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146 KiB
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Theme: Default
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Description: Original highlight.js style
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License: see project LICENSE
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Touched: 2021
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rel=tag>Mybatis</a><span class=tag-list-count>13</span><li class=tag-list-item><a class=tag-list-link href=/tags/Mysql/ rel=tag>Mysql</a><span class=tag-list-count>13</span><li class=tag-list-item><a class=tag-list-link href=/tags/NameServer/ rel=tag>NameServer</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/PHP/ rel=tag>PHP</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/Preorder-Traversal/ rel=tag>Preorder Traversal</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/Print-FooBar-Alternately/ rel=tag>Print FooBar Alternately</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/RPC/ rel=tag>RPC</a><span class=tag-list-count>4</span><li class=tag-list-item><a class=tag-list-link href=/tags/Redis/ rel=tag>Redis</a><span class=tag-list-count>2</span><li class=tag-list-item><a class=tag-list-link href=/tags/Remove-Duplicates-from-Sorted-List/ rel=tag>Remove Duplicates from Sorted List</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/RocketMQ/ rel=tag>RocketMQ</a><span class=tag-list-count>9</span><li class=tag-list-item><a class=tag-list-link href=/tags/Rotate-Image/ rel=tag>Rotate Image</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/Rust/ rel=tag>Rust</a><span class=tag-list-count>3</span><li class=tag-list-item><a class=tag-list-link href=/tags/SPI/ rel=tag>SPI</a><span class=tag-list-count>2</span><li class=tag-list-item><a class=tag-list-link href=/tags/Servlet/ rel=tag>Servlet</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/Sharding-Jdbc/ rel=tag>Sharding-Jdbc</a><span class=tag-list-count>3</span><li class=tag-list-item><a class=tag-list-link href=/tags/Shift-2D-Grid/ rel=tag>Shift 2D Grid</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/Singleton/ rel=tag>Singleton</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/Spring/ rel=tag>Spring</a><span class=tag-list-count>7</span><li class=tag-list-item><a class=tag-list-link href=/tags/Spring-Event/ rel=tag>Spring Event</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/SpringBoot/ rel=tag>SpringBoot</a><span class=tag-list-count>22</span><li class=tag-list-item><a class=tag-list-link href=/tags/Sql%E6%B3%A8%E5%85%A5/ rel=tag>Sql注入</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/Stream/ rel=tag>Stream</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/Synchronized/ rel=tag>Synchronized</a><span class=tag-list-count>2</span><li class=tag-list-item><a class=tag-list-link href=/tags/Thread-dump/ rel=tag>Thread dump</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/ThreadLocal/ rel=tag>ThreadLocal</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/ThreadPool/ rel=tag>ThreadPool</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/Tomcat/ rel=tag>Tomcat</a><span class=tag-list-count>13</span><li class=tag-list-item><a class=tag-list-link href=/tags/Trapping-Rain-Water/ rel=tag>Trapping Rain Water</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/WeakReference/ rel=tag>WeakReference</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/Web/ rel=tag>Web</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/Webhook/ rel=tag>Webhook</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/Windows/ rel=tag>Windows</a><span class=tag-list-count>5</span><li class=tag-list-item><a class=tag-list-link href=/tags/WordPress/ rel=tag>WordPress</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/aqs/ rel=tag>aqs</a><span class=tag-list-count>3</span><li class=tag-list-item><a class=tag-list-link href=/tags/await/ rel=tag>await</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/bloom-filter/ rel=tag>bloom filter</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/c/ rel=tag>c++</a><span class=tag-list-count>14</span><li class=tag-list-item><a class=tag-list-link href=/tags/cglib/ rel=tag>cglib</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/cgroup/ rel=tag>cgroup</a><span class=tag-list-count>2</span><li class=tag-list-item><a class=tag-list-link href=/tags/cluster/ rel=tag>cluster</a><span 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class=tag-list-item><a class=tag-list-link href=/tags/gc/ rel=tag>gc</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/git/ rel=tag>git</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/grep/ rel=tag>grep</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/hadoop/ rel=tag>hadoop</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/headscale/ rel=tag>headscale</a><span class=tag-list-count>5</span><li class=tag-list-item><a class=tag-list-link href=/tags/hexo/ rel=tag>hexo</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/http/ rel=tag>http</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/icu4c/ rel=tag>icu4c</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/im/ rel=tag>im</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/is-not-null/ rel=tag>is not null</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/is-null/ rel=tag>is null</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/j-u-c/ rel=tag>j.u.c</a><span class=tag-list-count>2</span><li class=tag-list-item><a class=tag-list-link href=/tags/java/ rel=tag>java</a><span class=tag-list-count>40</span><li class=tag-list-item><a class=tag-list-link href=/tags/jvm/ rel=tag>jvm</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/leetcode/ rel=tag>leetcode</a><span class=tag-list-count>44</span><li class=tag-list-item><a class=tag-list-link href=/tags/leetcode-155/ rel=tag>leetcode 155</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/linked-list/ rel=tag>linked list</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/linux/ rel=tag>linux</a><span class=tag-list-count>4</span><li class=tag-list-item><a class=tag-list-link href=/tags/lock/ rel=tag>lock</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/mfc/ rel=tag>mfc</a><span class=tag-list-count>2</span><li class=tag-list-item><a class=tag-list-link href=/tags/min-stack/ rel=tag>min stack</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/mq/ rel=tag>mq</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/mvcc/ rel=tag>mvcc</a><span class=tag-list-count>3</span><li class=tag-list-item><a class=tag-list-link href=/tags/mysql/ rel=tag>mysql</a><span class=tag-list-count>7</span><li class=tag-list-item><a class=tag-list-link href=/tags/namespace/ rel=tag>namespace</a><span class=tag-list-count>3</span><li class=tag-list-item><a class=tag-list-link href=/tags/nas/ rel=tag>nas</a><span class=tag-list-count>6</span><li class=tag-list-item><a class=tag-list-link href=/tags/next-key-lock/ rel=tag>next-key lock</a><span class=tag-list-count>2</span><li class=tag-list-item><a class=tag-list-link href=/tags/nginx/ rel=tag>nginx</a><span class=tag-list-count>3</span><li class=tag-list-item><a class=tag-list-link href=/tags/nullsfirst/ rel=tag>nullsfirst</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/openresty/ rel=tag>openresty</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/openwrt/ rel=tag>openwrt</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/php/ rel=tag>php</a><span class=tag-list-count>5</span><li class=tag-list-item><a class=tag-list-link href=/tags/powershell/ rel=tag>powershell</a><span class=tag-list-count>2</span><li class=tag-list-item><a class=tag-list-link href=/tags/procedure/ rel=tag>procedure</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/python/ rel=tag>python</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/read-view/ rel=tag>read view</a><span class=tag-list-count>3</span><li class=tag-list-item><a class=tag-list-link href=/tags/redis/ rel=tag>redis</a><span class=tag-list-count>12</span><li class=tag-list-item><a class=tag-list-link href=/tags/scp/ rel=tag>scp</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/signal/ rel=tag>signal</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/sort/ rel=tag>sort</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/spark/ rel=tag>spark</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/ssh/ rel=tag>ssh</a><span class=tag-list-count>3</span><li class=tag-list-item><a class=tag-list-link href=/tags/stack/ rel=tag>stack</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/stream/ rel=tag>stream</a><span class=tag-list-count>2</span><li class=tag-list-item><a class=tag-list-link href=/tags/string/ rel=tag>string</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/swoole/ rel=tag>swoole</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/top/ rel=tag>top</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/uname/ rel=tag>uname</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/unlock/ rel=tag>unlock</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/utf8/ rel=tag>utf8</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/utf8mb4/ rel=tag>utf8mb4</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/utf8mb4-0900-ai-ci/ rel=tag>utf8mb4_0900_ai_ci</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/utf8mb4-general-ci/ rel=tag>utf8mb4_general_ci</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/utf8mb4-unicode-ci/ rel=tag>utf8mb4_unicode_ci</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/value/ rel=tag>value</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/websocket/ rel=tag>websocket</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/windows/ rel=tag>windows</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/wsl/ rel=tag>wsl</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/zookeeper/ rel=tag>zookeeper</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/zsh/ rel=tag>zsh</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E4%B8%89%E9%98%B6%E6%AE%B5%E6%8F%90%E4%BA%A4/ rel=tag>三阶段提交</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E4%B8%8D%E5%8F%AF%E5%8F%98%E5%BC%95%E7%94%A8/ rel=tag>不可变引用</a><span class=tag-list-count>2</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E4%B8%9C%E4%BA%AC%E5%A5%A5%E8%BF%90%E4%BC%9A/ rel=tag>东京奥运会</a><span class=tag-list-count>2</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E4%B8%A4%E9%98%B6%E6%AE%B5%E6%8F%90%E4%BA%A4/ rel=tag>两阶段提交</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E4%B8%AD%E5%B1%B1%E8%B7%AF/ rel=tag>中山路</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E4%B8%AD%E5%BA%8F/ rel=tag>中序</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E4%B8%AD%E9%97%B4%E4%BB%B6/ rel=tag>中间件</a><span class=tag-list-count>4</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E4%B8%BE%E9%87%8D/ rel=tag>举重</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E4%B9%92%E4%B9%93%E7%90%83/ rel=tag>乒乓球</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E4%BA%8B%E5%8A%A1/ rel=tag>事务</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E4%BA%8C%E5%8F%89%E6%A0%91/ rel=tag>二叉树</a><span class=tag-list-count>3</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E4%BA%91%E6%9C%8D%E5%8A%A1%E5%99%A8/ rel=tag>云服务器</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E4%BA%92%E6%96%A5%E9%94%81/ rel=tag>互斥锁</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E4%BB%A3%E7%A0%81%E9%A2%98%E8%A7%A3/ rel=tag>代码题解</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E4%BF%AE%E7%94%B5%E8%84%91%E7%9A%84/ rel=tag>修电脑的</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E5%81%8F%E5%90%91%E9%94%81/ rel=tag>偏向锁</a><span class=tag-list-count>2</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E5%81%A5%E5%BA%B7%E7%A0%81/ rel=tag>健康码</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E5%85%AC%E4%BA%A4/ rel=tag>公交</a><span class=tag-list-count>3</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E5%85%AC%E4%BA%A4%E8%BD%A6/ rel=tag>公交车</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E5%86%85%E5%AD%98%E5%88%86%E5%B8%83/ rel=tag>内存分布</a><span class=tag-list-count>3</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E5%86%85%E5%AD%98%E6%B3%84%E6%BC%8F/ rel=tag>内存泄漏</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E5%87%86%E5%A4%87/ rel=tag>准备</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E5%87%8F%E8%82%A5/ rel=tag>减肥</a><span class=tag-list-count>7</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E5%88%86%E5%B8%83%E5%BC%8F%E4%BA%8B%E5%8A%A1/ rel=tag>分布式事务</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E5%88%86%E5%B8%83%E5%BC%8F%E9%94%81/ rel=tag>分布式锁</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E5%88%87%E7%89%87/ rel=tag>切片</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E5%88%9D%E5%A7%8B%E5%8C%96/ rel=tag>初始化</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E5%89%8A%E5%B3%B0%E5%A1%AB%E8%B0%B7/ rel=tag>削峰填谷</a><span class=tag-list-count>4</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E5%89%8D%E5%BA%8F/ rel=tag>前序</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E5%8A%A0%E5%A1%9E/ rel=tag>加塞</a><span class=tag-list-count>3</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E5%8A%A0%E8%BD%BD/ rel=tag>加载</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E5%8D%95%E4%BE%8B/ rel=tag>单例</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E5%8D%9A%E5%AE%A2%EF%BC%8C%E6%96%87%E7%AB%A0/ rel=tag>博客，文章</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E5%8E%A6%E9%97%A8/ rel=tag>厦门</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E5%8F%8C%E4%BA%B2%E5%A7%94%E6%B4%BE/ rel=tag>双亲委派</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E5%8F%91%E8%A1%8C%E7%89%88/ rel=tag>发行版</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E5%8F%A3%E7%BD%A9/ rel=tag>口罩</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E5%8F%AF%E5%8F%98%E5%BC%95%E7%94%A8/ rel=tag>可变引用</a><span class=tag-list-count>2</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E5%90%90%E6%A7%BD/ rel=tag>吐槽</a><span class=tag-list-count>2</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E5%9B%A4%E7%89%A9%E8%B5%84/ rel=tag>囤物资</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E5%9E%83%E5%9C%BE%E5%9B%9E%E6%94%B6/ rel=tag>垃圾回收</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E5%9F%BA%E7%A1%80%E8%AE%BE%E6%96%BD/ rel=tag>基础设施</a><span class=tag-list-count>2</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E5%A4%A7%E6%89%AB%E9%99%A4/ rel=tag>大扫除</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E5%AD%97%E7%AC%A6%E9%9B%86/ rel=tag>字符集</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E5%AE%89%E5%85%A8/ rel=tag>安全</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E5%AE%B9%E9%94%99%E6%9C%BA%E5%88%B6/ rel=tag>容错机制</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E5%AF%84%E7%94%9F%E8%99%AB/ rel=tag>寄生虫</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E5%B0%84%E5%87%BB/ rel=tag>射击</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E5%B0%8F%E6%8A%80%E5%B7%A7/ rel=tag>小技巧</a><span class=tag-list-count>6</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E5%B1%80%E5%8F%A3%E8%A1%97/ rel=tag>局口街</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E5%B7%A5%E5%85%B7/ rel=tag>工具</a><span class=tag-list-count>2</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E5%B8%83%E9%9A%86%E8%BF%87%E6%BB%A4%E5%99%A8/ rel=tag>布隆过滤器</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E5%B9%B2%E6%B4%BB/ rel=tag>干活</a><span class=tag-list-count>6</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E5%B9%B4%E4%B8%AD%E6%80%BB%E7%BB%93/ rel=tag>年中总结</a><span class=tag-list-count>2</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E5%B9%B4%E7%BB%88%E6%80%BB%E7%BB%93/ rel=tag>年终总结</a><span class=tag-list-count>4</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E5%B9%B6%E5%8F%91/ rel=tag>并发</a><span class=tag-list-count>2</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E5%B9%B8%E7%A6%8F%E4%BA%86%E5%90%97/ rel=tag>幸福了吗</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E5%B9%BB%E8%AF%BB/ rel=tag>幻读</a><span class=tag-list-count>2</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E5%BA%94%E7%94%A8/ rel=tag>应用</a><span class=tag-list-count>2</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E5%BC%80%E8%BD%A6/ rel=tag>开车</a><span class=tag-list-count>3</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E5%BC%B1%E5%BC%95%E7%94%A8/ rel=tag>弱引用</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E5%BD%B1%E8%AF%84/ rel=tag>影评</a><span class=tag-list-count>2</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E6%89%80%E6%9C%89%E6%9D%83/ rel=tag>所有权</a><span class=tag-list-count>3</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E6%89%93%E5%8D%A1/ rel=tag>打卡</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E6%89%B6%E6%A2%AF/ rel=tag>扶梯</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E6%8A%80%E6%9C%AF/ rel=tag>技术</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E6%8A%98%E8%85%BE/ rel=tag>折腾</a><span class=tag-list-count>3</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E6%8B%96%E6%9B%B4/ rel=tag>拖更</a><span class=tag-list-count>2</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E6%8D%A2%E8%BD%A6%E7%89%8C/ rel=tag>换车牌</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E6%8E%92%E5%BA%8F/ rel=tag>排序</a><span class=tag-list-count>2</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E6%8E%A5%E9%9B%A8%E6%B0%B4/ rel=tag>接雨水</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E6%95%B0%E6%8D%AE%E6%BA%90%E5%8A%A8%E6%80%81%E5%88%87%E6%8D%A2/ rel=tag>数据源动态切换</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84/ rel=tag>数据结构</a><span class=tag-list-count>11</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E6%96%B0%E8%AF%AD%E8%A8%80/ rel=tag>新语言</a><span class=tag-list-count>3</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E6%97%85%E6%B8%B8/ rel=tag>旅游</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E6%97%A5%E5%BF%97/ rel=tag>日志</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E6%9B%BE%E5%8E%9D%E5%9E%B5/ rel=tag>曾厝垵</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E6%9C%80%E5%B0%8F%E6%A0%88/ rel=tag>最小栈</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E6%9D%80%E4%BA%BA%E8%AF%9B%E5%BF%83/ rel=tag>杀人诛心</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E6%9D%AD%E5%B7%9E/ rel=tag>杭州</a><span class=tag-list-count>4</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E6%A0%87%E8%AE%B0%E6%95%B4%E7%90%86/ rel=tag>标记整理</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E6%A4%8D%E7%89%A9%E5%9B%AD/ rel=tag>植物园</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E6%B2%99%E8%8C%B6%E9%9D%A2/ rel=tag>沙茶面</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E6%B3%A8%E8%A7%A3/ rel=tag>注解</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E6%B5%B7%E8%9B%8E%E7%85%8E/ rel=tag>海蛎煎</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E6%B6%88%E6%81%AF%E9%98%9F%E5%88%97/ rel=tag>消息队列</a><span class=tag-list-count>9</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E6%B7%98%E6%B1%B0%E7%AD%96%E7%95%A5/ rel=tag>淘汰策略</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E6%B7%B1%E5%BA%A6%E5%AD%A6%E4%B9%A0/ rel=tag>深度学习</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E6%BA%90%E7%A0%81/ rel=tag>源码</a><span class=tag-list-count>11</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E6%BA%90%E7%A0%81%E8%A7%A3%E6%9E%90/ rel=tag>源码解析</a><span class=tag-list-count>3</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E7%94%9F%E6%B4%BB/ rel=tag>生活</a><span class=tag-list-count>42</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E7%94%B5%E7%93%B6%E8%BD%A6/ rel=tag>电瓶车</a><span class=tag-list-count>2</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E7%96%AB%E6%83%85/ rel=tag>疫情</a><span class=tag-list-count>2</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E7%9C%8B%E4%B9%A6/ rel=tag>看书</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E7%9C%8B%E5%89%A7/ rel=tag>看剧</a><span class=tag-list-count>3</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E7%9F%A9%E9%98%B5/ rel=tag>矩阵</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E7%AB%AF%E5%8F%A3%E8%BD%AC%E5%8F%91/ rel=tag>端口转发</a><span class=tag-list-count>3</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E7%AE%97%E6%B3%95/ rel=tag>算法</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E7%B1%BB%E5%8A%A0%E8%BD%BD/ rel=tag>类加载</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E7%B3%9F%E5%BF%83%E4%BA%8B/ rel=tag>糟心事</a><span class=tag-list-count>5</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E7%B4%A2%E5%BC%95/ rel=tag>索引</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E7%BA%BF%E7%A8%8B%E6%B1%A0/ rel=tag>线程池</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E7%BC%93%E5%AD%98/ rel=tag>缓存</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E7%BC%93%E5%AD%98%E5%87%BB%E7%A9%BF/ rel=tag>缓存击穿</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E7%BC%93%E5%AD%98%E7%A9%BF%E9%80%8F/ rel=tag>缓存穿透</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E7%BC%93%E5%AD%98%E9%9B%AA%E5%B4%A9/ rel=tag>缓存雪崩</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E7%BC%96%E7%A0%81/ rel=tag>编码</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E7%BE%8E%E5%9B%BD/ rel=tag>美国</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E8%80%81%E7%94%B5%E8%84%91/ rel=tag>老电脑</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E8%87%AA%E5%8A%A8%E8%A3%85%E9%85%8D/ rel=tag>自动装配</a><span class=tag-list-count>2</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E8%87%AA%E6%97%8B/ rel=tag>自旋</a><span class=tag-list-count>2</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E8%87%AA%E9%80%82%E5%BA%94%E6%8B%93%E5%B1%95/ rel=tag>自适应拓展</a><span class=tag-list-count>1</span><li class=tag-list-item><a class=tag-list-link href=/tags/%E8%A3%85%E7%94%B5%E8%84%91/ rel=tag>装电脑</a><span class=tag-list-count>1</span><li 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class=post-content