21\u56de\u5bb6\u9047\u5230\u4e86\u6211\u5b66\u751f\u65f6\u4ee3\u7684\u5973\u795e\uff0c\u5f53\u5e74\u5979\u5728\u6211\u5fc3\u76ee\u4e2d\u90a3\u662f<\/p>\n<blockquote>\n<p>&#8220;\u51fa\u6de4\u6ce5\u800c\u4e0d\u67d3\u3001\u6fef\u6e05\u6d9f\u800c\u4e0d\u5996&#8221;<\/p>\n<\/blockquote>\n<p>\u6ca1\u60f3\u5230\u8fd9\u6b21\u9047\u5230\u4e86\u5979\uff0c\u8eab\u4f53\u53d1\u798f\uff0c\u5fc3\u76ee\u4e2d\u5973\u795e\u7684\u5f62\u8c61\u77ac\u95f4\u788e\u4e86\uff0c\u5c31\u50cf\u8fbe\u82ac\u5947\u518d\u6b21\u9047\u5230\u4e86\u8499\u5a1c\u4e3d\u838e<\/p>\n<blockquote>\n<p>&#8220;\u83e1\u840f\u9999\u9500\u7fe0\u53f6\u6b8b&#8221;<\/p>\n<\/blockquote>\n<p>\u597d\u4e86\uff0c\u8a00\u5f52\u6b63\u4f20\u3002<\/p>\n<p>\u6709\u65f6\u5019\u6211\u4eec\u53ef\u4ee5\u9700\u8981\u5224\u65ad\u5728\u5927\u578b\u7f51\u7edc\u4e2d\u4e24\u53f0\u8ba1\u7b97\u673a\u662f\u5426\u76f8\u8fde\uff0c\u662f\u5426\u9700\u8981\u5efa\u7acb\u4e00\u6761\u65b0\u7684\u8fde\u63a5\u624d\u80fd\u901a\u4fe1\uff1b\u6216\u8005\u662f\u5728\u793e\u4ea4\u7f51\u7edc\u4e2d\u5224\u65ad\u4e24\u4e2a\u4eba\u662f\u5426\u662f\u670b\u53cb\u5173\u7cfb\uff08\u76f8\u8fde\u8868\u793a\u662f\u670b\u53cb\u5173\u7cfb\uff09\u3002\u5728\u8fd9\u79cd\u5e94\u7528\u4e2d\uff0c\u901a\u5e38\u6211\u4eec\u53ef\u80fd\u9700\u8981\u5904\u7406\u6570\u767e\u4e07\u7684\u5bf9\u8c61\u548c\u6570\u4ebf\u7684\u8fde\u63a5\uff0c\u5982\u4f55\u80fd\u591f\u5feb\u901f\u7684\u5224\u65ad\u51fa\u662f\u5426\u76f8\u8fde\u5462\uff1f\u8fd9\u5c31\u9700\u8981\u4f7f\u7528\u5230 union-find \u7b97\u6cd5<\/p>\n<h2>\u6982\u5ff5<\/h2>\n<h4>\u76f8\u8fde<\/h4>\n<p>\u5047\u5982\u8f93\u5165\u4e00\u5bf9\u6574\u6570\uff0c\u5176\u4e2d\u6bcf\u4e2a\u6570\u5b57\u8868\u793a\u7684\u662f\u67d0\u79cd\u5bf9\u8c61\uff08\u4eba\u3001\u5730\u5740\u6216\u8005\u8ba1\u7b97\u673a\u7b49\u7b49\uff09\uff0c\u6574\u6570\u5bf9 p,q \u7406\u89e3\u4e3a\u201cp \u4e0e q \u76f8\u8fde\u201d\uff0c\u76f8\u8fde\u5177\u6709\u4ee5\u4e0b\u7279\u6027\uff1a<\/p>\n<ul>\n<li>\u81ea\u53cd\u6027\uff1ap \u4e0e p \u662f\u76f8\u8fde\u7684<\/li>\n<li>\u5bf9\u79f0\u6027\uff1a\u5982\u679c p \u4e0e q \u76f8\u8fde\uff0c\u90a3\u4e48 q \u4e0e p \u76f8\u8fde<\/li>\n<li>\u4f20\u9012\u6027\uff1a\u5982\u679c p \u4e0e q \u76f8\u8fde\uff0cq \u4e0e r \u76f8\u8fde\uff0c\u90a3\u4e48 p \u4e0e r \u4e5f\u76f8\u8fde<\/li>\n<\/ul>\n<blockquote>\n<p>\u5bf9\u8c61\u5982\u4f55\u4e0e\u6570\u5b57\u5173\u8054\u8d77\u6765\uff0c\u540e\u9762\u6211\u4eec\u804a\u5230\u4e00\u79cd\u7b97\u6cd5\u7b26\u53f7\u8868<\/p>\n<\/blockquote>\n<h4>\u7b49\u4ef7\u7c7b<\/h4>\n<p>\u5047\u8bbe\u76f8\u8fde\u662f\u4e00\u4e2a\u79cd\u7b49\u4ef7\u5173\u7cfb\uff0c\u90a3\u4e48\u7b49\u4ef7\u5173\u7cfb\u80fd\u591f\u5c06\u5bf9\u8c61\u5212\u5206\u4e3a\u591a\u4e2a\u7b49\u4ef7\u7c7b\uff0c\u5728\u8be5\u7b97\u6cd5\u4e2d\uff0c\u5f53\u4e14\u4ec5\u5f53\u4e24\u4e2a\u5bf9\u8c61\u76f8\u8fde\u65f6\u4ed6\u4eec\u624d\u5c5e\u4e8e\u540c\u4e00\u4e2a\u7b49\u4ef7\u7c7b<\/p>\n<h4>\u89e6\u70b9<\/h4>\n<p>\u6574\u4e2a\u7f51\u7edc\u4e2d\u7684\u67d0\u79cd\u5bf9\u8c61\u79f0\u4e3a\u89e6\u70b9<\/p>\n<h4>\u8fde\u901a\u5206\u91cf<\/h4>\n<p>\u5c06\u6574\u6570\u5bf9\u79f0\u4e3a\u8fde\u63a5\uff0c\u5c06\u7b49\u4ef7\u7c7b\u79f0\u4f5c\u8fde\u901a\u5206\u91cf\u6216\u8005\u7b80\u79f0\u5206\u91cf<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" referrerpolicy=\"no-referrer\" rel=\"noreferrer\" src=\"http:\/\/4563.org\/wp-content\/uploads\/2021\/02\/20210224_603625cce508e.jpg\" alt=\"\u5982\u4f55\u68c0\u6d4b\u793e\u4ea4\u7f51\u7edc\u4e2d\u4e24\u4e2a\u4eba\u662f\u5426\u662f\u670b\u53cb\u5173\u7cfb\uff08union-find \u7b97\u6cd5\uff09\" \/><\/p>\n<h4>\u52a8\u6001\u8fde\u901a\u6027<\/h4>\n<p>union-find \u7b97\u6cd5\u7684\u76ee\u6807\u662f\u5f53\u7a0b\u5e8f\u4ece\u8f93\u5165\u4e2d\u8bfb\u53d6\u4e86\u6574\u6570\u5bf9 p q \u65f6\uff0c\u5982\u679c\u5df2\u77e5\u7684\u6240\u6709\u6574\u6570\u5bf9\u90fd\u4e0d\u80fd\u8bf4\u660e p q \u662f\u76f8\u8fde\u7684\uff0c\u90a3\u4e48\u5c06\u8fd9\u4e00\u5bf9\u6574\u6570\u8f93\u51fa\uff0c\u5426\u5219\u5ffd\u7565\u6389\u8fd9\u5bf9\u6574\u6570\uff1b\u6211\u4eec\u9700\u8981\u8bbe\u8ba1\u6570\u636e\u7ed3\u6784\u6765\u4fdd\u5b58\u5df2\u77e5\u7684\u6240\u6709\u6574\u6570\u5bf9\u7684\u4fe1\u606f\uff0c\u5224\u65ad\u51fa\u8f93\u5165\u7684\u6574\u6570\u5bf9\u662f\u5426\u662f\u76f8\u8fde\u7684\uff0c\u8fd9\u79cd\u95ee\u9898\u53eb\u505a\u52a8\u6001\u8fde\u901a\u6027\u95ee\u9898\u3002<\/p>\n<h2>union-find \u7b97\u6cd5 API \u5b9a\u4e49<\/h2>\n<pre><code>public interface UF {     void union(int p, int q); \/\/\u5728 p \u4e0e q \u4e4b\u95f4\u6dfb\u52a0\u4e00\u6761\u8fde\u63a5      int find(int p); \/\/\u8fd4\u56de p \u6240\u5728\u5206\u91cf\u7684\u6807\u8bc6\u7b26      boolean connected(int p, int q); \/\/\u5224\u65ad\u51fa p \u4e0e q \u662f\u5426\u5b58\u5728\u4e8e\u540c\u4e00\u4e2a\u5206\u91cf\u4e2d      int count(); \/\/\u7edf\u8ba1\u51fa\u8fde\u901a\u5206\u91cf\u7684\u6570\u91cf } <\/code><\/pre>\n<p>\u5982\u679c\u4e24\u4e2a\u89e6\u70b9\u5728\u4e0d\u540c\u7684\u5206\u91cf\u4e2d\uff0cunion \u64cd\u4f5c\u4f1a\u4f7f\u4e24\u4e2a\u5206\u91cf\u5f52\u5e76\u3002\u4e00\u5f00\u59cb\u6211\u4eec\u6709 N \u4e2a\u5206\u91cf\uff08\u6bcf\u4e2a\u89e6\u70b9\u8868\u793a\u4e00\u4e2a\u5206\u91cf\uff09\uff0c\u5c06\u4e24\u4e2a\u5206\u91cf\u5f52\u5e76\u4e4b\u540e\u6570\u91cf\u51cf\u4e00\u3002<\/p>\n<p>\u62bd\u8c61\u5b9e\u73b0\u5982\u4e0b\uff1a<\/p>\n<pre><code>public