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Some bug fixes and improvements (#1063)
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* Prevent the line breaks of buttons on Safari

* Fix a math symbol

* Small improvements

* Bug fixes and improvements.
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krahets authored Jan 25, 2024
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2 changes: 1 addition & 1 deletion docs-en/index.md
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</div>

<div class="admonition quote">
<p align="center">"Knowledge increases by sharing."</p>
<p align="center">"Learning by teaching."</p>
</div>

---
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2 changes: 1 addition & 1 deletion docs/chapter_computational_complexity/space_complexity.md
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对数阶常见于分治算法。例如归并排序，输入长度为 $n$ 的数组，每轮递归将数组从中点处划分为两半，形成高度为 $\log n$ 的递归树，使用 $O(\log n)$ 栈帧空间。

再例如将数字转化为字符串，输入一个正整数 $n$ ，它的位数为 $\lfloor \log_{10} n \rfloor + 1$ ，即对应字符串长度为 $\lfloor \log_{10} n \rfloor + 1$ ，因此空间复杂度为 $O(\lfloor \log_{10} n \rfloor + 1) = O(\log n)$ 。
再例如将数字转化为字符串，输入一个正整数 $n$ ，它的位数为 $\lfloor \log_{10} n \rfloor + 1$ ，即对应字符串长度为 $\lfloor \log_{10} n \rfloor + 1$ ，因此空间复杂度为 $O(\log_{10} n + 1) = O(\log n)$ 。

## 权衡时间与空间

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2 changes: 1 addition & 1 deletion docs/chapter_sorting/insertion_sort.md
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插入排序的时间复杂度为 $O(n^2)$ ，而我们即将学习的快速排序的时间复杂度为 $O(n \log n)$ 。尽管插入排序的时间复杂度更高，**但在数据量较小的情况下，插入排序通常更快**。

这个结论与线性查找和二分查找的适用情况的结论类似。快速排序这类 $O(n \log n)$ 的算法属于基于分治策略的排序算法，往往包含更多单元计算操作。而在数据量较小时，$n^2$ 和 $n \log n$ 的数值比较接近，复杂度不占主导地位；每轮中的单元操作数量起到决定性作用。
这个结论与线性查找和二分查找的适用情况的结论类似。快速排序这类 $O(n \log n)$ 的算法属于基于分治策略的排序算法，往往包含更多单元计算操作。而在数据量较小时，$n^2$ 和 $n \log n$ 的数值比较接近，复杂度不占主导地位，每轮中的单元操作数量起到决定性作用。

实际上，许多编程语言（例如 Java）的内置排序函数采用了插入排序，大致思路为：对于长数组，采用基于分治策略的排序算法，例如快速排序；对于短数组，直接使用插入排序。

