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<span class="md-ellipsis">
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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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0.2 如何使用本書
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<nav class="md-nav md-nav--secondary" aria-label="目錄">
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0.2.1 行文風格約定
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0.2.2 在動畫圖解中高效學習
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0.2.3 在程式碼實踐中加深理解
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0.2.4 在提問討論中共同成長
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0.2.5 演算法學習路線
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0.3 小結
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第 1 章 初識演算法
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第 1 章 初識演算法
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1.1 演算法無處不在
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1.2 演算法是什麼
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1.3 小結
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<span class="md-ellipsis">
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第 2 章 複雜度分析
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第 2 章 複雜度分析
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<span class="md-ellipsis">
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2.1 演算法效率評估
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</span>
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<span class="md-ellipsis">
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2.2 迭代與遞迴
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</span>
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<span class="md-ellipsis">
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2.3 時間複雜度
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<a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
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<span class="md-ellipsis">
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2.4 空間複雜度
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</span>
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<a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
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<span class="md-ellipsis">
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2.5 小結
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</span>
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</a>
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<span class="md-ellipsis">
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第 3 章 資料結構
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</a>
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<span class="md-nav__icon md-icon"></span>
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第 3 章 資料結構
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<ul class="md-nav__list" data-md-scrollfix>
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<span class="md-ellipsis">
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3.1 資料結構分類
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<span class="md-ellipsis">
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3.2 基本資料型別
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</span>
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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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</a>
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</li>
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<span class="md-ellipsis">
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第 4 章 陣列與鏈結串列
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</span>
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</a>
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<span class="md-nav__icon md-icon"></span>
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第 4 章 陣列與鏈結串列
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<ul class="md-nav__list" data-md-scrollfix>
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<span class="md-ellipsis">
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4.1 陣列
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</span>
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</a>
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<span class="md-ellipsis">
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4.2 鏈結串列
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</span>
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</a>
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<span class="md-ellipsis">
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4.3 串列
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</span>
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
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<span class="md-ellipsis">
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4.4 記憶體與快取 *
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</span>
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<span class="md-status md-status--new" title="最近新增">
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</span>
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</a>
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<li class="md-nav__item">
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<a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
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<span class="md-ellipsis">
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4.5 小結
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</span>
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</a>
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</li>
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</ul>
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</nav>
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<li class="md-nav__item md-nav__item--nested">
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
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<div class="md-nav__link md-nav__container">
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<a href="../../chapter_stack_and_queue/" class="md-nav__link ">
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
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<span class="md-ellipsis">
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第 5 章 堆疊與佇列
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</span>
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</a>
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<label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
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<span class="md-nav__icon md-icon"></span>
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</label>
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</div>
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
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<label class="md-nav__title" for="__nav_7">
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<span class="md-nav__icon md-icon"></span>
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第 5 章 堆疊與佇列
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</label>
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<ul class="md-nav__list" data-md-scrollfix>
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<li class="md-nav__item">
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<a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
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<span class="md-ellipsis">
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5.1 堆疊
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</span>
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
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<span class="md-ellipsis">
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5.2 佇列
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</span>
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</a>
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<li class="md-nav__item">
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<a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
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<span class="md-ellipsis">
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5.3 雙向佇列
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</span>
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</a>
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<li class="md-nav__item">
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<a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
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<span class="md-ellipsis">
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5.4 小結