itemscope itemtype=http://schema.org/Article><link href=https://nicksxs.me/2024/06/23/%E4%BB%8B%E7%BB%8D%E4%B8%80%E4%B8%8BHNSW%E7%AE%97%E6%B3%95/ itemprop=mainEntityOfPage><span hidden itemprop=author itemscope itemtype=http://schema.org/Person><meta content=/uploads/avatar.jpg itemprop=image><meta content=Nicksxs itemprop=name></span><span hidden itemprop=publisher itemscope itemtype=http://schema.org/Organization><meta content="Nicksxs's Blog" itemprop=name><meta content="learn from zero,技术博客，Nicksxs，史学森" itemprop=description></span><span hidden itemprop=post itemscope itemtype=http://schema.org/CreativeWork><meta content="undefined | Nicksxs's Blog" itemprop=name><meta itemprop=description></span><header class=post-header><h2 itemprop="name headline" class=post-title><a class=post-title-link href=/2024/06/23/%E4%BB%8B%E7%BB%8D%E4%B8%80%E4%B8%8BHNSW%E7%AE%97%E6%B3%95/ itemprop=url>向量数据库学习-介绍一下HNSW算法</a></h2><div class=post-meta-container><div class=post-meta><span class=post-meta-item><span class=post-meta-item-icon><i class="far fa-calendar"></i> </span><span class=post-meta-item-text>发表于</span> <time itemprop="dateCreated datePublished" title="创建时间：2024-06-23 22:47:47" datetime=2024-06-23T22:47:47+08:00>2024-06-23</time> </span><span class="post-meta-item leancloud_visitors" data-flag-title=向量数据库学习-介绍一下HNSW算法 id=/2024/06/23/%E4%BB%8B%E7%BB%8D%E4%B8%80%E4%B8%8BHNSW%E7%AE%97%E6%B3%95/ title=阅读次数><span class=post-meta-item-icon><i class="far fa-eye"></i> </span><span class=post-meta-item-text>阅读次数：</span> <span class=leancloud-visitors-count></span> </span><span class=post-meta-item><span class=post-meta-item-icon><i class="far fa-comment"></i> </span><span class=post-meta-item-text>Disqus：</span> <a href=/2024/06/23/%E4%BB%8B%E7%BB%8D%E4%B8%80%E4%B8%8BHNSW%E7%AE%97%E6%B3%95/#disqus_thread itemprop=discussionUrl title=disqus><span class="post-comments-count disqus-comment-count" data-disqus-identifier=2024/06/23/介绍一下HNSW算法/ itemprop=commentCount></span></a></span></div></div></header><div class=post-body itemprop=articleBody><p>结合AI帮我生成的一篇HNSW的介绍视频，算是向量数据库中比较核心的算法<h2 id=1-引言><a title="1. 引言" class=headerlink href=#1-引言></a>1. 引言</h2><p>向量数据库在当今人工智能和机器学习领域扮演着越来越重要的角色。随着数据规模的不断扩大和应用场景的日益复杂,传统的数据库系统已经难以满足高维向量数据的快速检索需求。在这个背景下,近似最近邻(Approximate Nearest Neighbor, ANN)搜索问题成为了一个热点研究方向。<p>HNSW(Hierarchical Navigable Small World)算法是解决ANN问题的一种高效方法。它通过构建一个多层次的图结构,结合小世界网络的特性,实现了对高维向量数据的快速、精确检索。本文将深入浅出地介绍HNSW算法的核心思想、工作原理以及实际应用。<h2 id=2-HNSW算法的核心思想><a title="2. HNSW算法的核心思想" class=headerlink href=#2-HNSW算法的核心思想></a>2. HNSW算法的核心思想</h2><p>HNSW算法的核心思想可以概括为三个关键点：分层结构、小世界图和近似搜索。<h3 id=分层结构><a class=headerlink href=#分层结构 title=分层结构></a>分层结构</h3><p>HNSW采用了一种多层次的图结构。想象一下,如果我们要在一个大城市中找到一个特定的地址,我们通常会先看城市地图,然后逐步缩小范围到区、街道,最后定位到具体门牌号。HNSW的分层结构就类似于这种由粗到细的搜索过程。<h3 id=小世界图><a class=headerlink href=#小世界图 title=小世界图></a>小世界图</h3><p>小世界网络是一种特殊的图结构,它具有较短的平均路径长度和较高的聚类系数。在HNSW中,每一层都是一个小世界图。这种结构使得在图中的任意两点之间都存在一条相对较短的路径,大大提高了搜索效率。<h3 id=近似搜索><a class=headerlink href=#近似搜索 title=近似搜索></a>近似搜索</h3><p>与传统的KNN(K-Nearest Neighbors)算法不同,HNSW通过牺牲一小部分精度来换取显著的速度提升。它不保证一定能找到真正的最近邻,但可以以极高的概率找到足够接近的点,而且搜索速度要快得多。<h2 id=3-HNSW的工作原理><a title="3. HNSW的工作原理" class=headerlink href=#3-HNSW的工作原理></a>3. HNSW的工作原理</h2><h3 id=数据结构-多层图的构建过程><a class=headerlink href=#数据结构-多层图的构建过程 title=数据结构:多层图的构建过程></a>数据结构:多层图的构建过程</h3><ol><li>HNSW从底层开始构建,每个数据点都会出现在底层。<li>对于每个新插入的点,算法会随机决定它是否应该出现在上一层。这个过程一直持续到某一层,该点不再被选中。<li>在每一层,新点会与该层的其他点建立连接,形成小世界图结构。</ol><h3 id=搜索过程-自顶向下的贪婪搜索><a class=headerlink href=#搜索过程-自顶向下的贪婪搜索 title=搜索过程:自顶向下的贪婪搜索></a>搜索过程:自顶向下的贪婪搜索</h3><ol><li>搜索从最顶层开始,选择一个随机起点。<li>在当前层进行贪婪搜索,不断移动到离目标更近的邻居。<li>当在当前层无法找到更近的点时,下降到下一层继续搜索。<li>重复这个过程直到达到底层,得到最终结果。<br><img data-src=https://img.nicksxs.com/blog/xg85mb.png></ol><h3 id=插入新向量的过程><a class=headerlink href=#插入新向量的过程 title=插入新向量的过程></a>插入新向量的过程</h3><ol><li>确定新向量应该出现在哪些层。<li>从顶层开始,在每一层执行类似于搜索的过程,找到适合连接的邻居点。<li>建立连接,同时可能需要删除一些现有连接以维持图的结构特性。<br><img data-src=https://img.nicksxs.com/blog/ytU7Ct.png></ol><ul><li><p>红色节点表示新插入的数据点。在这个例子中,新节点被插入到了层级0和层级1。<li><p>红色实线表示新建立的同层连接。新节点与其邻近节点建立了连接。<li><p>红色虚线表示新建立的跨层连接。新节点在不同层级之间建立了连接。<li><p>绿色虚线箭头表示插入过程的路径。这条路径展示了算法如何从顶层开始,逐层下降,最终确定新节点的插入位置。<li><p>其他颜色的节点和灰色的连接线表示原有的HNSW结构。<li><p>插入过程从顶层开始,沿着绿色虚线所示的路径向下搜索。<li><p>在每一层,算法都会寻找最近的邻居节点,并决定是否在该层插入新节点。<li><p>在本例中,新节点被插入到了层级0(基础层)和层级1。这是因为HNSW使用概率方法来决定节点应该出现在哪些层级。<li><p>插入后,新节点与其邻近节点建立连接(红色实线),以维持图的小世界特性。<li><p>同时,新节点也与其在不同层级的对应节点建立跨层连接(红色虚线),以确保层级之间的快速访问。</ul><h2 id=4-HNSW的性能分析><a title="4. HNSW的性能分析" class=headerlink href=#4-HNSW的性能分析></a>4. HNSW的性能分析</h2><h3 id=时间复杂度分析><a class=headerlink href=#时间复杂度分析 title=时间复杂度分析></a>时间复杂度分析</h3><ul><li>搜索时间复杂度: O(log N),其中N是数据点的总数。<li>插入时间复杂度: 平均情况下为O(log N)。</ul><h3 id=空间复杂度分析><a class=headerlink href=#空间复杂度分析 title=空间复杂度分析></a>空间复杂度分析</h3><ul><li>空间复杂度: O(N log N),因为上层节点数量呈指数衰减。</ul><h3 id=与其他ANN算法的比较><a class=headerlink href=#与其他ANN算法的比较 title=与其他ANN算法的比较></a>与其他ANN算法的比较</h3><p>相比LSH(Locality-Sensitive Hashing)和Annoy等算法,HNSW在大多数场景下都能提供更好的查询性能和更高的准确率。然而,HNSW的内存消耗相对较高,这是它的一个潜在缺点。<h2 id=5-HNSW的实际应用><a title="5. HNSW的实际应用" class=headerlink href=#5-HNSW的实际应用></a>5. HNSW的实际应用</h2><h3 id=在推荐系统中的应用><a class=headerlink href=#在推荐系统中的应用 title=在推荐系统中的应用></a>在推荐系统中的应用</h3><p>HNSW可以用于快速检索相似用户或物品,提高推荐系统的响应速度和准确性。例如,在音乐推荐中,可以用HNSW快速找到与用户喜好相似的歌曲。<h3 id=在图像检索中的应用><a class=headerlink href=#在图像检索中的应用 title=在图像检索中的应用></a>在图像检索中的应用</h3><p>在大规模图像数据库中,HNSW可以实现快速的相似图像搜索。这在图像搜索引擎、视觉商品搜索等场景中非常有用。<h3 id=在自然语言处理中的应用><a class=headerlink href=#在自然语言处理中的应用 title=在自然语言处理中的应用></a>在自然语言处理中的应用</h3><p>HNSW可以用于词嵌入或句子嵌入的快速检索,支持语义相似度计算、文本分类等任务。<h2 id=6-HNSW的优化和变种><a title="6. HNSW的优化和变种" class=headerlink href=#6-HNSW的优化和变种></a>6. HNSW的优化和变种</h2><h3 id=参数调优技巧><a class=headerlink href=#参数调优技巧 title=参数调优技巧></a>参数调优技巧</h3><ul><li>层数选择:影响搜索速度和内存使用<li>每层连接数:影响搜索准确度和构建时间<li>候选集大小:影响搜索质量和速度的平衡</ul><h3 id=常见的HNSW变种算法介绍><a class=headerlink href=#常见的HNSW变种算法介绍 title=常见的HNSW变种算法介绍></a>常见的HNSW变种算法介绍</h3><ul><li>NSW-G:改进了图的构建方法,提高了搜索效率<li>HCNNG:结合了层次聚类,提高了在某些数据集上的性能</ul><h2 id=7-实现HNSW的挑战与解决方案><a title="7. 实现HNSW的挑战与解决方案" class=headerlink href=#7-实现HNSW的挑战与解决方案></a>7. 实现HNSW的挑战与解决方案</h2><h3 id=大规模数据集的处理><a class=headerlink href=#大规模数据集的处理 title=大规模数据集的处理></a>大规模数据集的处理</h3><ul><li>使用外部存储和分批处理<li>采用压缩技术减少内存占用</ul><h3 id=并行化和分布式实现><a class=headerlink href=#并行化和分布式实现 title=并行化和分布式实现></a>并行化和分布式实现</h3><ul><li>搜索过程的并行化<li>分布式索引构建和查询</ul><h3 id=动态更新和删除操作的处理><a class=headerlink href=#动态更新和删除操作的处理 title=动态更新和删除操作的处理></a>动态更新和删除操作的处理</h3><ul><li>软删除技术<li>定期重建索引</ul><h2 id=8-总结与展望><a title="8. 总结与展望" class=headerlink href=#8-总结与展望></a>8. 总结与展望</h2><p>HNSW算法通过其独特的分层小世界图结构,在保证高准确率的同时实现了对高维向量数据的快速检索。它在推荐系统、图像检索、自然语言处理等多个领域都有广泛应用。<p>未来,向量数据库技术可能会朝着以下方向发展:<ol><li>更高效的压缩和索引技术<li>更好的动态更新支持<li>与深度学习模型的更紧密集成<li>针对特定领域的优化变体</ol><p>随着人工智能和大数据技术的不断发展,HNSW等高效的向量检索算法将在更广阔的应用场景中发挥重要作用。