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  189. <h1 class="post-title" itemprop="name headline">
  190. <a href="/2020/03/04/computer/" class="post-title-link" itemprop="url">How do computers work?</a>
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  210. <h3 id="introduction"><a class="markdownIt-Anchor" href="#introduction"></a> Introduction</h3>
  211. <p>We all know computers, and we basically know how to use it, but we have no idea about how does it work.</p>
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  245. <h1 class="post-title" itemprop="name headline">
  246. <a href="/2020/03/02/segment-tree/" class="post-title-link" itemprop="url">线段树</a>
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  254. <time title="Created: 2020-Mar-02 11:37:36" itemprop="dateCreated datePublished" datetime="2020-03-02T11:37:36+08:00">2020-Mar-02</time>
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  260. <span class="post-meta-item-text">Edited on</span>
  261. <time title="Modified: 2020-Mar-06 18:43:32" itemprop="dateModified" datetime="2020-03-06T18:43:32+08:00">2020-Mar-06</time>
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  265. <div class="post-body" itemprop="articleBody">
  266. <h3 id="前置知识"><a class="markdownIt-Anchor" href="#前置知识"></a> 前置知识</h3>
  267. <p>数组,结构体,二叉树</p>
  268. <h3 id="引入"><a class="markdownIt-Anchor" href="#引入"></a> 引入</h3>
  269. <p>有时候我们会遇到一些大规模的区间查找和区间修改问题,比如让你维护一个 <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mn>1</mn><msup><mn>0</mn><mn>5</mn></msup></mrow><annotation encoding="application/x-tex">10^5</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8141079999999999em;vertical-align:0em;"></span><span class="mord">1</span><span class="mord"><span class="mord">0</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">5</span></span></span></span></span></span></span></span></span></span></span> 长度的数列,要求操作有区间求和、区间加(区间每个数加上一个值),让你在一秒内完成 <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mn>1</mn><msup><mn>0</mn><mn>5</mn></msup></mrow><annotation encoding="application/x-tex">10^5</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8141079999999999em;vertical-align:0em;"></span><span class="mord">1</span><span class="mord"><span class="mord">0</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">5</span></span></span></span></span></span></span></span></span></span></span> 次操作。<br />
  270. 暴力是肯定不行的,数据范围太大,操作太多,会超时。<br />
  271. 所以我们就有一种专门解决大范围区间修改查询的数据结构:线段树。</p>
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  305. <h1 class="post-title" itemprop="name headline">
  306. <a href="/2020/03/02/ferbonacci/" class="post-title-link" itemprop="url">斐波那契数列-O(1)</a>
  307. </h1>
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  313. <span class="post-meta-item-text">Posted on</span>
  314. <time title="Created: 2020-Mar-02 11:35:44" itemprop="dateCreated datePublished" datetime="2020-03-02T11:35:44+08:00">2020-Mar-02</time>
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  316. <span class="post-meta-item">
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  319. </span>
  320. <span class="post-meta-item-text">Edited on</span>
  321. <time title="Modified: 2020-Mar-03 20:40:56" itemprop="dateModified" datetime="2020-03-03T20:40:56+08:00">2020-Mar-03</time>
  322. </span>
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  325. <div class="post-body" itemprop="articleBody">
  326. <p>引自:《信息学奥赛之-数学一本通》<br />
  327. 揍是这样:</p>
  328. <p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">F</mi><mo>⁡</mo><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo><mo>=</mo><mfrac><msqrt><mn>5</mn></msqrt><mn>5</mn></mfrac><mo>⋅</mo><mrow><mo fence="true">[</mo><msup><mrow><mo fence="true">(</mo><mn>1</mn><mo>+</mo><msqrt><mn>5</mn></msqrt><mo fence="true">)</mo></mrow><mi>n</mi></msup><mo>−</mo><msup><mrow><mo fence="true">(</mo><mn>1</mn><mo>−</mo><msqrt><mn>5</mn></msqrt><mo fence="true">)</mo></mrow><mi>n</mi></msup><mo fence="true">]</mo></mrow></mrow><annotation encoding="application/x-tex">\operatorname{F}(n)=\dfrac{\sqrt{5}}{5}\cdot\left[\left(1+\sqrt{5}\right)^n-\left(1-\sqrt{5}\right)^n\right]
  329. </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mop"><span class="mord mathrm">F</span></span><span class="mopen">(</span><span class="mord mathdefault">n</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:2.27022em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.5842200000000002em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">5</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.90722em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style="padding-left:0.833em;"><span class="mord">5</span></span></span><span style="top:-2.86722em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail" style="min-width:0.853em;height:1.08em;"><svg width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,
  330. -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,