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</span>
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</a>
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</li>
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</ul>
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</nav>
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<li class="md-nav__item md-nav__item--nested">
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
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<div class="md-nav__link md-nav__container">
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<a href="../../chapter_hashing/" class="md-nav__link ">
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
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<span class="md-ellipsis">
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第 6 章 雜湊表
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</span>
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</a>
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<label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
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<span class="md-nav__icon md-icon"></span>
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</label>
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</div>
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
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<label class="md-nav__title" for="__nav_8">
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<span class="md-nav__icon md-icon"></span>
|
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|
第 6 章 雜湊表
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</label>
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<ul class="md-nav__list" data-md-scrollfix>
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<li class="md-nav__item">
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<a href="../../chapter_hashing/hash_map/" class="md-nav__link">
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<span class="md-ellipsis">
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6.1 雜湊表
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</span>
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
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<span class="md-ellipsis">
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6.2 雜湊衝突
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</span>
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
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<span class="md-ellipsis">
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6.3 雜湊演算法
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</span>
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../../chapter_hashing/summary/" class="md-nav__link">
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<span class="md-ellipsis">
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6.4 小結
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</span>
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</a>
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</li>
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</ul>
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</nav>
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<li class="md-nav__item md-nav__item--nested">
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
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<div class="md-nav__link md-nav__container">
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<a href="../../chapter_tree/" class="md-nav__link ">
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
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<span class="md-ellipsis">
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第 7 章 樹
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</span>
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</a>
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<label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
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<span class="md-nav__icon md-icon"></span>
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</label>
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</div>
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
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<label class="md-nav__title" for="__nav_9">
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<span class="md-nav__icon md-icon"></span>
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第 7 章 樹
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</label>
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<ul class="md-nav__list" data-md-scrollfix>
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<li class="md-nav__item">
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<a href="../../chapter_tree/binary_tree/" class="md-nav__link">
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<span class="md-ellipsis">
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7.1 二元樹
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</span>
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
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<span class="md-ellipsis">
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7.2 二元樹走訪
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</span>
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
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<span class="md-ellipsis">
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7.3 二元樹陣列表示
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</span>
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
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<span class="md-ellipsis">
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7.4 二元搜尋樹
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</span>
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../../chapter_tree/avl_tree/" class="md-nav__link">
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<span class="md-ellipsis">
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7.5 AVL *
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</span>
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</a>
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<li class="md-nav__item">
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<a href="../../chapter_tree/summary/" class="md-nav__link">
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<span class="md-ellipsis">
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7.6 小結
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</span>
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</a>
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</li>
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<li class="md-nav__item md-nav__item--nested">
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
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<div class="md-nav__link md-nav__container">
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<a href="../../chapter_heap/" class="md-nav__link ">
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><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"/></svg>
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<span class="md-ellipsis">
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第 8 章 堆積
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</span>
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</a>
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<label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
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<span class="md-nav__icon md-icon"></span>
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</label>
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</div>
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
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<label class="md-nav__title" for="__nav_10">
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<span class="md-nav__icon md-icon"></span>
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第 8 章 堆積
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</label>
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<ul class="md-nav__list" data-md-scrollfix>
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<li class="md-nav__item">
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<a href="../../chapter_heap/heap/" class="md-nav__link">
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<span class="md-ellipsis">
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8.1 堆積
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</span>
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</a>
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<li class="md-nav__item">
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<a href="../../chapter_heap/build_heap/" class="md-nav__link">