abstract class AbstractUF implements UF {     protected int[] id;     protected int count;      public AbstractUF(int N) {         count = N;          id = new int[N];         for (int i = 0; i &lt; N; i++) {             id[i] = i;         }     }      @Override     public boolean connected(int p, int q) {         return find(p) == find(q);     }      @Override     public int count() {         return count;     } } <\/code><\/pre>\n<p>\u63a5\u4e0b\u6765\u6211\u4eec\u5c31\u4e3b\u8981\u6765\u8ba8\u8bba\u5982\u4f55\u5b9e\u73b0 union \u65b9\u6cd5\u548c find \u65b9\u6cd5<\/p>\n<h2>quick-find \u7b97\u6cd5<\/h2>\n<p>\u8fd9\u79cd\u7b97\u6cd5\u7684\u5b9e\u73b0\u601d\u8def\u662f\u5728\u540c\u4e00\u4e2a\u8fde\u901a\u5206\u91cf\u4e2d\u6240\u6709\u89e6\u70b9\u5728 id[]\u4e2d\u7684\u503c\u90fd\u662f\u76f8\u540c\u7684\uff0c\u5224\u65ad\u662f\u5426\u8fde\u901a\u7684 connected \u7684\u65b9\u6cd5\u5c31\u662f\u5224\u65ad id[p]\u662f\u5426\u7b49\u4e8e id[q]\u3002<\/p>\n<pre><code>public class QuickFindImpl extends AbstractUF {     public QuickFindImpl(int N) {         super(N);     }      @Override     public int find(int p) {         return id[p];     }      @Override     public void union(int p, int q) {         int pId = find(p);         int qId = find(q);          if (pId == qId) { \/\/\u5982\u679c\u76f8\u7b49\u8868\u793a p \u4e0e q \u5df2\u7ecf\u5c5e\u4e8e\u540c\u4e00\u5206\u91cf\u4e2d             return;         }          for (int i = 0; i &lt; id.length; i++) {             if (id[i] == pId) {                 id[i] = qId; \/\/\u628a\u5206\u91cf\u4e2d\u6240\u6709\u7684\u503c\u90fd\u7edf\u4e00\u6210 qId             }         }         count--; \/\/\u8fde\u901a\u5206\u91cf\u6570\u51cf\u4e00     }  } <\/code><\/pre>\n<ul>\n<li>\u7b97\u6cd5\u5206\u6790\uff1a find()\u64cd\u4f5c\u663e\u7136\u662f\u5f88\u5feb\u7684\uff0c\u65f6\u95f4\u590d\u6742\u5ea6 O(1), \u4f46\u662f union \u7684\u7b97\u6cd5\u662f\u65e0\u6cd5\u5904\u7406\u5927\u578b\u6570\u636e\u7684\uff0c\u56e0\u4e3a\u6bcf\u6b21\u90fd\u9700\u8981\u53d8\u91cf\u6574\u4e2a\u6570\u7ec4\uff0c\u90a3\u4e48 union \u65b9\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u662f O(n)<\/li>\n<\/ul>\n<h2>quick-union \u7b97\u6cd5<\/h2>\n<p>\u4e3a\u4e86\u63d0\u9ad8 union \u65b9\u6cd5\u7684\u901f\u5ea6\uff0c\u6211\u4eec\u9700\u8981\u8003\u8651\u53e6\u5916\u4e00\u79cd\u7b97\u6cd5\uff1b\u4f7f\u7528\u540c\u6837\u7684\u6570\u636e\u7ed3\u6784\uff0c\u53ea\u662f\u91cd\u65b0\u5b9a\u4e49 id[]\u8868\u793a\u7684\u610f\u4e49\uff0c\u6bcf\u4e2a\u89e6\u70b9\u6240\u5bf9\u5e94\u7684 