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## 11.5.4 基准数优化
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## 11.5.4 基准数优化
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**快速排序在某些输入下的时间效率可能降低**。举一个极端例子，假设输入数组是完全倒序的，由于我们选择最左端元素作为基准数，那么在哨兵划分完成后，基准数被交换至数组最右端，导致左子数组长度为 $n - 1$、右子数组长度为 $0$ 。如此递归下去，每轮哨兵划分后的右子数组长度都为 $0$ ，分治策略失效，快速排序退化为“冒泡排序”。
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**快速排序在某些输入下的时间效率可能降低**。举一个极端例子，假设输入数组是完全倒序的，由于我们选择最左端元素作为基准数，那么在哨兵划分完成后，基准数被交换至数组最右端，导致左子数组长度为 $n - 1$、右子数组长度为 $0$ 。如此递归下去，每轮哨兵划分后都有一个子数组的长度为 $0$ ，分治策略失效，快速排序退化为“冒泡排序”的近似形式。
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为了尽量避免这种情况发生，**我们可以优化哨兵划分中的基准数的选取策略**。例如，我们可以随机选取一个元素作为基准数。然而，如果运气不佳，每次都选到不理想的基准数，效率仍然不尽如人意。
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为了尽量避免这种情况发生，**我们可以优化哨兵划分中的基准数的选取策略**。例如，我们可以随机选取一个元素作为基准数。然而，如果运气不佳，每次都选到不理想的基准数，效率仍然不尽如人意。
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<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>
|
|
||||||
</a>
|
|
||||||
<a href="https://www.hello-algo.com/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>
|
|
||||||
</a>
|
|
||||||
<a href="https://www.hello-algo.com/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>
|
|
||||||
</a>
|
|
||||||
<a href="https://www.hello-algo.com/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>
|
|
||||||
</a>
|
|
||||||
<a href="https://www.hello-algo.com/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>
|
|
||||||
</a>
|
|
||||||
<a href="https://www.hello-algo.com/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>
|
|
||||||
</a>
|
|
||||||
<a href="https://www.hello-algo.com/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>
|
|
||||||
</a>
|
|
||||||
<a href="https://www.hello-algo.com/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>
|
|
||||||
</a>
|
|
||||||
<a href="https://www.hello-algo.com/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>
|
|
||||||
</a>
|
|
||||||
<a href="https://www.hello-algo.com/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>
|
|
||||||
</a>
|
|
||||||
<a href="https://www.hello-algo.com/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>
|
|
||||||
</a>
|
|
||||||
<a href="https://www.hello-algo.com/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>
|
|
||||||
</a>
|
|
||||||
<a href="https://www.hello-algo.com/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>
|
|
||||||
</a>
|
|
||||||
<a href="https://www.hello-algo.com/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>
|
|
||||||
</a>
|
|
||||||
</div>
|
|
||||||
</section>
|
</section>
|
||||||
|
|
||||||
<!-- Section: brief introduction -->
|
<!-- Section: brief introduction -->
|
||||||
|
|
@ -177,6 +167,18 @@ hide:
|
||||||
<img class="device-on-hover" src="assets/hero/web_iphone.png" style="height: 57.27%; left: 2%; bottom: 0%;">
|
<img class="device-on-hover" src="assets/hero/web_iphone.png" style="height: 57.27%; left: 2%; bottom: 0%;">
|
||||||
</div>
|
</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-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>
|
||||||
|
<div class="text-button-container">
|
||||||
|
<a href="https://github.com/krahets/hello-algo/releases">
|
||||||
|
<div class="text-button">
|
||||||
|
<p>下载 PDF</p>
|
||||||
|
<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
|
||||||
|
d="M278.6 233.4c12.5 12.5 12.5 32.8 0 45.3l-160 160c-12.5 12.5-32.8 12.5-45.3 0s-12.5-32.8 0-45.3L210.7 256 73.4 118.6c-12.5-12.5-12.5-32.8 0-45.3s32.8-12.5 45.3 0l160 160z" />
|
||||||
|
</svg>
|
||||||
|
</div>
|
||||||
|
</a>
|
||||||
|
</div>
|
||||||
</div>
|
</div>
|
||||||
</section>
|
</section>
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -112,6 +112,11 @@
|
||||||
text-transform: none;
|
text-transform: none;
|
||||||
}
|
}
|
||||||
|
|
||||||
|
.md-typeset a:hover {
|
||||||
|
color: var(--md-typeset-a-color);
|
||||||
|
text-decoration: underline;
|
||||||
|
}
|
||||||
|
|
||||||