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<span class="md-ellipsis">
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8.2 建堆積操作
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</span>
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</a>
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<li class="md-nav__item">
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<a href="../../chapter_heap/top_k/" class="md-nav__link">
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<span class="md-ellipsis">
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8.3 Top-k 問題
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</span>
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</a>
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<li class="md-nav__item">
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<a href="../../chapter_heap/summary/" class="md-nav__link">
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<span class="md-ellipsis">
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8.4 小結
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</span>
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</a>
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</li>
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</ul>
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</nav>
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<li class="md-nav__item md-nav__item--nested">
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
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<div class="md-nav__link md-nav__container">
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<a href="../../chapter_graph/" class="md-nav__link ">
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
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<span class="md-ellipsis">
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第 9 章 圖
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</span>
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</a>
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<label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
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<span class="md-nav__icon md-icon"></span>
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</label>
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</div>
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
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<label class="md-nav__title" for="__nav_11">
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<span class="md-nav__icon md-icon"></span>
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第 9 章 圖
|
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</label>
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<ul class="md-nav__list" data-md-scrollfix>
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<li class="md-nav__item">
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<a href="../../chapter_graph/graph/" class="md-nav__link">
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<span class="md-ellipsis">
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9.1 圖
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</span>
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../../chapter_graph/graph_operations/" class="md-nav__link">
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<span class="md-ellipsis">
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9.2 圖基礎操作
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</span>
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
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<span class="md-ellipsis">
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9.3 圖的走訪
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</span>
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</a>
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<li class="md-nav__item">
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<a href="../../chapter_graph/summary/" class="md-nav__link">
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<span class="md-ellipsis">
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9.4 小結
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</span>
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</a>
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</li>
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</ul>
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<li class="md-nav__item md-nav__item--nested">
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
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<div class="md-nav__link md-nav__container">
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<a href="../../chapter_searching/" class="md-nav__link ">
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
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<span class="md-ellipsis">
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第 10 章 搜尋
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</span>
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</a>
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<label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
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<span class="md-nav__icon md-icon"></span>
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</label>
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</div>
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
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<label class="md-nav__title" for="__nav_12">
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<span class="md-nav__icon md-icon"></span>
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第 10 章 搜尋
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</label>
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<ul class="md-nav__list" data-md-scrollfix>
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<li class="md-nav__item">
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<a href="../../chapter_searching/binary_search/" class="md-nav__link">
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<span class="md-ellipsis">
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10.1 二分搜尋
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</span>
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</a>
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<li class="md-nav__item">
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<a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
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<span class="md-ellipsis">
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10.2 二分搜尋插入點
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</span>
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<li class="md-nav__item">
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<a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
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<span class="md-ellipsis">
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10.3 二分搜尋邊界
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</span>
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</a>
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<a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
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<span class="md-ellipsis">
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10.4 雜湊最佳化策略
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</span>
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</a>
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<li class="md-nav__item">
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<a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
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<span class="md-ellipsis">
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10.5 重識搜尋演算法
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</span>
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</a>
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<li class="md-nav__item">
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<a href="../../chapter_searching/summary/" class="md-nav__link">
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<span class="md-ellipsis">
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10.6 小結
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</span>
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</a>
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</li>
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</ul>
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<li class="md-nav__item md-nav__item--nested">
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
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<div class="md-nav__link md-nav__container">
