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樹
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堆積
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</a>
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<a href="chapter_graph/">
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圖
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搜尋
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排序
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<a href="chapter_divide_and_conquer/">
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分治
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回溯
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動態規劃
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<a href="chapter_greedy/">
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貪婪
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<div class="heading-div">
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<p style="margin-top: max(-1vh, -2vw); margin-bottom: min(2vh, 3.5vw);">
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動畫圖解、一鍵執行的資料結構與演算法教程
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</p>
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<a class="rounded-button" href="chapter_hello_algo/">
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開始閱讀
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<a class="rounded-button" href="https://github.com/krahets/hello-algo">
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<span>
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程式碼倉庫
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</a>
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</section>
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<section class="home-div" data-md-color-scheme="slate">
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<div class="section-content">
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<img alt="Preview" src="index.assets/hello_algo_header.png" style="width: 100%; max-width: 41.5em;"/>
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<div class="code-badge">
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<img alt="" src="https://img.shields.io/badge/Python-snow?logo=python&logoColor=3776AB"/>
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<img alt="" src="https://img.shields.io/badge/Java-snow?logo=coffeescript&logoColor=FC4C02"/>
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<img alt="" src="https://img.shields.io/badge/C%2B%2B-snow?logo=c%2B%2B&logoColor=00599C"/>
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<img alt="" src="https://img.shields.io/badge/C-snow?logo=c&logoColor=A8B9CC"/>
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<img alt="" src="https://img.shields.io/badge/C%23-snow?logo=csharp&logoColor=512BD4"/>
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<img alt="" src="https://img.shields.io/badge/JS-snow?logo=javascript&logoColor=E9CE30"/>
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<img alt="" src="https://img.shields.io/badge/Go-snow?logo=go&logoColor=00ADD8"/>
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<img alt="" src="https://img.shields.io/badge/Swift-snow?logo=swift&logoColor=F05138"/>
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<img alt="" src="https://img.shields.io/badge/Rust-snow?logo=rust&logoColor=000000"/>
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<img alt="" src="https://img.shields.io/badge/Ruby-snow?logo=ruby&logoColor=CC342D"/>
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<img alt="" src="https://img.shields.io/badge/Kotlin-snow?logo=kotlin&logoColor=7F52FF"/>
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<img alt="" src="https://img.shields.io/badge/TS-snow?logo=typescript&logoColor=3178C6"/>
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<img alt="" src="https://img.shields.io/badge/Dart-snow?logo=dart&logoColor=0175C2"/>
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<img alt="" src="https://img.shields.io/badge/Zig-snow?logo=zig&logoColor=F7A41D"/>
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<p style="margin-top: 2em;">
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500 幅動畫圖解、14 種程式語言程式碼、3000 條社群問答，助你快速入門資料結構與演算法
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</p>
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</section>
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<a href="/chapter_paperbook/">
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<div class="text-button">
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<span>
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紙質書（簡中）
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</span>
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<svg viewbox="0 0 320 512" xmlns="http://www.w3.org/2000/svg">
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<a href="chapter_hello_algo/">
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線上閱讀
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<svg viewbox="0 0 320 512" xmlns="http://www.w3.org/2000/svg">
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<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">
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</a>
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</div>
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<div class="media-block">
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<a href="https://github.com/krahets/hello-algo/releases">
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<img alt="" class="device-on-hover" src="../assets/hero/pdf_ipad.png" style="height: 75%;"/>
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<div class="text-button">
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<span>
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PDF（簡中）
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<svg viewbox="0 0 320 512" xmlns="http://www.w3.org/2000/svg">
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<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">
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</svg>