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46 changes: 23 additions & 23 deletions docs/index.md
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style="position: absolute; width: auto; height: 78.751%; left: 10.545%; top: 7.326%;">
<a href="/chapter_introduction/">
<img class="hero-on-hover" src="assets/hero/astronaut.png" style="height: 46.673%; left: 35.413%; top: 24.343%;">
<p class="hero-caption" style="left: 52.244%; top: 20.919%;">初识算法</p>
<span class="hero-caption" style="left: 52.244%; top: 20.919%;">初识算法</span>
</a>
<a href="/chapter_computational_complexity/">
<img class="hero-on-hover" src="assets/hero/chapter_computational_complexity.png"
style="height: 12.347%; left: 36.267%; top: 37.653%;">
<p class="hero-caption" style="left: 39.244%; top: 33.919%;">复杂度</p>
<span class="hero-caption" style="left: 39.244%; top: 33.919%;">复杂度</span>
</a>
<a href="/chapter_array_and_linkedlist/">
<img class="hero-on-hover" src="assets/hero/chapter_array_and_linkedlist.png"
style="height: 22.242%; left: 73.242%; top: 52.481%;">
<p class="hero-caption" style="left: 90.897%; top: 76.259%;">数组与链表</p>
<span class="hero-caption" style="left: 90.897%; top: 76.259%;">数组与链表</span>
</a>
<a href="/chapter_stack_and_queue/">
<img class="hero-on-hover" src="assets/hero/chapter_stack_and_queue.png"
style="height: 14.302%; left: 62.646%; top: 77.875%;">
<p class="hero-caption" style="left: 78.371%; top: 90.25%;">栈与队列</p>
<span class="hero-caption" style="left: 77.571%; top: 91.25%;">栈与队列</span>
</a>
<a href="/chapter_hashing/">
<img class="hero-on-hover" src="assets/hero/chapter_hashing.png"
style="height: 15.266%; left: 63.281%; top: 27.933%;">
<p class="hero-caption" style="left: 68.862%; top: 46.292%;">哈希表</p>
<span class="hero-caption" style="left: 68.862%; top: 46.292%;">哈希表</span>
</a>
<a href="/chapter_tree/">
<img class="hero-on-hover" src="assets/hero/chapter_tree.png"
style="height: 19.615%; left: 80.137%; top: 26.678%;">
<p class="hero-caption" style="left: 96.159%; top: 44.8%;">树</p>
<span class="hero-caption" style="left: 96.159%; top: 44.8%;">树</span>
</a>
<a href="/chapter_heap/">
<img class="hero-on-hover" src="assets/hero/chapter_heap.png"
style="height: 10.566%; left: 77.226%; top: 11.559%;">
<p class="hero-caption" style="left: 88.103%; top: 15.422%;">堆</p>
<span class="hero-caption" style="left: 88.103%; top: 15.422%;">堆</span>
</a>
<a href="/chapter_graph/">
<img class="hero-on-hover" src="assets/hero/chapter_graph.png"
style="height: 16.112%; left: 51.854%; top: 5.575%;">
<p class="hero-caption" style="left: 71.195%; top: 6.503%;">图</p>
<span class="hero-caption" style="left: 71.195%; top: 6.503%;">图</span>
</a>
<a href="/chapter_searching/">
<img class="hero-on-hover" src="assets/hero/chapter_searching.png"
style="height: 15.149%; left: 18.185%; top: 16.404%;">
<p class="hero-caption" style="left: 14.556%; top: 20.876%;">搜索</p>
<span class="hero-caption" style="left: 14.556%; top: 20.876%;">搜索</span>
</a>
<a href="/chapter_sorting/">
<img class="hero-on-hover" src="assets/hero/chapter_sorting.png"
style="height: 9.574%; left: 25.409%; top: 40.747%;">
<p class="hero-caption" style="left: 28.805%; top: 53.808%;">排序</p>
<span class="hero-caption" style="left: 28.805%; top: 53.808%;">排序</span>
</a>
<a href="/chapter_divide_and_conquer/">
<img class="hero-on-hover" src="assets/hero/chapter_divide_and_conquer.png"
style="height: 18.681%; left: 32.721%; top: 4.816%;">
<p class="hero-caption" style="left: 31.42%; top: 8.679%;">分治</p>
<span class="hero-caption" style="left: 31.42%; top: 8.679%;">分治</span>
</a>
<a href="/chapter_backtracking/">
<img class="hero-on-hover" src="assets/hero/chapter_backtracking.png"
style="height: 17.338%; left: 4.875%; top: 32.925%;">
<p class="hero-caption" style="left: 4.742%; top: 50.113%;">回溯</p>
<span class="hero-caption" style="left: 4.742%; top: 50.113%;">回溯</span>
</a>
<a href="/chapter_dynamic_programming/">
<img class="hero-on-hover" src="assets/hero/chapter_dynamic_programming.png"
style="height: 15.47%; left: 9.406%; top: 57.472%;">
<p class="hero-caption" style="left: 8.561%; top: 75.351%;">动态规划</p>
<span class="hero-caption" style="left: 8.561%; top: 75.351%;">动态规划</span>
</a>
<a href="/chapter_greedy/">
<img class="hero-on-hover" src="assets/hero/chapter_greedy.png"
style="height: 14.127%; left: 23.132%; top: 75.803%;">
<p class="hero-caption" style="left: 21.619%; top: 86.85%;">贪心</p>
<span class="hero-caption" style="left: 21.619%; top: 86.85%;">贪心</span>
</a>
</div>