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<a href="../../chapter_sorting/" class="md-nav__link ">
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
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<span class="md-ellipsis">
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第 11 章 排序
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</span>
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</a>
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<label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
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<span class="md-nav__icon md-icon"></span>
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</div>
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
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<label class="md-nav__title" for="__nav_13">
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<span class="md-nav__icon md-icon"></span>
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第 11 章 排序
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</label>
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<ul class="md-nav__list" data-md-scrollfix>
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<li class="md-nav__item">
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<a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
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<span class="md-ellipsis">
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11.1 排序演算法
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</span>
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
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<span class="md-ellipsis">
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11.2 選擇排序
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</span>
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
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<span class="md-ellipsis">
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11.3 泡沫排序
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</span>
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
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<span class="md-ellipsis">
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11.4 插入排序
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</span>
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
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<span class="md-ellipsis">
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11.5 快速排序
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</span>
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
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<span class="md-ellipsis">
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11.6 合併排序
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</span>
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
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<span class="md-ellipsis">
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11.7 堆積排序
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</span>
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
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<span class="md-ellipsis">
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11.8 桶排序
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</span>
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
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<span class="md-ellipsis">
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11.9 計數排序
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</span>
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
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<span class="md-ellipsis">
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11.10 基數排序
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</span>
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../../chapter_sorting/summary/" class="md-nav__link">
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<span class="md-ellipsis">
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11.11 小結
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</span>
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</a>
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</li>
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</ul>
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</nav>
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</li>
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<li class="md-nav__item md-nav__item--nested">
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<a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
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<span class="md-ellipsis">
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第 12 章 分治
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</span>
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</a>
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<label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
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<span class="md-nav__icon md-icon"></span>
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</div>
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
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<label class="md-nav__title" for="__nav_14">
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<span class="md-nav__icon md-icon"></span>
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第 12 章 分治
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</label>
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<ul class="md-nav__list" data-md-scrollfix>
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<li class="md-nav__item">
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<a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
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<span class="md-ellipsis">
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12.1 分治演算法
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</span>
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
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<span class="md-ellipsis">
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12.2 分治搜尋策略
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</span>
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
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<span class="md-ellipsis">
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12.3 構建樹問題
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</span>
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
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<span class="md-ellipsis">
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12.4 河內塔問題
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</span>
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
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<span class="md-ellipsis">
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12.5 小結
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</span>
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</a>
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</li>
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</ul>
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</nav>
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<li class="md-nav__item md-nav__item--nested">
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<a href="../../chapter_backtracking/" class="md-nav__link ">
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
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<span class="md-ellipsis">
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第 13 章 回溯
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</span>
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</a>
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<label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
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<span class="md-nav__icon md-icon"></span>
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</label>
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</div>
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
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<label class="md-nav__title" for="__nav_15">
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<span class="md-nav__icon md-icon"></span>
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第 13 章 回溯
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</label>
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<ul class="md-nav__list" data-md-scrollfix>
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<a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
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<span class="md-ellipsis">
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13.1 回溯演算法