</div><footer class=post-footer><div class=post-eof></div></footer></article></div><div class=post-block><article class=post-content itemscope itemtype=http://schema.org/Article><link href=https://nicksxs.me/2024/06/16/NX30Pro-%E5%88%B7%E6%88%90-Openwrt-ImmortalWrt-%E5%90%8E%E4%BD%9C%E4%B8%BA%E6%9C%89%E7%BA%BF%E4%B8%AD%E7%BB%A7%E7%9A%84%E9%85%8D%E7%BD%AE%E6%96%B9%E6%B3%95/ itemprop=mainEntityOfPage><span hidden itemprop=author itemscope itemtype=http://schema.org/Person><meta content=/uploads/avatar.jpg itemprop=image><meta content=Nicksxs itemprop=name></span><span hidden itemprop=publisher itemscope itemtype=http://schema.org/Organization><meta content="Nicksxs's Blog" itemprop=name><meta content="learn from zero,技术博客，Nicksxs，史学森" 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class=post-meta-item-text>分类于</span> <span itemprop=about itemscope itemtype=http://schema.org/Thing><a href=/categories/openwrt/ itemprop=url rel=index><span itemprop=name>openwrt</span></a> </span></span><span class="post-meta-item leancloud_visitors" data-flag-title="NX30Pro 刷成 Openwrt-ImmortalWrt 后作为有线中继的配置方法" id=/2024/06/16/NX30Pro-%E5%88%B7%E6%88%90-Openwrt-ImmortalWrt-%E5%90%8E%E4%BD%9C%E4%B8%BA%E6%9C%89%E7%BA%BF%E4%B8%AD%E7%BB%A7%E7%9A%84%E9%85%8D%E7%BD%AE%E6%96%B9%E6%B3%95/ title=阅读次数><span class=post-meta-item-icon><i class="far fa-eye"></i> </span><span class=post-meta-item-text>阅读次数：</span> <span class=leancloud-visitors-count></span> </span><span class=post-meta-item><span class=post-meta-item-icon><i class="far fa-comment"></i> </span><span class=post-meta-item-text>Disqus：</span> <a href=/2024/06/16/NX30Pro-%E5%88%B7%E6%88%90-Openwrt-ImmortalWrt-%E5%90%8E%E4%BD%9C%E4%B8%BA%E6%9C%89%E7%BA%BF%E4%B8%AD%E7%BB%A7%E7%9A%84%E9%85%8D%E7%BD%AE%E6%96%B9%E6%B3%95/#disqus_thread itemprop=discussionUrl title=disqus><span class="post-comments-count disqus-comment-count" data-disqus-identifier=2024/06/16/NX30Pro-刷成-Openwrt-ImmortalWrt-后作为有线中继的配置方法/ itemprop=commentCount></span></a></span></div></div></header><div class=post-body itemprop=articleBody><p>因为买了两个NX30Pro，主要是奔着可以刷Openwrt，然后把两个都刷成了ImmortalWrt，结果发现要作为有线中继的话设置还有点麻烦，所以记录下<br>首先要设置个与主路由相同网段的静态地址，方便管理<br>在网络-LAN-基本设置-协议设置成“静态地址”<br>然后IPv4地址就是刚才说的静态地址，可以设个好记的<br>子网掩码就默认的，255.255.255.0，<br>IPv4网关就是主路由地址，DNS也设置成主路由地址<br>基础设置改成忽略此接口-不提供DHCP服务，由主路由提供<br>然后在高级设置中将IPv6的 路由通告服务和DHCPv6服务跟NDP代理禁用掉，<br>物理设置中勾选桥接接口<br>目前我是这样设置可以作为有线中继连通网络了，后续有变化继续更新</div><footer class=post-footer><div class=post-eof></div></footer></article></div><div class=post-block><article class=post-content itemscope itemtype=http://schema.org/Article><link href=https://nicksxs.me/2024/06/16/%E5%90%91%E9%87%8F%E6%95%B0%E6%8D%AE%E5%BA%93%E5%AD%A6%E4%B9%A0%E5%9F%BA%E7%A1%80%E4%B9%8B%E8%B7%B3%E8%A1%A8/ itemprop=mainEntityOfPage><span hidden itemprop=author itemscope itemtype=http://schema.org/Person><meta content=/uploads/avatar.jpg itemprop=image><meta content=Nicksxs itemprop=name></span><span hidden itemprop=publisher itemscope itemtype=http://schema.org/Organization><meta content="Nicksxs's Blog" itemprop=name><meta content="learn from zero,技术博客，Nicksxs，史学森" itemprop=description></span><span hidden itemprop=post itemscope itemtype=http://schema.org/CreativeWork><meta content="undefined | Nicksxs's Blog" itemprop=name><meta itemprop=description></span><header class=post-header><h2 itemprop="name headline" class=post-title><a class=post-title-link href=/2024/06/16/%E5%90%91%E9%87%8F%E6%95%B0%E6%8D%AE%E5%BA%93%E5%AD%A6%E4%B9%A0%E5%9F%BA%E7%A1%80%E4%B9%8B%E8%B7%B3%E8%A1%A8/ itemprop=url>向量数据库学习基础之跳表</a></h2><div class=post-meta-container><div class=post-meta><span class=post-meta-item><span class=post-meta-item-icon><i class="far fa-calendar"></i> </span><span class=post-meta-item-text>发表于</span> <time itemprop="dateCreated datePublished" title="创建时间：2024-06-16 22:30:37" datetime=2024-06-16T22:30:37+08:00>2024-06-16</time> </span><span class=post-meta-item><span class=post-meta-item-icon><i class="far fa-folder"></i> </span><span class=post-meta-item-text>分类于</span> <span itemprop=about itemscope itemtype=http://schema.org/Thing><a href=/categories/%E7%AE%97%E6%B3%95/ itemprop=url rel=index><span itemprop=name>算法</span></a> </span></span><span class="post-meta-item leancloud_visitors" data-flag-title=向量数据库学习基础之跳表 id=/2024/06/16/%E5%90%91%E9%87%8F%E6%95%B0%E6%8D%AE%E5%BA%93%E5%AD%A6%E4%B9%A0%E5%9F%BA%E7%A1%80%E4%B9%8B%E8%B7%B3%E8%A1%A8/ title=阅读次数><span class=post-meta-item-icon><i class="far fa-eye"></i> </span><span class=post-meta-item-text>阅读次数：</span> <span class=leancloud-visitors-count></span> </span><span class=post-meta-item><span class=post-meta-item-icon><i class="far fa-comment"></i> </span><span class=post-meta-item-text>Disqus：</span> <a href=/2024/06/16/%E5%90%91%E9%87%8F%E6%95%B0%E6%8D%AE%E5%BA%93%E5%AD%A6%E4%B9%A0%E5%9F%BA%E7%A1%80%E4%B9%8B%E8%B7%B3%E8%A1%A8/#disqus_thread itemprop=discussionUrl title=disqus><span class="post-comments-count disqus-comment-count" data-disqus-identifier=2024/06/16/向量数据库学习基础之跳表/ itemprop=commentCount></span></a></span></div></div></header><div class=post-body itemprop=articleBody><p>在学习向量数据库的时候，发现检索的算法 <code>HNSW</code> 是个比较重要且核心的概念，直接学习（面向小白）可能有一定的门槛，所以我们先通过常见算法的跳表来做个引入<br>跳表的前置基础就是最常见的序列结构之一的链表，链表的特点是添加插入元素效率非常高，查询检索则需要线性复杂度，比如Java中的hashmap，在jdk1.8以后就把<br>单纯链表的结构改成了链表和红黑树结合的方式，因为当链表比较长的时候，线性时间复杂度也是个比较慢的方法相比对数时间复杂度，而对于链表，也有直接在它基础<br>优化而来的跳表结构，跳表是在链表的基础上引入了分层的概念，通过投硬币概率来决定是否生成新层，先用比较通俗的话来讲一下我的理解<br>因为链表查找只能从前往后一个一个找（单向链表），那么有没有办法可以跳过一些，加速我的查找，那么引入了分层的结构，在更上层以更稀疏的数据链表来索引数据，<br>举个例子，我原来是一个<figure class="highlight plaintext"><table><tr><td class=gutter><pre><span class=line>1</span><br></pre><td class=code><pre><span class=line>1 --> 2 --> 3 --> 4 --> 5 --> 6 --> 7 --> 8 --> 9 </span><br></pre></table></figure><p>这样的链表，我要查找8个元素是否存在，那我需要查找八次才能找到<br>如果我把结构改成<figure class="highlight plaintext"><table><tr><td class=gutter><pre><span class=line>1</span><br><span class=line>2</span><br><span class=line>3</span><br></pre><td class=code><pre><span class=line>1 --------------> 4 --------------> 7 ---------> null </span><br><span class=line>| | |</span><br><span class=line>1 --> 2 --> 3 --> 4 --> 5 --> 6 --> 7 --> 8 --> 9 --> null</span><br></pre></table></figure><p>变成这样的结构，我现在第一层找最后一个比8小的元素，就是7，然后再到下一层查找，这样我的查找路径就是 <code>1 --> 4 --> 7 --> 8</code> 速度加快了一倍<br>直观来说这样是能够提升很多查询效率，但是具体怎么实现我们也来看一下<br>首先定义个简单的Node<figure class="highlight java"><table><tr><td class=gutter><pre><span class=line>1</span><br><span class=line>2</span><br><span class=line>3</span><br><span class=line>4</span><br><span class=line>5</span><br><span class=line>6</span><br><span class=line>7</span><br><span class=line>8</span><br><span class=line>9</span><br></pre><td class=code><pre><span class=line><span class=keyword>public</span> <span class=keyword>class</span> <span class="title class_">Node</span> {</span><br><span class=line> <span class=keyword>public</span> <span class=type>int</span> <span class=variable>data</span> <span class=operator>=</span> -<span class=number>1</span>;</span><br><span class=line></span><br><span class=line> <span class=keyword>public</span> Node[] forwards;</span><br><span class=line></span><br><span class=line> <span class=keyword>public</span> <span class="title function_">Node</span><span class=params>(<span class=type>int</span> level)</span> {</span><br><span class=line> forwards = <span class=keyword>new</span> <span class="title class_">Node</span>[level];</span><br><span class=line> }</span><br><span class=line>}</span><br></pre></table></figure><p>接下去是SkipList的主体结构<figure class="highlight java"><table><tr><td class=gutter><pre><span class=line>1</span><br><span class=line>2</span><br><span class=line>3</span><br><span class=line>4</span><br><span class=line>5</span><br><span class=line>6</span><br><span class=line>7</span><br><span class=line>8</span><br></pre><td class=code><pre><span class=line><span