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<meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
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<title>9.2 グラフの基本操作 - Hello アルゴリズム</title>
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<span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
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Hello アルゴリズム
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9.2 グラフの基本操作
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简体中文
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繁體中文
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<a href="/en/chapter_graph/graph_operations/" hreflang="en" class="md-select__link">
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English
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<a href="/ja/chapter_graph/graph_operations/" hreflang="ja" class="md-select__link">
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日本語
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Русский
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検索を初期化
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<span class="md-ellipsis">
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序
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序
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<span class="md-ellipsis">
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第 0 章 前書き
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第 0 章 前書き
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0.1 本書について
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</a>
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0.2 本書の使い方
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</span>
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</a>
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0.3 まとめ
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第 1 章 アルゴリズムを知る
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第 1 章 アルゴリズムを知る
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1.1 アルゴリズムはどこにでもある
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1.2 アルゴリズムとは何か
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1.3 まとめ
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<span class="md-ellipsis">
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第 2 章 計算量解析
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</a>
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
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<span class="md-nav__icon md-icon"></span>
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第 2 章 計算量解析
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</label>
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<ul class="md-nav__list" data-md-scrollfix>
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2.1 アルゴリズムの効率評価
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|
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|
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|
||
</span>
|
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|
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|
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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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2.2 反復と再帰
|
||
|
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|
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|
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</span>
|
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|
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|
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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="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
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|
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|
||
2.3 時間計算量
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
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|
||
</a>
|
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</li>
|
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<li class="md-nav__item">
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<a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
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|
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|
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|
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2.4 空間計算量
|
||
|
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|
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|
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</span>
|
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|
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|
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|
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</a>
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</li>
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|
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<li class="md-nav__item">
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<a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
|
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<span class="md-ellipsis">
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|
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|
||
2.5 まとめ
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
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</a>
|
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|
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|
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</ul>
|
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</nav>
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<div class="md-nav__link md-nav__container">
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|
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|
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<span class="md-ellipsis">
|
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|
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|
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第 3 章 データ構造
|
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|
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|
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|
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<span class="md-nav__icon md-icon"></span>
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第 3 章 データ構造
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|
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</label>
|
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<ul class="md-nav__list" data-md-scrollfix>
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<span class="md-ellipsis">
|
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|
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|
||
3.1 データ構造の分類
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
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</li>
|
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<li class="md-nav__item">
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<a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
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|
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|
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|
||
3.2 基本データ型
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
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<li class="md-nav__item">
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<a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
|
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<span class="md-ellipsis">
|
||
|
||
|
||
3.3 数値の符号化 *
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
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|
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|
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<li class="md-nav__item">
|
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<a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
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<span class="md-ellipsis">
|
||
|
||
|
||
3.4 文字の符号化 *
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
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<li class="md-nav__item">
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<a href="../../chapter_data_structure/summary/" class="md-nav__link">
|
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<span class="md-ellipsis">
|
||
|
||
|
||
3.5 まとめ
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
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|
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|
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|
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|
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</ul>
|
||
</nav>
|
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||
</li>
|
||
|
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|
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|
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|
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|
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|
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||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
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<li class="md-nav__item md-nav__item--nested">
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<div class="md-nav__link md-nav__container">
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|
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|
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<span class="md-ellipsis">
|
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|
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|
||
第 4 章 配列と連結リスト
|
||
|
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|
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|
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</span>
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|
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</a>
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
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<span class="md-nav__icon md-icon"></span>
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第 4 章 配列と連結リスト
|
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|
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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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<span class="md-ellipsis">
|
||
|
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|
||
4.1 配列
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
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|
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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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|
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|
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|
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<span class="md-ellipsis">
|
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|
||
|
||
4.2 連結リスト
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
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|
||
|
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|
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|
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|
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|
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|
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|
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|
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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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|
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|
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|
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<span class="md-ellipsis">
|
||
|
||
|
||
4.3 リスト
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
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|
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|
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|
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|
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|
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<li class="md-nav__item">
|
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<a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
4.4 メモリとキャッシュ *
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
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|
||
|
||
|
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|
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|
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|
