http://xilyfeAAAA.github.io/series/%E8%AF%BE%E7%A8%8B%E7%AC%94%E8%AE%B0/ Recent content in 课程笔记 on 多辣加香菜 Hugo zh-CN Wed, 18 Mar 2026 01:01:16 +0800 http://xilyfeAAAA.github.io/posts/ustc-combinatorics-review/ Wed, 18 Mar 2026 10:52:02 +0800 http://xilyfeAAAA.github.io/posts/ustc-combinatorics-review/ <h2 id="鸽巢原理" class="headerLink"> <a href="#%e9%b8%bd%e5%b7%a2%e5%8e%9f%e7%90%86" class="header-mark"></a>鸽巢原理</h2><h3 id="定理" class="headerLink"> <a href="#%e5%ae%9a%e7%90%86" class="header-mark"></a>定理</h3><ol> <li>若有 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">n</span></span></span></span> 个笼子和 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><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:0.6667em;vertical-align:-0.0833em;"></span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1</span></span></span></span> 只鸽子，所有的鸽子都被关在鸽笼里，那么至少有一个笼子有至少 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2</mn></mrow><annotation encoding="application/x-tex">2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">2</span></span></span></span> 只鸽子。</li> <li>一堆实数 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>a</mi><mn>1</mn></msub><mo separator="true">,</mo><msub><mi>a</mi><mn>2</mn></msub><mo separator="true">,</mo><mo>…</mo><mo separator="true">,</mo><msub><mi>a</mi><mi>n</mi></msub></mrow><annotation encoding="application/x-tex">a_1,a_2,\ldots,a_n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord"><span class="mord mathnormal">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span> 若他们的平均值大于 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">x</span></span></span></span>，那么至少存在一个 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>a</mi><mi>i</mi></msub><mo>&gt;</mo><mi>x</mi></mrow><annotation encoding="application/x-tex">a_i&gt;x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6891em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">x</span></span></span></span>。</li> </ol> <h3 id="例题" class="headerLink"> <a href="#%e4%be%8b%e9%a2%98" class="header-mark"></a>例题</h3><blockquote> <p>任意 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><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:0.6667em;vertical-align:-0.0833em;"></span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1</span></span></span></span> 个整数中，必存在两个不同的数 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>a</mi></mrow><annotation encoding="application/x-tex">a</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">a</span></span></span></span>,<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>b</mi></mrow><annotation encoding="application/x-tex">b</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal">b</span></span></span></span>，使得 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi><mo>∣</mo><mi>a</mi><mo>−</mo><mi>b</mi></mrow><annotation encoding="application/x-tex">n\mid a - b</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 mathnormal">n</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">∣</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord mathnormal">a</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal">b</span></span></span></span>。</p> http://xilyfeAAAA.github.io/posts/ustc-db-review/ Tue, 13 Jan 2026 13:31:14 +0800 http://xilyfeAAAA.github.io/posts/ustc-db-review/ <div class="details admonition tip open"> <div class="details-summary admonition-title"> <span class="icon"><svg class="icon" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 352 512"><!-- Font Awesome Free 5.15.4 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) --><path d="M96.06 454.35c.01 6.29 1.87 12.45 5.36 17.69l17.09 25.69a31.99 31.99 0 0 0 26.64 14.28h61.71a31.99 31.99 0 0 0 26.64-14.28l17.09-25.69a31.989 31.989 0 0 0 5.36-17.69l.04-38.35H96.01l.05 38.35zM0 176c0 44.37 16.45 84.85 43.56 115.78 16.52 18.85 42.36 58.23 52.21 91.45.04.26.07.52.11.78h160.24c.04-.26.07-.51.11-.78 9.85-33.22 35.69-72.6 52.21-91.45C335.55 260.85 352 220.37 352 176 352 78.61 272.91-.3 175.45 0 73.44.31 0 82.97 0 176zm176-80c-44.11 0-80 35.89-80 80 0 8.84-7.16 16-16 16s-16-7.16-16-16c0-61.76 50.24-112 112-112 8.84 0 16 7.16 16 16s-7.16 16-16 16z"/></svg></span>复习提纲<span class="details-icon"><svg class="icon" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 256 512"><!