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<title>9.2. 图基础操作 - Hello 算法</title>
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跳转至
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Hello 算法
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9.2. 图基础操作
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</span>
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正在初始化搜索引擎
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<div class="md-header__source">
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<a href="https://github.com/krahets/hello-algo" title="前往仓库" class="md-source" data-md-component="source">
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 496 512"><!--! Font Awesome Free 6.2.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2022 Fonticons, Inc.--><path d="M165.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6zm-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3zm44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9zM244.8 8C106.1 8 0 113.3 0 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C428.2 457.8 496 362.9 496 252 496 113.3 383.5 8 244.8 8zM97.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1zm-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7zm32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6 0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2z"/></svg>
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krahets/hello-algo
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</label>
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<span class="md-nav__icon md-icon"></span>
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0. 写在前面
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0.1. 关于本书
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0.2. 如何使用本书
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0.3. 编程环境安装
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1. 引言
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<span class="md-nav__icon md-icon"></span>
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1. 引言
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1.1. 算法无处不在
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</a>
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</li>
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1.2. 算法是什么
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</nav>
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<label class="md-nav__link" for="__nav_3" id="__nav_3_label" tabindex="0">
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2. 计算复杂度
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<span class="md-nav__icon md-icon"></span>
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</label>
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
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<span class="md-nav__icon md-icon"></span>
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2. 计算复杂度
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</label>
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<ul class="md-nav__list" data-md-scrollfix>
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<a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
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2.1. 算法效率评估
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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_computational_complexity/time_complexity/" class="md-nav__link">
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2.2. 时间复杂度
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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_computational_complexity/space_complexity/" class="md-nav__link">
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2.3. 空间复杂度
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</a>
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</li>
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<a href="../../chapter_computational_complexity/space_time_tradeoff/" class="md-nav__link">
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2.4. 权衡时间与空间
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</a>
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</li>
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<a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
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2.5. 小结
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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--section md-nav__item--nested">
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
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<label class="md-nav__link" for="__nav_4" id="__nav_4_label" tabindex="0">
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3. 数据结构简介
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<span class="md-nav__icon md-icon"></span>
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</label>
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
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<label class="md-nav__title" for="__nav_4">
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<span class="md-nav__icon md-icon"></span>
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3. 数据结构简介
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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_data_structure/data_and_memory/" class="md-nav__link">
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3.1. 数据与内存
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</a>
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</li>
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<a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
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3.2. 数据结构分类
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</a>
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<a href="../../chapter_data_structure/summary/" class="md-nav__link">
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3.3. 小结
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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--section md-nav__item--nested">
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
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<label class="md-nav__link" for="__nav_5" id="__nav_5_label" tabindex="0">
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4. 数组与链表
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<span class="md-nav__icon md-icon"></span>
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</label>
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
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<label class="md-nav__title" for="__nav_5">
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<span class="md-nav__icon md-icon"></span>
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4. 数组与链表
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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_array_and_linkedlist/array/" class="md-nav__link">
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4.1. 数组（Array）
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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/linked_list/" class="md-nav__link">
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4.2. 链表（LinkedList）
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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/list/" class="md-nav__link">
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4.3. 列表（List）
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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/summary/" class="md-nav__link">
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4.4. 小结
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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--section md-nav__item--nested">
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
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<label class="md-nav__link" for="__nav_6" id="__nav_6_label" tabindex="0">
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5. 栈与队列
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<span class="md-nav__icon md-icon"></span>
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</label>
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
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<label class="md-nav__title" for="__nav_6">
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<span class="md-nav__icon md-icon"></span>
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5. 栈与队列
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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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5.1. 栈（Stack）
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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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5.2. 队列（Queue）
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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/deque/" class="md-nav__link">
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5.3. 双向队列（Deque）
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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/summary/" class="md-nav__link">
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5.4. 小结
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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--section md-nav__item--nested">
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
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<label class="md-nav__link" for="__nav_7" id="__nav_7_label" tabindex="0">
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6. 散列表
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<span class="md-nav__icon md-icon"></span>
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</label>
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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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6. 散列表
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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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6.1. 哈希表（HashMap）
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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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6.2. 哈希冲突处理
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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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6.3. 小结
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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--section md-nav__item--nested">
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
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<label class="md-nav__link" for="__nav_8" id="__nav_8_label" tabindex="0">
|
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7. 二叉树
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<span class="md-nav__icon md-icon"></span>
|
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</label>
|
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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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7. 二叉树
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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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7.1. 二叉树（Binary Tree）
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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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7.2. 二叉树遍历
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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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7.3. 二叉搜索树
|
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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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7.4. AVL 树 *
|
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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/summary/" class="md-nav__link">
|
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7.5. 小结
|
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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--section md-nav__item--nested">
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
|
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<label class="md-nav__link" for="__nav_9" id="__nav_9_label" tabindex="0">
|
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8. 堆
|
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<span class="md-nav__icon md-icon"></span>
|
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</label>
|
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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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8. 堆
|
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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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8.1. 堆（Heap）
|
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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--active md-nav__item--section md-nav__item--nested">
|
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" checked>
|
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<label class="md-nav__link" for="__nav_10" id="__nav_10_label" tabindex="0">
|
|
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|
|
9. 图
|
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|
<span class="md-nav__icon md-icon"></span>
|
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|
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</label>
|
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|
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="true">
|
|
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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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|
|
9. 图
|
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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="../graph/" class="md-nav__link">
|
|
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|
|
9.1. 图（Graph）
|
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|
|
</a>
|
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</li>
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<li class="md-nav__item md-nav__item--active">
|
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|
|
<input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
|
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|
<label class="md-nav__link md-nav__link--active" for="__toc">
|
|
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|
|
9.2. 图基础操作
|
|
|
|
|
|
<span class="md-nav__icon md-icon"></span>
|
|
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|
|
|
</label>
|
|
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|
|
<a href="./" class="md-nav__link md-nav__link--active">
|
|
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|
|
9.2. 图基础操作
|
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</a>
|
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|
<nav class="md-nav md-nav--secondary" aria-label="目录">
|
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<label class="md-nav__title" for="__toc">
|
|
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|
|
<span class="md-nav__icon md-icon"></span>
|
|
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|
|
目录
|
|
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|
|
</label>
|
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|
|
<ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
|
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|
<li class="md-nav__item">
|
|
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|
|
<a href="#921" class="md-nav__link">
|
|
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|
|
|
9.2.1. 基于邻接矩阵的实现
|
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|
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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="#922" class="md-nav__link">
|
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|
|
9.2.2. 基于邻接表的实现
|
|
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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="#923" class="md-nav__link">
|
|
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|
|
9.2.3. 效率对比
|
|
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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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</ul>
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</nav>
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</li>
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<li class="md-nav__item md-nav__item--section md-nav__item--nested">
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
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<label class="md-nav__link" for="__nav_11" id="__nav_11_label" tabindex="0">
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10. 查找算法
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<span class="md-nav__icon md-icon"></span>
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</label>
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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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10. 查找算法
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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/linear_search/" class="md-nav__link">
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10.1. 线性查找
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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_searching/binary_search/" class="md-nav__link">
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10.2. 二分查找
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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_searching/hashing_search/" class="md-nav__link">
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10.3. 哈希查找
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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_searching/summary/" class="md-nav__link">
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10.4. 小结
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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--section md-nav__item--nested">
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
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<label class="md-nav__link" for="__nav_12" id="__nav_12_label" tabindex="0">
|
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11. 排序算法
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<span class="md-nav__icon md-icon"></span>
|
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</label>
|
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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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|
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11. 排序算法
|
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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/intro_to_sort/" class="md-nav__link">
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11.1. 排序简介
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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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11.2. 冒泡排序
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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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11.3. 插入排序