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|
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|
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|
||
<li class="md-nav__item">
|
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<a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
|
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|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
4.5 まとめ
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
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</li>
|
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|
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|
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|
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|
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</ul>
|
||
</nav>
|
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|
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</li>
|
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|
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|
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|
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|
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|
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|
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|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
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|
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|
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|
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<li class="md-nav__item md-nav__item--nested">
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
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<div class="md-nav__link md-nav__container">
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<a href="../../chapter_stack_and_queue/" class="md-nav__link ">
|
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38zM6.77 14.32l.37-1.76 8.79 1.85-.37 1.76zm1.16-4.21.76-1.61 8.14 3.78-.76 1.62zm2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37zm4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21zM6.59 18.41v-1.8h8.98v1.8z"/></svg>
|
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|
||
<span class="md-ellipsis">
|
||
|
||
|
||
第 5 章 スタックとキュー
|
||
|
||
|
||
|
||
</span>
|
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|
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|
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|
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</a>
|
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<label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
|
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<span class="md-nav__icon md-icon"></span>
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</div>
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|
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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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|
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|
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第 5 章 スタックとキュー
|
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|
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|
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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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|
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|
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|
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<span class="md-ellipsis">
|
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|
||
|
||
5.1 スタック
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
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</li>
|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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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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|
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|
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|
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<span class="md-ellipsis">
|
||
|
||
|
||
5.2 キュー
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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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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|
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|
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|
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<span class="md-ellipsis">
|
||
|
||
|
||
5.3 両端キュー
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
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|
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|
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|
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|
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|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
|
||
|
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|
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|
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<span class="md-ellipsis">
|
||
|
||
|
||
5.4 まとめ
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
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|
||
|
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</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
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|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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<li class="md-nav__item md-nav__item--nested">
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
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|
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<div class="md-nav__link md-nav__container">
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<a href="../../chapter_hashing/" class="md-nav__link ">
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|
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|
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<span class="md-ellipsis">
|
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|
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|
||
第 6 章 ハッシュ表
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
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|
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|
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<label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
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<span class="md-nav__icon md-icon"></span>
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</div>
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|
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
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<span class="md-nav__icon md-icon"></span>
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|
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|
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第 6 章 ハッシュ表
|
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|
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|
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</label>
|
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<ul class="md-nav__list" data-md-scrollfix>
|
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|
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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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|
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|
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|
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<span class="md-ellipsis">
|
||
|
||
|
||
6.1 ハッシュ表
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
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|
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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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|
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|
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<span class="md-ellipsis">
|
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|
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|
||
6.2 ハッシュ衝突
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
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</li>
|
||
|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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<li class="md-nav__item">
|
||
<a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
6.3 ハッシュアルゴリズム
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
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|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_hashing/summary/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
6.4 まとめ
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
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|
||
|
||
|
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|
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|
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||
|
||
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||
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||
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||
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||
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||
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||
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||
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||
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||
|
||
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||
|
||
|
||
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|
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|
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|
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|
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|
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|
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|
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|
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|
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<li class="md-nav__item md-nav__item--nested">
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
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<div class="md-nav__link md-nav__container">
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<a href="../../chapter_tree/" class="md-nav__link ">
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1"/></svg>
|
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|
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<span class="md-ellipsis">
|
||
|
||
|
||
第 7 章 木
|
||
|
||
|
||
|
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</span>
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</a>
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<label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
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<span class="md-nav__icon md-icon"></span>
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</div>
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
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<label class="md-nav__title" for="__nav_9">
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<span class="md-nav__icon md-icon"></span>
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|
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|
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第 7 章 木
|
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|
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|
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</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
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|
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<li class="md-nav__item">
|
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<a href="../../chapter_tree/binary_tree/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
7.1 二分木
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
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|
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|
||
|
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|
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|
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|
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|
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<li class="md-nav__item">
|
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<a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
7.2 二分木の走査
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