-- Font Awesome Free 5.15.4 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) --><path d="M224.3 273l-136 136c-9.4 9.4-24.6 9.4-33.9 0l-22.6-22.6c-9.4-9.4-9.4-24.6 0-33.9l96.4-96.4-96.4-96.4c-9.4-9.4-9.4-24.6 0-33.9L54.3 103c9.4-9.4 24.6-9.4 33.9 0l136 136c9.5 9.4 9.5 24.6.1 34z"/></svg></span> </div> <div class="details-content"> <div class="admonition-content"><p><strong>第1章 概述</strong></p> http://xilyfeAAAA.github.io/posts/ustc-alg-review/ Thu, 08 Jan 2026 11:27:53 +0800 http://xilyfeAAAA.github.io/posts/ustc-alg-review/ <h2 id="第二章-算法初步" class="headerLink"> <a href="#%e7%ac%ac%e4%ba%8c%e7%ab%a0-%e7%ae%97%e6%b3%95%e5%88%9d%e6%ad%a5" class="header-mark"></a>第二章 算法初步</h2><h3 id="插入排序" class="headerLink"> <a href="#%e6%8f%92%e5%85%a5%e6%8e%92%e5%ba%8f" class="header-mark"></a>插入排序</h3><div class="code-block highlight is-open show-line-numbers tw-group tw-my-2"> <div class=" tw-flex tw-flex-row tw-flex-1 tw-justify-between tw-w-full tw-bg-bgColor-secondary "> <button class=" code-block-button tw-mx-2 tw-flex tw-flex-row tw-flex-1" aria-hidden="true"> <div class="group-[.is-open]:tw-rotate-90 tw-transition-[transform] tw-duration-500 tw-ease-in-out print:!tw-hidden tw-w-min tw-h-min tw-my-1 tw-mx-1"><svg class="icon" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 320 512"><!-- Font Awesome Free 5.15.4 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) --><path d="M285.476 272.971L91.132 467.314c-9.373 9.373-24.569 9.373-33.941 0l-22.667-22.667c-9.357-9.357-9.375-24.522-.04-33.901L188.505 256 34.484 101.255c-9.335-9.379-9.317-24.544.04-33.901l22.667-22.667c9.373-9.373 24.569-9.373 33.941 0L285.475 239.03c9.373 9.372 9.373 24.568.001 33.941z"/></svg></div> <p class="tw-select-none !tw-my-1">python</p> http://xilyfeAAAA.github.io/posts/cs336/ Wed, 17 Dec 2025 13:05:11 +0800 http://xilyfeAAAA.github.io/posts/cs336/ <h2 id="1-lecture-1" class="headerLink"> <a href="#1-lecture-1" class="header-mark"></a>1. Lecture 1</h2><p>!!! abstract 本节主要讲解常见的几种 Tokenizer 以及它们的优劣，最后介绍了 BPE 的实现思路。</p> <h3 id="11-tokenizer-主要类型" class="headerLink"> <a href="#11-tokenizer-%e4%b8%bb%e8%a6%81%e7%b1%bb%e5%9e%8b" class="header-mark"></a>1.1 Tokenizer 主要类型</h3><ol> <li> <p>Character-based</p> <ul> <li>优点：不会出现 Out of vocabulary 的情况</li> <li>缺点：词表大小爆炸，需要涵盖每一种语言的每一个字符</li> </ul> </li> <li> <p>Byte-based</p> http://xilyfeAAAA.github.io/posts/cs224n/ Sun, 30 Nov 2025 11:24:11 +0800 http://xilyfeAAAA.github.io/posts/cs224n/ <h2 id="1-lecture-1" class="headerLink"> <a href="#1-lecture-1" class="header-mark"></a>1. Lecture 1</h2><p> <div class="post-img-view"> <a data-fancybox="gallery" href="http://img.xilyfe.top/img/20260130144846647.png"> <img src="http://img.xilyfe.top/img/20260130144846647.png" alt="" /> </a> </div> </p> <h3 id="11-独热编码" class="headerLink"> <a href="#11-%e7%8b%ac%e7%83%ad%e7%bc%96%e7%a0%81" class="header-mark"></a>1.1 独热编码</h3><p>每个不同的向量代表一个单词，例如:</p> <div class="code-block highlight is-open show-line-numbers tw-group tw-my-2"> <div class=" tw-flex tw-flex-row tw-flex-1 tw-justify-between tw-w-full tw-bg-bgColor-secondary "> <button class=" code-block-button tw-mx-2 tw-flex tw-flex-row tw-flex-1" aria-hidden="true"> <div class="group-[.is-open]:tw-rotate-90 tw-transition-[transform] tw-duration-500 tw-ease-in-out print:!tw-hidden tw-w-min tw-h-min tw-my-1 tw-mx-1"><svg class="icon" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 320 512"><!-- Font Awesome Free 5.15.4 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) --><path d="M285.476 272.971L91.132 467.314c-9.373 9.373-24.569 9.373-33.941 0l-22.667-22.667c-9.357-9.357-9.375-24.522-.04-33.901L188.505 256 34.484 101.255c-9.335-9.379-9.317-24.544.04-33.901l22.667-22.667c9.373-9.373 24.569-9.373 33.941 0L285.475 239.03c9.373 9.372 9.373 24.568.001 33.941z"/></svg></div> <p class="tw-select-none !tw-my-1">text</p>