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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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11.4. 快速排序
|
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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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11.5. 归并排序
|
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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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11.6. 小结
|
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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--section 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__link--index ">
|
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<a href="../../chapter_reference/">参考文献</a>
|
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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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|
|
参考文献
|
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</label>
|
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<ul class="md-nav__list" data-md-scrollfix>
|
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</ul>
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</nav>
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</li>
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</ul>
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</nav>
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</div>
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</div>
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</div>
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|
<div class="md-sidebar md-sidebar--secondary" data-md-component="sidebar" data-md-type="toc" >
|
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|
|
<div class="md-sidebar__scrollwrap">
|
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<div class="md-sidebar__inner">
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<nav class="md-nav md-nav--secondary" aria-label="目录">
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<label class="md-nav__title" for="__toc">
|
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|
<span class="md-nav__icon md-icon"></span>
|
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|
|
目录
|
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</label>
|
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<ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
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<li class="md-nav__item">
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<a href="#921" class="md-nav__link">
|
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|
|
9.2.1. 基于邻接矩阵的实现
|
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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="#922" class="md-nav__link">
|
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|
|
9.2.2. 基于邻接表的实现
|
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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="#923" class="md-nav__link">
|
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|
9.2.3. 效率对比
|
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</a>
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</li>
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</ul>
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</nav>
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</div>
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</div>
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</div>
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<div class="md-content" data-md-component="content">
|
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|
<article class="md-content__inner md-typeset">
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|
<a href="https://github.com/krahets/hello-algo/tree/main/docs/chapter_graph/graph_operations.md" title="编辑此页" class="md-content__button md-icon">
|
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M10 20H6V4h7v5h5v3.1l2-2V8l-6-6H6c-1.1 0-2 .9-2 2v16c0 1.1.9 2 2 2h4v-2m10.2-7c.1 0 .3.1.4.2l1.3 1.3c.2.2.2.6 0 .8l-1 1-2.1-2.1 1-1c.1-.1.2-.2.4-.2m0 3.9L14.1 23H12v-2.1l6.1-6.1 2.1 2.1Z"/></svg>
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</a>
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<h1 id="92">9.2. 图基础操作<a class="headerlink" href="#92" title="Permanent link">¶</a></h1>
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<p>图的基础操作分为对「边」的操作和对「顶点」的操作，在「邻接矩阵」和「邻接表」这两种表示下的实现方式不同。</p>
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<h2 id="921">9.2.1. 基于邻接矩阵的实现<a class="headerlink" href="#921" title="Permanent link">¶</a></h2>
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<p>设图的顶点总数为 <span class="arithmatex">\(n\)</span> ，则有：</p>
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<ul>
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<li><strong>添加或删除边</strong>：直接在邻接矩阵中修改指定边的对应元素即可，使用 <span class="arithmatex">\(O(1)\)</span> 时间。而由于是无向图，因此需要同时更新两个方向的边。</li>
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<li><strong>添加顶点</strong>：在邻接矩阵的尾部添加一行一列，并全部填 <span class="arithmatex">\(0\)</span> 即可，使用 <span class="arithmatex">\(O(n)\)</span> 时间。</li>
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<li><strong>删除顶点</strong>：在邻接矩阵中删除一行一列。当删除首行首列时达到最差情况，需要将 <span class="arithmatex">\((n-1)^2\)</span> 个元素“向左上移动”，从而使用 <span class="arithmatex">\(O(n^2)\)</span> 时间。</li>
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<li><strong>初始化</strong>：传入 <span class="arithmatex">\(n\)</span> 个顶点，初始化长度为 <span class="arithmatex">\(n\)</span> 的顶点列表 <code>vertices</code> ，使用 <span class="arithmatex">\(O(n)\)</span> 时间；初始化 <span class="arithmatex">\(n \times n\)</span> 大小的邻接矩阵 <code>adjMat</code> ，使用 <span class="arithmatex">\(O(n^2)\)</span> 时间。</li>
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</ul>
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<div class="tabbed-set tabbed-alternate" data-tabs="1:5"><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" /><div class="tabbed-labels"><label for="__tabbed_1_1">初始化邻接矩阵</label><label for="__tabbed_1_2">添加边</label><label for="__tabbed_1_3">删除边</label><label for="__tabbed_1_4">添加顶点</label><label for="__tabbed_1_5">删除顶点</label></div>
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<div class="tabbed-content">
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<div class="tabbed-block">
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<p><img alt="adjacency_matrix_initialization" src="../graph_operations.assets/adjacency_matrix_initialization.png" /></p>
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</div>
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<div class="tabbed-block">
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<p><img alt="adjacency_matrix_add_edge" src="../graph_operations.assets/adjacency_matrix_add_edge.png" /></p>
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</div>
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<div class="tabbed-block">
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<p><img alt="adjacency_matrix_remove_edge" src="../graph_operations.assets/adjacency_matrix_remove_edge.png" /></p>
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</div>
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<div class="tabbed-block">
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<p><img alt="adjacency_matrix_add_vertex" src="../graph_operations.assets/adjacency_matrix_add_vertex.png" /></p>
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</div>
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<div class="tabbed-block">
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<p><img alt="adjacency_matrix_remove_vertex" src="../graph_operations.assets/adjacency_matrix_remove_vertex.png" /></p>
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</div>
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</div>
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</div>
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<p>以下是基于邻接矩阵表示图的实现代码。</p>
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<div class="tabbed-set tabbed-alternate" data-tabs="2:10"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Java</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Python</label><label for="__tabbed_2_4">Go</label><label for="__tabbed_2_5">JavaScript</label><label for="__tabbed_2_6">TypeScript</label><label for="__tabbed_2_7">C</label><label for="__tabbed_2_8">C#</label><label for="__tabbed_2_9">Swift</label><label for="__tabbed_2_10">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"><span class="filename">graph_adjacency_matrix.java</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="cm">/* 基于邻接矩阵实现的无向图类 */</span>
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<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="kd">class</span> <span class="nc">GraphAdjMat</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">Integer</span><span class="o">></span><span class="w"> </span><span class="n">vertices</span><span class="p">;</span><span class="w"> </span><span class="c1">// 顶点列表，元素代表“顶点值”，索引代表“顶点索引”</span>
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<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">List</span><span class="o"><</span><span class="n">Integer</span><span class="o">>></span><span class="w"> </span><span class="n">adjMat</span><span class="p">;</span><span class="w"> </span><span class="c1">// 邻接矩阵，行列索引对应“顶点索引”</span>
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<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>
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<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a><span class="w"> </span><span class="cm">/* 构造函数 */</span>
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<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="nf">GraphAdjMat</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">vertices</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">[][]</span><span class="w"> </span><span class="n">edges</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="na">vertices</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o"><></span><span class="p">();</span>
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<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="na">adjMat</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o"><></span><span class="p">();</span>
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<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a><span class="w"> </span><span class="c1">// 添加顶点</span>
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<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">vertices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a><span class="w"> </span><span class="n">addVertex</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
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<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a><span class="w"> </span><span class="c1">// 添加边</span>
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<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a><span class="w"> </span><span class="c1">// 请注意，edges 元素代表顶点索引，即对应 vertices 元素索引</span>
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<a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">e</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">edges</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a><span class="w"> </span><span class="n">addEdge</span><span class="p">(</span><span class="n">e</span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">e</span><span class="o">[</span><span class="mi">1</span><span class="o">]</span><span class="p">);</span>
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<a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-0-19" name="__codelineno-0-19" href="#__codelineno-0-19"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-0-20" name="__codelineno-0-20" href="#__codelineno-0-20"></a>
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<a id="__codelineno-0-21" name="__codelineno-0-21" href="#__codelineno-0-21"></a><span class="w"> </span><span class="cm">/* 获取顶点数量 */</span>
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<a id="__codelineno-0-22" name="__codelineno-0-22" href="#__codelineno-0-22"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-0-23" name="__codelineno-0-23" href="#__codelineno-0-23"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">vertices</span><span class="p">.</span><span class="na">size</span><span class="p">();</span>
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<a id="__codelineno-0-24" name="__codelineno-0-24" href="#__codelineno-0-24"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-0-25" name="__codelineno-0-25" href="#__codelineno-0-25"></a>
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<a id="__codelineno-0-26" name="__codelineno-0-26" href="#__codelineno-0-26"></a><span class="w"> </span><span class="cm">/* 添加顶点 */</span>
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<a id="__codelineno-0-27" name="__codelineno-0-27" href="#__codelineno-0-27"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">addVertex</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-0-28" name="__codelineno-0-28" href="#__codelineno-0-28"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">size</span><span class="p">();</span>
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<a id="__codelineno-0-29" name="__codelineno-0-29" href="#__codelineno-0-29"></a><span class="w"> </span><span class="c1">// 向顶点列表中添加新顶点的值</span>
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<a id="__codelineno-0-30" name="__codelineno-0-30" href="#__codelineno-0-30"></a><span class="w"> </span><span class="n">vertices</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
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<a id="__codelineno-0-31" name="__codelineno-0-31" href="#__codelineno-0-31"></a><span class="w"> </span><span class="c1">// 在邻接矩阵中添加一行</span>
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<a id="__codelineno-0-32" name="__codelineno-0-32" href="#__codelineno-0-32"></a><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">Integer</span><span class="o">></span><span class="w"> </span><span class="n">newRow</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o"><></span><span class="p">(</span><span class="n">n</span><span class="p">);</span>
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<a id="__codelineno-0-33" name="__codelineno-0-33" href="#__codelineno-0-33"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-0-34" name="__codelineno-0-34" href="#__codelineno-0-34"></a><span class="w"> </span><span class="n">newRow</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
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<a id="__codelineno-0-35" name="__codelineno-0-35" href="#__codelineno-0-35"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-0-36" name="__codelineno-0-36" href="#__codelineno-0-36"></a><span class="w"> </span><span class="n">adjMat</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">newRow</span><span class="p">);</span>
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<a id="__codelineno-0-37" name="__codelineno-0-37" href="#__codelineno-0-37"></a><span class="w"> </span><span class="c1">// 在邻接矩阵中添加一列</span>
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<a id="__codelineno-0-38" name="__codelineno-0-38" href="#__codelineno-0-38"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">List</span><span class="o"><</span><span class="n">Integer</span><span class="o">></span><span class="w"> </span><span class="n">row</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">adjMat</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-0-39" name="__codelineno-0-39" href="#__codelineno-0-39"></a><span class="w"> </span><span class="n">row</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
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<a id="__codelineno-0-40" name="__codelineno-0-40" href="#__codelineno-0-40"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-0-41" name="__codelineno-0-41" href="#__codelineno-0-41"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-0-42" name="__codelineno-0-42" href="#__codelineno-0-42"></a>
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<a id="__codelineno-0-43" name="__codelineno-0-43" href="#__codelineno-0-43"></a><span class="w"> </span><span class="cm">/* 删除顶点 */</span>
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<a id="__codelineno-0-44" name="__codelineno-0-44" href="#__codelineno-0-44"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">removeVertex</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-0-45" name="__codelineno-0-45" href="#__codelineno-0-45"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">>=</span><span class="w"> </span><span class="n">size</span><span class="p">())</span>
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<a id="__codelineno-0-46" name="__codelineno-0-46" href="#__codelineno-0-46"></a><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">();</span>
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<a id="__codelineno-0-47" name="__codelineno-0-47" href="#__codelineno-0-47"></a><span class="w"> </span><span class="c1">// 在顶点列表中移除索引 index 的顶点</span>
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<a id="__codelineno-0-48" name="__codelineno-0-48" href="#__codelineno-0-48"></a><span class="w"> </span><span class="n">vertices</span><span class="p">.</span><span class="na">remove</span><span class="p">(</span><span class="n">index</span><span class="p">);</span>
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<a id="__codelineno-0-49" name="__codelineno-0-49" href="#__codelineno-0-49"></a><span class="w"> </span><span class="c1">// 在邻接矩阵中删除索引 index 的行</span>
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<a id="__codelineno-0-50" name="__codelineno-0-50" href="#__codelineno-0-50"></a><span class="w"> </span><span class="n">adjMat</span><span class="p">.</span><span class="na">remove</span><span class="p">(</span><span class="n">index</span><span class="p">);</span>
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<a id="__codelineno-0-51" name="__codelineno-0-51" href="#__codelineno-0-51"></a><span class="w"> </span><span class="c1">// 在邻接矩阵中删除索引 index 的列</span>
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<a id="__codelineno-0-52" name="__codelineno-0-52" href="#__codelineno-0-52"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">List</span><span class="o"><</span><span class="n">Integer</span><span class="o">></span><span class="w"> </span><span class="n">row</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">adjMat</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-0-53" name="__codelineno-0-53" href="#__codelineno-0-53"></a><span class="w"> </span><span class="n">row</span><span class="p">.</span><span class="na">remove</span><span class="p">(</span><span class="n">index</span><span class="p">);</span>
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<a id="__codelineno-0-54" name="__codelineno-0-54" href="#__codelineno-0-54"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-0-55" name="__codelineno-0-55" href="#__codelineno-0-55"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-0-56" name="__codelineno-0-56" href="#__codelineno-0-56"></a>