  331. -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,
  332. 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,
  333. -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467
  334. s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422
  335. s-65,47,-65,47z M834 80H400000v40H845z'/></svg></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.13278em;"><span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1.854312em;vertical-align:-0.65002em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size2">[</span></span><span class="minner"><span class="minner"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size2">(</span></span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.956095em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style="padding-left:0.833em;"><span class="mord">5</span></span></span><span style="top:-2.916095em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail" style="min-width:0.853em;height:1.08em;"><svg width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,
  336. -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,
  337. -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,
  338. 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,
  339. -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467
  340. s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422
  341. s-65,47,-65,47z M834 80H400000v40H845z'/></svg></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.08390500000000001em;"><span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em;"><span class="delimsizing size2">)</span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:1.204292em;"><span style="top:-3.6029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="minner"><span class="minner"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size2">(</span></span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.956095em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style="padding-left:0.833em;"><span class="mord">5</span></span></span><span style="top:-2.916095em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail" style="min-width:0.853em;height:1.08em;"><svg width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,
  342. -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,
  343. -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,
  344. 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,
  345. -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467
  346. s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422
  347. s-65,47,-65,47z M834 80H400000v40H845z'/></svg></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.08390500000000001em;"><span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em;"><span class="delimsizing size2">)</span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:1.204292em;"><span style="top:-3.6029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em;"><span class="delimsizing size2">]</span></span></span></span></span></span></span></p>
  348. <p>代码揍这么简单:</p>
  349. <figure class="highlight cpp"><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><td class="code"><pre><span class="line"><span class="function"><span class="keyword">int</span> <span class="title">ferbo</span><span class="params">(<span class="keyword">int</span> n)</span></span>&#123;</span><br><span class="line"> <span class="keyword">return</span> (<span class="built_in">sqrt</span>(<span class="number">5</span>)/<span class="number">5</span>)*(<span class="built_in">pow</span>((<span class="number">1</span>+<span class="built_in">sqrt</span>(<span class="number">5</span>))/<span class="number">2</span>,n)-<span class="built_in">pow</span>((<span class="number">1</span>-<span class="built_in">sqrt</span>(<span class="number">5</span>))/<span class="number">2</span>,n));</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
  350. <p>要是再加个快速幂就更棒了(够快了,懒得写)</p>
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  377. <h1 class="post-title" itemprop="name headline">
  378. <a href="/2020/03/02/dinic/" class="post-title-link" itemprop="url">网络最大流-Dinic</a>
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  386. <time title="Created: 2020-Mar-02 11:31:22" itemprop="dateCreated datePublished" datetime="2020-03-02T11:31:22+08:00">2020-Mar-02</time>
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  392. <span class="post-meta-item-text">Edited on</span>
  393. <time title="Modified: 2020-Mar-03 20:41:19" itemprop="dateModified" datetime="2020-03-03T20:41:19+08:00">2020-Mar-03</time>
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  397. <div class="post-body" itemprop="articleBody">
  398. <h3 id="前置知识"><a class="markdownIt-Anchor" href="#前置知识"></a> 前置知识</h3>