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|
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|
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|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
7.3 二分木の配列表現
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
7.4 二分探索木
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_tree/avl_tree/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
7.5 AVL木 *
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
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|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_tree/summary/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
7.6 まとめ
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
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|
||
|
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</ul>
|
||
</nav>
|
||
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||
</li>
|
||
|
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|
||
|
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|
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|
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|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
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|
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|
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|
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|
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|
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|
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<li class="md-nav__item md-nav__item--nested">
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
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|
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<div class="md-nav__link md-nav__container">
|
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<a href="../../chapter_heap/" class="md-nav__link ">
|
||
|
||
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1"/></svg>
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
第 8 章 ヒープ
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
|
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|
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<label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
|
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<span class="md-nav__icon md-icon"></span>
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</label>
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|
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</div>
|
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|
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
|
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<label class="md-nav__title" for="__nav_10">
|
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<span class="md-nav__icon md-icon"></span>
|
||
|
||
|
||
第 8 章 ヒープ
|
||
|
||
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
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|
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|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_heap/heap/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
8.1 ヒープ
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
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|
||
|
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|
||
|
||
|
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|
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|
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|
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|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_heap/build_heap/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
8.2 ヒープ構築操作
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
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|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_heap/top_k/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
8.3 Top-k 問題
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
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|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_heap/summary/" class="md-nav__link">
|
||
|
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|
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|
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<span class="md-ellipsis">
|
||
|
||
|
||
8.4 まとめ
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
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|
||
|
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</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
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|
||
|
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|
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|
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|
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|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
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|
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|
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|
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|
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<li class="md-nav__item md-nav__item--active md-nav__item--nested">
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<div class="md-nav__link md-nav__container">
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<a href="../" class="md-nav__link ">
|
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|
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|
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|
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59zM6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43s.83.16 1.12.43l4.28-2.53zM12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68s1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25zm2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24z"/></svg>
|
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|
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<span class="md-ellipsis">
|
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|
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|
||
第 9 章 グラフ
|
||
|
||
|
||
|
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</span>
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|
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|
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|
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</a>
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<label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="true">
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<span class="md-nav__icon md-icon"></span>
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|
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第 9 章 グラフ
|
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|
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|
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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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|
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|
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|
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<span class="md-ellipsis">
|
||
|
||
|
||
9.1 グラフ
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
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|
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|
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<li class="md-nav__item md-nav__item--active">
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<label class="md-nav__link md-nav__link--active" for="__toc">
|
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|
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|
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|
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<span class="md-ellipsis">
|
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|
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|
||
9.2 グラフの基本操作
|
||
|
||
|
||
|
||
</span>
|
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|
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|
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|
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<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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|
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|
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|
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<span class="md-ellipsis">
|
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|
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|
||
9.2 グラフの基本操作
|
||
|
||
|
||
|
||
</span>
|
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|
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|
||
|
||
</a>
|
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|
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|
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|
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<nav class="md-nav md-nav--secondary" aria-label="目次">
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|
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|
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|
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<span class="md-nav__icon md-icon"></span>
|
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目次
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|
||
|
||
<li class="md-nav__item">
|
||
<a href="#921" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
9.2.1 隣接行列に基づく実装
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#922" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
9.2.2 隣接リストに基づく実装
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
<li class="md-nav__item">
|
||
<a href="#923" class="md-nav__link">
|
||
<span class="md-ellipsis">
|
||
|
||
9.2.3 効率の比較
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
||
|
||
</ul>
|
||
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../graph_traversal/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
9.3 グラフの走査
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../summary/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
9.4 まとめ
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
|
||
|
||
|
||
<div class="md-nav__link md-nav__container">
|
||
<a href="../../chapter_searching/" class="md-nav__link ">
|
||
|
||
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4zM3 16v-2h6v2zm0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1z"/></svg>
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
第 10 章 探索
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
|
||
|
||
<label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
</div>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_12">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
|
||
|
||
第 10 章 探索
|
||
|
||
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_searching/binary_search/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
10.1 二分探索
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
10.2 二分探索の挿入点
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
10.3 二分探索の境界
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
10.4 ハッシュ最適化戦略
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
10.5 探索アルゴリズムの再認識
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_searching/summary/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
10.6 まとめ
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
|
||
|
||
|
||
<div class="md-nav__link md-nav__container">
|
||
<a href="../../chapter_sorting/" class="md-nav__link ">
|
||
|
||
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2z"/></svg>
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
第 11 章 ソート
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
|
||
|
||
<label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
</div>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_13">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
|
||
|
||
第 11 章 ソート
|
||
|
||
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
11.1 ソートアルゴリズム
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
11.2 選択ソート
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
11.3 バブルソート
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
11.4 挿入ソート
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
11.5 クイックソート
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
11.6 マージソート
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
11.7 ヒープソート
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
11.8 バケットソート
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
11.9 計数ソート
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
11.10 基数ソート
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/summary/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
11.11 まとめ