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<a id="__codelineno-0-57" name="__codelineno-0-57" href="#__codelineno-0-57"></a><span class="w"> </span><span class="cm">/* 添加边 */</span>
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<a id="__codelineno-0-58" name="__codelineno-0-58" href="#__codelineno-0-58"></a><span class="w"> </span><span class="c1">// 参数 i, j 对应 vertices 元素索引</span>
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<a id="__codelineno-0-59" name="__codelineno-0-59" href="#__codelineno-0-59"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">addEdge</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-0-60" name="__codelineno-0-60" href="#__codelineno-0-60"></a><span class="w"> </span><span class="c1">// 索引越界与相等处理</span>
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<a id="__codelineno-0-61" name="__codelineno-0-61" href="#__codelineno-0-61"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">>=</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">>=</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">j</span><span class="p">)</span>
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<a id="__codelineno-0-62" name="__codelineno-0-62" href="#__codelineno-0-62"></a><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">();</span>
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<a id="__codelineno-0-63" name="__codelineno-0-63" href="#__codelineno-0-63"></a><span class="w"> </span><span class="c1">// 在无向图中，邻接矩阵沿主对角线对称，即满足 (i, j) == (j, i)</span>
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<a id="__codelineno-0-64" name="__codelineno-0-64" href="#__codelineno-0-64"></a><span class="w"> </span><span class="n">adjMat</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">i</span><span class="p">).</span><span class="na">set</span><span class="p">(</span><span class="n">j</span><span class="p">,</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
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<a id="__codelineno-0-65" name="__codelineno-0-65" href="#__codelineno-0-65"></a><span class="w"> </span><span class="n">adjMat</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">j</span><span class="p">).</span><span class="na">set</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
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<a id="__codelineno-0-66" name="__codelineno-0-66" href="#__codelineno-0-66"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-0-67" name="__codelineno-0-67" href="#__codelineno-0-67"></a>
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<a id="__codelineno-0-68" name="__codelineno-0-68" href="#__codelineno-0-68"></a><span class="w"> </span><span class="cm">/* 删除边 */</span>
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<a id="__codelineno-0-69" name="__codelineno-0-69" href="#__codelineno-0-69"></a><span class="w"> </span><span class="c1">// 参数 i, j 对应 vertices 元素索引</span>
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<a id="__codelineno-0-70" name="__codelineno-0-70" href="#__codelineno-0-70"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">removeEdge</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-0-71" name="__codelineno-0-71" href="#__codelineno-0-71"></a><span class="w"> </span><span class="c1">// 索引越界与相等处理</span>
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<a id="__codelineno-0-72" name="__codelineno-0-72" href="#__codelineno-0-72"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">>=</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">>=</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">j</span><span class="p">)</span>
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<a id="__codelineno-0-73" name="__codelineno-0-73" href="#__codelineno-0-73"></a><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">();</span>
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<a id="__codelineno-0-74" name="__codelineno-0-74" href="#__codelineno-0-74"></a><span class="w"> </span><span class="n">adjMat</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">i</span><span class="p">).</span><span class="na">set</span><span class="p">(</span><span class="n">j</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
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<a id="__codelineno-0-75" name="__codelineno-0-75" href="#__codelineno-0-75"></a><span class="w"> </span><span class="n">adjMat</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">j</span><span class="p">).</span><span class="na">set</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
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<a id="__codelineno-0-76" name="__codelineno-0-76" href="#__codelineno-0-76"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-0-77" name="__codelineno-0-77" href="#__codelineno-0-77"></a>
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<a id="__codelineno-0-78" name="__codelineno-0-78" href="#__codelineno-0-78"></a><span class="w"> </span><span class="cm">/* 打印邻接矩阵 */</span>
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<a id="__codelineno-0-79" name="__codelineno-0-79" href="#__codelineno-0-79"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">print</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-0-80" name="__codelineno-0-80" href="#__codelineno-0-80"></a><span class="w"> </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">print</span><span class="p">(</span><span class="s">"顶点列表 = "</span><span class="p">);</span>
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<a id="__codelineno-0-81" name="__codelineno-0-81" href="#__codelineno-0-81"></a><span class="w"> </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="n">vertices</span><span class="p">);</span>
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<a id="__codelineno-0-82" name="__codelineno-0-82" href="#__codelineno-0-82"></a><span class="w"> </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="s">"邻接矩阵 ="</span><span class="p">);</span>
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<a id="__codelineno-0-83" name="__codelineno-0-83" href="#__codelineno-0-83"></a><span class="w"> </span><span class="n">PrintUtil</span><span class="p">.</span><span class="na">printMatrix</span><span class="p">(</span><span class="n">adjMat</span><span class="p">);</span>
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<a id="__codelineno-0-84" name="__codelineno-0-84" href="#__codelineno-0-84"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-0-85" name="__codelineno-0-85" href="#__codelineno-0-85"></a><span class="p">}</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"><span class="filename">graph_adjacency_matrix.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a>
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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"><span class="filename">graph_adjacency_matrix.py</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a>
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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"><span class="filename">graph_adjacency_matrix.go</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 基于邻接矩阵实现的无向图类 */</span>
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<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="kd">type</span><span class="w"> </span><span class="nx">graphAdjMat</span><span class="w"> </span><span class="kd">struct</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w"> </span><span class="c1">// 顶点列表，元素代表“顶点值”，索引代表“顶点索引”</span>
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<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w"> </span><span class="nx">vertices</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span>
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<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w"> </span><span class="c1">// 邻接矩阵，行列索引对应“顶点索引”</span>
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<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w"> </span><span class="nx">adjMat</span><span class="w"> </span><span class="p">[][]</span><span class="kt">int</span>
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<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="p">}</span>
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<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a>
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<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="kd">func</span><span class="w"> </span><span class="nx">newGraphAdjMat</span><span class="p">(</span><span class="nx">vertices</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">edges</span><span class="w"> </span><span class="p">[][]</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="nx">graphAdjMat</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="w"> </span><span class="c1">// 添加顶点</span>
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<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">vertices</span><span class="p">)</span>
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<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="w"> </span><span class="nx">adjMat</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([][]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="p">)</span>
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<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">adjMat</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w"> </span><span class="nx">adjMat</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="p">)</span>
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<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="w"> </span><span class="c1">// 初始化图</span>
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<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="w"> </span><span class="nx">g</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="o">&</span><span class="nx">graphAdjMat</span><span class="p">{</span>
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<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="w"> </span><span class="nx">vertices</span><span class="p">:</span><span class="w"> </span><span class="nx">vertices</span><span class="p">,</span>
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<a id="__codelineno-3-19" name="__codelineno-3-19" href="#__codelineno-3-19"></a><span class="w"> </span><span class="nx">adjMat</span><span class="p">:</span><span class="w"> </span><span class="nx">adjMat</span><span class="p">,</span>
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<a id="__codelineno-3-20" name="__codelineno-3-20" href="#__codelineno-3-20"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-3-21" name="__codelineno-3-21" href="#__codelineno-3-21"></a><span class="w"> </span><span class="c1">// 添加边</span>
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<a id="__codelineno-3-22" name="__codelineno-3-22" href="#__codelineno-3-22"></a><span class="w"> </span><span class="c1">// 请注意，edges 元素代表顶点索引，即对应 vertices 元素索引</span>
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<a id="__codelineno-3-23" name="__codelineno-3-23" href="#__codelineno-3-23"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">edges</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-3-24" name="__codelineno-3-24" href="#__codelineno-3-24"></a><span class="w"> </span><span class="nx">g</span><span class="p">.</span><span class="nx">addEdge</span><span class="p">(</span><span class="nx">edges</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="mi">0</span><span class="p">],</span><span class="w"> </span><span class="nx">edges</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="mi">1</span><span class="p">])</span>
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<a id="__codelineno-3-25" name="__codelineno-3-25" href="#__codelineno-3-25"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-3-26" name="__codelineno-3-26" href="#__codelineno-3-26"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">g</span>
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<a id="__codelineno-3-27" name="__codelineno-3-27" href="#__codelineno-3-27"></a><span class="p">}</span>
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<a id="__codelineno-3-28" name="__codelineno-3-28" href="#__codelineno-3-28"></a>
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<a id="__codelineno-3-29" name="__codelineno-3-29" href="#__codelineno-3-29"></a><span class="cm">/* 获取顶点数量 */</span>
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<a id="__codelineno-3-30" name="__codelineno-3-30" href="#__codelineno-3-30"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">g</span><span class="w"> </span><span class="o">*</span><span class="nx">graphAdjMat</span><span class="p">)</span><span class="w"> </span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-3-31" name="__codelineno-3-31" href="#__codelineno-3-31"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">g</span><span class="p">.</span><span class="nx">vertices</span><span class="p">)</span>
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<a id="__codelineno-3-32" name="__codelineno-3-32" href="#__codelineno-3-32"></a><span class="p">}</span>
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<a id="__codelineno-3-33" name="__codelineno-3-33" href="#__codelineno-3-33"></a>
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<a id="__codelineno-3-34" name="__codelineno-3-34" href="#__codelineno-3-34"></a><span class="cm">/* 添加顶点 */</span>
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<a id="__codelineno-3-35" name="__codelineno-3-35" href="#__codelineno-3-35"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">g</span><span class="w"> </span><span class="o">*</span><span class="nx">graphAdjMat</span><span class="p">)</span><span class="w"> </span><span class="nx">addVertex</span><span class="p">(</span><span class="nx">val</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-3-36" name="__codelineno-3-36" href="#__codelineno-3-36"></a><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">g</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span>
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<a id="__codelineno-3-37" name="__codelineno-3-37" href="#__codelineno-3-37"></a><span class="w"> </span><span class="c1">// 向顶点列表中添加新顶点的值</span>
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<a id="__codelineno-3-38" name="__codelineno-3-38" href="#__codelineno-3-38"></a><span class="w"> </span><span class="nx">g</span><span class="p">.</span><span class="nx">vertices</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">g</span><span class="p">.</span><span class="nx">vertices</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">)</span>
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<a id="__codelineno-3-39" name="__codelineno-3-39" href="#__codelineno-3-39"></a><span class="w"> </span><span class="c1">// 在邻接矩阵中添加一行</span>
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<a id="__codelineno-3-40" name="__codelineno-3-40" href="#__codelineno-3-40"></a><span class="w"> </span><span class="nx">newRow</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="p">)</span>
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<a id="__codelineno-3-41" name="__codelineno-3-41" href="#__codelineno-3-41"></a><span class="w"> </span><span class="nx">g</span><span class="p">.</span><span class="nx">adjMat</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">g</span><span class="p">.</span><span class="nx">adjMat</span><span class="p">,</span><span class="w"> </span><span class="nx">newRow</span><span class="p">)</span>
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<a id="__codelineno-3-42" name="__codelineno-3-42" href="#__codelineno-3-42"></a><span class="w"> </span><span class="c1">// 在邻接矩阵中添加一列</span>
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<a id="__codelineno-3-43" name="__codelineno-3-43" href="#__codelineno-3-43"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">g</span><span class="p">.</span><span class="nx">adjMat</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-3-44" name="__codelineno-3-44" href="#__codelineno-3-44"></a><span class="w"> </span><span class="nx">g</span><span class="p">.</span><span class="nx">adjMat</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">g</span><span class="p">.</span><span class="nx">adjMat</span><span class="p">[</span><span class="nx">i</span><span class="p">],</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
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<a id="__codelineno-3-45" name="__codelineno-3-45" href="#__codelineno-3-45"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-3-46" name="__codelineno-3-46" href="#__codelineno-3-46"></a><span class="p">}</span>
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<a id="__codelineno-3-47" name="__codelineno-3-47" href="#__codelineno-3-47"></a>
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<a id="__codelineno-3-48" name="__codelineno-3-48" href="#__codelineno-3-48"></a><span class="cm">/* 删除顶点 */</span>
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<a id="__codelineno-3-49" name="__codelineno-3-49" href="#__codelineno-3-49"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">g</span><span class="w"> </span><span class="o">*</span><span class="nx">graphAdjMat</span><span class="p">)</span><span class="w"> </span><span class="nx">removeVertex</span><span class="p">(</span><span class="nx">index</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-3-50" name="__codelineno-3-50" href="#__codelineno-3-50"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">index</span><span class="w"> </span><span class="o">>=</span><span class="w"> </span><span class="nx">g</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-3-51" name="__codelineno-3-51" href="#__codelineno-3-51"></a><span class="w"> </span><span class="k">return</span>
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<a id="__codelineno-3-52" name="__codelineno-3-52" href="#__codelineno-3-52"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-3-53" name="__codelineno-3-53" href="#__codelineno-3-53"></a><span class="w"> </span><span class="c1">// 在顶点列表中移除索引 index 的顶点</span>
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<a id="__codelineno-3-54" name="__codelineno-3-54" href="#__codelineno-3-54"></a><span class="w"> </span><span class="nx">g</span><span class="p">.</span><span class="nx">vertices</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">g</span><span class="p">.</span><span class="nx">vertices</span><span class="p">[:</span><span class="nx">index</span><span class="p">],</span><span class="w"> </span><span class="nx">g</span><span class="p">.</span><span class="nx">vertices</span><span class="p">[</span><span class="nx">index</span><span class="o">+</span><span class="mi">1</span><span class="p">:]</span><span class="o">...</span><span class="p">)</span>
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<a id="__codelineno-3-55" name="__codelineno-3-55" href="#__codelineno-3-55"></a><span class="w"> </span><span class="c1">// 在邻接矩阵中删除索引 index 的行</span>
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<a id="__codelineno-3-56" name="__codelineno-3-56" href="#__codelineno-3-56"></a><span class="w"> </span><span class="nx">g</span><span class="p">.</span><span class="nx">adjMat</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">g</span><span class="p">.</span><span class="nx">adjMat</span><span class="p">[:</span><span class="nx">index</span><span class="p">],</span><span class="w"> </span><span class="nx">g</span><span class="p">.</span><span class="nx">adjMat</span><span class="p">[</span><span class="nx">index</span><span class="o">+</span><span class="mi">1</span><span class="p">:]</span><span class="o">...</span><span class="p">)</span>