.md-typeset code {
|
.md-typeset code {
|
||||||
border-radius: 0.2rem;
|
border-radius: 0.2rem;
|
||||||
}
|
}
|
||||||
|
|
@ -150,34 +155,6 @@ body {
|
||||||
width: 100%; /* Default to full width */
|
width: 100%; /* Default to full width */
|
||||||
}
|
}
|
||||||
|
|
||||||
/* rounded button */
|
|
||||||
.rounded-button {
|
|
||||||
display: inline-flex; /* Use flexbox for alignment */
|
|
||||||
align-items: center; /* Align items vertically */
|
|
||||||
justify-content: center; /* Center items horizontally */
|
|
||||||
border-radius: 100px; /* Circular corners */
|
|
||||||
padding: 9px 18px; /* Padding around the text */
|
|
||||||
margin: 0.15em 0;
|
|
||||||
border: none; /* Removes default border */
|
|
||||||
background-color: var(--md-typeset-btn-color); /* Background color */
|
|
||||||
color: var(--md-primary-fg-color) !important; /* Text color */
|
|
||||||
font-size: 0.85em; /* Font size */
|
|
||||||
text-align: center; /* Center the text */
|
|
||||||
text-decoration: none; /* Remove underline from anchor text */
|
|
||||||
cursor: pointer; /* Pointer cursor on hover */
|
|
||||||
}
|
|
||||||
|
|
||||||
.rounded-button:hover {
|
|
||||||
background-color: var(--md-typeset-btn-hover-color);
|
|
||||||
}
|
|
||||||
|
|
||||||
.rounded-button svg {
|
|
||||||
fill: var(--md-primary-fg-color); /* Fill SVG icon with text color */
|
|
||||||
width: 1.2em;
|
|
||||||
height: auto;
|
|
||||||
margin-right: 0.5em; /* Add some space between the SVG icon and the text */
|
|
||||||
}
|
|
||||||
|
|
||||||
/* Admonition for python tutor */
|
/* Admonition for python tutor */
|
||||||
.md-typeset .admonition.pythontutor,
|
.md-typeset .admonition.pythontutor,
|
||||||
.md-typeset details.pythontutor {
|
.md-typeset details.pythontutor {
|
||||||
|
|
@ -237,10 +214,69 @@ body {
|
||||||
max-width: 70vw;
|
max-width: 70vw;
|
||||||
}
|
}
|
||||||
|
|
||||||
.hero-btn {
|
/* rounded button */
|
||||||
|
.rounded-button {
|
||||||
|
display: inline-flex;
|
||||||
|
align-items: center;
|
||||||
|
justify-content: center;
|
||||||
|
border-radius: 10em;
|
||||||
margin: 0 0.1em;
|
margin: 0 0.1em;
|
||||||
padding: 0.5em 1.3em;
|
padding: 0.5em 1.3em;
|
||||||
font-size: 0.85em;
|
border: none;
|
||||||
|
background-color: var(--md-typeset-btn-color);
|
||||||
|
color: var(--md-primary-fg-color) !important;
|
||||||
|
text-align: center;
|
||||||
|
text-decoration: none;
|
||||||
|
cursor: pointer;
|
||||||
|
}
|
||||||
|
|
||||||
|
.rounded-button:hover {
|
||||||
|
background-color: var(--md-typeset-btn-hover-color);
|
||||||
|
}
|
||||||
|
|
||||||
|
.rounded-button p {
|
||||||
|
margin: 0;
|
||||||
|
margin-bottom: 0.1em;
|
||||||
|
}
|
||||||
|
|
||||||
|
.rounded-button svg {
|
||||||
|
fill: var(--md-primary-fg-color);
|
||||||
|
width: auto;
|
||||||
|
height: 1.2em;
|
||||||
|
margin-right: 0.5em;
|
||||||
|
}
|
||||||
|
|
||||||
|
/* text button */
|
||||||
|
.text-button-container {
|
||||||
|
width: 100%;
|
||||||
|
display: flex;
|
||||||
|
flex-direction: row;
|
||||||
|
justify-content: center;
|
||||||
|
height: auto;
|
||||||
|
margin: 0 auto;
|
||||||
|
}
|
||||||
|
|
||||||
|
.text-button {
|
||||||
|
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 svg {
|
||||||
|
display: inline-block;
|
||||||
|
fill: var(--md-typeset-btn-color);
|
||||||
|
width: auto;
|
||||||
|
height: 0.9em;
|
||||||
|
background-size: cover;
|
||||||
|
padding-top: 0.17em;
|
||||||
|
margin-left: 0.4em;
|
||||||
}
|
}
|
||||||
|
|
||||||
/* hero image */
|
/* hero image */
|
||||||
|
|
@ -284,8 +320,8 @@ a:hover .hero-on-hover {
|
||||||
}
|
}
|
||||||
|
|
||||||
a:hover .hero-caption {
|
a:hover .hero-caption {
|
||||||
|
text-decoration: underline;
|
||||||
color: var(--md-typeset-btn-color);
|
color: var(--md-typeset-btn-color);
|
||||||
font-weight: bold;
|
|
||||||
}
|
}
|
||||||
|
|
||||||
/* code badge */
|
/* code badge */
|
||||||
|
|
|
||||||
Loading…
Reference in a new issue