class=keyword>public</span> <span class=keyword>class</span> <span class="title class_">SkipList</span> {</span><br><span class=line> <span class=keyword>private</span> <span class=keyword>static</span> <span class=keyword>final</span> <span class=type>int</span> <span class=variable>MAX_LEVEL</span> <span class=operator>=</span> <span class=number>16</span>;</span><br><span class=line></span><br><span class=line> <span class=keyword>private</span> <span class=type>int</span> <span class=variable>currentLevel</span> <span class=operator>=</span> <span class=number>0</span>;</span><br><span class=line></span><br><span class=line> <span class=keyword>private</span> <span class=type>Node</span> <span class=variable>head</span> <span class=operator>=</span> <span class=keyword>new</span> <span class="title class_">Node</span>(MAX_LEVEL);</span><br><span class=line></span><br><span class=line> <span class=keyword>private</span> <span class=type>Random</span> <span class=variable>random</span> <span class=operator>=</span> <span class=keyword>new</span> <span class="title class_">Random</span>();</span><br></pre></table></figure><p>包含最大层数，当前层数，头结点，跟随机值<br>生成随机层数参考了redis的zset实现方法<figure class="highlight java"><table><tr><td class=gutter><pre><span class=line>1</span><br><span class=line>2</span><br><span class=line>3</span><br><span class=line>4</span><br><span class=line>5</span><br><span class=line>6</span><br><span class=line>7</span><br></pre><td class=code><pre><span class=line><span class=keyword>private</span> <span class=type>int</span> <span class="title function_">generateRandomLevel</span><span class=params>()</span> {</span><br><span class=line> <span class=comment>// 参考redis sorted set 实现</span></span><br><span class=line> <span class=type>int</span> <span class=variable>level</span> <span class=operator>=</span> <span class=number>1</span>;</span><br><span class=line> <span class=keyword>while</span> ((random.nextInt() & <span class=number>0xFFFF</span>) < (<span class=number>0.25</span> * <span class=number>0xFFFF</span>))</span><br><span class=line> level += <span class=number>1</span>;</span><br><span class=line> <span class=keyword>return</span> Math.min(level, MAX_LEVEL);</span><br><span class=line> }</span><br></pre></table></figure><p>接下去先看下<h2 id=插入元素><a class=headerlink href=#插入元素 title=插入元素></a>插入元素</h2><figure class="highlight java"><table><tr><td class=gutter><pre><span class=line>1</span><br><span class=line>2</span><br><span class=line>3</span><br><span class=line>4</span><br><span class=line>5</span><br><span class=line>6</span><br><span class=line>7</span><br><span class=line>8</span><br><span class=line>9</span><br><span class=line>10</span><br><span class=line>11</span><br><span class=line>12</span><br><span class=line>13</span><br><span class=line>14</span><br><span class=line>15</span><br><span class=line>16</span><br><span class=line>17</span><br><span class=line>18</span><br><span class=line>19</span><br><span class=line>20</span><br><span class=line>21</span><br><span class=line>22</span><br><span class=line>23</span><br><span class=line>24</span><br><span class=line>25</span><br><span class=line>26</span><br><span class=line>27</span><br><span class=line>28</span><br><span class=line>29</span><br></pre><td class=code><pre><span class=line><span class=keyword>public</span> <span class=keyword>void</span> <span class="title function_">insert</span><span class=params>(<span class=type>int</span> value)</span> {</span><br><span class=line> <span class=type>int</span> <span class=variable>level</span> <span class=operator>=</span> generateRandomLevel();</span><br><span class=line> <span class=keyword>if</span> (level >= currentLevel) {</span><br><span class=line> currentLevel = level;</span><br><span class=line> }</span><br><span class=line></span><br><span class=line> <span class=type>Node</span> <span class=variable>newNode</span> <span class=operator>=</span> <span class=keyword>new</span> <span class="title class_">Node</span>(level);</span><br><span class=line> newNode.setData(value);</span><br><span class=line> Node[] update = <span class=keyword>new</span> <span class="title class_">Node</span>[level];</span><br><span class=line></span><br><span class=line> Arrays.fill(update, head);</span><br><span class=line></span><br><span class=line> <span class=type>Node</span> <span class=variable>p</span> <span class=operator>=</span> head;</span><br><span class=line></span><br><span class=line> <span class=keyword>for</span> (<span class=type>int</span> <span class=variable>i</span> <span class=operator>=</span> level - <span class=number>1</span>; i >= <span class=number>0</span>; --i) {</span><br><span class=line> <span class=comment>// 找到应该处在的位置，把前一元素记录为待更新</span></span><br><span class=line> <span class=keyword>while</span> (p.forwards[i] != <span class=literal>null</span> && p.forwards[i].data < value) {</span><br><span class=line> p = p.forwards[i];</span><br><span class=line> }</span><br><span class=line> <span class=comment>// 对应这一层，更新新的位置p</span></span><br><span class=line> update[i] = p;</span><br><span class=line> }</span><br><span class=line> </span><br><span class=line> <span class=comment>// 每一层都处理前后链接</span></span><br><span class=line> <span class=keyword>for</span> (<span class=type>int</span> <span class=variable>i</span> <span class=operator>=</span> <span class=number>0</span>; i < level; i++) {</span><br><span class=line> newNode.forwards[i] = update[i].forwards[i];</span><br><span class=line> update[i].forwards[i] = newNode;</span><br><span class=line> }</span><br><span class=line> }</span><br></pre></table></figure><p>看下图片演示,类似于链表的插入，但是需要处理每一层的前后链接<br><img data-src=https://img.nicksxs.com/blog/%E9%93%BE%E8%A1%A8.png><h2 id=查找元素><a class=headerlink href=#查找元素 title=查找元素></a>查找元素</h2><figure class="highlight java"><table><tr><td class=gutter><pre><span class=line>1</span><br><span class=line>2</span><br><span class=line>3</span><br><span class=line>4</span><br><span class=line>5</span><br><span class=line>6</span><br><span class=line>7</span><br><span class=line>8</span><br><span class=line>9</span><br><span class=line>10</span><br><span class=line>11</span><br><span class=line>12</span><br><span class=line>13</span><br><span class=line>14</span><br><span class=line>15</span><br><span class=line>16</span><br></pre><td class=code><pre><span class=line><span class=keyword>public</span> Node <span class="title function_">search</span><span class=params>(<span class=type>int</span> value)</span> {</span><br><span class=line> <span class=type>Node</span> <span class=variable>p</span> <span class=operator>=</span> head;</span><br><span class=line> <span class=comment>// 逐层找到比目标元素小的最后一个元素</span></span><br><span class=line> <span class=comment>// 然后再往下一层找</span></span><br><span class=line> <span class=keyword>for</span> (<span class=type>int</span> <span class=variable>i</span> <span class=operator>=</span> currentLevel - <span class=number>1</span>; i >= <span class=number>0</span> ; i--) {</span><br><span class=line> <span class=keyword>while</span> (p.forwards[i] != <span class=literal>null</span> && p.forwards[i].data < value) {</span><br><span class=line> p = p.forwards[i];</span><br><span class=line> }</span><br><span class=line> }</span><br><span class=line> <span