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<a id="__codelineno-3-57" name="__codelineno-3-57" href="#__codelineno-3-57"></a><span class="w"> </span><span class="c1">// 在邻接矩阵中删除索引 index 的列</span>
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<a id="__codelineno-3-58" name="__codelineno-3-58" href="#__codelineno-3-58"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">g</span><span class="p">.</span><span class="nx">adjMat</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-3-59" name="__codelineno-3-59" href="#__codelineno-3-59"></a><span class="w"> </span><span class="nx">g</span><span class="p">.</span><span class="nx">adjMat</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">g</span><span class="p">.</span><span class="nx">adjMat</span><span class="p">[</span><span class="nx">i</span><span class="p">][:</span><span class="nx">index</span><span class="p">],</span><span class="w"> </span><span class="nx">g</span><span class="p">.</span><span class="nx">adjMat</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">index</span><span class="o">+</span><span class="mi">1</span><span class="p">:]</span><span class="o">...</span><span class="p">)</span>
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<a id="__codelineno-3-60" name="__codelineno-3-60" href="#__codelineno-3-60"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-3-61" name="__codelineno-3-61" href="#__codelineno-3-61"></a><span class="p">}</span>
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<a id="__codelineno-3-62" name="__codelineno-3-62" href="#__codelineno-3-62"></a>
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<a id="__codelineno-3-63" name="__codelineno-3-63" href="#__codelineno-3-63"></a><span class="cm">/* 添加边 */</span>
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<a id="__codelineno-3-64" name="__codelineno-3-64" href="#__codelineno-3-64"></a><span class="c1">// 参数 i, j 对应 vertices 元素索引</span>
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<a id="__codelineno-3-65" name="__codelineno-3-65" href="#__codelineno-3-65"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">g</span><span class="w"> </span><span class="o">*</span><span class="nx">graphAdjMat</span><span class="p">)</span><span class="w"> </span><span class="nx">addEdge</span><span class="p">(</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-3-66" name="__codelineno-3-66" href="#__codelineno-3-66"></a><span class="w"> </span><span class="c1">// 索引越界与相等处理</span>
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<a id="__codelineno-3-67" name="__codelineno-3-67" href="#__codelineno-3-67"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p"><</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="p"><</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">>=</span><span class="w"> </span><span class="nx">g</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">>=</span><span class="w"> </span><span class="nx">g</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-3-68" name="__codelineno-3-68" href="#__codelineno-3-68"></a><span class="w"> </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Errorf</span><span class="p">(</span><span class="s">"%s"</span><span class="p">,</span><span class="w"> </span><span class="s">"Index Out Of Bounds Exception"</span><span class="p">)</span>
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<a id="__codelineno-3-69" name="__codelineno-3-69" href="#__codelineno-3-69"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-3-70" name="__codelineno-3-70" href="#__codelineno-3-70"></a><span class="w"> </span><span class="c1">// 在无向图中，邻接矩阵沿主对角线对称，即满足 (i, j) == (j, i)</span>
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<a id="__codelineno-3-71" name="__codelineno-3-71" href="#__codelineno-3-71"></a><span class="w"> </span><span class="nx">g</span><span class="p">.</span><span class="nx">adjMat</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">1</span>
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<a id="__codelineno-3-72" name="__codelineno-3-72" href="#__codelineno-3-72"></a><span class="w"> </span><span class="nx">g</span><span class="p">.</span><span class="nx">adjMat</span><span class="p">[</span><span class="nx">j</span><span class="p">][</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">1</span>
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<a id="__codelineno-3-73" name="__codelineno-3-73" href="#__codelineno-3-73"></a><span class="p">}</span>
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<a id="__codelineno-3-74" name="__codelineno-3-74" href="#__codelineno-3-74"></a>
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<a id="__codelineno-3-75" name="__codelineno-3-75" href="#__codelineno-3-75"></a><span class="cm">/* 删除边 */</span>
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<a id="__codelineno-3-76" name="__codelineno-3-76" href="#__codelineno-3-76"></a><span class="c1">// 参数 i, j 对应 vertices 元素索引</span>
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<a id="__codelineno-3-77" name="__codelineno-3-77" href="#__codelineno-3-77"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">g</span><span class="w"> </span><span class="o">*</span><span class="nx">graphAdjMat</span><span class="p">)</span><span class="w"> </span><span class="nx">removeEdge</span><span class="p">(</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-3-78" name="__codelineno-3-78" href="#__codelineno-3-78"></a><span class="w"> </span><span class="c1">// 索引越界与相等处理</span>
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<a id="__codelineno-3-79" name="__codelineno-3-79" href="#__codelineno-3-79"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p"><</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="p"><</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">>=</span><span class="w"> </span><span class="nx">g</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">>=</span><span class="w"> </span><span class="nx">g</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-3-80" name="__codelineno-3-80" href="#__codelineno-3-80"></a><span class="w"> </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Errorf</span><span class="p">(</span><span class="s">"%s"</span><span class="p">,</span><span class="w"> </span><span class="s">"Index Out Of Bounds Exception"</span><span class="p">)</span>
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<a id="__codelineno-3-81" name="__codelineno-3-81" href="#__codelineno-3-81"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-3-82" name="__codelineno-3-82" href="#__codelineno-3-82"></a><span class="w"> </span><span class="nx">g</span><span class="p">.</span><span class="nx">adjMat</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
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<a id="__codelineno-3-83" name="__codelineno-3-83" href="#__codelineno-3-83"></a><span class="w"> </span><span class="nx">g</span><span class="p">.</span><span class="nx">adjMat</span><span class="p">[</span><span class="nx">j</span><span class="p">][</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
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<a id="__codelineno-3-84" name="__codelineno-3-84" href="#__codelineno-3-84"></a><span class="p">}</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"><span class="filename">graph_adjacency_matrix.js</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a>
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</code></pre></div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">graph_adjacency_matrix.ts</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a>
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</code></pre></div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">graph_adjacency_matrix.c</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a>
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</code></pre></div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">graph_adjacency_matrix.cs</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a>
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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"><span class="filename">graph_adjacency_matrix.swift</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 基于邻接矩阵实现的无向图类 */</span>
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<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kd">class</span> <span class="nc">GraphAdjMat</span> <span class="p">{</span>
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<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a> <span class="kd">private</span> <span class="kd">var</span> <span class="nv">vertices</span><span class="p">:</span> <span class="p">[</span><span class="nb">Int</span><span class="p">]</span> <span class="c1">// 顶点列表，元素代表“顶点值”，索引代表“顶点索引”</span>
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<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a> <span class="kd">private</span> <span class="kd">var</span> <span class="nv">adjMat</span><span class="p">:</span> <span class="p">[[</span><span class="nb">Int</span><span class="p">]]</span> <span class="c1">// 邻接矩阵，行列索引对应“顶点索引”</span>
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<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a>
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<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a> <span class="cm">/* 构造函数 */</span>
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<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a> <span class="kd">init</span><span class="p">(</span><span class="n">vertices</span><span class="p">:</span> <span class="p">[</span><span class="nb">Int</span><span class="p">],</span> <span class="n">edges</span><span class="p">:</span> <span class="p">[[</span><span class="nb">Int</span><span class="p">]])</span> <span class="p">{</span>
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<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a> <span class="kc">self</span><span class="p">.</span><span class="n">vertices</span> <span class="p">=</span> <span class="p">[]</span>
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<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a> <span class="n">adjMat</span> <span class="p">=</span> <span class="p">[]</span>
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<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a> <span class="c1">// 添加顶点</span>
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<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a> <span class="k">for</span> <span class="n">val</span> <span class="k">in</span> <span class="n">vertices</span> <span class="p">{</span>
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<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a> <span class="n">addVertex</span><span class="p">(</span><span class="n">val</span><span class="p">:</span> <span class="n">val</span><span class="p">)</span>
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<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a> <span class="p">}</span>
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<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a> <span class="c1">// 添加边</span>
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<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a> <span class="c1">// 请注意，edges 元素代表顶点索引，即对应 vertices 元素索引</span>
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<a id="__codelineno-8-16" name="__codelineno-8-16" href="#__codelineno-8-16"></a> <span class="k">for</span> <span class="n">e</span> <span class="k">in</span> <span class="n">edges</span> <span class="p">{</span>
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<a id="__codelineno-8-17" name="__codelineno-8-17" href="#__codelineno-8-17"></a> <span class="n">addEdge</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="n">e</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">j</span><span class="p">:</span> <span class="n">e</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
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<a id="__codelineno-8-18" name="__codelineno-8-18" href="#__codelineno-8-18"></a> <span class="p">}</span>
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<a id="__codelineno-8-19" name="__codelineno-8-19" href="#__codelineno-8-19"></a> <span class="p">}</span>
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<a id="__codelineno-8-20" name="__codelineno-8-20" href="#__codelineno-8-20"></a>
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<a id="__codelineno-8-21" name="__codelineno-8-21" href="#__codelineno-8-21"></a> <span class="cm">/* 获取顶点数量 */</span>
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<a id="__codelineno-8-22" name="__codelineno-8-22" href="#__codelineno-8-22"></a> <span class="kd">func</span> <span class="nf">size</span><span class="p">()</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span>
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<a id="__codelineno-8-23" name="__codelineno-8-23" href="#__codelineno-8-23"></a> <span class="n">vertices</span><span class="p">.</span><span class="bp">count</span>
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<a id="__codelineno-8-24" name="__codelineno-8-24" href="#__codelineno-8-24"></a> <span class="p">}</span>
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<a id="__codelineno-8-25" name="__codelineno-8-25" href="#__codelineno-8-25"></a>
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<a id="__codelineno-8-26" name="__codelineno-8-26" href="#__codelineno-8-26"></a> <span class="cm">/* 添加顶点 */</span>
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<a id="__codelineno-8-27" name="__codelineno-8-27" href="#__codelineno-8-27"></a> <span class="kd">func</span> <span class="nf">addVertex</span><span class="p">(</span><span class="n">val</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">{</span>
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<a id="__codelineno-8-28" name="__codelineno-8-28" href="#__codelineno-8-28"></a> <span class="kd">let</span> <span class="nv">n</span> <span class="p">=</span> <span class="n">size</span><span class="p">()</span>
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<a id="__codelineno-8-29" name="__codelineno-8-29" href="#__codelineno-8-29"></a> <span class="c1">// 向顶点列表中添加新顶点的值</span>
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<a id="__codelineno-8-30" name="__codelineno-8-30" href="#__codelineno-8-30"></a> <span class="n">vertices</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">val</span><span class="p">)</span>
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<a id="__codelineno-8-31" name="__codelineno-8-31" href="#__codelineno-8-31"></a> <span class="c1">// 在邻接矩阵中添加一行</span>
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<a id="__codelineno-8-32" name="__codelineno-8-32" href="#__codelineno-8-32"></a> <span class="kd">let</span> <span class="nv">newRow</span> <span class="p">=</span> <span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="bp">count</span><span class="p">:</span> <span class="n">n</span><span class="p">)</span>
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<a id="__codelineno-8-33" name="__codelineno-8-33" href="#__codelineno-8-33"></a> <span class="n">adjMat</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">newRow</span><span class="p">)</span>
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<a id="__codelineno-8-34" name="__codelineno-8-34" href="#__codelineno-8-34"></a> <span class="c1">// 在邻接矩阵中添加一列</span>
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<a id="__codelineno-8-35" name="__codelineno-8-35" href="#__codelineno-8-35"></a> <span class="k">for</span> <span class="n">i</span> <span class="k">in</span> <span class="n">adjMat</span><span class="p">.</span><span class="bp">indices</span> <span class="p">{</span>
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<a id="__codelineno-8-36" name="__codelineno-8-36" href="#__codelineno-8-36"></a> <span class="n">adjMat</span><span class="p">[</span><span class="n">i</span><span class="p">].</span><span class="n">append</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
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<a id="__codelineno-8-37" name="__codelineno-8-37" href="#__codelineno-8-37"></a> <span class="p">}</span>
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<a id="__codelineno-8-38" name="__codelineno-8-38" href="#__codelineno-8-38"></a> <span class="p">}</span>
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<a id="__codelineno-8-39" name="__codelineno-8-39" href="#__codelineno-8-39"></a>
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<a id="__codelineno-8-40" name="__codelineno-8-40" href="#__codelineno-8-40"></a> <span class="cm">/* 删除顶点 */</span>
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<a id="__codelineno-8-41" name="__codelineno-8-41" href="#__codelineno-8-41"></a> <span class="kd">func</span> <span class="nf">removeVertex</span><span class="p">(</span><span class="n">index</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">{</span>
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<a id="__codelineno-8-42" name="__codelineno-8-42" href="#__codelineno-8-42"></a> <span class="k">if</span> <span class="n">index</span> <span class="o">>=</span> <span class="n">size</span><span class="p">()</span> <span class="p">{</span>
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<a id="__codelineno-8-43" name="__codelineno-8-43" href="#__codelineno-8-43"></a> <span class="bp">fatalError</span><span class="p">(</span><span class="s">"越界"</span><span class="p">)</span>
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<a id="__codelineno-8-44" name="__codelineno-8-44" href="#__codelineno-8-44"></a> <span class="p">}</span>
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<a id="__codelineno-8-45" name="__codelineno-8-45" href="#__codelineno-8-45"></a> <span class="c1">// 在顶点列表中移除索引 index 的顶点</span>
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<a id="__codelineno-8-46" name="__codelineno-8-46" href="#__codelineno-8-46"></a> <span class="n">vertices</span><span class="p">.</span><span class="n">remove</span><span class="p">(</span><span class="n">at</span><span class="p">:</span> <span class="n">index</span><span class="p">)</span>
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<a id="__codelineno-8-47" name="__codelineno-8-47" href="#__codelineno-8-47"></a> <span class="c1">// 在邻接矩阵中删除索引 index 的行</span>
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<a id="__codelineno-8-48" name="__codelineno-8-48" href="#__codelineno-8-48"></a> <span class="n">adjMat</span><span class="p">.</span><span class="n">remove</span><span class="p">(</span><span class="n">at</span><span class="p">:</span> <span class="n">index</span><span class="p">)</span>
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<a id="__codelineno-8-49" name="__codelineno-8-49" href="#__codelineno-8-49"></a> <span class="c1">// 在邻接矩阵中删除索引 index 的列</span>