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<a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
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<span class="md-ellipsis">
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13.2 全排列問題
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<li class="md-nav__item">
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<a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
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<span class="md-ellipsis">
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13.3 子集和問題
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<a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
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<span class="md-ellipsis">
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13.4 N 皇后問題
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<a href="../../chapter_backtracking/summary/" class="md-nav__link">
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<span class="md-ellipsis">
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13.5 小結
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</a>
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<span class="md-ellipsis">
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第 14 章 動態規劃
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<span class="md-nav__icon md-icon"></span>
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第 14 章 動態規劃
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<ul class="md-nav__list" data-md-scrollfix>
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<span class="md-ellipsis">
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14.1 初探動態規劃
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<a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
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<span class="md-ellipsis">
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14.2 DP 問題特性
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<a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
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<span class="md-ellipsis">
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14.3 DP 解題思路
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<span class="md-ellipsis">
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14.4 0-1 背包問題
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<li class="md-nav__item">
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<a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
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<span class="md-ellipsis">
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14.5 完全背包問題
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</span>
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<li class="md-nav__item">
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<a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
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<span class="md-ellipsis">
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14.6 編輯距離問題
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</span>
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<a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
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<span class="md-ellipsis">
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14.7 小結
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</a>
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<span class="md-ellipsis">
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第 15 章 貪婪
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</span>
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</a>
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<span class="md-nav__icon md-icon"></span>
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第 15 章 貪婪
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<ul class="md-nav__list" data-md-scrollfix>
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<span class="md-ellipsis">
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15.1 貪婪演算法
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</span>
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<a href="../../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
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<span class="md-ellipsis">
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15.2 分數背包問題
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</span>
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<a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
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<span class="md-ellipsis">
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15.3 最大容量問題
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</span>
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<li class="md-nav__item">
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<a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
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<span class="md-ellipsis">
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15.4 最大切分乘積問題
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</span>
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<li class="md-nav__item">
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<span class="md-ellipsis">
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15.5 小結
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</span>
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</a>
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<span class="md-ellipsis">
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第 16 章 附錄
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</span>
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</a>
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第 16 章 附錄
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16.1 程式設計環境安裝
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16.3 術語表
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0.2.1 行文風格約定
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0.2.2 在動畫圖解中高效學習
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0.2.3 在程式碼實踐中加深理解
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0.2.4 在提問討論中共同成長
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0.2.5 演算法學習路線
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<h1 id="02">0.2 如何使用本書<a class="headerlink" href="#02" title="Permanent link">¶</a></h1>
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<div class="admonition tip">
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|
|
<p class="admonition-title">Tip</p>
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<p>為了獲得最佳的閱讀體驗，建議你通讀本節內容。</p>
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</div>
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<h2 id="021">0.2.1 行文風格約定<a class="headerlink" href="#021" title="Permanent link">¶</a></h2>
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<ul>
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|
<li>標題後標註 <code>*</code> 的是選讀章節，內容相對困難。如果你的時間有限，可以先跳過。</li>
|
|
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<li>專業術語會使用黑體（紙質版和 PDF 版）或新增下劃線（網頁版），例如<u>陣列（array）</u>。建議記住它們，以便閱讀文獻。</li>
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|
|
<li>重點內容和總結性語句會 <strong>加粗</strong>，這類文字值得特別關注。</li>
|
|
|
<li>有特指含義的詞句會使用“引號”標註，以避免歧義。</li>
|
|
|
<li>當涉及程式語言之間不一致的名詞時，本書均以 Python 為準，例如使用 <code>None</code> 來表示“空”。</li>
|
|
|
<li>本書部分放棄了程式語言的註釋規範，以換取更加緊湊的內容排版。註釋主要分為三種類型：標題註釋、內容註釋、多行註釋。</li>
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</ul>
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<div class="tabbed-set tabbed-alternate" data-tabs="1:14"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><input id="__tabbed_1_14" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label><label for="__tabbed_1_14">Zig</label></div>
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<div class="tabbed-content">
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<div class="tabbed-block">
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<div class="highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="sd">"""標題註釋，用於標註函式、類別、測試樣例等"""</span>
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<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a>
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<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a><span class="c1"># 內容註釋，用於詳解程式碼</span>
|
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<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>
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<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a><span class="sd">"""</span>
|
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|
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a><span class="sd">多行</span>
|