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
|
||
|
||
|
||
<div class="md-nav__link md-nav__container">
|
||
<a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
|
||
|
||
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7zM2 9v6h5V9zm10 0v2H9v2h3v2l3-3zm5 2v2h5v-2zm0 4v2h5v-2z"/></svg>
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
第 12 章 分割統治
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
|
||
|
||
<label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
</div>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_14">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
|
||
|
||
第 12 章 分割統治
|
||
|
||
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
12.1 分割統治アルゴリズム
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
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|
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|
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|
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|
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|
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|
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|
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<li class="md-nav__item">
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<a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
|
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|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
12.2 分割統治探索戦略
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
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|
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|
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|
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|
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|
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<li class="md-nav__item">
|
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<a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
|
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|
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|
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|
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<span class="md-ellipsis">
|
||
|
||
|
||
12.3 木の構築問題
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
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|
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|
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<span class="md-ellipsis">
|
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|
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|
||
12.4 ハノイの塔問題
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
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</li>
|
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<a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
|
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|
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|
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<span class="md-ellipsis">
|
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|
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|
||
12.5 まとめ
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
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</a>
|
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</ul>
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|
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<span class="md-ellipsis">
|
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|
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|
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第 13 章 バックトラッキング
|
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|
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|
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|
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第 13 章 バックトラッキング
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|
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|
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</label>
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|
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|
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|
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13.1 バックトラッキングアルゴリズム
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
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</a>
|
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</li>
|
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|
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|
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|
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<li class="md-nav__item">
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<a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
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<span class="md-ellipsis">
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|
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|
||
13.2 全順列問題
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
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</li>
|
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|
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|
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|
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|
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|
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|
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<li class="md-nav__item">
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<a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
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|
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|
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|
||
13.3 部分集合和問題
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
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</li>
|
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|
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|
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|
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<li class="md-nav__item">
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<a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
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<span class="md-ellipsis">
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|
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|
||
13.4 Nクイーン問題
|
||
|
||
|
||
|
||
</span>
|
||
|
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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="../../chapter_backtracking/summary/" class="md-nav__link">
|
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|
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|
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|
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|
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|
||
13.5 まとめ
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
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</a>
|
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|
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|
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</ul>
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</nav>
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|
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|
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|
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|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
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|
||
|
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|
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<span class="md-ellipsis">
|
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|
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|
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第 14 章 動的計画法
|
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|
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|
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|
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<span class="md-nav__icon md-icon"></span>
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第 14 章 動的計画法
|
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|
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</label>
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<ul class="md-nav__list" data-md-scrollfix>
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|
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|
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|
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|
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<span class="md-ellipsis">
|
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|
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|
||
14.1 動的計画法の初歩
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
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</li>
|
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<li class="md-nav__item">
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<a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
|
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|
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|
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|
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<span class="md-ellipsis">
|
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|
||
|
||
14.2 DP 問題の特性
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
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</li>
|
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|
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|
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|
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|
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|
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<li class="md-nav__item">
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<a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
|
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|
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|
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|
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<span class="md-ellipsis">
|
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|
||
|
||
14.3 DP の解法の考え方
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
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</li>
|
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|
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|
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<li class="md-nav__item">
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<a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
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|
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|
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|
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<span class="md-ellipsis">
|
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|
||
|
||
14.4 0-1ナップサック問題
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
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</li>
|
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|
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|
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|
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|
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<li class="md-nav__item">
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<a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
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|
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|
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|
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<span class="md-ellipsis">
|
||
|
||
|
||
14.5 完全ナップサック問題
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
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|
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|
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|
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<li class="md-nav__item">
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<a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
|
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|
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|
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|
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<span class="md-ellipsis">
|
||
|
||
|
||
14.6 編集距離問題
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
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|
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|
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|