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<a id="__codelineno-8-50" name="__codelineno-8-50" href="#__codelineno-8-50"></a> <span class="k">for</span> <span class="n">i</span> <span class="k">in</span> <span class="n">adjMat</span><span class="p">.</span><span class="bp">indices</span> <span class="p">{</span>
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<a id="__codelineno-8-51" name="__codelineno-8-51" href="#__codelineno-8-51"></a> <span class="n">adjMat</span><span class="p">[</span><span class="n">i</span><span class="p">].</span><span class="n">remove</span><span class="p">(</span><span class="n">at</span><span class="p">:</span> <span class="n">index</span><span class="p">)</span>
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<a id="__codelineno-8-52" name="__codelineno-8-52" href="#__codelineno-8-52"></a> <span class="p">}</span>
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<a id="__codelineno-8-53" name="__codelineno-8-53" href="#__codelineno-8-53"></a> <span class="p">}</span>
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<a id="__codelineno-8-54" name="__codelineno-8-54" href="#__codelineno-8-54"></a>
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<a id="__codelineno-8-55" name="__codelineno-8-55" href="#__codelineno-8-55"></a> <span class="cm">/* 添加边 */</span>
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<a id="__codelineno-8-56" name="__codelineno-8-56" href="#__codelineno-8-56"></a> <span class="c1">// 参数 i, j 对应 vertices 元素索引</span>
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<a id="__codelineno-8-57" name="__codelineno-8-57" href="#__codelineno-8-57"></a> <span class="kd">func</span> <span class="nf">addEdge</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="nb">Int</span><span class="p">,</span> <span class="n">j</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">{</span>
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<a id="__codelineno-8-58" name="__codelineno-8-58" href="#__codelineno-8-58"></a> <span class="c1">// 索引越界与相等处理</span>
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<a id="__codelineno-8-59" name="__codelineno-8-59" href="#__codelineno-8-59"></a> <span class="k">if</span> <span class="n">i</span> <span class="o"><</span> <span class="mi">0</span> <span class="o">||</span> <span class="n">j</span> <span class="o"><</span> <span class="mi">0</span> <span class="o">||</span> <span class="n">i</span> <span class="o">>=</span> <span class="n">size</span><span class="p">()</span> <span class="o">||</span> <span class="n">j</span> <span class="o">>=</span> <span class="n">size</span><span class="p">()</span> <span class="o">||</span> <span class="n">i</span> <span class="p">==</span> <span class="n">j</span> <span class="p">{</span>
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<a id="__codelineno-8-60" name="__codelineno-8-60" href="#__codelineno-8-60"></a> <span class="bp">fatalError</span><span class="p">(</span><span class="s">"越界"</span><span class="p">)</span>
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<a id="__codelineno-8-61" name="__codelineno-8-61" href="#__codelineno-8-61"></a> <span class="p">}</span>
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<a id="__codelineno-8-62" name="__codelineno-8-62" href="#__codelineno-8-62"></a> <span class="c1">// 在无向图中，邻接矩阵沿主对角线对称，即满足 (i, j) == (j, i)</span>
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<a id="__codelineno-8-63" name="__codelineno-8-63" href="#__codelineno-8-63"></a> <span class="n">adjMat</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span> <span class="p">=</span> <span class="mi">1</span>
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<a id="__codelineno-8-64" name="__codelineno-8-64" href="#__codelineno-8-64"></a> <span class="n">adjMat</span><span class="p">[</span><span class="n">j</span><span class="p">][</span><span class="n">i</span><span class="p">]</span> <span class="p">=</span> <span class="mi">1</span>
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<a id="__codelineno-8-65" name="__codelineno-8-65" href="#__codelineno-8-65"></a> <span class="p">}</span>
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<a id="__codelineno-8-66" name="__codelineno-8-66" href="#__codelineno-8-66"></a>
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<a id="__codelineno-8-67" name="__codelineno-8-67" href="#__codelineno-8-67"></a> <span class="cm">/* 删除边 */</span>
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<a id="__codelineno-8-68" name="__codelineno-8-68" href="#__codelineno-8-68"></a> <span class="c1">// 参数 i, j 对应 vertices 元素索引</span>
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<a id="__codelineno-8-69" name="__codelineno-8-69" href="#__codelineno-8-69"></a> <span class="kd">func</span> <span class="nf">removeEdge</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="nb">Int</span><span class="p">,</span> <span class="n">j</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">{</span>
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<a id="__codelineno-8-70" name="__codelineno-8-70" href="#__codelineno-8-70"></a> <span class="c1">// 索引越界与相等处理</span>
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<a id="__codelineno-8-71" name="__codelineno-8-71" href="#__codelineno-8-71"></a> <span class="k">if</span> <span class="n">i</span> <span class="o"><</span> <span class="mi">0</span> <span class="o">||</span> <span class="n">j</span> <span class="o"><</span> <span class="mi">0</span> <span class="o">||</span> <span class="n">i</span> <span class="o">>=</span> <span class="n">size</span><span class="p">()</span> <span class="o">||</span> <span class="n">j</span> <span class="o">>=</span> <span class="n">size</span><span class="p">()</span> <span class="o">||</span> <span class="n">i</span> <span class="p">==</span> <span class="n">j</span> <span class="p">{</span>
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<a id="__codelineno-8-72" name="__codelineno-8-72" href="#__codelineno-8-72"></a> <span class="bp">fatalError</span><span class="p">(</span><span class="s">"越界"</span><span class="p">)</span>
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<a id="__codelineno-8-73" name="__codelineno-8-73" href="#__codelineno-8-73"></a> <span class="p">}</span>
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<a id="__codelineno-8-74" name="__codelineno-8-74" href="#__codelineno-8-74"></a> <span class="n">adjMat</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span> <span class="p">=</span> <span class="mi">0</span>
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<a id="__codelineno-8-75" name="__codelineno-8-75" href="#__codelineno-8-75"></a> <span class="n">adjMat</span><span class="p">[</span><span class="n">j</span><span class="p">][</span><span class="n">i</span><span class="p">]</span> <span class="p">=</span> <span class="mi">0</span>
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<a id="__codelineno-8-76" name="__codelineno-8-76" href="#__codelineno-8-76"></a> <span class="p">}</span>
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<a id="__codelineno-8-77" name="__codelineno-8-77" href="#__codelineno-8-77"></a><span class="p">}</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"><span class="filename">graph_adjacency_matrix.zig</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a>
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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="922">9.2.2. 基于邻接表的实现<a class="headerlink" href="#922" title="Permanent link">¶</a></h2>
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<p>设图的顶点总数为 <span class="arithmatex">\(n\)</span> 、边总数为 <span class="arithmatex">\(m\)</span> ，则有：</p>
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<ul>
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<li><strong>添加边</strong>：在顶点对应链表的尾部添加边即可，使用 <span class="arithmatex">\(O(1)\)</span> 时间。因为是无向图，所以需要同时添加两个方向的边。</li>
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<li><strong>删除边</strong>：在顶点对应链表中查询与删除指定边，使用 <span class="arithmatex">\(O(m)\)</span> 时间。与添加边一样，需要同时删除两个方向的边。</li>
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<li><strong>添加顶点</strong>：在邻接表中添加一个链表即可，并以新增顶点为链表头结点，使用 <span class="arithmatex">\(O(1)\)</span> 时间。</li>
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<li><strong>删除顶点</strong>：需要遍历整个邻接表，删除包含指定顶点的所有边，使用 <span class="arithmatex">\(O(n + m)\)</span> 时间。</li>
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<li><strong>初始化</strong>：需要在邻接表中建立 <span class="arithmatex">\(n\)</span> 个结点和 <span class="arithmatex">\(2m\)</span> 条边，使用 <span class="arithmatex">\(O(n + m)\)</span> 时间。</li>
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</ul>
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<div class="tabbed-set tabbed-alternate" data-tabs="3:5"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">初始化邻接表</label><label for="__tabbed_3_2">添加边</label><label for="__tabbed_3_3">删除边</label><label for="__tabbed_3_4">添加顶点</label><label for="__tabbed_3_5">删除顶点</label></div>
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<div class="tabbed-content">
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<div class="tabbed-block">
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<p><img alt="adjacency_list_initialization" src="../graph_operations.assets/adjacency_list_initialization.png" /></p>
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</div>
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<div class="tabbed-block">
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<p><img alt="adjacency_list_add_edge" src="../graph_operations.assets/adjacency_list_add_edge.png" /></p>
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</div>
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<div class="tabbed-block">
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<p><img alt="adjacency_list_remove_edge" src="../graph_operations.assets/adjacency_list_remove_edge.png" /></p>
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</div>
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<div class="tabbed-block">
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<p><img alt="adjacency_list_add_vertex" src="../graph_operations.assets/adjacency_list_add_vertex.png" /></p>
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</div>
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<div class="tabbed-block">
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<p><img alt="adjacency_list_remove_vertex" src="../graph_operations.assets/adjacency_list_remove_vertex.png" /></p>
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</div>
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</div>
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</div>
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<p>基于邻接表实现图的代码如下所示。</p>
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<div class="tabbed-set tabbed-alternate" data-tabs="4:10"><input checked="checked" id="__tabbed_4_1" name="__tabbed_4" type="radio" /><input id="__tabbed_4_2" name="__tabbed_4" type="radio" /><input id="__tabbed_4_3" name="__tabbed_4" type="radio" /><input id="__tabbed_4_4" name="__tabbed_4" type="radio" /><input id="__tabbed_4_5" name="__tabbed_4" type="radio" /><input id="__tabbed_4_6" name="__tabbed_4" type="radio" /><input id="__tabbed_4_7" name="__tabbed_4" type="radio" /><input id="__tabbed_4_8" name="__tabbed_4" type="radio" /><input id="__tabbed_4_9" name="__tabbed_4" type="radio" /><input id="__tabbed_4_10" name="__tabbed_4" type="radio" /><div class="tabbed-labels"><label for="__tabbed_4_1">Java</label><label for="__tabbed_4_2">C++</label><label for="__tabbed_4_3">Python</label><label for="__tabbed_4_4">Go</label><label for="__tabbed_4_5">JavaScript</label><label for="__tabbed_4_6">TypeScript</label><label for="__tabbed_4_7">C</label><label for="__tabbed_4_8">C#</label><label for="__tabbed_4_9">Swift</label><label for="__tabbed_4_10">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"><span class="filename">graph_adjacency_list.java</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* 顶点类 */</span>
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<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="kd">class</span> <span class="nc">Vertex</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
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<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="nf">Vertex</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="na">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
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<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="p">}</span>
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<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a>
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<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="cm">/* 基于邻接表实现的无向图类 */</span>
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<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="kd">class</span> <span class="nc">GraphAdjList</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a><span class="w"> </span><span class="c1">// 请注意，vertices 和 adjList 中存储的都是 Vertex 对象</span>
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<a id="__codelineno-10-12" name="__codelineno-10-12" href="#__codelineno-10-12"></a><span class="w"> </span><span class="n">Map</span><span class="o"><</span><span class="n">Vertex</span><span class="p">,</span><span class="w"> </span><span class="n">Set</span><span class="o"><</span><span class="n">Vertex</span><span class="o">>></span><span class="w"> </span><span class="n">adjList</span><span class="p">;</span><span class="w"> </span><span class="c1">// 邻接表（使用哈希表实现）</span>
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<a id="__codelineno-10-13" name="__codelineno-10-13" href="#__codelineno-10-13"></a>
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<a id="__codelineno-10-14" name="__codelineno-10-14" href="#__codelineno-10-14"></a><span class="w"> </span><span class="cm">/* 构造函数 */</span>
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<a id="__codelineno-10-15" name="__codelineno-10-15" href="#__codelineno-10-15"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="nf">GraphAdjList</span><span class="p">(</span><span class="n">Vertex</span><span class="o">[][]</span><span class="w"> </span><span class="n">edges</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-10-16" name="__codelineno-10-16" href="#__codelineno-10-16"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="na">adjList</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">HashMap</span><span class="o"><></span><span class="p">();</span>
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<a id="__codelineno-10-17" name="__codelineno-10-17" href="#__codelineno-10-17"></a><span class="w"> </span><span class="c1">// 添加所有顶点和边</span>
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<a id="__codelineno-10-18" name="__codelineno-10-18" href="#__codelineno-10-18"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Vertex</span><span class="o">[]</span><span class="w"> </span><span class="n">edge</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">edges</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-10-19" name="__codelineno-10-19" href="#__codelineno-10-19"></a><span class="w"> </span><span class="n">addVertex</span><span class="p">(</span><span class="n">edge</span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="p">);</span>
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<a id="__codelineno-10-20" name="__codelineno-10-20" href="#__codelineno-10-20"></a><span class="w"> </span><span class="n">addVertex</span><span class="p">(</span><span class="n">edge</span><span class="o">[</span><span class="mi">1</span><span class="o">]</span><span class="p">);</span>
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<a id="__codelineno-10-21" name="__codelineno-10-21" href="#__codelineno-10-21"></a><span class="w"> </span><span class="n">addEdge</span><span class="p">(</span><span class="n">edge</span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">edge</span><span class="o">[</span><span class="mi">1</span><span class="o">]</span><span class="p">);</span>
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<a id="__codelineno-10-22" name="__codelineno-10-22" href="#__codelineno-10-22"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-10-23" name="__codelineno-10-23" href="#__codelineno-10-23"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-10-24" name="__codelineno-10-24" href="#__codelineno-10-24"></a>
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<a id="__codelineno-10-25" name="__codelineno-10-25" href="#__codelineno-10-25"></a><span class="w"> </span><span class="cm">/* 获取顶点数量 */</span>
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<a id="__codelineno-10-26" name="__codelineno-10-26" href="#__codelineno-10-26"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-10-27" name="__codelineno-10-27" href="#__codelineno-10-27"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">adjList</span><span class="p">.</span><span class="na">size</span><span class="p">();</span>
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<a id="__codelineno-10-28" name="__codelineno-10-28" href="#__codelineno-10-28"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-10-29" name="__codelineno-10-29" href="#__codelineno-10-29"></a>
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<a id="__codelineno-10-30" name="__codelineno-10-30" href="#__codelineno-10-30"></a><span class="w"> </span><span class="cm">/* 添加边 */</span>
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<a id="__codelineno-10-31" name="__codelineno-10-31" href="#__codelineno-10-31"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">addEdge</span><span class="p">(</span><span class="n">Vertex</span><span class="w"> </span><span class="n">vet1</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="n">vet2</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-10-32" name="__codelineno-10-32" href="#__codelineno-10-32"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">adjList</span><span class="p">.</span><span class="na">containsKey</span><span class="p">(</span><span class="n">vet1</span><span class="p">)</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="o">!</span><span class="n">adjList</span><span class="p">.</span><span class="na">containsKey</span><span class="p">(</span><span class="n">vet2</span><span class="p">)</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">vet1</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">vet2</span><span class="p">)</span>
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<a id="__codelineno-10-33" name="__codelineno-10-33" href="#__codelineno-10-33"></a><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">IllegalArgumentException</span><span class="p">();</span>
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<a id="__codelineno-10-34" name="__codelineno-10-34" href="#__codelineno-10-34"></a><span class="w"> </span><span class="c1">// 添加边 vet1 - vet2</span>
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<a id="__codelineno-10-35" name="__codelineno-10-35" href="#__codelineno-10-35"></a><span class="w"> </span><span class="n">adjList</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">vet1</span><span class="p">).</span><span class="na">add</span><span class="p">(</span><span class="n">vet2</span><span class="p">);</span>