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<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a><span class="sd">註釋</span>
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<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a><span class="sd">"""</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 標題註釋，用於標註函式、類別、測試樣例等 */</span>
|
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<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a>
|
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<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="c1">// 內容註釋，用於詳解程式碼</span>
|
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<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a>
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<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="cm">/**</span>
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<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="cm"> * 多行</span>
|
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<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="cm"> * 註釋</span>
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<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="cm"> */</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 標題註釋，用於標註函式、類別、測試樣例等 */</span>
|
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<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a>
|
|
|
<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="c1">// 內容註釋，用於詳解程式碼</span>
|
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<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a>
|
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<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="cm">/**</span>
|
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<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="cm"> * 多行</span>
|
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<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="cm"> * 註釋</span>
|
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<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="cm"> */</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
|
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<div class="highlight"><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 標題註釋，用於標註函式、類別、測試樣例等 */</span>
|
|
|
<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a>
|
|
|
<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="c1">// 內容註釋，用於詳解程式碼</span>
|
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|
<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a>
|
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|
<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="cm">/**</span>
|
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<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="cm"> * 多行</span>
|
|
|
<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="cm"> * 註釋</span>
|
|
|
<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="cm"> */</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
|
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<div class="highlight"><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* 標題註釋，用於標註函式、類別、測試樣例等 */</span>
|
|
|
<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a>
|
|
|
<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="c1">// 內容註釋，用於詳解程式碼</span>
|
|
|
<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a>
|
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|
<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="cm">/**</span>
|
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|
<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="cm"> * 多行</span>
|
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|
<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="cm"> * 註釋</span>
|
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|
<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="cm"> */</span>
|
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* 標題註釋，用於標註函式、類別、測試樣例等 */</span>
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<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a>
|
|
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<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="c1">// 內容註釋，用於詳解程式碼</span>
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<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a>
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<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="cm">/**</span>
|
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<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="cm"> * 多行</span>
|
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<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="cm"> * 註釋</span>
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<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="cm"> */</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* 標題註釋，用於標註函式、類別、測試樣例等 */</span>
|
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<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a>
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<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="c1">// 內容註釋，用於詳解程式碼</span>
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<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a>
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<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="cm">/**</span>
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<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="cm"> * 多行</span>
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<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="cm"> * 註釋</span>
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<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="cm"> */</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* 標題註釋，用於標註函式、類別、測試樣例等 */</span>
|
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<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a>
|
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<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="c1">// 內容註釋，用於詳解程式碼</span>
|
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<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a>
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<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="cm">/**</span>
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<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="cm"> * 多行</span>
|
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<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="cm"> * 註釋</span>
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<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="cm"> */</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 標題註釋，用於標註函式、類別、測試樣例等 */</span>
|
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<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a>
|
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|
<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="c1">// 內容註釋，用於詳解程式碼</span>
|
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<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a>
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<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="cm">/**</span>
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<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="cm"> * 多行</span>
|
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<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="cm"> * 註釋</span>
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<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="cm"> */</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* 標題註釋，用於標註函式、類別、測試樣例等 */</span>
|
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<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a>
|
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|
<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="c1">// 內容註釋，用於詳解程式碼</span>
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<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a>
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<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="sd">/**</span>
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<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="sd"> * 多行</span>
|
|
|
<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="sd"> * 註釋</span>
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<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="sd"> */</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* 標題註釋，用於標註函式、類別、測試樣例等 */</span>
|
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<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a>
|
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|
<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="c1">// 內容註釋，用於詳解程式碼</span>