id[]\u503c\u90fd\u662f\u5728\u540c\u4e00\u5206\u91cf\u4e2d\u7684\u53e6\u4e00\u4e2a\u89e6\u70b9\u7684\u540d\u79f0<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" referrerpolicy=\"no-referrer\" rel=\"noreferrer\" src=\"http:\/\/4563.org\/wp-content\/uploads\/2021\/02\/20210224_603625d20a0e1.jpg\" alt=\"\u5982\u4f55\u68c0\u6d4b\u793e\u4ea4\u7f51\u7edc\u4e2d\u4e24\u4e2a\u4eba\u662f\u5426\u662f\u670b\u53cb\u5173\u7cfb\uff08union-find \u7b97\u6cd5\uff09\" \/><\/p>\n<p>\u5728\u6570\u7ec4\u521d\u59cb\u5316\u4e4b\u540e\uff0c\u6bcf\u4e2a\u8282\u70b9\u7684\u94fe\u63a5\u90fd\u6307\u5411\u81ea\u5df1\uff1b id[]\u6570\u7ec4\u7528<code>\u7236\u94fe\u63a5<\/code>\u7684\u5f62\u5f0f\u8868\u793a\u4e86<code>\u68ee\u6797<\/code>\uff0c\u6bcf\u4e00\u6b21 union \u64cd\u4f5c\u90fd\u4f1a\u627e\u51fa\u6bcf\u4e2a\u5206\u91cf\u7684<code>\u6839\u8282\u70b9<\/code>\u8fdb\u884c\u5f52\u5e76\u3002<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" referrerpolicy=\"no-referrer\" rel=\"noreferrer\" src=\"http:\/\/4563.org\/wp-content\/uploads\/2021\/02\/20210224_603625d93dd4a.jpg\" alt=\"\u5982\u4f55\u68c0\u6d4b\u793e\u4ea4\u7f51\u7edc\u4e2d\u4e24\u4e2a\u4eba\u662f\u5426\u662f\u670b\u53cb\u5173\u7cfb\uff08union-find \u7b97\u6cd5\uff09\" \/><\/p>\n<pre><code>public class QuickUnionImpl extends AbstractUF {     public QuickUnionImpl(int N) {         super(N);     }      @Override     public int find(int p) {         \/\/\u627e\u51fa p \u6240\u5728\u5206\u91cf\u7684\u6839\u89e6\u70b9         while (p != id[p]) {             p = id[p];         }         return p;     }      @Override     public void union(int p, int q) {         int pRoot = find(p); \/\/\u627e\u51fa q p \u7684\u6839\u89e6\u70b9         int qRoot = find(q);         if (pRoot == qRoot) { \/\/\u5904\u4e8e\u540c\u4e00\u5206\u91cf\u4e0d\u505a\u5904\u7406             return;         }         id[pRoot] = qRoot; \/\/\u6839\u8282\u70b9         count--;     }  } <\/code><\/pre>\n<ul>\n<li>\u7b97\u6cd5\u5206\u6790\uff1a \u770b\u8d77\u6765 quick-union \u7b97\u6cd5\u6bd4 quick-find \u7b97\u6cd5\u66f4\u5feb\uff0c\u56e0\u4e3a union \u4e0d\u9700\u8981\u4e3a\u6bcf\u5bf9\u8f93\u5165\u904d\u5386\u6574\u4e2a\u6570\u7ec4\uff0c \u8003\u8651\u6700\u4f73\u60c5\u51b5\u4e0b\uff0cfind \u65b9\u6cd5\u53ea\u9700\u8981\u8bbf\u95ee\u4e00\u6b21\u6570\u7ec4\u5c31\u53ef\u4ee5\u5f97\u5230\u6839\u89e6\u70b9\uff0c\u90a3\u4e48 union \u65b9\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6 O(n)\uff1b \u8003\u8651\u5230\u6700\u7cdf\u7cd5\u7684\u8f93\u5165\u60c5\u51b5\uff0c\u5982\u4e0b\u56fe\uff1a<\/li>\n<\/ul>\n<p><img decoding=\"async\" loading=\"lazy\" referrerpolicy=\"no-referrer\" rel=\"noreferrer\" src=\"http:\/\/4563.org\/wp-content\/uploads\/2021\/02\/20210224_603625e14029e.jpg\" alt=\"\u5982\u4f55\u68c0\u6d4b\u793e\u4ea4\u7f51\u7edc\u4e2d\u4e24\u4e2a\u4eba\u662f\u5426\u662f\u670b\u53cb\u5173\u7cfb\uff08union-find \u7b97\u6cd5\uff09\" \/><\/p>\n<p>find \u65b9\u6cd5\u9700\u8981\u8bbf\u95ee\u6570\u7ec4 n-1 \u6b21\uff0c\u90a3\u4e48 union \u65b9\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u662f O(n\u00b2)<\/p>\n<h2>\u52a0\u6743 quick-union \u7b97\u6cd5<\/h2>\n<p>\u4e3a\u4e86\u4fdd\u8bc1 quick-union \u7b97\u6cd5\u6700\u7cdf\u7cd5\u7684\u60c5\u51b5\u4e0d\u5728\u51fa\u73b0\uff0c\u6211\u9700\u8981\u8bb0\u5f55\u6bcf\u4e00\u4e2a\u6811\u7684\u5927\u5c0f\uff0c\u5728\u8fdb\u884c\u5206\u91cf\u5f52\u5e76\u64cd\u4f5c\u65f6\u603b\u662f\u628a\u5c0f\u7684\u6811\u8fde\u63a5\u5230\u5927\u7684\u6811\u4e0a\uff0c\u8fd9\u79cd\u7b97\u6cd5\u6784\u9020\u51fa\u6765\u6811\u7684\u9ad8\u5ea6\u4f1a\u8fdc\u8fdc\u5c0f\u4e8e\u672a\u52a0\u6743\u7248\u672c\u6240\u6784\u9020\u7684\u6811\u9ad8\u5ea6\u3002<\/p>\n<pre><code>public class WeightedQuickUnionImpl extends AbstractUF {     private int[] sz;      public WeightedQuickUnionImpl(int N) {         super(N);         sz = new int[N];         for (int i = 0; i &lt; N; i++) {             sz[i] = 1;         }     }      @Override     public void union(int p, int q) {         int pRoot = find(p); \/\/\u627e\u51fa q p \u7684\u6839\u89e6\u70b9         int qRoot = find(q);         if (pRoot == qRoot) { \/\/\u5904\u4e8e\u540c\u4e00\u5206\u91cf\u4e0d\u505a\u5904\u7406             return;         }         \/\/\u5c0f\u6811\u5408\u5e76\u5230\u5927\u6811         if (sz[pRoot] &lt; sz[qRoot]) {             sz[qRoot] += sz[pRoot];              id[pRoot] = qRoot;         } else {             sz[pRoot] += sz[qRoot];             id[qRoot] = pRoot;         }         count--;     }      @Override     public int find(int p) {         \/\/\u627e\u51fa p \u6240\u5728\u5206\u91cf\u7684\u6839\u89e6\u70b9         while (p != id[p]) {             p = id[p];         }         return p;     } } <\/code><\/pre>\n<ul>\n<li>\u7b97\u6cd5\u5206\u6790\uff1a \u6700\u574f\u7684\u60c5\u51b5\u4e0b\uff0c\u6bcf\u6b21 union \u5f52\u5e76\u7684\u6811\u90fd\u662f\u5927\u5c0f\u76f8\u7b49\u7684\uff0c\u4ed6\u4eec\u90fd\u5305\u542b\u4e86 2 \u7684 n \u6b21\u65b9\u4e2a\u8282\u70b9\uff0c\u9ad8\u5ea6\u90fd\u662f n\uff0c\u5408\u5e76\u4e4b\u540e\u7684\u9ad8\u5ea6\u53d8\u6210\u4e86 n+1\uff0c\u7531\u6b64\u53ef\u4ee5\u5f97\u51fa union \u65b9\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u662f O(lgN)<\/li>\n<\/ul>\n<p><img decoding=\"async\" loading=\"lazy\" referrerpolicy=\"no-referrer\" rel=\"noreferrer\" src=\"http:\/\/4563.org\/wp-content\/uploads\/2021\/02\/20210224_603625e64fc55.jpg\" alt=\"\u5982\u4f55\u68c0\u6d4b\u793e\u4ea4\u7f51\u7edc\u4e2d\u4e24\u4e2a\u4eba\u662f\u5426\u662f\u670b\u53cb\u5173\u7cfb\uff08union-find \u7b97\u6cd5\uff09\" \/><\/p>\n<h2>\u603b\u7ed3<\/h2>\n<p>union-find \u7b97\u6cd5\u53ea\u80fd\u5224\u65ad\u51fa\u7ed9\u5b9a\u7684\u4e24\u4e2a\u6574\u6570\u662f\u5426\u662f\u76f8\u8fde\u7684\uff0c\u65e0\u6cd5\u7ed9\u51fa\u5177\u4f53\u8fbe\u5230\u7684\u8def\u5f84\uff1b\u540e\u671f\u6211\u4eec\u804a\u5230\u56fe\u7b97\u6cd5\u53ef\u4ee5\u7ed9\u51fa\u5177\u4f53\u7684\u8def\u5f84<\/p>\n<table>\n<thead>\n<tr>\n<th>\u7b97\u6cd5<\/th>\n<th>union()<\/th>\n<th>find()<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>quick-find \u7b97\u6cd5<\/td>\n<td>N<\/td>\n<td>1<\/td>\n<\/tr>\n<tr>\n<td>quick-union \u7b97\u6cd5<\/td>\n<td>\u6811\u7684\u9ad8\u5ea6<\/td>\n<td>\u6811\u7684\u9ad8\u5ea6<\/td>\n<\/tr>\n<tr>\n<td>\u52a0\u6743 quick-union \u7b97\u6cd5<\/td>\n<td>lgN<\/td>\n<td>lgN<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<blockquote>\n<p>\u6587\u4e2d\u6240\u6709\u6e90\u7801\u5df2\u653e\u5165\u5230\u4e86 github \u4ed3\u5e93https:\/\/github.com\/silently9527\/JavaCore<\/p>\n<p>\u53c2\u8003\u4e66\u7c4d\uff1a\u7b97\u6cd5\u7b2c\u56db\u7248<\/p>\n<\/blockquote><\/div>\n<div> <b>\u5927\u4f6c\u6709\u8a71\u8aaa<\/b> (<span>10<\/span>)        <\/div>\n<div> <\/div>\n<\/p><\/div>\n<\/p><\/div>\n<ul>\n<li data-pid=\"5341831\" data-uid=\"2\">\n<div>\n<div>\n<div> <span>\u8cc7\u6df1\u5927\u4f6c : Olament <\/span>  <\/div>\n<div> <i title=\"\u5f15\u7528\"><\/i>  <span>          <\/span> <\/div>\n<\/p><\/div>\n<div>                                                             Path compression \u5462                                                            <\/div>\n<\/p><\/div>\n<\/li>\n<li data-pid=\"5341832\" data-uid=\"2\">\n<div>\n<div>\n<div> <span>\u8cc7\u6df1\u5927\u4f6c : theRealWhexy <\/span>  <\/div>\n<div> <i title=\"\u5f15\u7528\"><\/i>  <span>          <\/span> <\/div>\n<\/p><\/div>\n<div>                                                             \u7b2c\u4e00\u6b21\u770b\u5230\u5e76\u67e5\u96c6\u5199\u5f97\u8fd9\u4e48\u957f\u3002\u5389\u5bb3\u4e86\uff01                                                            <\/div>\n<\/p><\/div>\n<\/li>\n<li data-pid=\"5341833\" data-uid=\"2\">\n<div>\n<div>\n<div> <span>\u8cc7\u6df1\u5927\u4f6c : Baratheon <\/span>  <\/div>\n<div> <i title=\"\u5f15\u7528\"><\/i>  <span>          <\/span> <\/div>\n<\/p><\/div>\n<div>                                                             \u6839\u636e\u9093\u5df4\u6307\u6570\u7684\u6307\u5bfc\u2026\u2026150 \u4e2a\u4eba\u4f5c\u4e3a\u793e\u4ea4\u5173\u7cfb\u4e0a\u9650\u7684\u60c5\u51b5\u4e0b\uff0c\u5bf9\u8fd9\u73a9\u610f\u513f\u7684\u68c0\u6d4b\u53ef\u80fd\u6709\u70b9\u591a\u4f59                                                            <\/div>\n<\/p><\/div>\n<\/li>\n<li data-pid=\"5341834\" data-uid=\"2\">\n<div>\n<div>\n<div> <span>\u8cc7\u6df1\u5927\u4f6c : ThanksSirAlex <\/span>  <\/div>\n<div> <i title=\"\u5f15\u7528\"><\/i>  <span>          <\/span> <\/div>\n<\/p><\/div>\n<div>                                                             \u5b9e\u9645\u4e1a\u52a1\u90fd\u7528\u56fe\u6570\u636e\u5e93\u4e86\uff0c\u53ea\u4e0d\u8fc7\u56fe\u6570\u636e\u5e93\u91cc\u9762\u672c\u8eab\u53ef\u80fd\u4f1a\u7528\u5e76\u67e5\u96c6\u505a\u67e5\u627e                                                            <\/div>\n<\/p><\/div>\n<\/li>\n<li data-pid=\"5341835\" data-uid=\"2\">\n<div>\n<div>\n<div> <span>\u8cc7\u6df1\u5927\u4f6c : lance6716 <\/span>  <\/div>\n<div> <i title=\"\u5f15\u7528\"><\/i>  <span>          <\/span> <\/div>\n<\/p><\/div>\n<div>                                                             \u6240\u4ee5\u5c31\u662f\u628a&lt;\u7b97\u6cd5\u7b2c\u56db\u7248&gt;\u7684\u4ee3\u7801\u642c\u8fd0\u4e86\u4e00\u4e0b\uff1f                                                            <\/div>\n<\/p><\/div>\n<\/li>\n<li data-pid=\"5341836\" data-uid=\"2\">\n<div>\n<div>\n<div> <span>\u8cc7\u6df1\u5927\u4f6c : jones2000 <\/span>  <\/div>\n<div> <i title=\"\u5f15\u7528\"><\/i>  <span>          <\/span> <\/div>\n<\/p><\/div>\n<div>                                                             &#8220;\u5982\u4f55\u68c0\u6d4b\u793e\u4ea4\u7f51\u7edc\u4e2d\u4e24\u4e2a\u4eba\u662f\u5426\u662f\u670b\u53cb\u5173\u7cfb?&#8221;<br \/>\u9996\u5148\u4f60\u8981\u628a\u8fd9\u4e24\u4e2a\u4eba\u7684\u4e2a\u4eba\u4fe1\u606f\u548c\u9690\u79c1\uff08\u540c\u5b66\uff0c\u4eb2\u621a\uff0c\u540c\u4e8b\uff0c\u5404\u4e2a\u804a\u5929\u8f6f\u4ef6\u91cc\u7684\u597d\u53cb\u7b49\u7b49&#8230;&#8230;.)\u90fd\u6536\u96c6\u5230\uff0c \u7136\u540e\u624d\u662f\u7b97\u6cd5\u3002                                                            <\/div>\n<\/p><\/div>\n<\/li>\n<li data-pid=\"5341837\" data-uid=\"2\">\n<div>\n<div>\n<div> <span>\u8cc7\u6df1\u5927\u4f6c : yianing <\/span>  <\/div>\n<div> <i title=\"\u5f15\u7528\"><\/i>  <span>          <\/span> <\/div>\n<\/p><\/div>\n<div>                                                             \u6211\u7684\u670b\u53cb\u7684\u670b\u53cb\uff0c\u4e0d\u4e00\u5b9a\u662f\u6211\u7684\u670b\u53cb                                                            <\/div>\n<\/p><\/div>\n<\/li>\n<li data-pid=\"5341838\" data-uid=\"2\">\n<div>\n<div>\n<div> <span>\u8cc7\u6df1\u5927\u4f6c : no1xsyzy <\/span>  <\/div>\n<div> <i title=\"\u5f15\u7528\"><\/i>  <span>          <\/span> <\/div>\n<\/p><\/div>\n<div>                                                             \u5e76\u67e5\u96c6\u7684\u82f1\u6587\u662f Disjoint-set<br \/>\u65f6\u95f4\u590d\u6742\u5ea6\u662f\u53cd Ackermann \u51fd\u6570\u2026\u2026<br \/>\u987a\u4fbf\uff0c\u6bcf\u6b21\u641c\u7d22\u53ef\u4ee5\u628a\u6574\u6761\u8def\u4e0a\u7684\u8282\u70b9\u5168\u90e8\u8bbe\u5230\u6839\u8282\u70b9\u4e0a\u53bb\u3002<br \/>\u7528\u9012\u5f52\u5199\u8fd9\u4e00\u6bb5\u975e\u5e38\u723d find_parent(s): s.parent = find_parent(s.parent)                                                            <\/div>\n<\/p><\/div>\n<\/li>\n<li data-pid=\"5341839\" data-uid=\"2\">\n<div>\n<div>\n<div> <span>\u8cc7\u6df1\u5927\u4f6c : hanxiV2EX <\/span>  <\/div>\n<div> <i title=\"\u5f15\u7528\"><\/i>  <span>          <\/span> <\/div>\n<\/p><\/div>\n<div>                                                             @yianing \u53ef\u80fd\u662f\u654c\u4eba                                                            <\/div>\n<\/p><\/div>\n<\/li>\n<li data-pid=\"5341840\" data-uid=\"2\">\n<div>\n<div>\n<div> <span>\u8cc7\u6df1\u5927\u4f6c : Ethson <\/span>  <\/div>\n<div> <i title=\"\u5f15\u7528\"><\/i>  <span>          <\/span> <\/div>\n<\/p><\/div>\n<div>                                                             https:\/\/ethsonliu.com\/2019\/12\/union-find-sets.html                                                            <\/div>\n<\/p><\/div>\n<\/li>\n<li>\n","protected":false},"excerpt":{"rendered":"<p>\u5982\u4f55\u68c0\u6d4b\u793e\u4ea4\u7f51\u7edc\u4e2d\u4e24\u4e2a\u4eba\u662f\u5426\u662f\u670b\u53cb&hellip;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[],"tags":[],"_links":{"self":[{"href":"http:\/\/4563.org\/index.php?rest_route=\/wp\/v2\/posts\/353210"}],"collection":[{"href":"http:\/\/4563.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/4563.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/4563.org\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/4563.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=353210"}],"version-history":[{"count":0,"href":"http:\/\/4563.org\/index.php?rest_route=\/wp\/v2\/posts\/353210\/revisions"}],"wp:attachment":[{"href":"http:\/\/4563.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=353210"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/4563.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=353210"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/4563.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=353210"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}