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<a id="__codelineno-10-36" name="__codelineno-10-36" href="#__codelineno-10-36"></a><span class="w"> </span><span class="n">adjList</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">vet2</span><span class="p">).</span><span class="na">add</span><span class="p">(</span><span class="n">vet1</span><span class="p">);</span>
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<a id="__codelineno-10-37" name="__codelineno-10-37" href="#__codelineno-10-37"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-10-38" name="__codelineno-10-38" href="#__codelineno-10-38"></a>
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<a id="__codelineno-10-39" name="__codelineno-10-39" href="#__codelineno-10-39"></a><span class="w"> </span><span class="cm">/* 删除边 */</span>
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<a id="__codelineno-10-40" name="__codelineno-10-40" href="#__codelineno-10-40"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">removeEdge</span><span class="p">(</span><span class="n">Vertex</span><span class="w"> </span><span class="n">vet1</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="n">vet2</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-10-41" name="__codelineno-10-41" href="#__codelineno-10-41"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">adjList</span><span class="p">.</span><span class="na">containsKey</span><span class="p">(</span><span class="n">vet1</span><span class="p">)</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="o">!</span><span class="n">adjList</span><span class="p">.</span><span class="na">containsKey</span><span class="p">(</span><span class="n">vet2</span><span class="p">)</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">vet1</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">vet2</span><span class="p">)</span>
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<a id="__codelineno-10-42" name="__codelineno-10-42" href="#__codelineno-10-42"></a><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">IllegalArgumentException</span><span class="p">();</span>
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<a id="__codelineno-10-43" name="__codelineno-10-43" href="#__codelineno-10-43"></a><span class="w"> </span><span class="c1">// 删除边 vet1 - vet2</span>
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<a id="__codelineno-10-44" name="__codelineno-10-44" href="#__codelineno-10-44"></a><span class="w"> </span><span class="n">adjList</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">vet1</span><span class="p">).</span><span class="na">remove</span><span class="p">(</span><span class="n">vet2</span><span class="p">);</span>
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<a id="__codelineno-10-45" name="__codelineno-10-45" href="#__codelineno-10-45"></a><span class="w"> </span><span class="n">adjList</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">vet2</span><span class="p">).</span><span class="na">remove</span><span class="p">(</span><span class="n">vet1</span><span class="p">);</span>
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<a id="__codelineno-10-46" name="__codelineno-10-46" href="#__codelineno-10-46"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-10-47" name="__codelineno-10-47" href="#__codelineno-10-47"></a>
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<a id="__codelineno-10-48" name="__codelineno-10-48" href="#__codelineno-10-48"></a><span class="w"> </span><span class="cm">/* 添加顶点 */</span>
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<a id="__codelineno-10-49" name="__codelineno-10-49" href="#__codelineno-10-49"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">addVertex</span><span class="p">(</span><span class="n">Vertex</span><span class="w"> </span><span class="n">vet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-10-50" name="__codelineno-10-50" href="#__codelineno-10-50"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">adjList</span><span class="p">.</span><span class="na">containsKey</span><span class="p">(</span><span class="n">vet</span><span class="p">))</span>
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<a id="__codelineno-10-51" name="__codelineno-10-51" href="#__codelineno-10-51"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
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<a id="__codelineno-10-52" name="__codelineno-10-52" href="#__codelineno-10-52"></a><span class="w"> </span><span class="c1">// 在邻接表中添加一个新链表（即 HashSet）</span>
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<a id="__codelineno-10-53" name="__codelineno-10-53" href="#__codelineno-10-53"></a><span class="w"> </span><span class="n">adjList</span><span class="p">.</span><span class="na">put</span><span class="p">(</span><span class="n">vet</span><span class="p">,</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">HashSet</span><span class="o"><></span><span class="p">());</span>
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<a id="__codelineno-10-54" name="__codelineno-10-54" href="#__codelineno-10-54"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-10-55" name="__codelineno-10-55" href="#__codelineno-10-55"></a>
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<a id="__codelineno-10-56" name="__codelineno-10-56" href="#__codelineno-10-56"></a><span class="w"> </span><span class="cm">/* 删除顶点 */</span>
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<a id="__codelineno-10-57" name="__codelineno-10-57" href="#__codelineno-10-57"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">removeVertex</span><span class="p">(</span><span class="n">Vertex</span><span class="w"> </span><span class="n">vet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-10-58" name="__codelineno-10-58" href="#__codelineno-10-58"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">adjList</span><span class="p">.</span><span class="na">containsKey</span><span class="p">(</span><span class="n">vet</span><span class="p">))</span>
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<a id="__codelineno-10-59" name="__codelineno-10-59" href="#__codelineno-10-59"></a><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">IllegalArgumentException</span><span class="p">();</span>
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<a id="__codelineno-10-60" name="__codelineno-10-60" href="#__codelineno-10-60"></a><span class="w"> </span><span class="c1">// 在邻接表中删除顶点 vet 对应的链表（即 HashSet）</span>
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<a id="__codelineno-10-61" name="__codelineno-10-61" href="#__codelineno-10-61"></a><span class="w"> </span><span class="n">adjList</span><span class="p">.</span><span class="na">remove</span><span class="p">(</span><span class="n">vet</span><span class="p">);</span>
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<a id="__codelineno-10-62" name="__codelineno-10-62" href="#__codelineno-10-62"></a><span class="w"> </span><span class="c1">// 遍历其它顶点的链表（即 HashSet），删除所有包含 vet 的边</span>
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<a id="__codelineno-10-63" name="__codelineno-10-63" href="#__codelineno-10-63"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Set</span><span class="o"><</span><span class="n">Vertex</span><span class="o">></span><span class="w"> </span><span class="n">set</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">adjList</span><span class="p">.</span><span class="na">values</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-10-64" name="__codelineno-10-64" href="#__codelineno-10-64"></a><span class="w"> </span><span class="n">set</span><span class="p">.</span><span class="na">remove</span><span class="p">(</span><span class="n">vet</span><span class="p">);</span>
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<a id="__codelineno-10-65" name="__codelineno-10-65" href="#__codelineno-10-65"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-10-66" name="__codelineno-10-66" href="#__codelineno-10-66"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-10-67" name="__codelineno-10-67" href="#__codelineno-10-67"></a>
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<a id="__codelineno-10-68" name="__codelineno-10-68" href="#__codelineno-10-68"></a><span class="w"> </span><span class="cm">/* 打印邻接表 */</span>
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<a id="__codelineno-10-69" name="__codelineno-10-69" href="#__codelineno-10-69"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">print</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-10-70" name="__codelineno-10-70" href="#__codelineno-10-70"></a><span class="w"> </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="s">"邻接表 ="</span><span class="p">);</span>
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<a id="__codelineno-10-71" name="__codelineno-10-71" href="#__codelineno-10-71"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Map</span><span class="p">.</span><span class="na">Entry</span><span class="o"><</span><span class="n">Vertex</span><span class="p">,</span><span class="w"> </span><span class="n">Set</span><span class="o"><</span><span class="n">Vertex</span><span class="o">>></span><span class="w"> </span><span class="n">entry</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">adjList</span><span class="p">.</span><span class="na">entrySet</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-10-72" name="__codelineno-10-72" href="#__codelineno-10-72"></a><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">Integer</span><span class="o">></span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o"><></span><span class="p">();</span>
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<a id="__codelineno-10-73" name="__codelineno-10-73" href="#__codelineno-10-73"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Vertex</span><span class="w"> </span><span class="n">vertex</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">entry</span><span class="p">.</span><span class="na">getValue</span><span class="p">())</span>
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<a id="__codelineno-10-74" name="__codelineno-10-74" href="#__codelineno-10-74"></a><span class="w"> </span><span class="n">tmp</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">vertex</span><span class="p">.</span><span class="na">val</span><span class="p">);</span>
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<a id="__codelineno-10-75" name="__codelineno-10-75" href="#__codelineno-10-75"></a><span class="w"> </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="n">entry</span><span class="p">.</span><span class="na">getKey</span><span class="p">().</span><span class="na">val</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="s">": "</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="s">","</span><span class="p">);</span>
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<a id="__codelineno-10-76" name="__codelineno-10-76" href="#__codelineno-10-76"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-10-77" name="__codelineno-10-77" href="#__codelineno-10-77"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-10-78" name="__codelineno-10-78" href="#__codelineno-10-78"></a><span class="p">}</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"><span class="filename">graph_adjacency_list.cpp</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a>
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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"><span class="filename">graph_adjacency_list.py</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a>
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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"><span class="filename">graph_adjacency_list.go</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="cm">/* 顶点类 */</span>
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<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="kd">type</span><span class="w"> </span><span class="nx">vertex</span><span class="w"> </span><span class="kd">struct</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="kt">int</span>
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<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a><span class="p">}</span>
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<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a>
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<a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a><span class="kd">func</span><span class="w"> </span><span class="nx">newVertex</span><span class="p">(</span><span class="nx">val</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="nx">vertex</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">vertex</span><span class="p">{</span>
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<a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a><span class="w"> </span><span class="nx">val</span><span class="p">:</span><span class="w"> </span><span class="nx">val</span><span class="p">,</span>
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<a id="__codelineno-13-9" name="__codelineno-13-9" href="#__codelineno-13-9"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-13-10" name="__codelineno-13-10" href="#__codelineno-13-10"></a><span class="p">}</span>
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<a id="__codelineno-13-11" name="__codelineno-13-11" href="#__codelineno-13-11"></a>
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<a id="__codelineno-13-12" name="__codelineno-13-12" href="#__codelineno-13-12"></a><span class="cm">/* 基于邻接表实现的无向图类 */</span>
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<a id="__codelineno-13-13" name="__codelineno-13-13" href="#__codelineno-13-13"></a><span class="kd">type</span><span class="w"> </span><span class="nx">graphAdjList</span><span class="w"> </span><span class="kd">struct</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-13-14" name="__codelineno-13-14" href="#__codelineno-13-14"></a><span class="w"> </span><span class="c1">// 请注意，vertices 和 adjList 中存储的都是 Vertex 对象</span>
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<a id="__codelineno-13-15" name="__codelineno-13-15" href="#__codelineno-13-15"></a><span class="w"> </span><span class="c1">// 邻接表（使用哈希表实现）, 使用哈希表模拟集合</span>
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<a id="__codelineno-13-16" name="__codelineno-13-16" href="#__codelineno-13-16"></a><span class="w"> </span><span class="nx">adjList</span><span class="w"> </span><span class="kd">map</span><span class="p">[</span><span class="nx">vertex</span><span class="p">]</span><span class="kd">map</span><span class="p">[</span><span class="nx">vertex</span><span class="p">]</span><span class="kd">struct</span><span class="p">{}</span>
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<a id="__codelineno-13-17" name="__codelineno-13-17" href="#__codelineno-13-17"></a><span class="p">}</span>
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<a id="__codelineno-13-18" name="__codelineno-13-18" href="#__codelineno-13-18"></a>
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<a id="__codelineno-13-19" name="__codelineno-13-19" href="#__codelineno-13-19"></a><span class="cm">/* 构造函数 */</span>
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<a id="__codelineno-13-20" name="__codelineno-13-20" href="#__codelineno-13-20"></a><span class="kd">func</span><span class="w"> </span><span class="nx">newGraphAdjList</span><span class="p">(</span><span class="nx">edges</span><span class="w"> </span><span class="p">[][]</span><span class="nx">vertex</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="nx">graphAdjList</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-13-21" name="__codelineno-13-21" href="#__codelineno-13-21"></a><span class="w"> </span><span class="nx">g</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="o">&</span><span class="nx">graphAdjList</span><span class="p">{</span>
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<a id="__codelineno-13-22" name="__codelineno-13-22" href="#__codelineno-13-22"></a><span class="w"> </span><span class="nx">adjList</span><span class="p">:</span><span class="w"> </span><span class="nb">make</span><span class="p">(</span><span class="kd">map</span><span class="p">[</span><span class="nx">vertex</span><span class="p">]</span><span class="kd">map</span><span class="p">[</span><span class="nx">vertex</span><span class="p">]</span><span class="kd">struct</span><span class="p">{}),</span>
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<a id="__codelineno-13-23" name="__codelineno-13-23" href="#__codelineno-13-23"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-13-24" name="__codelineno-13-24" href="#__codelineno-13-24"></a><span class="w"> </span><span class="c1">// 添加所有顶点和边</span>
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<a id="__codelineno-13-25" name="__codelineno-13-25" href="#__codelineno-13-25"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">edge</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">edges</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-13-26" name="__codelineno-13-26" href="#__codelineno-13-26"></a><span class="w"> </span><span class="nx">g</span><span class="p">.</span><span class="nx">addVertex</span><span class="p">(</span><span class="nx">edge</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
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<a id="__codelineno-13-27" name="__codelineno-13-27" href="#__codelineno-13-27"></a><span class="w"> </span><span class="nx">g</span><span class="p">.</span><span class="nx">addVertex</span><span class="p">(</span><span class="nx">edge</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
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<a id="__codelineno-13-28" name="__codelineno-13-28" href="#__codelineno-13-28"></a><span class="w"> </span><span class="nx">g</span><span class="p">.</span><span class="nx">addEdge</span><span class="p">(</span><span class="nx">edge</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span><span class="w"> </span><span class="nx">edge</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
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<a id="__codelineno-13-29" name="__codelineno-13-29" href="#__codelineno-13-29"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-13-30" name="__codelineno-13-30" href="#__codelineno-13-30"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">g</span>
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<a id="__codelineno-13-31" name="__codelineno-13-31" href="#__codelineno-13-31"></a><span class="p">}</span>
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<a id="__codelineno-13-32" name="__codelineno-13-32" href="#__codelineno-13-32"></a>
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<a id="__codelineno-13-33" name="__codelineno-13-33" href="#__codelineno-13-33"></a><span class="cm">/* 获取顶点数量 */</span>
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<a id="__codelineno-13-34" name="__codelineno-13-34" href="#__codelineno-13-34"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">g</span><span class="w"> </span><span class="o">*</span><span class="nx">graphAdjList</span><span class="p">)</span><span class="w"> </span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-13-35" name="__codelineno-13-35" href="#__codelineno-13-35"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">g</span><span class="p">.</span><span class="nx">adjList</span><span class="p">)</span>