<!-- heading and buttons -->
<div style="width: 100%; position: absolute; transform: translateX(-50%); left: 50%; bottom: min(2vh, 3vw);">
<div style="width: 100%; position: absolute; transform: translateX(-50%); left: 50%; bottom: min(2vh, 3vw); pointer-events: none;">
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src="https://readme-typing-svg.demolab.com/?font=Noto+Sans+SC&weight=400&duration=3500&pause=2000&color=FFF&center=true&vCenter=true&random=false&width=200&lines=Hello%2C+%E7%AE%97%E6%B3%95+!"
alt="hello-algo-typing-svg" />
<p style="color: #fff; margin-top: max(-1vh, -2vw); margin-bottom: min(2vh, 3.5vw);">
动画图解、一键运行的数据结构与算法教程
</p>
<div>
<div style="pointer-events: auto;">
<a href="/chapter_preface/" class="rounded-button">
<svg xmlns="http://www.w3.org/2000/svg"
viewBox="0 0 512 512"><!--!Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free Copyright 2024 Fonticons, Inc.-->
<path
d="M160 96a96 96 0 1 1 192 0A96 96 0 1 1 160 96zm80 152V512l-48.4-24.2c-20.9-10.4-43.5-17-66.8-19.3l-96-9.6C12.5 457.2 0 443.5 0 427V224c0-17.7 14.3-32 32-32H62.3c63.6 0 125.6 19.6 177.7 56zm32 264V248c52.1-36.4 114.1-56 177.7-56H480c17.7 0 32 14.3 32 32V427c0 16.4-12.5 30.2-28.8 31.8l-96 9.6c-23.2 2.3-45.9 8.9-66.8 19.3L272 512z" />
</svg>
<p>开始阅读</p>
<span>开始阅读</span>
</a>
<a href="https://github.com/krahets/hello-algo" class="rounded-button">
<svg xmlns="http://www.w3.org/2000/svg"
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</svg>
<p>代码仓库</p>
<span>代码仓库</span>
</a>
</div>
<!-- arrow -->
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<!-- Section: reading -->
<section data-md-color-scheme="default" data-md-color-primary="white" class="home-div">
<div class="section-content">
<div style="height: min(37vh, 33vw); width: min(75vh, 75vw); position: relative; margin: 1em auto;">
<div style="height: min(37vh, 33vw); width: min(75vh, 75vw); position: relative; margin: 0.5em auto;">
<!-- devices -->
<!-- mac height = 248.1 mm -->
<!-- ipad height = 280.6mm -->
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<img class="device-on-hover" src="assets/hero/pdf_ipad.png" style="height: 100%; left: 60%; bottom: 0%;">
<img class="device-on-hover" src="assets/hero/web_iphone.png" style="height: 57.27%; left: 2%; bottom: 0%;">
</div>
<p style="margin-top: 2em;">提供网页版和 PDF 版，兼容 PC、平板和手机，随时随地阅读</p>
<p style="margin: 2em auto;">提供网页版和 PDF 版，兼容 PC、平板和手机，随时随地阅读</p>
<div class="text-button-container">
<a href="https://github.com/krahets/hello-algo/releases">
<div class="text-button">
<p>下载 PDF</p>
<span>下载 PDF</span>
<svg xmlns="http://www.w3.org/2000/svg"
viewBox="0 0 320 512"><!--!Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free Copyright 2024 Fonticons, Inc.-->
<path
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<section data-md-color-scheme="slate" data-md-color-primary="grey" class="home-div">
<div class="section-content">
<h3 style="text-align: center; margin: 1em auto;">推荐语</h3>
<div class="intro-container" style="margin-bottom: 1em;">
<div class="intro-container" style="margin: 0 auto;">
<div class="intro-text endor-text">
<p style="margin-bottom: 0;">“一本通俗易懂的数据结构与算法入门书，引导读者手脑并用地学习，强烈推荐算法初学者阅读。”</p>
<p style="font-weight: bold;">—— 邓俊辉，清华大学计算机系教授</p>
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<h3 style="margin-left: 0.5em;">互助学习</h3>
</div>
<p style="margin: 0;">欢迎讨论与提问，读者间携手共进</p>
<p class="intro-quote">"Knowledge increases by sharing."</br>“知识在分享中得以增长”</p>
<p class="intro-quote">"Learning by teaching."</br>“教学相长”</p>
</div>
</div>
<img class="intro-image" src="index.assets/comment.gif">
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17 changes: 11 additions & 6 deletions overrides/stylesheets/extra.css
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background-color: var(--md-default-bg-color);
color: var(--md-default-fg-color);
font-size: 0.9rem;
padding: 2em;
padding: 3em 2em;
text-align: center;
}

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justify-content: center;
border-radius: 10em;
margin: 0 0.1em;
padding: 0.5em 1.3em;
padding: 0.6em 1.3em;
border: none;
background-color: var(--md-typeset-btn-color);
color: var(--md-primary-fg-color) !important;
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background-color: var(--md-typeset-btn-hover-color);
}

.rounded-button p {
.rounded-button span {
margin: 0;
margin-bottom: 0.1em;
margin-bottom: 0.07em;
white-space: nowrap;
}

.rounded-button svg {
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}

.text-button {
width: 100%;
display: flex;
flex-direction: row;
align-items: center;
color: var(--md-typeset-btn-color);
text-decoration: none;
margin: 0 1em;
}

.text-button:hover {
text-decoration: underline;
}

.text-button span {
white-space: nowrap;
}

.text-button svg {
display: inline-block;
fill: var(--md-typeset-btn-color);
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padding: 0;
position: relative;
color: white;
font-size: min(2vh, 2.5vw);
font-size: min(1.8vh, 2.5vw);
font-weight: 500;
}

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