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</div>
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</a>
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</div>
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</div>
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</div>
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</section>
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<section class="home-div" data-md-color-primary="grey" data-md-color-scheme="slate">
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<div class="section-content">
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<h3 style="text-align: center; margin: 1em auto;">
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推薦語
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</h3>
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<div class="intro-container" style="margin: 0 auto;">
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<div class="intro-text endor-text">
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<p style="margin-bottom: 0;">
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|
|
“一本通俗易懂的資料結構與演算法入門書，引導讀者手腦並用地學習，強烈推薦演算法初學者閱讀。”
|
|
|
</p>
|
|
|
<p style="font-weight: bold;">
|
|
|
—— 鄧俊輝，清華大學計算機系教授
|
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|
</p>
|
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</div>
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|
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<div class="intro-text endor-text">
|
|
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<p style="margin-bottom: 0;">
|
|
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“如果我當年學資料結構與演算法的時候有《Hello 演算法》，學起來應該會簡單 10 倍！”
|
|
|
</p>
|
|
|
<p style="font-weight: bold;">
|
|
|
—— 李沐，亞馬遜資深首席科學家
|
|
|
</p>
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|
</div>
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</div>
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</div>
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</section>
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<section class="home-div" data-md-color-primary="white" data-md-color-scheme="default">
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<div class="section-content">
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<div class="intro-container">
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<div class="intro-text">
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<div>
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<div style="display: flex; align-items: center;">
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<svg height="1.5em" viewbox="0 0 640 512" width="1.5em" xmlns="http://www.w3.org/2000/svg">
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<path d="M256 0H576c35.3 0 64 28.7 64 64V288c0 35.3-28.7 64-64 64H256c-35.3 0-64-28.7-64-64V64c0-35.3 28.7-64 64-64zM476 106.7C471.5 100 464 96 456 96s-15.5 4-20 10.7l-56 84L362.7 169c-4.6-5.7-11.5-9-18.7-9s-14.2 3.3-18.7 9l-64 80c-5.8 7.2-6.9 17.1-2.9 25.4s12.4 13.6 21.6 13.6h80 48H552c8.9 0 17-4.9 21.2-12.7s3.7-17.3-1.2-24.6l-96-144zM336 96a32 32 0 1 0 -64 0 32 32 0 1 0 64 0zM64 128h96V384v32c0 17.7 14.3 32 32 32H320c17.7 0 32-14.3 32-32V384H512v64c0 35.3-28.7 64-64 64H64c-35.3 0-64-28.7-64-64V192c0-35.3 28.7-64 64-64zm8 64c-8.8 0-16 7.2-16 16v16c0 8.8 7.2 16 16 16H88c8.8 0 16-7.2 16-16V208c0-8.8-7.2-16-16-16H72zm0 104c-8.8 0-16 7.2-16 16v16c0 8.8 7.2 16 16 16H88c8.8 0 16-7.2 16-16V312c0-8.8-7.2-16-16-16H72zm0 104c-8.8 0-16 7.2-16 16v16c0 8.8 7.2 16 16 16H88c8.8 0 16-7.2 16-16V416c0-8.8-7.2-16-16-16H72zm336 16v16c0 8.8 7.2 16 16 16h16c8.8 0 16-7.2 16-16V416c0-8.8-7.2-16-16-16H424c-8.8 0-16 7.2-16 16z" fill="var(--md-primary-bg-color)">
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</path>
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</svg>
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|
<h3 style="margin-left: 0.5em;">
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|
|
動畫圖解
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|
|
</h3>
|
|
|
</div>
|
|
|
<p style="margin: 0;">
|
|
|
內容清晰易懂，學習曲線平滑
|
|
|
</p>
|
|
|
<p class="intro-quote">
|
|
|
"A picture is worth a thousand words."
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|
<br/>
|
|
|
“一圖勝千言”
|
|
|
</p>
|
|
|
</div>
|
|
|
</div>
|
|
|
<img alt="Animation example" class="intro-image" src="index.assets/animation.gif"/>
|
|
|
</div>
|
|
|
<div class="intro-container">
|
|
|
<img alt="Running code example" class="intro-image" src="index.assets/running_code.gif"/>
|
|
|
<div class="intro-text">
|
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|
<div>
|
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|
<div style="display: flex; align-items: center;">
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<svg height="1.5em" viewbox="0 0 640 512" width="1.5em" xmlns="http://www.w3.org/2000/svg">
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<path d="M392.8 1.2c-17-4.9-34.7 5-39.6 22l-128 448c-4.9 17 5 34.7 22 39.6s34.7-5 39.6-22l128-448c4.9-17-5-34.7-22-39.6zm80.6 120.1c-12.5 12.5-12.5 32.8 0 45.3L562.7 256l-89.4 89.4c-12.5 12.5-12.5 32.8 0 45.3s32.8 12.5 45.3 0l112-112c12.5-12.5 12.5-32.8 0-45.3l-112-112c-12.5-12.5-32.8-12.5-45.3 0zm-306.7 0c-12.5-12.5-32.8-12.5-45.3 0l-112 112c-12.5 12.5-12.5 32.8 0 45.3l112 112c12.5 12.5 32.8 12.5 45.3 0s12.5-32.8 0-45.3L77.3 256l89.4-89.4c12.5-12.5 12.5-32.8 0-45.3z" fill="var(--md-primary-bg-color)">
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</path>
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</svg>
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<h3 style="margin-left: 0.5em;">
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|
一鍵執行
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|
|
</h3>
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|
|
</div>
|
|
|
<p style="margin: 0;">
|
|
|
十餘種程式語言，程式碼視覺化執行
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|
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</p>
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<p class="intro-quote">
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"Talk is cheap. Show me the code."