class=comment>// 此时如果前一元素就是目标元素就返回该元素</span></span><br><span class=line> <span class=keyword>if</span> (p.forwards[<span class=number>0</span>] != <span class=literal>null</span> && p.forwards[<span class=number>0</span>].data == value) {</span><br><span class=line> <span class=keyword>return</span> p.forwards[<span class=number>0</span>];</span><br><span class=line> } <span class=keyword>else</span> {</span><br><span class=line> <span class=keyword>return</span> <span class=literal>null</span>;</span><br><span class=line> }</span><br><span class=line> }</span><br></pre></table></figure><p>也可以看下图里的演示，按红色的线寻找元素<br><img data-src=https://img.nicksxs.com/blog/UbOCGZ.png><h2 id=删除元素><a class=headerlink href=#删除元素 title=删除元素></a>删除元素</h2><figure class="highlight java"><table><tr><td class=gutter><pre><span class=line>1</span><br><span class=line>2</span><br><span class=line>3</span><br><span class=line>4</span><br><span class=line>5</span><br><span class=line>6</span><br><span class=line>7</span><br><span class=line>8</span><br><span class=line>9</span><br><span class=line>10</span><br><span class=line>11</span><br><span class=line>12</span><br><span class=line>13</span><br><span class=line>14</span><br><span class=line>15</span><br><span class=line>16</span><br><span class=line>17</span><br><span class=line>18</span><br><span class=line>19</span><br></pre><td class=code><pre><span class=line><span class=keyword>public</span> <span class=keyword>void</span> <span class="title function_">delete</span><span class=params>(<span class=type>int</span> value)</span> {</span><br><span class=line> Node[] update = <span class=keyword>new</span> <span class="title class_">Node</span>[currentLevel];</span><br><span class=line> <span class=type>Node</span> <span class=variable>p</span> <span class=operator>=</span> head;</span><br><span class=line> <span class=comment>// 找到待删除元素的前一元素</span></span><br><span class=line> <span class=keyword>for</span> (<span class=type>int</span> <span class=variable>i</span> <span class=operator>=</span> currentLevel - <span class=number>1</span>; i >= <span class=number>0</span>; i--) {</span><br><span class=line> <span class=keyword>while</span> (p.forwards[i] != <span class=literal>null</span> && p.forwards[i].data < value) {</span><br><span class=line> p = p.forwards[i];</span><br><span class=line> }</span><br><span class=line> update[i] = p;</span><br><span class=line> }</span><br><span class=line> <span class=comment>// 判断如果该层有这个元素就更新链接</span></span><br><span class=line> <span class=keyword>if</span> (p.forwards[<span class=number>0</span>] != <span class=literal>null</span> && p.forwards[<span class=number>0</span>].data == value) {</span><br><span class=line> <span class=keyword>for</span> (<span class=type>int</span> <span class=variable>i</span> <span class=operator>=</span> currentLevel - <span class=number>1</span>; i >= <span class=number>0</span>; i--) {</span><br><span class=line> <span class=keyword>if</span> (update[i].forwards[i] != <span class=literal>null</span> && update[i].forwards[i].data == value) {</span><br><span class=line> update[i].forwards[i] = update[i].forwards[i].forwards[i];</span><br><span class=line> }</span><br><span class=line> }</span><br><span class=line> }</span><br><span class=line> }</span><br></pre></table></figure><p>删除操作就类似于插入操作。了解了跳表原理以后其实<code>HNSW</code>就是个在空间层面的跳表</div><footer class=post-footer><div class=post-eof></div></footer></article></div><div class=post-block><article class=post-content itemscope itemtype=http://schema.org/Article><link href=https://nicksxs.me/2024/06/02/%E7%BB%99%E5%B1%80%E5%9F%9F%E7%BD%91%E4%B8%AD%E7%9A%84Ubuntu%E5%9B%BA%E5%AE%9A%E4%B8%8Bip/ itemprop=mainEntityOfPage><span hidden itemprop=author itemscope itemtype=http://schema.org/Person><meta content=/uploads/avatar.jpg itemprop=image><meta content=Nicksxs itemprop=name></span><span hidden itemprop=publisher itemscope itemtype=http://schema.org/Organization><meta content="Nicksxs's Blog" itemprop=name><meta content="learn from zero,技术博客，Nicksxs，史学森" itemprop=description></span><span hidden itemprop=post itemscope itemtype=http://schema.org/CreativeWork><meta content="undefined | Nicksxs's Blog" itemprop=name><meta itemprop=description></span><header class=post-header><h2 itemprop="name headline" class=post-title><a class=post-title-link href=/2024/06/02/%E7%BB%99%E5%B1%80%E5%9F%9F%E7%BD%91%E4%B8%AD%E7%9A%84Ubuntu%E5%9B%BA%E5%AE%9A%E4%B8%8Bip/ itemprop=url>给局域网中的Ubuntu固定下ip</a></h2><div class=post-meta-container><div class=post-meta><span class=post-meta-item><span class=post-meta-item-icon><i class="far fa-calendar"></i> </span><span class=post-meta-item-text>发表于</span> <time itemprop="dateCreated datePublished" title="创建时间：2024-06-02 23:32:18 / 修改时间：23:32:28" datetime=2024-06-02T23:32:18+08:00>2024-06-02</time> </span><span class=post-meta-item><span class=post-meta-item-icon><i class="far fa-folder"></i> </span><span class=post-meta-item-text>分类于</span> <span itemprop=about itemscope itemtype=http://schema.org/Thing><a href=/categories/linux/ itemprop=url rel=index><span itemprop=name>linux</span></a> </span></span><span class="post-meta-item leancloud_visitors" data-flag-title=给局域网中的Ubuntu固定下ip id=/2024/06/02/%E7%BB%99%E5%B1%80%E5%9F%9F%E7%BD%91%E4%B8%AD%E7%9A%84Ubuntu%E5%9B%BA%E5%AE%9A%E4%B8%8Bip/ title=阅读次数><span class=post-meta-item-icon><i class="far fa-eye"></i> </span><span class=post-meta-item-text>阅读次数：</span> <span class=leancloud-visitors-count></span> </span><span class=post-meta-item><span class=post-meta-item-icon><i class="far fa-comment"></i> </span><span class=post-meta-item-text>Disqus：</span> <a href=/2024/06/02/%E7%BB%99%E5%B1%80%E5%9F%9F%E7%BD%91%E4%B8%AD%E7%9A%84Ubuntu%E5%9B%BA%E5%AE%9A%E4%B8%8Bip/#disqus_thread itemprop=discussionUrl title=disqus><span class="post-comments-count disqus-comment-count" data-disqus-identifier=2024/06/02/给局域网中的Ubuntu固定下ip/ itemprop=commentCount></span></a></span></div></div></header><div class=post-body itemprop=articleBody><p>将一个小点，在局域网中包括类似于homelab的或者仅仅只是搭一个用来当实验环境的，在局域网内机器比较少的时候大部分DHCP会给分配相同的ip，但是这不是一定的，当机器比较多，并且上下线比较频繁时就会出现ip地址变动，这对于一些使用场景比较讨厌，所以我想把ip固定下来，先简单引用下DHCP的原理，他分为下面几个阶段<h3 id=DHCP发现（DISCOVER）><a class=headerlink href=#DHCP发现（DISCOVER） title=DHCP发现（DISCOVER）></a>DHCP发现（DISCOVER）</h3><p>client在物理子网上发送广播来寻找可用的服务器。网络管理员可以配置一个本地路由来转发DHCP包给另一个子网上的DHCP服务器。该client实现生成一个目的地址为255.255.255.255或者一个子网广播地址的UDP包。<p>客户也可以申请它使用的最后一个IP地址（在下面的例子里为192.168.1.100）。如果该客户所在的网络中此IP仍然可用，服务器就可以准许该申请。否则，就要看该服务器是授权的还是非授权的。授权服务器会拒绝请求，使得客户立刻申请一个新的IP。非授权服务器仅仅忽略掉请求，导致一个客户端请求的超时，于是客户端就会放弃此请求而去申请一个新的IP地址。<h3 id=DHCP提供（OFFER）><a class=headerlink href=#DHCP提供（OFFER） title=DHCP提供（OFFER）></a>DHCP提供（OFFER）</h3><p>当DHCP服务器收到一个来自客户的IP租约请求时，它会提供一个IP租约。DHCP为客户保留一个IP地址，然后通过网络单播一个DHCPOFFER消息给客户。该消息包含客户的MAC地址、服务器提供的IP地址、子网掩码、租期以及提供IP的DHCP服务器的IP。<p>服务器基于在CHADDR字段指定的客户硬件地址来检查配置。这里的服务器，192.168.1.1，将IP地址指定于YIADDR字段。<h3 id=DHCP请求（REQUEST）><a class=headerlink href=#DHCP请求（REQUEST） title=DHCP请求（REQUEST）></a>DHCP请求（REQUEST）</h3><p>当客户PC收到一个IP租约提供时，它必须告诉所有其他的DHCP服务器它已经接受了一个租约提供。因此，该客户会发送一个DHCPREQUEST消息，其中包含提供租约的服务器的IP。当其他DHCP服务器收到了该消息后，它们会收回所有可能已提供给该客户的租约。然后它们把曾经给该客户保留的那个地址重新放回到可用地址池中，这样，它们就可以为其他计算机分配这个地址。任意数量的DHCP服务器都可以响应同一个IP租约请求，但是每一个客户网卡只能接受一个租约提供。