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|
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|
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|
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|
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<li class="md-nav__item">
|
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<a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
|
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|
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|
||
|
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<span class="md-ellipsis">
|
||
|
||
|
||
14.7 まとめ
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
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</a>
|
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|
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|
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|
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|
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|
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</ul>
|
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|
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|
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|
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|
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|
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|
||
|
||
|
||
|
||
|
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|
||
|
||
|
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|
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|
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|
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|
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|
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<span class="md-ellipsis">
|
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|
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|
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第 15 章 貪欲法
|
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|
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|
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|
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</span>
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</a>
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第 15 章 貪欲法
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|
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<ul class="md-nav__list" data-md-scrollfix>
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|
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|
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|
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15.1 貪欲アルゴリズム
|
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|
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|
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|
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</span>
|
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|
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|
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|
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</a>
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<span class="md-ellipsis">
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|
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|
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15.2 分数ナップサック問題
|
||
|
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|
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|
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</span>
|
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|
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|
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|
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</a>
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</li>
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|
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|
||
15.3 最大容量問題
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
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|
||
</a>
|
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</li>
|
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|
||
|
||
|
||
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<h1 id="92">9.2 グラフの基本操作<a class="headerlink" href="#92" title="Permanent link">¶</a></h1>
|
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<p>グラフの基本操作は「辺」に対する操作と「頂点」に対する操作に分けることができます。「隣接行列」と「隣接リスト」の2つの表現方法の下では、実装が異なります。</p>
|
||
<h2 id="921">9.2.1 隣接行列に基づく実装<a class="headerlink" href="#921" title="Permanent link">¶</a></h2>
|
||
<p><span class="arithmatex">\(n\)</span>個の頂点を持つ無向グラフが与えられた場合、さまざまな操作は下図のように実装されます。</p>
|
||
<ul>
|
||
<li><strong>辺の追加または削除</strong>：隣接行列内の指定された辺を直接変更し、<span class="arithmatex">\(O(1)\)</span>時間を使用します。無向グラフであるため、両方向の辺を同時に更新する必要があります。</li>
|
||
<li><strong>頂点の追加</strong>：隣接行列の末尾に行と列を追加し、すべて<span class="arithmatex">\(0\)</span>で埋めます。<span class="arithmatex">\(O(n)\)</span>時間を使用します。</li>
|
||
<li><strong>頂点の削除</strong>：隣接行列内の行と列を削除します。最悪の場合は最初の行と列が削除されるときで、<span class="arithmatex">\((n-1)^2\)</span>個の要素を「上と左に移動」する必要があり、<span class="arithmatex">\(O(n^2)\)</span>時間を使用します。</li>
|
||
<li><strong>初期化</strong>：<span class="arithmatex">\(n\)</span>個の頂点を渡し、長さ<span class="arithmatex">\(n\)</span>の頂点リスト<code>vertices</code>を初期化し、<span class="arithmatex">\(O(n)\)</span>時間を使用します。<span class="arithmatex">\(n \times n\)</span>サイズの隣接行列<code>adjMat</code>を初期化し、<span class="arithmatex">\(O(n^2)\)</span>時間を使用します。</li>
|
||
</ul>
|
||
<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">隣接行列の初期化</label><label for="__tabbed_1_2">辺の追加</label><label for="__tabbed_1_3">辺の削除</label><label for="__tabbed_1_4">頂点の追加</label><label for="__tabbed_1_5">頂点の削除</label></div>
|
||
<div class="tabbed-content">
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../graph_operations.assets/adjacency_matrix_step1_initialization.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="隣接行列での初期化、辺の追加と削除、頂点の追加と削除" class="animation-figure" src="../graph_operations.assets/adjacency_matrix_step1_initialization.png" /></a></p>
|
||
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|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../graph_operations.assets/adjacency_matrix_step2_add_edge.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="adjacency_matrix_add_edge" class="animation-figure" src="../graph_operations.assets/adjacency_matrix_step2_add_edge.png" /></a></p>
|
||
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|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../graph_operations.assets/adjacency_matrix_step3_remove_edge.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="adjacency_matrix_remove_edge" class="animation-figure" src="../graph_operations.assets/adjacency_matrix_step3_remove_edge.png" /></a></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../graph_operations.assets/adjacency_matrix_step4_add_vertex.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="adjacency_matrix_add_vertex" class="animation-figure" src="../graph_operations.assets/adjacency_matrix_step4_add_vertex.png" /></a></p>
|
||
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|
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<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../graph_operations.assets/adjacency_matrix_step5_remove_vertex.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="adjacency_matrix_remove_vertex" class="animation-figure" src="../graph_operations.assets/adjacency_matrix_step5_remove_vertex.png" /></a></p>
|
||
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|
||
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|
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|
||
<p align="center"> 図 9-7 隣接行列での初期化、辺の追加と削除、頂点の追加と削除 </p>
|
||
|
||
<p>以下は隣接行列を使用して表現されたグラフの実装コードです：</p>
|
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<div class="tabbed-set tabbed-alternate" data-tabs="2:13"><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" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Ruby</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.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">class</span><span class="w"> </span><span class="nc">GraphAdjMat</span><span class="p">:</span>
|
||
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w"> </span><span class="sd">"""隣接行列に基づく無向グラフクラス"""</span>
|
||
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>
|
||
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a> <span class="k">def</span><span class="w"> </span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">vertices</span><span class="p">:</span> <span class="nb">list</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="nb">list</span><span class="p">[</span><span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]]):</span>
|
||
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a><span class="w"> </span><span class="sd">"""コンストラクタ"""</span>
|
||
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a> <span class="c1"># 頂点リスト、要素は「頂点値」を表し、インデックスは「頂点インデックス」を表す</span>
|
||
<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a> <span class="bp">self</span><span class="o">.</span><span class="n">vertices</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]</span> <span class="o">=</span> <span class="p">[]</span>
|
||
<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a> <span class="c1"># 隣接行列、行と列のインデックスは「頂点インデックス」に対応</span>
|
||
<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a> <span class="bp">self</span><span class="o">.</span><span class="n">adj_mat</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]]</span> <span class="o">=</span> <span class="p">[]</span>
|
||
<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a> <span class="c1"># 頂点を追加</span>
|
||
<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a> <span class="k">for</span> <span class="n">val</span> <span class="ow">in</span> <span class="n">vertices</span><span class="p">:</span>
|
||
<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a> <span class="bp">self</span><span class="o">.</span><span class="n">add_vertex</span><span class="p">(</span><span class="n">val</span><span class="p">)</span>
|
||
<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a> <span class="c1"># 辺を追加</span>
|
||
<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a> <span class="c1"># edges要素は頂点インデックスを表す</span>
|
||
<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a> <span class="k">for</span> <span class="n">e</span> <span class="ow">in</span> <span class="n">edges</span><span class="p">:</span>
|
||
<a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a> <span class="bp">self</span><span class="o">.</span><span class="n">add_edge</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">e</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
|
||
<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a>
|
||
<a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a> <span class="k">def</span><span class="w"> </span><span class="nf">size</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-></span> <span class="nb">int</span><span class="p">:</span>
|
||
<a id="__codelineno-0-19" name="__codelineno-0-19" href="#__codelineno-0-19"></a><span class="w"> </span><span class="sd">"""頂点数を取得"""</span>
|
||
<a id="__codelineno-0-20" name="__codelineno-0-20" href="#__codelineno-0-20"></a> <span class="k">return</span> <span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">vertices</span><span class="p">)</span>
|
||
<a id="__codelineno-0-21" name="__codelineno-0-21" href="#__codelineno-0-21"></a>
|
||
<a id="__codelineno-0-22" name="__codelineno-0-22" href="#__codelineno-0-22"></a> <span class="k">def</span><span class="w"> </span><span class="nf">add_vertex</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
|
||
<a id="__codelineno-0-23" name="__codelineno-0-23" href="#__codelineno-0-23"></a><span class="w"> </span><span class="sd">"""頂点を追加"""</span>
|
||
<a id="__codelineno-0-24" name="__codelineno-0-24" href="#__codelineno-0-24"></a> <span class="n">n</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">()</span>
|
||
<a id="__codelineno-0-25" name="__codelineno-0-25" href="#__codelineno-0-25"></a> <span class="c1"># 頂点リストに新しい頂点値を追加</span>
|
||
<a id="__codelineno-0-26" name="__codelineno-0-26" href="#__codelineno-0-26"></a> <span class="bp">self</span><span class="o">.</span><span class="n">vertices</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">val</span><span class="p">)</span>
|
||
<a id="__codelineno-0-27" name="__codelineno-0-27" href="#__codelineno-0-27"></a> <span class="c1"># 隣接行列に行を追加</span>
|
||
<a id="__codelineno-0-28" name="__codelineno-0-28" href="#__codelineno-0-28"></a> <span class="n">new_row</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">n</span>