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<br/>
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“少吹牛，看程式碼”
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</p>
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</div>
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</div>
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</div>
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<div class="intro-container">
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<div class="intro-text">
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<div>
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<div style="display: flex; align-items: center;">
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<svg height="1.5em" viewbox="0 0 640 512" width="1.5em" xmlns="http://www.w3.org/2000/svg">
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<path d="M88.2 309.1c9.8-18.3 6.8-40.8-7.5-55.8C59.4 230.9 48 204 48 176c0-63.5 63.8-128 160-128s160 64.5 160 128s-63.8 128-160 128c-13.1 0-25.8-1.3-37.8-3.6c-10.4-2-21.2-.6-30.7 4.2c-4.1 2.1-8.3 4.1-12.6 6c-16 7.2-32.9 13.5-49.9 18c2.8-4.6 5.4-9.1 7.9-13.6c1.1-1.9 2.2-3.9 3.2-5.9zM0 176c0 41.8 17.2 80.1 45.9 110.3c-.9 1.7-1.9 3.5-2.8 5.1c-10.3 18.4-22.3 36.5-36.6 52.1c-6.6 7-8.3 17.2-4.6 25.9C5.8 378.3 14.4 384 24 384c43 0 86.5-13.3 122.7-29.7c4.8-2.2 9.6-4.5 14.2-6.8c15.1 3 30.9 4.5 47.1 4.5c114.9 0 208-78.8 208-176S322.9 0 208 0S0 78.8 0 176zM432 480c16.2 0 31.9-1.6 47.1-4.5c4.6 2.3 9.4 4.6 14.2 6.8C529.5 498.7 573 512 616 512c9.6 0 18.2-5.7 22-14.5c3.8-8.8 2-19-4.6-25.9c-14.2-15.6-26.2-33.7-36.6-52.1c-.9-1.7-1.9-3.4-2.8-5.1C622.8 384.1 640 345.8 640 304c0-94.4-87.9-171.5-198.2-175.8c4.1 15.2 6.2 31.2 6.2 47.8l0 .6c87.2 6.7 144 67.5 144 127.4c0 28-11.4 54.9-32.7 77.2c-14.3 15-17.3 37.6-7.5 55.8c1.1 2 2.2 4 3.2 5.9c2.5 4.5 5.2 9 7.9 13.6c-17-4.5-33.9-10.7-49.9-18c-4.3-1.9-8.5-3.9-12.6-6c-9.5-4.8-20.3-6.2-30.7-4.2c-12.1 2.4-24.7 3.6-37.8 3.6c-61.7 0-110-26.5-136.8-62.3c-16 5.4-32.8 9.4-50 11.8C279 439.8 350 480 432 480z" fill="var(--md-primary-bg-color)">
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</path>
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</svg>
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<h3 style="margin-left: 0.5em;">
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互助學習
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</h3>
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</div>
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<p style="margin: 0;">
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|
|
歡迎討論與提問，讀者間攜手共進
|
|
|
</p>
|
|
|
<p class="intro-quote">
|
|
|
"Learning by teaching."