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<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a>
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<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="cm">/**</span>
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<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a><span class="cm"> * 多行</span>
|
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<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="cm"> * 註釋</span>
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<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="cm"> */</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* 標題註釋，用於標註函式、類別、測試樣例等 */</span>
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<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a>
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<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="c1">// 內容註釋，用於詳解程式碼</span>
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<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a>
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<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="cm">/**</span>
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<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="cm"> * 多行</span>
|
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<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="cm"> * 註釋</span>
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<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="cm"> */</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### 標題註釋，用於標註函式、類別、測試樣例等 ###</span>
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<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a>
|
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<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="c1"># 內容註釋，用於詳解程式碼</span>
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<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a>
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<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="c1"># 多行</span>
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<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="c1"># 註釋</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
|
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<div class="highlight"><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="c1">// 標題註釋，用於標註函式、類別、測試樣例等</span>
|
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|
<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a>
|
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|
<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a><span class="c1">// 內容註釋，用於詳解程式碼</span>
|
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|
<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a>
|
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<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a><span class="c1">// 多行</span>
|
|
|
<a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a><span class="c1">// 註釋</span>
|
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|
</code></pre></div>
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|
</div>
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</div>
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</div>
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<h2 id="022">0.2.2 在動畫圖解中高效學習<a class="headerlink" href="#022" title="Permanent link">¶</a></h2>
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<p>相較於文字，影片和圖片具有更高的資訊密度和結構化程度，更易於理解。在本書中，<strong>重點和難點知識將主要透過動畫以圖解形式展示</strong>，而文字則作為解釋與補充。</p>
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|
|
<p>如果你在閱讀本書時，發現某段內容提供瞭如圖 0-2 所示的動畫圖解，<strong>請以圖為主、以文字為輔</strong>，綜合兩者來理解內容。</p>
|
|
|
<p><a class="glightbox" href="../../index.assets/animation.gif" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="動畫圖解示例" class="animation-figure" src="../../index.assets/animation.gif" /></a></p>
|
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|
<p align="center"> 圖 0-2 動畫圖解示例 </p>
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<h2 id="023">0.2.3 在程式碼實踐中加深理解<a class="headerlink" href="#023" title="Permanent link">¶</a></h2>
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<p>本書的配套程式碼託管在 <a href="https://github.com/krahets/hello-algo">GitHub 倉庫</a>。如圖 0-3 所示，<strong>源程式碼附有測試樣例，可一鍵執行</strong>。</p>
|
|
|
<p>如果時間允許，<strong>建議你參照程式碼自行敲一遍</strong>。如果學習時間有限，請至少通讀並執行所有程式碼。</p>
|
|
|
<p>與閱讀程式碼相比，編寫程式碼的過程往往能帶來更多收穫。<strong>動手學，才是真的學</strong>。</p>
|
|
|
<p><a class="glightbox" href="../../index.assets/running_code.gif" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="執行程式碼示例" class="animation-figure" src="../../index.assets/running_code.gif" /></a></p>
|
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<p align="center"> 圖 0-3 執行程式碼示例 </p>
|
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|
<p>執行程式碼的前置工作主要分為三步。</p>
|
|
|
<p><strong>第一步：安裝本地程式設計環境</strong>。請參照附錄所示的<a href="https://www.hello-algo.com/chapter_appendix/installation/">教程</a>進行安裝，如果已安裝，則可跳過此步驟。</p>
|
|
|
<p><strong>第二步：克隆或下載程式碼倉庫</strong>。前往 <a href="https://github.com/krahets/hello-algo">GitHub 倉庫</a>。如果已經安裝 <a href="https://git-scm.com/downloads">Git</a> ，可以透過以下命令克隆本倉庫：</p>
|
|
|
<div class="highlight"><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a>git<span class="w"> </span>clone<span class="w"> </span>https://github.com/krahets/hello-algo.git
|
|
|
</code></pre></div>
|
|
|
<p>當然，你也可以在圖 0-4 所示的位置，點選“Download ZIP”按鈕直接下載程式碼壓縮包，然後在本地解壓即可。</p>
|
|
|
<p><a class="glightbox" href="../suggestions.assets/download_code.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="克隆倉庫與下載程式碼" class="animation-figure" src="../suggestions.assets/download_code.png" /></a></p>
|
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|
<p align="center"> 圖 0-4 克隆倉庫與下載程式碼 </p>
|
|
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|
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|
<p><strong>第三步：執行源程式碼</strong>。如圖 0-5 所示，對於頂部標有檔案名稱的程式碼塊，我們可以在倉庫的 <code>codes</code> 檔案夾內找到對應的源程式碼檔案。源程式碼檔案可一鍵執行，將幫助你節省不必要的除錯時間，讓你能夠專注於學習內容。</p>
|
|
|
<p><a class="glightbox" href="../suggestions.assets/code_md_to_repo.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="程式碼塊與對應的源程式碼檔案" class="animation-figure" src="../suggestions.assets/code_md_to_repo.png" /></a></p>
|
|
|
<p align="center"> 圖 0-5 程式碼塊與對應的源程式碼檔案 </p>
|
|
|
|
|
|
<p>除了本地執行程式碼，<strong>網頁版還支持 Python 程式碼的視覺化執行</strong>（基於 <a href="https://pythontutor.com/">pythontutor</a> 實現）。如圖 0-6 所示，你可以點選程式碼塊下方的“視覺化執行”來展開檢視，觀察演算法程式碼的執行過程；也可以點選“全屏觀看”，以獲得更好的閱覽體驗。</p>
|
|
|
<p><a class="glightbox" href="../suggestions.assets/pythontutor_example.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Python 程式碼的視覺化執行" class="animation-figure" src="../suggestions.assets/pythontutor_example.png" /></a></p>
|
|
|
<p align="center"> 圖 0-6 Python 程式碼的視覺化執行 </p>
|
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|
<h2 id="024">0.2.4 在提問討論中共同成長<a class="headerlink" href="#024" title="Permanent link">¶</a></h2>
|
|
|
<p>在閱讀本書時，請不要輕易跳過那些沒學明白的知識點。<strong>歡迎在評論區提出你的問題</strong>，我和小夥伴們將竭誠為你解答，一般情況下可在兩天內回覆。</p>
|
|
|
<p>如圖 0-7 所示，網頁版每個章節的底部都配有評論區。希望你能多關注評論區的內容。一方面，你可以瞭解大家遇到的問題，從而查漏補缺，激發更深入的思考。另一方面，期待你能慷慨地回答其他小夥伴的問題，分享你的見解，幫助他人進步。</p>
|
|
|
<p><a class="glightbox" href="../../index.assets/comment.gif" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="評論區示例" class="animation-figure" src="../../index.assets/comment.gif" /></a></p>
|
|
|
<p align="center"> 圖 0-7 評論區示例 </p>
|
|
|
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|
|
<h2 id="025">0.2.5 演算法學習路線<a class="headerlink" href="#025" title="Permanent link">¶</a></h2>
|
|
|
<p>從總體上看，我們可以將學習資料結構與演算法的過程劃分為三個階段。</p>
|
|
|
<ol>
|
|
|
<li><strong>階段一：演算法入門</strong>。我們需要熟悉各種資料結構的特點和用法，學習不同演算法的原理、流程、用途和效率等方面的內容。</li>
|
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<li><strong>階段二：刷演算法題</strong>。建議從熱門題目開刷，先積累至少 100 道題目，熟悉主流的演算法問題。初次刷題時，“知識遺忘”可能是一個挑戰，但請放心，這是很正常的。我們可以按照“艾賓浩斯遺忘曲線”來複習題目，通常在進行 3～5 輪的重複後，就能將其牢記在心。推薦的題單和刷題計劃請見此 <a href="https://github.com/krahets/LeetCode-Book">GitHub 倉庫</a>。</li>
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<li><strong>階段三：搭建知識體系</strong>。在學習方面，我們可以閱讀演算法專欄文章、解題框架和演算法教材，以不斷豐富知識體系。在刷題方面，可以嘗試採用進階刷題策略，如按專題分類、一題多解、一解多題等，相關的刷題心得可以在各個社群找到。</li>
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</ol>
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<p>如圖 0-8 所示，本書內容主要涵蓋“階段一”，旨在幫助你更高效地展開階段二和階段三的學習。</p>
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<p><a class="glightbox" href="../suggestions.assets/learning_route.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="演算法學習路線" class="animation-figure" src="../suggestions.assets/learning_route.png" /></a></p>
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<p align="center"> 圖 0-8 演算法學習路線 </p>
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