|
||
<a id="__codelineno-0-29" name="__codelineno-0-29" href="#__codelineno-0-29"></a> <span class="bp">self</span><span class="o">.</span><span class="n">adj_mat</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">new_row</span><span class="p">)</span>
|
||
<a id="__codelineno-0-30" name="__codelineno-0-30" href="#__codelineno-0-30"></a> <span class="c1"># 隣接行列に列を追加</span>
|
||
<a id="__codelineno-0-31" name="__codelineno-0-31" href="#__codelineno-0-31"></a> <span class="k">for</span> <span class="n">row</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">adj_mat</span><span class="p">:</span>
|
||
<a id="__codelineno-0-32" name="__codelineno-0-32" href="#__codelineno-0-32"></a> <span class="n">row</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
|
||
<a id="__codelineno-0-33" name="__codelineno-0-33" href="#__codelineno-0-33"></a>
|
||
<a id="__codelineno-0-34" name="__codelineno-0-34" href="#__codelineno-0-34"></a> <span class="k">def</span><span class="w"> </span><span class="nf">remove_vertex</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">index</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
|
||
<a id="__codelineno-0-35" name="__codelineno-0-35" href="#__codelineno-0-35"></a><span class="w"> </span><span class="sd">"""頂点を削除"""</span>
|
||
<a id="__codelineno-0-36" name="__codelineno-0-36" href="#__codelineno-0-36"></a> <span class="k">if</span> <span class="n">index</span> <span class="o">>=</span> <span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">():</span>
|
||
<a id="__codelineno-0-37" name="__codelineno-0-37" href="#__codelineno-0-37"></a> <span class="k">raise</span> <span class="ne">IndexError</span><span class="p">()</span>
|
||
<a id="__codelineno-0-38" name="__codelineno-0-38" href="#__codelineno-0-38"></a> <span class="c1"># 頂点リストから`index`の頂点を削除</span>
|
||
<a id="__codelineno-0-39" name="__codelineno-0-39" href="#__codelineno-0-39"></a> <span class="bp">self</span><span class="o">.</span><span class="n">vertices</span><span class="o">.</span><span class="n">pop</span><span class="p">(</span><span class="n">index</span><span class="p">)</span>
|
||
<a id="__codelineno-0-40" name="__codelineno-0-40" href="#__codelineno-0-40"></a> <span class="c1"># 隣接行列から`index`の行を削除</span>
|
||
<a id="__codelineno-0-41" name="__codelineno-0-41" href="#__codelineno-0-41"></a> <span class="bp">self</span><span class="o">.</span><span class="n">adj_mat</span><span class="o">.</span><span class="n">pop</span><span class="p">(</span><span class="n">index</span><span class="p">)</span>
|
||
<a id="__codelineno-0-42" name="__codelineno-0-42" href="#__codelineno-0-42"></a> <span class="c1"># 隣接行列から`index`の列を削除</span>
|
||
<a id="__codelineno-0-43" name="__codelineno-0-43" href="#__codelineno-0-43"></a> <span class="k">for</span> <span class="n">row</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">adj_mat</span><span class="p">:</span>
|
||
<a id="__codelineno-0-44" name="__codelineno-0-44" href="#__codelineno-0-44"></a> <span class="n">row</span><span class="o">.</span><span class="n">pop</span><span class="p">(</span><span class="n">index</span><span class="p">)</span>
|
||
<a id="__codelineno-0-45" name="__codelineno-0-45" href="#__codelineno-0-45"></a>
|
||
<a id="__codelineno-0-46" name="__codelineno-0-46" href="#__codelineno-0-46"></a> <span class="k">def</span><span class="w"> </span><span class="nf">add_edge</span><span class="p">(</span><span class="bp">self</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>
|
||
<a id="__codelineno-0-47" name="__codelineno-0-47" href="#__codelineno-0-47"></a><span class="w"> </span><span class="sd">"""辺を追加"""</span>
|
||
<a id="__codelineno-0-48" name="__codelineno-0-48" href="#__codelineno-0-48"></a> <span class="c1"># パラメータi、jは頂点要素のインデックスに対応</span>
|
||
<a id="__codelineno-0-49" name="__codelineno-0-49" href="#__codelineno-0-49"></a> <span class="c1"># インデックスの範囲外と等価性を処理</span>
|
||
<a id="__codelineno-0-50" name="__codelineno-0-50" href="#__codelineno-0-50"></a> <span class="k">if</span> <span class="n">i</span> <span class="o"><</span> <span class="mi">0</span> <span class="ow">or</span> <span class="n">j</span> <span class="o"><</span> <span class="mi">0</span> <span class="ow">or</span> <span class="n">i</span> <span class="o">>=</span> <span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">()</span> <span class="ow">or</span> <span class="n">j</span> <span class="o">>=</span> <span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">()</span> <span class="ow">or</span> <span class="n">i</span> <span class="o">==</span> <span class="n">j</span><span class="p">:</span>
|
||
<a id="__codelineno-0-51" name="__codelineno-0-51" href="#__codelineno-0-51"></a> <span class="k">raise</span> <span class="ne">IndexError</span><span class="p">()</span>
|
||
<a id="__codelineno-0-52" name="__codelineno-0-52" href="#__codelineno-0-52"></a> <span class="c1"># 無向グラフでは、隣接行列は主対角線について対称、すなわち (i, j) == (j, i) を満たす</span>
|
||
<a id="__codelineno-0-53" name="__codelineno-0-53" href="#__codelineno-0-53"></a> <span class="bp">self</span><span class="o">.</span><span class="n">adj_mat</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="o">=</span> <span class="mi">1</span>
|
||
<a id="__codelineno-0-54" name="__codelineno-0-54" href="#__codelineno-0-54"></a> <span class="bp">self</span><span class="o">.</span><span class="n">adj_mat</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="o">=</span> <span class="mi">1</span>
|
||
<a id="__codelineno-0-55" name="__codelineno-0-55" href="#__codelineno-0-55"></a>
|
||
<a id="__codelineno-0-56" name="__codelineno-0-56" href="#__codelineno-0-56"></a> <span class="k">def</span><span class="w"> </span><span class="nf">remove_edge</span><span class="p">(</span><span class="bp">self</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>
|
||
<a id="__codelineno-0-57" name="__codelineno-0-57" href="#__codelineno-0-57"></a><span class="w"> </span><span class="sd">"""辺を削除"""</span>
|
||
<a id="__codelineno-0-58" name="__codelineno-0-58" href="#__codelineno-0-58"></a> <span class="c1"># パラメータi、jは頂点要素のインデックスに対応</span>
|
||
<a id="__codelineno-0-59" name="__codelineno-0-59" href="#__codelineno-0-59"></a> <span class="c1"># インデックスの範囲外と等価性を処理</span>
|
||
<a id="__codelineno-0-60" name="__codelineno-0-60" href="#__codelineno-0-60"></a> <span class="k">if</span> <span class="n">i</span> <span class="o"><</span> <span class="mi">0</span> <span class="ow">or</span> <span class="n">j</span> <span class="o"><</span> <span class="mi">0</span> <span class="ow">or</span> <span class="n">i</span> <span class="o">>=</span> <span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">()</span> <span class="ow">or</span> <span class="n">j</span> <span class="o">>=</span> <span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">()</span> <span class="ow">or</span> <span class="n">i</span> <span class="o">==</span> <span class="n">j</span><span class="p">:</span>
|
||
<a id="__codelineno-0-61" name="__codelineno-0-61" href="#__codelineno-0-61"></a> <span class="k">raise</span> <span class="ne">IndexError</span><span class="p">()</span>
|
||
<a id="__codelineno-0-62" name="__codelineno-0-62" href="#__codelineno-0-62"></a> <span class="bp">self</span><span class="o">.</span><span class="n">adj_mat</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="o">=</span> <span class="mi">0</span>
|
||
<a id="__codelineno-0-63" name="__codelineno-0-63" href="#__codelineno-0-63"></a> <span class="bp">self</span><span class="o">.</span><span class="n">adj_mat</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="o">=</span> <span class="mi">0</span>
|
||
<a id="__codelineno-0-64" name="__codelineno-0-64" href="#__codelineno-0-64"></a>
|
||
<a id="__codelineno-0-65" name="__codelineno-0-65" href="#__codelineno-0-65"></a> <span class="k">def</span><span class="w"> </span><span class="nf">print</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
|
||
<a id="__codelineno-0-66" name="__codelineno-0-66" href="#__codelineno-0-66"></a><span class="w"> </span><span class="sd">"""隣接行列を出力"""</span>
|
||
<a id="__codelineno-0-67" name="__codelineno-0-67" href="#__codelineno-0-67"></a> <span class="nb">print</span><span class="p">(</span><span class="s2">"頂点リスト ="</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">vertices</span><span class="p">)</span>
|
||
<a id="__codelineno-0-68" name="__codelineno-0-68" href="#__codelineno-0-68"></a> <span class="nb">print</span><span class="p">(</span><span class="s2">"隣接行列 ="</span><span class="p">)</span>
|
||
<a id="__codelineno-0-69" name="__codelineno-0-69" href="#__codelineno-0-69"></a> <span class="n">print_matrix</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">adj_mat</span><span class="p">)</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<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><span class="cm">/* 隣接行列に基づく無向グラフクラス */</span>
|
||
<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">GraphAdjMat</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w"> </span><span class="n">vector</span><span class="o"><</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="c1">// 頂点リスト、要素は「頂点値」を表し、インデックスは「頂点インデックス」を表す</span>
|
||
<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w"> </span><span class="n">vector</span><span class="o"><</span><span class="n">vector</span><span class="o"><</span><span class="kt">int</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">// 隣接行列、行と列のインデックスは「頂点インデックス」に対応</span>
|
||
<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a>
|
||
<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w"> </span><span class="k">public</span><span class="o">:</span>
|
||
<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w"> </span><span class="cm">/* コンストラクタ */</span>
|
||
<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w"> </span><span class="n">GraphAdjMat</span><span class="p">(</span><span class="k">const</span><span class="w"> </span><span class="n">vector</span><span class="o"><</span><span class="kt">int</span><span class="o">></span><span class="w"> </span><span class="o">&</span><span class="n">vertices</span><span class="p">,</span><span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="n">vector</span><span class="o"><</span><span class="n">vector</span><span class="o"><</span><span class="kt">int</span><span class="o">>></span><span class="w"> </span><span class="o">&</span><span class="n">edges</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w"> </span><span class="c1">// 頂点を追加</span>
|
||
<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></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="o">:</span><span class="w"> </span><span class="n">vertices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w"> </span><span class="n">addVertex</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
|
||
<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w"> </span><span class="c1">// 辺を追加</span>
|
||
<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w"> </span><span class="c1">// 辺の要素は頂点インデックスを表す</span>
|
||
<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="k">const</span><span class="w"> </span><span class="n">vector</span><span class="o"><</span><span class="kt">int</span><span class="o">></span><span class="w"> </span><span class="o">&</span><span class="n">edge</span><span class="w"> </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>
|
||
<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="w"> </span><span class="n">addEdge</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="w"> </span><span class="n">edge</span><span class="p">[</span><span class="mi">1</span><span class="p">]);</span>
|
||
<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a>
|
||
<a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="w"> </span><span class="cm">/* 頂点数を取得 */</span>
|
||
<a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-1-22" name="__codelineno-1-22" href="#__codelineno-1-22"></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="n">size</span><span class="p">();</span>
|
||
<a id="__codelineno-1-23" name="__codelineno-1-23" href="#__codelineno-1-23"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-1-24" name="__codelineno-1-24" href="#__codelineno-1-24"></a>
|
||
<a id="__codelineno-1-25" name="__codelineno-1-25" href="#__codelineno-1-25"></a><span class="w"> </span><span class="cm">/* 頂点を追加 */</span>
|
||
<a id="__codelineno-1-26" name="__codelineno-1-26" href="#__codelineno-1-26"></a><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="n">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>
|
||
<a id="__codelineno-1-27" name="__codelineno-1-27" href="#__codelineno-1-27"></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>
|
||
<a id="__codelineno-1-28" name="__codelineno-1-28" href="#__codelineno-1-28"></a><span class="w"> </span><span class="c1">// 頂点リストに新しい頂点値を追加</span>