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|
|
<br/>
|
|
|
“教學相長”
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</p>
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|
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</div>
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</div>
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|
|
<img alt="Comments example" class="intro-image" src="index.assets/comment.gif"/>
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</div>
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</div>
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</section>
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<section class="home-div" data-md-color-primary="grey" data-md-color-scheme="slate">
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<div class="section-content" style="max-width: 90vw;">
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<div style="margin: 2em auto;">
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<h3>
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|
作者
|
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</h3>
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<div class="profile-div">
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|
<div class="profile-cell">
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|
<a href="https://github.com/krahets">
|
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|
<img alt="Author: yudongjin" class="profile-img" src="../assets/avatar/avatar_yudongjin.jpg"/>
|
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|
<br/>
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<b>
|
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|
靳宇棟（@krahets）
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</b>
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</a>
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</div>
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</div>
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|
</div>
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|
|
<div style="margin: 2em auto;">
|
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|
<h3>
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|
程式碼審閱者
|
|
|
</h3>
|
|
|
<div class="profile-div">
|
|
|
<div class="profile-cell">
|
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|
<a href="https://github.com/codingonion">
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|
<img alt="Reviewer: codingonion" class="profile-img" src="../assets/avatar/avatar_codingonion.jpg"/>
|
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<br/>
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<b>
|
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|
codingonion
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|
</b>
|
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|
<br/>
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|
|
<sub>
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|
|
Zig, Rust
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</sub>
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|
</a>
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|
</div>
|
|
|
<div class="profile-cell">
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|
<a href="https://github.com/Gonglja">
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|
<img alt="Reviewer: Gonglja" class="profile-img" src="../assets/avatar/avatar_Gonglja.jpg"/>
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|
<br/>
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<b>
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|
Gonglja
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</b>
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|
<br/>
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<sub>
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|
C, C++
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|
</sub>
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</a>
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</div>
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|
<div class="profile-cell">
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|
<a href="https://github.com/gvenusleo">
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|
<img alt="Reviewer: gvenusleo" class="profile-img" src="../assets/avatar/avatar_gvenusleo.jpg"/>
|
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<br/>
|
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<b>
|
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|
gvenusleo
|
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|
</b>
|
|
|
<br/>
|
|
|
<sub>
|
|
|
Dart
|
|
|
</sub>
|
|
|
</a>
|
|
|
</div>
|
|
|
<div class="profile-cell">
|
|
|
<a href="https://github.com/hpstory">
|
|
|
<img alt="Reviewer: hpstory" class="profile-img" src="../assets/avatar/avatar_hpstory.jpg"/>
|
|
|
<br/>
|
|
|
<b>
|
|
|
hpstory
|
|
|
</b>
|
|
|
<br/>
|
|
|
<sub>
|
|
|
C#
|
|
|
</sub>
|
|
|
</a>
|
|
|
</div>
|
|
|
<div class="profile-cell">
|
|
|
<a href="https://github.com/justin-tse">
|
|
|
<img alt="Reviewer: justin-tse" class="profile-img" src="../assets/avatar/avatar_justin-tse.jpg"/>
|
|
|
<br/>
|
|
|
<b>
|
|
|
justin-tse
|
|
|
</b>
|
|
|
<br/>
|
|
|
<sub>
|
|
|
JS, TS
|
|
|
</sub>
|
|
|
</a>
|
|
|
</div>
|
|
|
<div class="profile-cell">
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<a href="https://github.com/krahets">
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<img alt="Reviewer: krahets" class="profile-img" src="../assets/avatar/avatar_krahets.jpg"/>
|
|
|
<br/>
|
|
|
<b>
|
|
|
krahets
|
|
|
</b>
|
|
|
<br/>
|
|
|
<sub>
|
|
|
Python, Java
|
|
|
</sub>
|
|
|
</a>
|
|
|
</div>
|
|
|
<div class="profile-cell">
|
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|
<a href="https://github.com/night-cruise">
|
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|
<img alt="Reviewer: night-cruise" class="profile-img" src="../assets/avatar/avatar_night-cruise.jpg"/>
|
|
|
<br/>
|
|
|
<b>
|
|
|
night-cruise
|
|
|
</b>
|
|
|
<br/>
|
|
|
<sub>
|
|
|
Rust
|
|
|
</sub>
|
|
|
</a>
|
|
|
</div>
|
|
|
<div class="profile-cell">
|
|
|
<a href="https://github.com/nuomi1">
|
|
|
<img alt="Reviewer: nuomi1" class="profile-img" src="../assets/avatar/avatar_nuomi1.jpg"/>
|
|
|
<br/>
|
|
|
<b>
|
|
|
nuomi1
|
|
|
</b>
|
|
|
<br/>
|
|
|
<sub>
|
|
|
Swift
|
|
|
</sub>
|
|
|
</a>
|
|
|
</div>
|
|
|
<div class="profile-cell">
|
|
|
<a href="https://github.com/Reanon">
|
|
|
<img alt="Reviewer: Reanon" class="profile-img" src="../assets/avatar/avatar_Reanon.jpg"/>
|
|
|
<br/>
|
|
|
<b>
|
|
|
Reanon
|
|
|
</b>
|
|
|
<br/>
|
|
|
<sub>
|
|
|
Go, C
|
|
|
</sub>
|
|
|
</a>
|
|
|
</div>
|
|
|
</div>
|
|
|
</div>
|
|
|
<div style="margin: 2em auto;">
|
|
|
<h3>
|
|
|
貢獻者
|
|
|
</h3>
|
|
|
<p>
|
|
|
本書在開源社群一百多位貢獻者的共同努力下不斷完善，感謝他們付出的時間與精力！
|
|
|
</p>
|
|
|
<a href="https://github.com/krahets/hello-algo/graphs/contributors">
|
|
|
<img alt="Contributors" src="https://contrib.rocks/image?repo=krahets/hello-algo&max=300&columns=16" style="width: 100%; max-width: 38.5em;"/>
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</a>
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</div>
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</div>
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</section>
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Hello 演算法