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<a id="__codelineno-13-36" name="__codelineno-13-36" href="#__codelineno-13-36"></a><span class="p">}</span>
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<a id="__codelineno-13-37" name="__codelineno-13-37" href="#__codelineno-13-37"></a>
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<a id="__codelineno-13-38" name="__codelineno-13-38" href="#__codelineno-13-38"></a><span class="cm">/* 添加边 */</span>
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<a id="__codelineno-13-39" name="__codelineno-13-39" href="#__codelineno-13-39"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">g</span><span class="w"> </span><span class="o">*</span><span class="nx">graphAdjList</span><span class="p">)</span><span class="w"> </span><span class="nx">addEdge</span><span class="p">(</span><span class="nx">vet1</span><span class="w"> </span><span class="nx">vertex</span><span class="p">,</span><span class="w"> </span><span class="nx">vet2</span><span class="w"> </span><span class="nx">vertex</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-13-40" name="__codelineno-13-40" href="#__codelineno-13-40"></a><span class="w"> </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">ok1</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">g</span><span class="p">.</span><span class="nx">adjList</span><span class="p">[</span><span class="nx">vet1</span><span class="p">]</span>
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<a id="__codelineno-13-41" name="__codelineno-13-41" href="#__codelineno-13-41"></a><span class="w"> </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">ok2</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">g</span><span class="p">.</span><span class="nx">adjList</span><span class="p">[</span><span class="nx">vet2</span><span class="p">]</span>
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<a id="__codelineno-13-42" name="__codelineno-13-42" href="#__codelineno-13-42"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">!</span><span class="nx">ok1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="p">!</span><span class="nx">ok2</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">vet1</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nx">vet2</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-13-43" name="__codelineno-13-43" href="#__codelineno-13-43"></a><span class="w"> </span><span class="nb">panic</span><span class="p">(</span><span class="s">"error"</span><span class="p">)</span>
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<a id="__codelineno-13-44" name="__codelineno-13-44" href="#__codelineno-13-44"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-13-45" name="__codelineno-13-45" href="#__codelineno-13-45"></a><span class="w"> </span><span class="c1">// 添加边 vet1 - vet2, 添加匿名 struct{},</span>
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<a id="__codelineno-13-46" name="__codelineno-13-46" href="#__codelineno-13-46"></a><span class="w"> </span><span class="nx">g</span><span class="p">.</span><span class="nx">adjList</span><span class="p">[</span><span class="nx">vet1</span><span class="p">][</span><span class="nx">vet2</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="kd">struct</span><span class="p">{}{}</span>
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<a id="__codelineno-13-47" name="__codelineno-13-47" href="#__codelineno-13-47"></a><span class="w"> </span><span class="nx">g</span><span class="p">.</span><span class="nx">adjList</span><span class="p">[</span><span class="nx">vet2</span><span class="p">][</span><span class="nx">vet1</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="kd">struct</span><span class="p">{}{}</span>
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<a id="__codelineno-13-48" name="__codelineno-13-48" href="#__codelineno-13-48"></a><span class="p">}</span>
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<a id="__codelineno-13-49" name="__codelineno-13-49" href="#__codelineno-13-49"></a>
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<a id="__codelineno-13-50" name="__codelineno-13-50" href="#__codelineno-13-50"></a><span class="cm">/* 删除边 */</span>
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<a id="__codelineno-13-51" name="__codelineno-13-51" href="#__codelineno-13-51"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">g</span><span class="w"> </span><span class="o">*</span><span class="nx">graphAdjList</span><span class="p">)</span><span class="w"> </span><span class="nx">removeEdge</span><span class="p">(</span><span class="nx">vet1</span><span class="w"> </span><span class="nx">vertex</span><span class="p">,</span><span class="w"> </span><span class="nx">vet2</span><span class="w"> </span><span class="nx">vertex</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-13-52" name="__codelineno-13-52" href="#__codelineno-13-52"></a><span class="w"> </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">ok1</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">g</span><span class="p">.</span><span class="nx">adjList</span><span class="p">[</span><span class="nx">vet1</span><span class="p">]</span>
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<a id="__codelineno-13-53" name="__codelineno-13-53" href="#__codelineno-13-53"></a><span class="w"> </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">ok2</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">g</span><span class="p">.</span><span class="nx">adjList</span><span class="p">[</span><span class="nx">vet2</span><span class="p">]</span>
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<a id="__codelineno-13-54" name="__codelineno-13-54" href="#__codelineno-13-54"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">!</span><span class="nx">ok1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="p">!</span><span class="nx">ok2</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">vet1</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nx">vet2</span><span class="w"> </span><span class="p">{</span>
|
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<a id="__codelineno-13-55" name="__codelineno-13-55" href="#__codelineno-13-55"></a><span class="w"> </span><span class="nb">panic</span><span class="p">(</span><span class="s">"error"</span><span class="p">)</span>
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<a id="__codelineno-13-56" name="__codelineno-13-56" href="#__codelineno-13-56"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-13-57" name="__codelineno-13-57" href="#__codelineno-13-57"></a><span class="w"> </span><span class="c1">// 删除边 vet1 - vet2, 借助 delete 来删除 map 中的键</span>
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<a id="__codelineno-13-58" name="__codelineno-13-58" href="#__codelineno-13-58"></a><span class="w"> </span><span class="nb">delete</span><span class="p">(</span><span class="nx">g</span><span class="p">.</span><span class="nx">adjList</span><span class="p">[</span><span class="nx">vet1</span><span class="p">],</span><span class="w"> </span><span class="nx">vet2</span><span class="p">)</span>
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<a id="__codelineno-13-59" name="__codelineno-13-59" href="#__codelineno-13-59"></a><span class="w"> </span><span class="nb">delete</span><span class="p">(</span><span class="nx">g</span><span class="p">.</span><span class="nx">adjList</span><span class="p">[</span><span class="nx">vet2</span><span class="p">],</span><span class="w"> </span><span class="nx">vet1</span><span class="p">)</span>
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<a id="__codelineno-13-60" name="__codelineno-13-60" href="#__codelineno-13-60"></a><span class="p">}</span>
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<a id="__codelineno-13-61" name="__codelineno-13-61" href="#__codelineno-13-61"></a>
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<a id="__codelineno-13-62" name="__codelineno-13-62" href="#__codelineno-13-62"></a><span class="cm">/* 添加顶点 */</span>
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<a id="__codelineno-13-63" name="__codelineno-13-63" href="#__codelineno-13-63"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">g</span><span class="w"> </span><span class="o">*</span><span class="nx">graphAdjList</span><span class="p">)</span><span class="w"> </span><span class="nx">addVertex</span><span class="p">(</span><span class="nx">vet</span><span class="w"> </span><span class="nx">vertex</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-13-64" name="__codelineno-13-64" href="#__codelineno-13-64"></a><span class="w"> </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">ok</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">g</span><span class="p">.</span><span class="nx">adjList</span><span class="p">[</span><span class="nx">vet</span><span class="p">]</span>
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<a id="__codelineno-13-65" name="__codelineno-13-65" href="#__codelineno-13-65"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">ok</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-13-66" name="__codelineno-13-66" href="#__codelineno-13-66"></a><span class="w"> </span><span class="k">return</span>
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<a id="__codelineno-13-67" name="__codelineno-13-67" href="#__codelineno-13-67"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-13-68" name="__codelineno-13-68" href="#__codelineno-13-68"></a><span class="w"> </span><span class="c1">// 在邻接表中添加一个新链表（即 set）</span>
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<a id="__codelineno-13-69" name="__codelineno-13-69" href="#__codelineno-13-69"></a><span class="w"> </span><span class="nx">g</span><span class="p">.</span><span class="nx">adjList</span><span class="p">[</span><span class="nx">vet</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">make</span><span class="p">(</span><span class="kd">map</span><span class="p">[</span><span class="nx">vertex</span><span class="p">]</span><span class="kd">struct</span><span class="p">{})</span>
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<a id="__codelineno-13-70" name="__codelineno-13-70" href="#__codelineno-13-70"></a><span class="p">}</span>
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<a id="__codelineno-13-71" name="__codelineno-13-71" href="#__codelineno-13-71"></a>
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<a id="__codelineno-13-72" name="__codelineno-13-72" href="#__codelineno-13-72"></a><span class="cm">/* 删除顶点 */</span>
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<a id="__codelineno-13-73" name="__codelineno-13-73" href="#__codelineno-13-73"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">g</span><span class="w"> </span><span class="o">*</span><span class="nx">graphAdjList</span><span class="p">)</span><span class="w"> </span><span class="nx">removeVertex</span><span class="p">(</span><span class="nx">vet</span><span class="w"> </span><span class="nx">vertex</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-13-74" name="__codelineno-13-74" href="#__codelineno-13-74"></a><span class="w"> </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">ok</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">g</span><span class="p">.</span><span class="nx">adjList</span><span class="p">[</span><span class="nx">vet</span><span class="p">]</span>
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<a id="__codelineno-13-75" name="__codelineno-13-75" href="#__codelineno-13-75"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">!</span><span class="nx">ok</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-13-76" name="__codelineno-13-76" href="#__codelineno-13-76"></a><span class="w"> </span><span class="nb">panic</span><span class="p">(</span><span class="s">"error"</span><span class="p">)</span>
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<a id="__codelineno-13-77" name="__codelineno-13-77" href="#__codelineno-13-77"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-13-78" name="__codelineno-13-78" href="#__codelineno-13-78"></a><span class="w"> </span><span class="c1">// 在邻接表中删除顶点 vet 对应的链表</span>
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<a id="__codelineno-13-79" name="__codelineno-13-79" href="#__codelineno-13-79"></a><span class="w"> </span><span class="nb">delete</span><span class="p">(</span><span class="nx">g</span><span class="p">.</span><span class="nx">adjList</span><span class="p">,</span><span class="w"> </span><span class="nx">vet</span><span class="p">)</span>
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<a id="__codelineno-13-80" name="__codelineno-13-80" href="#__codelineno-13-80"></a><span class="w"> </span><span class="c1">// 遍历其它顶点的链表（即 Set），删除所有包含 vet 的边</span>
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<a id="__codelineno-13-81" name="__codelineno-13-81" href="#__codelineno-13-81"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">set</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">g</span><span class="p">.</span><span class="nx">adjList</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-13-82" name="__codelineno-13-82" href="#__codelineno-13-82"></a><span class="w"> </span><span class="c1">// 操作</span>
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<a id="__codelineno-13-83" name="__codelineno-13-83" href="#__codelineno-13-83"></a><span class="w"> </span><span class="nb">delete</span><span class="p">(</span><span class="nx">set</span><span class="p">,</span><span class="w"> </span><span class="nx">vet</span><span class="p">)</span>
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<a id="__codelineno-13-84" name="__codelineno-13-84" href="#__codelineno-13-84"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-13-85" name="__codelineno-13-85" href="#__codelineno-13-85"></a><span class="p">}</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"><span class="filename">graph_adjacency_list.js</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a>
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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"><span class="filename">graph_adjacency_list.ts</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a>
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</code></pre></div>
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<div class="highlight"><span class="filename">graph_adjacency_list.c</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a>
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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"><span class="filename">graph_adjacency_list.cs</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a>
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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"><span class="filename">graph_adjacency_list.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="cm">/* 顶点类 */</span>
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<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a><span class="kd">class</span> <span class="nc">Vertex</span><span class="p">:</span> <span class="nb">Hashable</span> <span class="p">{</span>
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<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a> <span class="kd">var</span> <span class="nv">val</span><span class="p">:</span> <span class="nb">Int</span>
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<a id="__codelineno-18-4" name="__codelineno-18-4" href="#__codelineno-18-4"></a>
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<a id="__codelineno-18-5" name="__codelineno-18-5" href="#__codelineno-18-5"></a> <span class="kd">init</span><span class="p">(</span><span class="n">val</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">{</span>
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<a id="__codelineno-18-6" name="__codelineno-18-6" href="#__codelineno-18-6"></a> <span class="kc">self</span><span class="p">.</span><span class="n">val</span> <span class="p">=</span> <span class="n">val</span>
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<a id="__codelineno-18-7" name="__codelineno-18-7" href="#__codelineno-18-7"></a> <span class="p">}</span>
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<a id="__codelineno-18-8" name="__codelineno-18-8" href="#__codelineno-18-8"></a>
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<a id="__codelineno-18-9" name="__codelineno-18-9" href="#__codelineno-18-9"></a> <span class="kd">static</span> <span class="kd">func</span> <span class="p">==</span> <span class="p">(</span><span class="n">lhs</span><span class="p">:</span> <span class="n">Vertex</span><span class="p">,</span> <span class="n">rhs</span><span class="p">:</span> <span class="n">Vertex</span><span class="p">)</span> <span class="p">-></span> <span class="nb">Bool</span> <span class="p">{</span>
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<a id="__codelineno-18-10" name="__codelineno-18-10" href="#__codelineno-18-10"></a> <span class="n">lhs</span><span class="p">.</span><span class="n">val</span> <span class="p">==</span> <span class="n">rhs</span><span class="p">.</span><span class="n">val</span>
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<a id="__codelineno-18-11" name="__codelineno-18-11" href="#__codelineno-18-11"></a> <span class="p">}</span>
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<a id="__codelineno-18-12" name="__codelineno-18-12" href="#__codelineno-18-12"></a>
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<a id="__codelineno-18-13" name="__codelineno-18-13" href="#__codelineno-18-13"></a> <span class="kd">func</span> <span class="nf">hash</span><span class="p">(</span><span class="n">into</span> <span class="n">hasher</span><span class="p">:</span> <span class="kr">inout</span> <span class="n">Hasher</span><span class="p">)</span> <span class="p">{</span>
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<a id="__codelineno-18-14" name="__codelineno-18-14" href="#__codelineno-18-14"></a> <span class="n">hasher</span><span class="p">.</span><span class="n">combine</span><span class="p">(</span><span class="n">val</span><span class="p">)</span>
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<a id="__codelineno-18-15" name="__codelineno-18-15" href="#__codelineno-18-15"></a> <span class="p">}</span>
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<a id="__codelineno-18-16" name="__codelineno-18-16" href="#__codelineno-18-16"></a><span class="p">}</span>
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<a id="__codelineno-18-17" name="__codelineno-18-17" href="#__codelineno-18-17"></a>
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<a id="__codelineno-18-18" name="__codelineno-18-18" href="#__codelineno-18-18"></a><span class="cm">/* 基于邻接表实现的无向图类 */</span>
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<a id="__codelineno-18-19" name="__codelineno-18-19" href="#__codelineno-18-19"></a><span class="kd">class</span> <span class="nc">GraphAdjList</span> <span class="p">{</span>
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<a id="__codelineno-18-20" name="__codelineno-18-20" href="#__codelineno-18-20"></a> <span class="c1">// 请注意，vertices 和 adjList 中存储的都是 Vertex 对象</span>