<h3 id=DHCP确认（Acknowledge，ACK）><a class=headerlink href=#DHCP确认（Acknowledge，ACK） title=DHCP确认（Acknowledge，ACK）></a>DHCP确认（Acknowledge，ACK）</h3><p>当DHCP服务器收到来自客户的REQUEST消息后，它就开始了配置过程的最后阶段。这个响应阶段包括发送一个DHCPACK包给客户。这个包包含租期和客户可能请求的其他所有配置信息。这时候，TCP/IP配置过程就完成了。<p>该服务器响应请求并发送响应给客户。整个系统期望客户来根据选项来配置其网卡。<h3 id=DHCP释放（RELEASE）><a class=headerlink href=#DHCP释放（RELEASE） title=DHCP释放（RELEASE）></a>DHCP释放（RELEASE）</h3><p>客户端向DHCP服务器发送一个请求以释放DHCP资源，并注销其IP地址。鉴于客户端更多的时候并不清楚何时用户会将其从网络中移除，此协议不会托管“DHCP释放的发送”。<h3 id=DHCP-NAK><a title="DHCP NAK" class=headerlink href=#DHCP-NAK></a>DHCP NAK</h3><p>服务器回复客户，客户要求的IP不能被分配。<h1 id=Ubuntu><a class=headerlink href=#Ubuntu title=Ubuntu></a>Ubuntu</h1><p>而对于Ubuntu，现在较新版本的设置方式也有点变化，比如我用的是22.04<figure class="highlight shell"><table><tr><td class=gutter><pre><span class=line>1</span><br></pre><td class=code><pre><span class=line>cd /etc/netplan/</span><br></pre></table></figure><p>先去这个目录下查看配置文件<br>我们要找的是这个 <code>00-installer-config.yaml</code> 文件<br><img data-src=https://img.nicksxs.com/blog/2vQ0nG.png><br>原本的是长这样<br><img data-src=https://img.nicksxs.com/blog/pHOYwe.png><br>默认是通过dhcp分配ip<br>我们要改成静态ip<figure class="highlight yaml"><table><tr><td class=gutter><pre><span class=line>1</span><br><span class=line>2</span><br><span class=line>3</span><br><span class=line>4</span><br><span class=line>5</span><br><span class=line>6</span><br><span class=line>7</span><br><span class=line>8</span><br><span class=line>9</span><br><span class=line>10</span><br><span class=line>11</span><br><span class=line>12</span><br></pre><td class=code><pre><span class=line><span class=attr>network:</span></span><br><span class=line> <span class=attr>renderer:</span> <span class=string>networkd</span></span><br><span class=line> <span class=attr>ethernets:</span></span><br><span class=line> <span class=attr>ens33:</span></span><br><span class=line> <span class=attr>addresses:</span></span><br><span class=line> <span class=bullet>-</span> <span class=number>192.168</span><span class=number>.1</span><span class=string>.xx/24</span></span><br><span class=line> <span class=attr>nameservers:</span></span><br><span class=line> <span class=attr>addresses:</span> [<span class=number>114.114</span><span class=number>.114</span><span class=number>.114</span>, <span class=number>233.5</span><span class=number>.5</span><span class=number>.5</span>]</span><br><span class=line> <span class=attr>routes:</span></span><br><span class=line> <span class=bullet>-</span> <span class=attr>to:</span> <span class=string>default</span></span><br><span class=line> <span class=attr>via:</span> <span class=number>192.168</span><span class=number>.1</span><span class=number>.1</span></span><br><span class=line> <span class=attr>version:</span> <span class=number>2</span></span><br></pre></table></figure><p>解释一下 ethernets中的ens33表示我们的网卡接口的标识<br>可以通过 <code>ip addr</code> 查看<br><img data-src=https://img.nicksxs.com/blog/1gipDk.png><br>第一个是本地回环，第二个可以看下是否跟内网ip对应上，如果是的话就这个ens33<br>然后就是addresses填的地址，就是我们想要固定的ip地址，记得得是自己局域网网段的<br>上面只是个示例，然后是nameservers里的是dns服务器，也是按需填写<br>这里的114.114.114.114跟233.5.5.5分别是电信跟阿里云的，仅供参考<br>然后是routes就是网关地址，按自己的环境填写，网络没有任何特殊处理的一般就是路由器<br>接下去就是应用这个配置<figure class="highlight shell"><table><tr><td class=gutter><pre><span class=line>1</span><br></pre><td class=code><pre><span class=line>sudo netplan apply</span><br></pre></table></figure><p>这样ip配置就生效了<br>可以通过<br><code>ip addr show ens33</code>查看</div><footer class=post-footer><div class=post-eof></div></footer></article></div><div class=post-block><article class=post-content itemscope itemtype=http://schema.org/Article><link href=https://nicksxs.me/2024/05/26/Headscale%E6%B8%90%E5%85%A5%E4%BD%B3%E5%A2%83%E8%A1%A5%E5%85%85%E7%AF%87-%E8%87%AA%E5%AE%9A%E4%B9%89%E4%B8%AD%E8%BD%ACderper%E7%9A%84%E8%AF%81%E4%B9%A6%E9%97%AE%E9%A2%98/ itemprop=mainEntityOfPage><span hidden itemprop=author itemscope itemtype=http://schema.org/Person><meta content=/uploads/avatar.jpg itemprop=image><meta content=Nicksxs itemprop=name></span><span hidden itemprop=publisher itemscope itemtype=http://schema.org/Organization><meta content="Nicksxs's Blog" itemprop=name><meta content="learn from zero,技术博客，Nicksxs，史学森" itemprop=description></span><span hidden itemprop=post itemscope itemtype=http://schema.org/CreativeWork><meta content="undefined | Nicksxs's Blog" itemprop=name><meta itemprop=description></span><header class=post-header><h2 itemprop="name headline" class=post-title><a class=post-title-link href=/2024/05/26/Headscale%E6%B8%90%E5%85%A5%E4%BD%B3%E5%A2%83%E8%A1%A5%E5%85%85%E7%AF%87-%E8%87%AA%E5%AE%9A%E4%B9%89%E4%B8%AD%E8%BD%ACderper%E7%9A%84%E8%AF%81%E4%B9%A6%E9%97%AE%E9%A2%98/ itemprop=url>Headscale渐入佳境补充篇-自定义中转derper的证书问题</a></h2><div class=post-meta-container><div class=post-meta><span class=post-meta-item><span class=post-meta-item-icon><i class="far fa-calendar"></i> </span><span class=post-meta-item-text>发表于</span> <time itemprop="dateCreated datePublished" title="创建时间：2024-05-26 23:32:56" datetime=2024-05-26T23:32:56+08:00>2024-05-26</time> </span><span class=post-meta-item><span class=post-meta-item-icon><i class="far fa-folder"></i> </span><span class=post-meta-item-text>分类于</span> <span itemprop=about itemscope itemtype=http://schema.org/Thing><a href=/categories/headscale/ itemprop=url rel=index><span itemprop=name>headscale</span></a> </span></span><span class="post-meta-item leancloud_visitors" data-flag-title=Headscale渐入佳境补充篇-自定义中转derper的证书问题 id=/2024/05/26/Headscale%E6%B8%90%E5%85%A5%E4%BD%B3%E5%A2%83%E8%A1%A5%E5%85%85%E7%AF%87-%E8%87%AA%E5%AE%9A%E4%B9%89%E4%B8%AD%E8%BD%ACderper%E7%9A%84%E8%AF%81%E4%B9%A6%E9%97%AE%E9%A2%98/ title=阅读次数><span class=post-meta-item-icon><i class="far fa-eye"></i> </span><span class=post-meta-item-text>阅读次数：</span> <span class=leancloud-visitors-count></span> </span><span class=post-meta-item><span class=post-meta-item-icon><i class="far fa-comment"></i> </span><span class=post-meta-item-text>Disqus：</span> <a href=/2024/05/26/Headscale%E6%B8%90%E5%85%A5%E4%BD%B3%E5%A2%83%E8%A1%A5%E5%85%85%E7%AF%87-%E8%87%AA%E5%AE%9A%E4%B9%89%E4%B8%AD%E8%BD%ACderper%E7%9A%84%E8%AF%81%E4%B9%A6%E9%97%AE%E9%A2%98/#disqus_thread itemprop=discussionUrl title=disqus><span class="post-comments-count disqus-comment-count" data-disqus-identifier=2024/05/26/Headscale渐入佳境补充篇-自定义中转derper的证书问题/ itemprop=commentCount></span></a></span></div></div></header><div class=post-body itemprop=articleBody><p>之前自定义部署的derper在Mac端和Windows使用时没啥问题，但是在我想作为网关的Armbian小机器上一直会报 “x509: certificate signed by unknown authority”<br>错误，原因在于之前在通过acme生成证书以后我是直接把cer证书重命名成crt就映射到derper的docker目录里，对于Mac和Windows客户端应该是有兼容逻辑，而实际使用需要完整的证书去识别认证机构，否则就会被认为是自定义证书，在一些常规的证书认证逻辑里就会报上面的问题<br>这边需要先把生成的 <code>fullchain.cer</code> 完整证书转成crt格式的<figure class="highlight shell"><table><tr><td class=gutter><pre><span class=line>1</span><br></pre><td class=code><pre><span class=line>openssl x509 -inform PEM -in fullchain.cer -out derper.demo.com.crt</span><br></pre></table></figure><p>这边是PEM格式的证书，如果是DER的话就改一下<figure class="highlight shell"><table><tr><td class=gutter><pre><span class=line>1</span><br></pre><td class=code><pre><span class=line>openssl x509 -inform DER -in certificate.cer -out certificate.crt</span><br></pre></table></figure><p>转换完成后就重新启动下docker<br>这里的原因主要是fullchain.cer是包含了完整的证书链，而ca.cer只是包含用户证书，所以需要替换一下，这算是个小问题</div><footer class=post-footer><div 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