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序
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第 0 章 前言
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第 0 章 前言
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0.1 關於本書
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0.2 如何使用本書
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0.3 小結
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第 2 章 複雜度分析
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2.1 演算法效率評估
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2.3 時間複雜度
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2.4 空間複雜度
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2.5 小結
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第 3 章 資料結構
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第 3 章 資料結構
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3.1 資料結構分類
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3.2 基本資料型別
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3.3 數字編碼 *
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3.4 字元編碼 *
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3.5 小結
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第 4 章 陣列與鏈結串列
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第 4 章 陣列與鏈結串列
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4.1 陣列
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4.2 鏈結串列
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4.3 串列
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4.4 記憶體與快取 *
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4.5 小結
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第 5 章 堆疊與佇列
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第 5 章 堆疊與佇列
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5.1 堆疊
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5.2 佇列
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5.3 雙向佇列
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5.4 小結
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第 6 章 雜湊表
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第 6 章 雜湊表
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6.1 雜湊表
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6.2 雜湊衝突
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6.3 雜湊演算法
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6.4 小結
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第 7 章 樹
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第 7 章 樹
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7.1 二元樹
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7.2 二元樹走訪
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7.3 二元樹陣列表示
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7.4 二元搜尋樹
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7.5 AVL *
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7.6 小結
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<a class="md-nav__link" href="chapter_heap/">
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<path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z">
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第 8 章 堆積
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第 8 章 堆積
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8.1 堆積
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8.2 建堆積操作
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<a class="md-nav__link" href="chapter_heap/top_k/">
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8.3 Top-k 問題
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<a class="md-nav__link" href="chapter_heap/summary/">
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8.4 小結
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第 9 章 圖
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第 9 章 圖
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9.1 圖
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9.2 圖基礎操作
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9.3 圖的走訪
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9.4 小結
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第 10 章 搜尋
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第 10 章 搜尋
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10.1 二分搜尋
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</a>
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<a class="md-nav__link" href="chapter_searching/binary_search_insertion/">
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10.2 二分搜尋插入點
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</a>
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<a class="md-nav__link" href="chapter_searching/binary_search_edge/">
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10.3 二分搜尋邊界
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10.4 雜湊最佳化策略
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10.5 重識搜尋演算法
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10.6 小結
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第 11 章 排序
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第 11 章 排序
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<ul class="md-nav__list" data-md-scrollfix="">
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11.1 排序演算法
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</a>
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11.2 選擇排序
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11.3 泡沫排序
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11.4 插入排序
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11.5 快速排序
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11.6 合併排序
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11.7 堆積排序
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11.8 桶排序
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11.9 計數排序
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11.10 基數排序
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11.11 小結
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12.1 分治演算法
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12.3 構建樹問題
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12.5 小結
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第 13 章 回溯
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13.1 回溯演算法
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13.2 全排列問題
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13.3 子集和問題
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13.4 N 皇后問題
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13.5 小結
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第 14 章 動態規劃
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第 14 章 動態規劃
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14.1 初探動態規劃
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14.2 DP 問題特性
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14.3 DP 解題思路
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14.4 0-1 背包問題
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14.5 完全背包問題
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14.6 編輯距離問題
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14.7 小結
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第 15 章 貪婪
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第 15 章 貪婪
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15.1 貪婪演算法
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15.4 最大切分乘積問題
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15.5 小結
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