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<a id="__codelineno-18-21" name="__codelineno-18-21" href="#__codelineno-18-21"></a> <span class="kd">private</span> <span class="kd">var</span> <span class="nv">adjList</span><span class="p">:</span> <span class="p">[</span><span class="n">Vertex</span><span class="p">:</span> <span class="n">Set</span><span class="p"><</span><span class="n">Vertex</span><span class="p">>]</span> <span class="c1">// 邻接表（使用哈希表实现）</span>
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<a id="__codelineno-18-22" name="__codelineno-18-22" href="#__codelineno-18-22"></a>
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<a id="__codelineno-18-23" name="__codelineno-18-23" href="#__codelineno-18-23"></a> <span class="kd">init</span><span class="p">(</span><span class="n">edges</span><span class="p">:</span> <span class="p">[[</span><span class="n">Vertex</span><span class="p">]])</span> <span class="p">{</span>
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<a id="__codelineno-18-24" name="__codelineno-18-24" href="#__codelineno-18-24"></a> <span class="n">adjList</span> <span class="p">=</span> <span class="p">[:]</span>
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<a id="__codelineno-18-25" name="__codelineno-18-25" href="#__codelineno-18-25"></a> <span class="c1">// 添加所有顶点和边</span>
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<a id="__codelineno-18-26" name="__codelineno-18-26" href="#__codelineno-18-26"></a> <span class="k">for</span> <span class="n">edge</span> <span class="k">in</span> <span class="n">edges</span> <span class="p">{</span>
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<a id="__codelineno-18-27" name="__codelineno-18-27" href="#__codelineno-18-27"></a> <span class="n">addVertex</span><span class="p">(</span><span class="n">vet</span><span class="p">:</span> <span class="n">edge</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
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<a id="__codelineno-18-28" name="__codelineno-18-28" href="#__codelineno-18-28"></a> <span class="n">addVertex</span><span class="p">(</span><span class="n">vet</span><span class="p">:</span> <span class="n">edge</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
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<a id="__codelineno-18-29" name="__codelineno-18-29" href="#__codelineno-18-29"></a> <span class="n">addEdge</span><span class="p">(</span><span class="n">vet1</span><span class="p">:</span> <span class="n">edge</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">vet2</span><span class="p">:</span> <span class="n">edge</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
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<a id="__codelineno-18-30" name="__codelineno-18-30" href="#__codelineno-18-30"></a> <span class="p">}</span>
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<a id="__codelineno-18-31" name="__codelineno-18-31" href="#__codelineno-18-31"></a> <span class="p">}</span>
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<a id="__codelineno-18-32" name="__codelineno-18-32" href="#__codelineno-18-32"></a>
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<a id="__codelineno-18-33" name="__codelineno-18-33" href="#__codelineno-18-33"></a> <span class="cm">/* 获取顶点数量 */</span>
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<a id="__codelineno-18-34" name="__codelineno-18-34" href="#__codelineno-18-34"></a> <span class="kd">func</span> <span class="nf">size</span><span class="p">()</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span>
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<a id="__codelineno-18-35" name="__codelineno-18-35" href="#__codelineno-18-35"></a> <span class="n">adjList</span><span class="p">.</span><span class="bp">count</span>
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<a id="__codelineno-18-36" name="__codelineno-18-36" href="#__codelineno-18-36"></a> <span class="p">}</span>
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<a id="__codelineno-18-37" name="__codelineno-18-37" href="#__codelineno-18-37"></a>
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<a id="__codelineno-18-38" name="__codelineno-18-38" href="#__codelineno-18-38"></a> <span class="cm">/* 添加边 */</span>
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<a id="__codelineno-18-39" name="__codelineno-18-39" href="#__codelineno-18-39"></a> <span class="kd">func</span> <span class="nf">addEdge</span><span class="p">(</span><span class="n">vet1</span><span class="p">:</span> <span class="n">Vertex</span><span class="p">,</span> <span class="n">vet2</span><span class="p">:</span> <span class="n">Vertex</span><span class="p">)</span> <span class="p">{</span>
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<a id="__codelineno-18-40" name="__codelineno-18-40" href="#__codelineno-18-40"></a> <span class="k">if</span> <span class="n">adjList</span><span class="p">[</span><span class="n">vet1</span><span class="p">]</span> <span class="p">==</span> <span class="kc">nil</span> <span class="o">||</span> <span class="n">adjList</span><span class="p">[</span><span class="n">vet2</span><span class="p">]</span> <span class="p">==</span> <span class="kc">nil</span> <span class="o">||</span> <span class="n">vet1</span> <span class="p">==</span> <span class="n">vet2</span> <span class="p">{</span>
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<a id="__codelineno-18-41" name="__codelineno-18-41" href="#__codelineno-18-41"></a> <span class="bp">fatalError</span><span class="p">(</span><span class="s">"参数错误"</span><span class="p">)</span>
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<a id="__codelineno-18-42" name="__codelineno-18-42" href="#__codelineno-18-42"></a> <span class="p">}</span>
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<a id="__codelineno-18-43" name="__codelineno-18-43" href="#__codelineno-18-43"></a> <span class="c1">// 添加边 vet1 - vet2</span>
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<a id="__codelineno-18-44" name="__codelineno-18-44" href="#__codelineno-18-44"></a> <span class="n">adjList</span><span class="p">[</span><span class="n">vet1</span><span class="p">]?.</span><span class="bp">insert</span><span class="p">(</span><span class="n">vet2</span><span class="p">)</span>
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<a id="__codelineno-18-45" name="__codelineno-18-45" href="#__codelineno-18-45"></a> <span class="n">adjList</span><span class="p">[</span><span class="n">vet2</span><span class="p">]?.</span><span class="bp">insert</span><span class="p">(</span><span class="n">vet1</span><span class="p">)</span>
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<a id="__codelineno-18-46" name="__codelineno-18-46" href="#__codelineno-18-46"></a> <span class="p">}</span>
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<a id="__codelineno-18-47" name="__codelineno-18-47" href="#__codelineno-18-47"></a>
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<a id="__codelineno-18-48" name="__codelineno-18-48" href="#__codelineno-18-48"></a> <span class="cm">/* 删除边 */</span>
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<a id="__codelineno-18-49" name="__codelineno-18-49" href="#__codelineno-18-49"></a> <span class="kd">func</span> <span class="nf">removeEdge</span><span class="p">(</span><span class="n">vet1</span><span class="p">:</span> <span class="n">Vertex</span><span class="p">,</span> <span class="n">vet2</span><span class="p">:</span> <span class="n">Vertex</span><span class="p">)</span> <span class="p">{</span>
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<a id="__codelineno-18-50" name="__codelineno-18-50" href="#__codelineno-18-50"></a> <span class="k">if</span> <span class="n">adjList</span><span class="p">[</span><span class="n">vet1</span><span class="p">]</span> <span class="p">==</span> <span class="kc">nil</span> <span class="o">||</span> <span class="n">adjList</span><span class="p">[</span><span class="n">vet2</span><span class="p">]</span> <span class="p">==</span> <span class="kc">nil</span> <span class="o">||</span> <span class="n">vet1</span> <span class="p">==</span> <span class="n">vet2</span> <span class="p">{</span>
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<a id="__codelineno-18-51" name="__codelineno-18-51" href="#__codelineno-18-51"></a> <span class="bp">fatalError</span><span class="p">(</span><span class="s">"参数错误"</span><span class="p">)</span>
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<a id="__codelineno-18-52" name="__codelineno-18-52" href="#__codelineno-18-52"></a> <span class="p">}</span>
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<a id="__codelineno-18-53" name="__codelineno-18-53" href="#__codelineno-18-53"></a> <span class="c1">// 删除边 vet1 - vet2</span>
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<a id="__codelineno-18-54" name="__codelineno-18-54" href="#__codelineno-18-54"></a> <span class="n">adjList</span><span class="p">[</span><span class="n">vet1</span><span class="p">]?.</span><span class="n">remove</span><span class="p">(</span><span class="n">vet2</span><span class="p">)</span>
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<a id="__codelineno-18-55" name="__codelineno-18-55" href="#__codelineno-18-55"></a> <span class="n">adjList</span><span class="p">[</span><span class="n">vet2</span><span class="p">]?.</span><span class="n">remove</span><span class="p">(</span><span class="n">vet1</span><span class="p">)</span>
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<a id="__codelineno-18-56" name="__codelineno-18-56" href="#__codelineno-18-56"></a> <span class="p">}</span>
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<a id="__codelineno-18-57" name="__codelineno-18-57" href="#__codelineno-18-57"></a>
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<a id="__codelineno-18-58" name="__codelineno-18-58" href="#__codelineno-18-58"></a> <span class="cm">/* 添加顶点 */</span>
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<a id="__codelineno-18-59" name="__codelineno-18-59" href="#__codelineno-18-59"></a> <span class="kd">func</span> <span class="nf">addVertex</span><span class="p">(</span><span class="n">vet</span><span class="p">:</span> <span class="n">Vertex</span><span class="p">)</span> <span class="p">{</span>
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<a id="__codelineno-18-60" name="__codelineno-18-60" href="#__codelineno-18-60"></a> <span class="k">if</span> <span class="n">adjList</span><span class="p">[</span><span class="n">vet</span><span class="p">]</span> <span class="o">!=</span> <span class="kc">nil</span> <span class="p">{</span>
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<a id="__codelineno-18-61" name="__codelineno-18-61" href="#__codelineno-18-61"></a> <span class="k">return</span>
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<a id="__codelineno-18-62" name="__codelineno-18-62" href="#__codelineno-18-62"></a> <span class="p">}</span>
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<a id="__codelineno-18-63" name="__codelineno-18-63" href="#__codelineno-18-63"></a> <span class="c1">// 在邻接表中添加一个新链表（即 HashSet）</span>
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<a id="__codelineno-18-64" name="__codelineno-18-64" href="#__codelineno-18-64"></a> <span class="n">adjList</span><span class="p">[</span><span class="n">vet</span><span class="p">]</span> <span class="p">=</span> <span class="p">[]</span>
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<a id="__codelineno-18-65" name="__codelineno-18-65" href="#__codelineno-18-65"></a> <span class="p">}</span>
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<a id="__codelineno-18-66" name="__codelineno-18-66" href="#__codelineno-18-66"></a>
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<a id="__codelineno-18-67" name="__codelineno-18-67" href="#__codelineno-18-67"></a> <span class="cm">/* 删除顶点 */</span>
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<a id="__codelineno-18-68" name="__codelineno-18-68" href="#__codelineno-18-68"></a> <span class="kd">func</span> <span class="nf">removeVertex</span><span class="p">(</span><span class="n">vet</span><span class="p">:</span> <span class="n">Vertex</span><span class="p">)</span> <span class="p">{</span>
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<a id="__codelineno-18-69" name="__codelineno-18-69" href="#__codelineno-18-69"></a> <span class="k">if</span> <span class="n">adjList</span><span class="p">[</span><span class="n">vet</span><span class="p">]</span> <span class="p">==</span> <span class="kc">nil</span> <span class="p">{</span>
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<a id="__codelineno-18-70" name="__codelineno-18-70" href="#__codelineno-18-70"></a> <span class="bp">fatalError</span><span class="p">(</span><span class="s">"参数错误"</span><span class="p">)</span>
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<a id="__codelineno-18-71" name="__codelineno-18-71" href="#__codelineno-18-71"></a> <span class="p">}</span>
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<a id="__codelineno-18-72" name="__codelineno-18-72" href="#__codelineno-18-72"></a> <span class="c1">// 在邻接表中删除顶点 vet 对应的链表（即 HashSet）</span>
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<a id="__codelineno-18-73" name="__codelineno-18-73" href="#__codelineno-18-73"></a> <span class="n">adjList</span><span class="p">.</span><span class="n">removeValue</span><span class="p">(</span><span class="n">forKey</span><span class="p">:</span> <span class="n">vet</span><span class="p">)</span>
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<a id="__codelineno-18-74" name="__codelineno-18-74" href="#__codelineno-18-74"></a> <span class="c1">// 遍历其它顶点的链表（即 HashSet），删除所有包含 vet 的边</span>
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<a id="__codelineno-18-75" name="__codelineno-18-75" href="#__codelineno-18-75"></a> <span class="k">for</span> <span class="n">key</span> <span class="k">in</span> <span class="n">adjList</span><span class="p">.</span><span class="n">keys</span> <span class="p">{</span>
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<a id="__codelineno-18-76" name="__codelineno-18-76" href="#__codelineno-18-76"></a> <span class="n">adjList</span><span class="p">[</span><span class="n">key</span><span class="p">]?.</span><span class="n">remove</span><span class="p">(</span><span class="n">vet</span><span class="p">)</span>
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<a id="__codelineno-18-77" name="__codelineno-18-77" href="#__codelineno-18-77"></a> <span class="p">}</span>
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<a id="__codelineno-18-78" name="__codelineno-18-78" href="#__codelineno-18-78"></a> <span class="p">}</span>
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<a id="__codelineno-18-79" name="__codelineno-18-79" href="#__codelineno-18-79"></a><span class="p">}</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"><span class="filename">graph_adjacency_list.zig</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a>
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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="923">9.2.3. 效率对比<a class="headerlink" href="#923" title="Permanent link">¶</a></h2>
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<p>设图中共有 <span class="arithmatex">\(n\)</span> 个顶点和 <span class="arithmatex">\(m\)</span> 条边，下表为邻接矩阵和邻接表的时间和空间效率对比。</p>
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<div class="center-table">
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<table>
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<thead>
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<tr>
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<th></th>
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<th>邻接矩阵</th>
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<th>邻接表（链表）</th>
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<th>邻接表（哈希表）</th>
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</tr>
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</thead>
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<tbody>
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<tr>
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<td>判断是否邻接</td>
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<td><span class="arithmatex">\(O(1)\)</span></td>
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<td><span class="arithmatex">\(O(m)\)</span></td>
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<td><span class="arithmatex">\(O(1)\)</span></td>
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</tr>
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<tr>
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<td>添加边</td>
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<td><span class="arithmatex">\(O(1)\)</span></td>
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<td><span class="arithmatex">\(O(1)\)</span></td>
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<td><span class="arithmatex">\(O(1)\)</span></td>
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</tr>
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<tr>
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<td>删除边</td>
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<td><span class="arithmatex">\(O(1)\)</span></td>
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<td><span class="arithmatex">\(O(m)\)</span></td>
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<td><span class="arithmatex">\(O(1)\)</span></td>
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</tr>
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<tr>
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<td>添加顶点</td>
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<td><span class="arithmatex">\(O(n)\)</span></td>
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<td><span class="arithmatex">\(O(1)\)</span></td>
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<td><span class="arithmatex">\(O(1)\)</span></td>
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</tr>
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<tr>
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<td>删除顶点</td>
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<td><span class="arithmatex">\(O(n^2)\)</span></td>
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<td><span class="arithmatex">\(O(n + m)\)</span></td>
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<td><span class="arithmatex">\(O(n)\)</span></td>
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</tr>
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<tr>
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<td>内存空间占用</td>
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<td><span class="arithmatex">\(O(n^2)\)</span></td>
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<td><span class="arithmatex">\(O(n + m)\)</span></td>
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<td><span class="arithmatex">\(O(n + m)\)</span></td>
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</tr>
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</tbody>
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</table>
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</div>
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<p>观察上表，貌似邻接表（哈希表）的时间与空间效率最优。但实际上，在邻接矩阵中操作边的效率更高，只需要一次数组访问或赋值操作即可。总结以上，<strong>邻接矩阵体现“以空间换时间”，邻接表体现“以时间换空间”</strong>。</p>
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