|
||
<a id="__codelineno-1-29" name="__codelineno-1-29" href="#__codelineno-1-29"></a><span class="w"> </span><span class="n">vertices</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
|
||
<a id="__codelineno-1-30" name="__codelineno-1-30" href="#__codelineno-1-30"></a><span class="w"> </span><span class="c1">// 隣接行列に行を追加</span>
|
||
<a id="__codelineno-1-31" name="__codelineno-1-31" href="#__codelineno-1-31"></a><span class="w"> </span><span class="n">adjMat</span><span class="p">.</span><span class="n">emplace_back</span><span class="p">(</span><span class="n">vector</span><span class="o"><</span><span class="kt">int</span><span class="o">></span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">));</span>
|
||
<a id="__codelineno-1-32" name="__codelineno-1-32" href="#__codelineno-1-32"></a><span class="w"> </span><span class="c1">// 隣接行列に列を追加</span>
|
||
<a id="__codelineno-1-33" name="__codelineno-1-33" href="#__codelineno-1-33"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">vector</span><span class="o"><</span><span class="kt">int</span><span class="o">></span><span class="w"> </span><span class="o">&</span><span class="n">row</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">adjMat</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-1-34" name="__codelineno-1-34" href="#__codelineno-1-34"></a><span class="w"> </span><span class="n">row</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
|
||
<a id="__codelineno-1-35" name="__codelineno-1-35" href="#__codelineno-1-35"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-1-36" name="__codelineno-1-36" href="#__codelineno-1-36"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-1-37" name="__codelineno-1-37" href="#__codelineno-1-37"></a>
|
||
<a id="__codelineno-1-38" name="__codelineno-1-38" href="#__codelineno-1-38"></a><span class="w"> </span><span class="cm">/* 頂点を削除 */</span>
|
||
<a id="__codelineno-1-39" name="__codelineno-1-39" href="#__codelineno-1-39"></a><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="n">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>
|
||
<a id="__codelineno-1-40" name="__codelineno-1-40" href="#__codelineno-1-40"></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><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-1-41" name="__codelineno-1-41" href="#__codelineno-1-41"></a><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="n">out_of_range</span><span class="p">(</span><span class="s">"Vertex does not exist"</span><span class="p">);</span>
|
||
<a id="__codelineno-1-42" name="__codelineno-1-42" href="#__codelineno-1-42"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-1-43" name="__codelineno-1-43" href="#__codelineno-1-43"></a><span class="w"> </span><span class="c1">// 頂点リストから`index`の頂点を削除</span>
|
||
<a id="__codelineno-1-44" name="__codelineno-1-44" href="#__codelineno-1-44"></a><span class="w"> </span><span class="n">vertices</span><span class="p">.</span><span class="n">erase</span><span class="p">(</span><span class="n">vertices</span><span class="p">.</span><span class="n">begin</span><span class="p">()</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">index</span><span class="p">);</span>
|
||
<a id="__codelineno-1-45" name="__codelineno-1-45" href="#__codelineno-1-45"></a><span class="w"> </span><span class="c1">// 隣接行列から`index`の行を削除</span>
|
||
<a id="__codelineno-1-46" name="__codelineno-1-46" href="#__codelineno-1-46"></a><span class="w"> </span><span class="n">adjMat</span><span class="p">.</span><span class="n">erase</span><span class="p">(</span><span class="n">adjMat</span><span class="p">.</span><span class="n">begin</span><span class="p">()</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">index</span><span class="p">);</span>
|
||
<a id="__codelineno-1-47" name="__codelineno-1-47" href="#__codelineno-1-47"></a><span class="w"> </span><span class="c1">// 隣接行列から`index`の列を削除</span>
|
||
<a id="__codelineno-1-48" name="__codelineno-1-48" href="#__codelineno-1-48"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">vector</span><span class="o"><</span><span class="kt">int</span><span class="o">></span><span class="w"> </span><span class="o">&</span><span class="n">row</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">adjMat</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-1-49" name="__codelineno-1-49" href="#__codelineno-1-49"></a><span class="w"> </span><span class="n">row</span><span class="p">.</span><span class="n">erase</span><span class="p">(</span><span class="n">row</span><span class="p">.</span><span class="n">begin</span><span class="p">()</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">index</span><span class="p">);</span>
|
||
<a id="__codelineno-1-50" name="__codelineno-1-50" href="#__codelineno-1-50"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-1-51" name="__codelineno-1-51" href="#__codelineno-1-51"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-1-52" name="__codelineno-1-52" href="#__codelineno-1-52"></a>
|
||
<a id="__codelineno-1-53" name="__codelineno-1-53" href="#__codelineno-1-53"></a><span class="w"> </span><span class="cm">/* 辺を追加 */</span>
|
||
<a id="__codelineno-1-54" name="__codelineno-1-54" href="#__codelineno-1-54"></a><span class="w"> </span><span class="c1">// パラメータi、jは頂点要素のインデックスに対応</span>
|
||
<a id="__codelineno-1-55" name="__codelineno-1-55" href="#__codelineno-1-55"></a><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="n">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>
|
||
<a id="__codelineno-1-56" name="__codelineno-1-56" href="#__codelineno-1-56"></a><span class="w"> </span><span class="c1">// インデックス範囲外と等価性を処理</span>
|
||
<a id="__codelineno-1-57" name="__codelineno-1-57" href="#__codelineno-1-57"></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><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-1-58" name="__codelineno-1-58" href="#__codelineno-1-58"></a><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="n">out_of_range</span><span class="p">(</span><span class="s">"Vertex does not exist"</span><span class="p">);</span>
|
||
<a id="__codelineno-1-59" name="__codelineno-1-59" href="#__codelineno-1-59"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-1-60" name="__codelineno-1-60" href="#__codelineno-1-60"></a><span class="w"> </span><span class="c1">// 無向グラフでは、隣接行列は主対角線について対称、即ち(i, j) == (j, i)を満たす</span>
|
||
<a id="__codelineno-1-61" name="__codelineno-1-61" href="#__codelineno-1-61"></a><span class="w"> </span><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="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
||
<a id="__codelineno-1-62" name="__codelineno-1-62" href="#__codelineno-1-62"></a><span class="w"> </span><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="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
||
<a id="__codelineno-1-63" name="__codelineno-1-63" href="#__codelineno-1-63"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-1-64" name="__codelineno-1-64" href="#__codelineno-1-64"></a>
|
||
<a id="__codelineno-1-65" name="__codelineno-1-65" href="#__codelineno-1-65"></a><span class="w"> </span><span class="cm">/* 辺を削除 */</span>
|
||
<a id="__codelineno-1-66" name="__codelineno-1-66" href="#__codelineno-1-66"></a><span class="w"> </span><span class="c1">// パラメータi、jは頂点要素のインデックスに対応</span>
|
||
<a id="__codelineno-1-67" name="__codelineno-1-67" href="#__codelineno-1-67"></a><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="n">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>
|
||
<a id="__codelineno-1-68" name="__codelineno-1-68" href="#__codelineno-1-68"></a><span class="w"> </span><span class="c1">// インデックス範囲外と等価性を処理</span>
|
||
<a id="__codelineno-1-69" name="__codelineno-1-69" href="#__codelineno-1-69"></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><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-1-70" name="__codelineno-1-70" href="#__codelineno-1-70"></a><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="n">out_of_range</span><span class="p">(</span><span class="s">"Vertex does not exist"</span><span class="p">);</span>
|
||
<a id="__codelineno-1-71" name="__codelineno-1-71" href="#__codelineno-1-71"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-1-72" name="__codelineno-1-72" href="#__codelineno-1-72"></a><span class="w"> </span><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="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||
<a id="__codelineno-1-73" name="__codelineno-1-73" href="#__codelineno-1-73"></a><span class="w"> </span><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="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||
<a id="__codelineno-1-74" name="__codelineno-1-74" href="#__codelineno-1-74"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-1-75" name="__codelineno-1-75" href="#__codelineno-1-75"></a>
|
||
<a id="__codelineno-1-76" name="__codelineno-1-76" href="#__codelineno-1-76"></a><span class="w"> </span><span class="cm">/* 隣接行列を印刷 */</span>
|
||
<a id="__codelineno-1-77" name="__codelineno-1-77" href="#__codelineno-1-77"></a><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="n">print</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-1-78" name="__codelineno-1-78" href="#__codelineno-1-78"></a><span class="w"> </span><span class="n">cout</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="s">"頂点リスト = "</span><span class="p">;</span>
|
||
<a id="__codelineno-1-79" name="__codelineno-1-79" href="#__codelineno-1-79"></a><span class="w"> </span><span class="n">printVector</span><span class="p">(</span><span class="n">vertices</span><span class="p">);</span>
|
||
<a id="__codelineno-1-80" name="__codelineno-1-80" href="#__codelineno-1-80"></a><span class="w"> </span><span class="n">cout</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="s">"隣接行列 ="</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span>
|
||
<a id="__codelineno-1-81" name="__codelineno-1-81" href="#__codelineno-1-81"></a><span class="w"> </span><span class="n">printVectorMatrix</span><span class="p">(</span><span class="n">adjMat</span><span class="p">);</span>
|
||
<a id="__codelineno-1-82" name="__codelineno-1-82" href="#__codelineno-1-82"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-1-83" name="__codelineno-1-83" href="#__codelineno-1-83"></a><span class="p">};</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">graph_adjacency_matrix.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 隣接行列に基づく無向グラフクラス */</span>
|
||
<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kd">class</span> <span class="nc">GraphAdjMat</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></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">// 頂点リスト、要素は「頂点値」を表し、インデックスは「頂点インデックス」を表す</span>
|
||
<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></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">// 隣接行列、行と列のインデックスは「頂点インデックス」に対応</span>
|
||
<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a>
|
||
<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w"> </span><span class="cm">/* コンストラクタ */</span>
|
||
<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></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>
|
||
<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></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>
|
||
<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></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>
|
||
<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w"> </span><span class="c1">// 頂点を追加</span>
|
||
<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></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>
|
||
<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w"> </span><span class="n">addVertex</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
|
||
<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w"> </span><span class="c1">// 辺を追加</span>
|
||
<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w"> </span><span class="c1">// 辺の要素は頂点インデックスを表す</span>
|
||
<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></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>
|
||
<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></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>
|
||
<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a>
|
||
<a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a><span class="w"> </span><span class="cm">/* 頂点数を取得 */</span>
|
||
<a id="__codelineno-2-22" name="__codelineno-2-22" href="#__codelineno-2-22"></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>
|
||
<a id="__codelineno-2-23" name="__codelineno-2-23" href="#__codelineno-2-23"></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>
|
||
<a id="__codelineno-2-24" name="__codelineno-2-24" href="#__codelineno-2-24"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-2-25" name="__codelineno-2-25" href="#__codelineno-2-25"></a>
