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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.
This commit is contained in:
Yudong Jin
2024-01-25 12:50:53 +08:00
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parent 82da279c60
commit c69ae9534d
5 changed files with 37 additions and 32 deletions
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</div> </div>
<div class="admonition quote"> <div class="admonition quote">
<p align="center">"Knowledge increases by sharing."</p> <p align="center">"Learning by teaching."</p>
</div> </div>
--- ---

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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。 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 ## 权衡时间与空间

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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**。 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。 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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style="position: absolute; width: auto; height: 78.751%; left: 10.545%; top: 7.326%;"> style="position: absolute; width: auto; height: 78.751%; left: 10.545%; top: 7.326%;">
<a href="/chapter_introduction/"> <a href="/chapter_introduction/">
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<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>
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<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>
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<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>
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<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>
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<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>
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<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>
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<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>
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<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>
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<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>
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<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>
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<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>
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动画图解、一键运行的数据结构与算法教程 动画图解、一键运行的数据结构与算法教程
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<p>开始阅读</p> <span>开始阅读</span>
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<p>下载 PDF</p> <span>下载 PDF</span>
<svg xmlns="http://www.w3.org/2000/svg" <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.--> 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 <path
@ -186,7 +186,7 @@ hide:
<section data-md-color-scheme="slate" data-md-color-primary="grey" class="home-div"> <section data-md-color-scheme="slate" data-md-color-primary="grey" class="home-div">
<div class="section-content"> <div class="section-content">
<h3 style="text-align: center; margin: 1em auto;">推荐语</h3> <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"> <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="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> <p style="font-weight: bold;">—— 邓俊辉，清华大学计算机系教授</p>
@ -250,7 +250,7 @@ hide:
<h3 style="margin-left: 0.5em;">互助学习</h3> <h3 style="margin-left: 0.5em;">互助学习</h3>
</div> </div>
<p style="margin: 0;">欢迎讨论与提问，读者间携手共进</p> <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>
</div> </div>
<img class="intro-image" src="index.assets/comment.gif"> <img class="intro-image" src="index.assets/comment.gif">

17
overrides/stylesheets/extra.css
View File

@ -204,7 +204,7 @@ body {
background-color: var(--md-default-bg-color); background-color: var(--md-default-bg-color);
color: var(--md-default-fg-color); color: var(--md-default-fg-color);
font-size: 0.9rem; font-size: 0.9rem;
padding: 2em; padding: 3em 2em;
text-align: center; text-align: center;
} }
@ -221,7 +221,7 @@ body {
justify-content: center; justify-content: center;
border-radius: 10em; border-radius: 10em;
margin: 0 0.1em; margin: 0 0.1em;
padding: 0.5em 1.3em; padding: 0.6em 1.3em;
border: none; border: none;
background-color: var(--md-typeset-btn-color); background-color: var(--md-typeset-btn-color);
color: var(--md-primary-fg-color) !important; color: var(--md-primary-fg-color) !important;
@ -234,9 +234,10 @@ body {
background-color: var(--md-typeset-btn-hover-color); background-color: var(--md-typeset-btn-hover-color);
} }
.rounded-button p { .rounded-button span {
margin: 0; margin: 0;
margin-bottom: 0.1em; margin-bottom: 0.07em;
white-space: nowrap;
} }
.rounded-button svg { .rounded-button svg {
@ -257,18 +258,22 @@ body {
} }
.text-button { .text-button {
width: 100%;
display: flex; display: flex;
flex-direction: row; flex-direction: row;
align-items: center; align-items: center;
color: var(--md-typeset-btn-color); color: var(--md-typeset-btn-color);
text-decoration: none; text-decoration: none;
margin: 0 1em;
} }
.text-button:hover { .text-button:hover {
text-decoration: underline; text-decoration: underline;
} }
.text-button span {
white-space: nowrap;
}
.text-button svg { .text-button svg {
display: inline-block; display: inline-block;
fill: var(--md-typeset-btn-color); fill: var(--md-typeset-btn-color);
@ -288,7 +293,7 @@ body {
padding: 0; padding: 0;
position: relative; position: relative;
color: white; color: white;
font-size: min(2vh, 2.5vw); font-size: min(1.8vh, 2.5vw);
font-weight: 500; font-weight: 500;
} }