  399. <p>存图方式(<a href="http://baidu.physton.com/?q=%E9%82%BB%E6%8E%A5%E8%A1%A8" target="_blank" rel="noopener" title="简单">邻接表</a>,<a href="http://baidu.physton.com/?q=%E9%82%BB%E6%8E%A5%E7%9F%A9%E9%98%B5" target="_blank" rel="noopener" title="都太简单了">邻接矩阵</a>),图的遍历(<a href="http://baidu.physton.com/?q=dfs" target="_blank" rel="noopener" title="简单">dfs</a>,<a href="http://baidu.physton.com/?q=bfs" target="_blank" rel="noopener" title="简单">bfs</a>)</p>
  400. <h3 id="引入"><a class="markdownIt-Anchor" href="#引入"></a> 引入</h3>
  401. <p>我们举个例子吧:<br />
  402. 有一个毒瘤水管工,他会造水管,有一天他造了一个水管网络,就像一个图。其中有一个点只有出边,就是起点,还有一个点只有入边,是终点。<br />
  403. 点之间有一些管子,这些管子都有单位时间内的容量,现在毒瘤水管工想知道,他的管子在<strong>单位时间内</strong>在起点终点之间最多能流多少水。</p>
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  437. <h1 class="post-title" itemprop="name headline">
  438. <a href="/2020/03/01/min-span-tree/" class="post-title-link" itemprop="url">最小生成树</a>
  439. </h1>
  440. <div class="post-meta">
  441. <span class="post-meta-item">
  442. <span class="post-meta-item-icon">
  443. <i class="fa fa-calendar-o"></i>
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  452. <span class="post-meta-item-text">Edited on</span>
  453. <time title="Modified: 2020-Mar-05 21:16:57" itemprop="dateModified" datetime="2020-03-05T21:16:57+08:00">2020-Mar-05</time>
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  457. <div class="post-body" itemprop="articleBody">
  458. <h3 id="前置知识"><a class="markdownIt-Anchor" href="#前置知识"></a> 前置知识</h3>
  459. <p>存图方式(<a href="http://baidu.physton.com/?q=%E9%82%BB%E6%8E%A5%E8%A1%A8" target="_blank" rel="noopener" title="简单">邻接表</a>,<a href="http://baidu.physton.com/?q=%E9%82%BB%E6%8E%A5%E7%9F%A9%E9%98%B5" target="_blank" rel="noopener" title="都太简单了,没有一个打得过的">邻接矩阵</a>),<a href="https://schtonn.github.io/2020/03/01/union-find">并查集</a>。<br />
  460. 不会的快进入链接学习吧!</p>
  461. <h3 id="引入"><a class="markdownIt-Anchor" href="#引入"></a> 引入</h3>
  462. <p>生成树,就是从一个图中选中<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">n-1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.66666em;vertical-align:-0.08333em;"></span><span class="mord mathdefault">n</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">1</span></span></span></span>条边,使得这些边构成一棵树,并包含图中的所有节点。<br />
  463. 最小生成树,就是找到一种生成树,使得这个生成树的边权和最小。</p>
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  497. <h1 class="post-title" itemprop="name headline">
  498. <a href="/2020/03/01/union-find/" class="post-title-link" itemprop="url">并查集</a>
  499. </h1>
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  505. <span class="post-meta-item-text">Posted on</span>
  506. <time title="Created: 2020-Mar-01 22:44:33" itemprop="dateCreated datePublished" datetime="2020-03-01T22:44:33+08:00">2020-Mar-01</time>
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  512. <span class="post-meta-item-text">Edited on</span>
  513. <time title="Modified: 2020-Mar-03 20:39:35" itemprop="dateModified" datetime="2020-03-03T20:39:35+08:00">2020-Mar-03</time>
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  518. <h3 id="前置知识"><a class="markdownIt-Anchor" href="#前置知识"></a> 前置知识</h3>
  519. <p>哈哈,简单到爆,没有。</p>
  520. <h3 id="引入"><a class="markdownIt-Anchor" href="#引入"></a> 引入</h3>
  521. <p>并查集是一种快到爆炸的集合算法,可以进行两项基本操作:合并两个集合(并)、查询两个参数是否在一个集合内(查)。这也是它名字的由来。</p>
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  564. <time title="Created: 2020-Mar-01 22:41:02" itemprop="dateCreated datePublished" datetime="2020-03-01T22:41:02+08:00">2020-Mar-01</time>
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  576. <h3 id="前置知识"><a class="markdownIt-Anchor" href="#前置知识"></a> 前置知识</h3>
  577. <p>必备:存图方式(<a href="http://baidu.physton.com/?q=%E9%82%BB%E6%8E%A5%E8%A1%A8" target="_blank" rel="noopener" title="简单">邻接表</a>,<a href="http://baidu.physton.com/?q=%E9%82%BB%E6%8E%A5%E7%9F%A9%E9%98%B5" target="_blank" rel="noopener" title="都太简单了,没有一个打得过的">邻接矩阵</a>),<a href="http://baidu.physton.com/?q=dfs%E5%BA%8F" target="_blank" rel="noopener">dfs序</a>。<br />
  578. 维护:<a href="http://baidu.physton.com/?q=%E7%BA%BF%E6%AE%B5%E6%A0%91" target="_blank" rel="noopener">线段树</a>、<a href="http://baidu.physton.com/?q=%E6%A0%91%E7%8A%B6%E6%95%B0%E7%BB%84" target="_blank" rel="noopener">树状数组</a>、<a href="http://baidu.physton.com/?q=BST" target="_blank" rel="noopener">BST</a>。<br />
  579. 不会的快进入链接学习吧!</p>
  580. <h3 id="引入"><a class="markdownIt-Anchor" href="#引入"></a> 引入</h3>
  581. <p>树链剖分,简单来说就是把树分割成链,然后维护每一条链。一般的维护算法有线段树,树状数组和BST。复杂度为<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>O</mi><mo stretchy="false">(</mo><mi>l</mi><mi>o</mi><mi>g</mi><mi>n</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">O(log n)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathdefault" style="margin-right:0.02778em;">O</span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.01968em;">l</span><span class="mord mathdefault">o</span><span class="mord mathdefault" style="margin-right:0.03588em;">g</span><span class="mord mathdefault">n</span><span class="mclose">)</span></span></span></span>。</p>
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