|
||
<a id="__codelineno-2-26" name="__codelineno-2-26" href="#__codelineno-2-26"></a><span class="w"> </span><span class="cm">/* 頂点を追加 */</span>
|
||
<a id="__codelineno-2-27" name="__codelineno-2-27" href="#__codelineno-2-27"></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>
|
||
<a id="__codelineno-2-28" name="__codelineno-2-28" href="#__codelineno-2-28"></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>
|
||
<a id="__codelineno-2-29" name="__codelineno-2-29" href="#__codelineno-2-29"></a><span class="w"> </span><span class="c1">// 頂点リストに新しい頂点値を追加</span>
|
||
<a id="__codelineno-2-30" name="__codelineno-2-30" href="#__codelineno-2-30"></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>
|
||
<a id="__codelineno-2-31" name="__codelineno-2-31" href="#__codelineno-2-31"></a><span class="w"> </span><span class="c1">// 隣接行列に行を追加</span>
|
||
<a id="__codelineno-2-32" name="__codelineno-2-32" href="#__codelineno-2-32"></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>
|
||
<a id="__codelineno-2-33" name="__codelineno-2-33" href="#__codelineno-2-33"></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>
|
||
<a id="__codelineno-2-34" name="__codelineno-2-34" href="#__codelineno-2-34"></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>
|
||
<a id="__codelineno-2-35" name="__codelineno-2-35" href="#__codelineno-2-35"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-2-36" name="__codelineno-2-36" href="#__codelineno-2-36"></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>
|
||
<a id="__codelineno-2-37" name="__codelineno-2-37" href="#__codelineno-2-37"></a><span class="w"> </span><span class="c1">// 隣接行列に列を追加</span>
|
||
<a id="__codelineno-2-38" name="__codelineno-2-38" href="#__codelineno-2-38"></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>
|
||
<a id="__codelineno-2-39" name="__codelineno-2-39" href="#__codelineno-2-39"></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>
|
||
<a id="__codelineno-2-40" name="__codelineno-2-40" href="#__codelineno-2-40"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-2-41" name="__codelineno-2-41" href="#__codelineno-2-41"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-2-42" name="__codelineno-2-42" href="#__codelineno-2-42"></a>
|
||
<a id="__codelineno-2-43" name="__codelineno-2-43" href="#__codelineno-2-43"></a><span class="w"> </span><span class="cm">/* 頂点を削除 */</span>
|
||
<a id="__codelineno-2-44" name="__codelineno-2-44" href="#__codelineno-2-44"></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>
|
||
<a id="__codelineno-2-45" name="__codelineno-2-45" href="#__codelineno-2-45"></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>
|
||
<a id="__codelineno-2-46" name="__codelineno-2-46" href="#__codelineno-2-46"></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>
|
||
<a id="__codelineno-2-47" name="__codelineno-2-47" href="#__codelineno-2-47"></a><span class="w"> </span><span class="c1">// 頂点リストから `index` の頂点を削除</span>
|
||
<a id="__codelineno-2-48" name="__codelineno-2-48" href="#__codelineno-2-48"></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>
|
||
<a id="__codelineno-2-49" name="__codelineno-2-49" href="#__codelineno-2-49"></a><span class="w"> </span><span class="c1">// 隣接行列から `index` の行を削除</span>
|
||
<a id="__codelineno-2-50" name="__codelineno-2-50" href="#__codelineno-2-50"></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>
|
||
<a id="__codelineno-2-51" name="__codelineno-2-51" href="#__codelineno-2-51"></a><span class="w"> </span><span class="c1">// 隣接行列から `index` の列を削除</span>
|
||
<a id="__codelineno-2-52" name="__codelineno-2-52" href="#__codelineno-2-52"></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>
|
||
<a id="__codelineno-2-53" name="__codelineno-2-53" href="#__codelineno-2-53"></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>
|
||
<a id="__codelineno-2-54" name="__codelineno-2-54" href="#__codelineno-2-54"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-2-55" name="__codelineno-2-55" href="#__codelineno-2-55"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-2-56" name="__codelineno-2-56" href="#__codelineno-2-56"></a>
|
||
<a id="__codelineno-2-57" name="__codelineno-2-57" href="#__codelineno-2-57"></a><span class="w"> </span><span class="cm">/* 辺を追加 */</span>
|
||
<a id="__codelineno-2-58" name="__codelineno-2-58" href="#__codelineno-2-58"></a><span class="w"> </span><span class="c1">// パラメータ i、j は頂点要素のインデックスに対応</span>
|
||
<a id="__codelineno-2-59" name="__codelineno-2-59" href="#__codelineno-2-59"></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>
|
||
<a id="__codelineno-2-60" name="__codelineno-2-60" href="#__codelineno-2-60"></a><span class="w"> </span><span class="c1">// インデックスの範囲外と等価性を処理</span>
|
||
<a id="__codelineno-2-61" name="__codelineno-2-61" href="#__codelineno-2-61"></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>
|
||
<a id="__codelineno-2-62" name="__codelineno-2-62" href="#__codelineno-2-62"></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>
|
||
<a id="__codelineno-2-63" name="__codelineno-2-63" href="#__codelineno-2-63"></a><span class="w"> </span><span class="c1">// 無向グラフでは、隣接行列は主対角線について対称、すなわち (i, j) == (j, i) を満たす</span>
|
||
<a id="__codelineno-2-64" name="__codelineno-2-64" href="#__codelineno-2-64"></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>
|
||
<a id="__codelineno-2-65" name="__codelineno-2-65" href="#__codelineno-2-65"></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>
|
||
<a id="__codelineno-2-66" name="__codelineno-2-66" href="#__codelineno-2-66"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-2-67" name="__codelineno-2-67" href="#__codelineno-2-67"></a>
|
||
<a id="__codelineno-2-68" name="__codelineno-2-68" href="#__codelineno-2-68"></a><span class="w"> </span><span class="cm">/* 辺を削除 */</span>
|
||
<a id="__codelineno-2-69" name="__codelineno-2-69" href="#__codelineno-2-69"></a><span class="w"> </span><span class="c1">// パラメータ i、j は頂点要素のインデックスに対応</span>
|
||
<a id="__codelineno-2-70" name="__codelineno-2-70" href="#__codelineno-2-70"></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>
|
||
<a id="__codelineno-2-71" name="__codelineno-2-71" href="#__codelineno-2-71"></a><span class="w"> </span><span class="c1">// インデックスの範囲外と等価性を処理</span>
|
||
<a id="__codelineno-2-72" name="__codelineno-2-72" href="#__codelineno-2-72"></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>
|
||
<a id="__codelineno-2-73" name="__codelineno-2-73" href="#__codelineno-2-73"></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>
|
||
<a id="__codelineno-2-74" name="__codelineno-2-74" href="#__codelineno-2-74"></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>
|
||
<a id="__codelineno-2-75" name="__codelineno-2-75" href="#__codelineno-2-75"></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>
|
||
<a id="__codelineno-2-76" name="__codelineno-2-76" href="#__codelineno-2-76"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-2-77" name="__codelineno-2-77" href="#__codelineno-2-77"></a>
|
||
<a id="__codelineno-2-78" name="__codelineno-2-78" href="#__codelineno-2-78"></a><span class="w"> </span><span class="cm">/* 隣接行列を出力 */</span>
|
||
<a id="__codelineno-2-79" name="__codelineno-2-79" href="#__codelineno-2-79"></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>
|
||
<a id="__codelineno-2-80" name="__codelineno-2-80" href="#__codelineno-2-80"></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">"頂点リスト = "</span><span class="p">);</span>
|
||
<a id="__codelineno-2-81" name="__codelineno-2-81" href="#__codelineno-2-81"></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>
|
||
<a id="__codelineno-2-82" name="__codelineno-2-82" href="#__codelineno-2-82"></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">"隣接行列 ="</span><span class="p">);</span>
|
||
<a id="__codelineno-2-83" name="__codelineno-2-83" href="#__codelineno-2-83"></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>
|
||
<a id="__codelineno-2-84" name="__codelineno-2-84" href="#__codelineno-2-84"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-2-85" name="__codelineno-2-85" href="#__codelineno-2-85"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">graph_adjacency_matrix.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">GraphAdjMat</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">graph_adjacency_matrix.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">graphAdjMat</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">graph_adjacency_matrix.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">GraphAdjMat</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">graph_adjacency_matrix.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">GraphAdjMat</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">graph_adjacency_matrix.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">GraphAdjMat</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">graph_adjacency_matrix.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">GraphAdjMat</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">graph_adjacency_matrix.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">GraphAdjMat</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">graph_adjacency_matrix.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">GraphAdjMat</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">graph_adjacency_matrix.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">GraphAdjMat</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">graph_adjacency_matrix.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">GraphAdjMat</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<h2 id="922">9.2.2 隣接リストに基づく実装<a class="headerlink" href="#922" title="Permanent link">¶</a></h2>
|
||
<p>総計<span class="arithmatex">\(n\)</span>個の頂点と<span class="arithmatex">\(m\)</span>個の辺を持つ無向グラフが与えられた場合、さまざまな操作は下図のように実装できます。</p>
|
||
<ul>
|
||
<li><strong>辺の追加</strong>：対応する頂点の連結リストの末尾に辺を追加するだけで、<span class="arithmatex">\(O(1)\)</span>時間を使用します。無向グラフであるため、両方向に同時に辺を追加する必要があります。</li>
|
||
<li><strong>辺の削除</strong>：対応する頂点の連結リスト内で指定された辺を見つけて削除し、<span class="arithmatex">\(O(m)\)</span>時間を使用します。無向グラフでは、両方向の辺を同時に削除する必要があります。</li>
|
||
<li><strong>頂点の追加</strong>：隣接リストに連結リストを追加し、新しい頂点をリストのヘッドノードにし、<span class="arithmatex">\(O(1)\)</span>時間を使用します。</li>
|
||
<li><strong>頂点の削除</strong>：隣接リスト全体を走査し、指定された頂点を含むすべての辺を削除する必要があり、<span class="arithmatex">\(O(n + m)\)</span>時間を使用します。</li>
|
||
<li><strong>初期化</strong>：隣接リストに<span class="arithmatex">\(n\)</span>個の頂点と<span class="arithmatex">\(2m\)</span>個の辺を作成し、<span class="arithmatex">\(O(n + m)\)</span>時間を使用します。</li>
|
||
</ul>
|
||
<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">隣接リストの初期化</label><label for="__tabbed_3_2">辺の追加</label><label for="__tabbed_3_3">辺の削除</label><label for="__tabbed_3_4">頂点の追加</label><label for="__tabbed_3_5">頂点の削除</label></div>
|
||
<div class="tabbed-content">
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../graph_operations.assets/adjacency_list_step1_initialization.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="隣接リストでの初期化、辺の追加と削除、頂点の追加と削除" class="animation-figure" src="../graph_operations.assets/adjacency_list_step1_initialization.png" /></a></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../graph_operations.assets/adjacency_list_step2_add_edge.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="adjacency_list_add_edge" class="animation-figure" src="../graph_operations.assets/adjacency_list_step2_add_edge.png" /></a></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../graph_operations.assets/adjacency_list_step3_remove_edge.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="adjacency_list_remove_edge" class="animation-figure" src="../graph_operations.assets/adjacency_list_step3_remove_edge.png" /></a></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../graph_operations.assets/adjacency_list_step4_add_vertex.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="adjacency_list_add_vertex" class="animation-figure" src="../graph_operations.assets/adjacency_list_step4_add_vertex.png" /></a></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../graph_operations.assets/adjacency_list_step5_remove_vertex.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="adjacency_list_remove_vertex" class="animation-figure" src="../graph_operations.assets/adjacency_list_step5_remove_vertex.png" /></a></p>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<p align="center"> 図 9-8 隣接リストでの初期化、辺の追加と削除、頂点の追加と削除 </p>
|
||
|
||
<p>以下は隣接リストのコード実装です。上図と比較して、実際のコードには以下の違いがあります。</p>
|
||
<ul>
|
||
<li>頂点の追加と削除の便宜、およびコードの簡素化のため、連結リストの代わりにリスト（動的配列）を使用します。</li>
|
||
<li>ハッシュテーブルを使用して隣接リストを格納し、<code>key</code>が頂点インスタンス、<code>value</code>がその頂点の隣接頂点のリスト（連結リスト）です。</li>
|
||
</ul>
|
||
<p>さらに、隣接リストで頂点を表現するために<code>Vertex</code>クラスを使用します。その理由は：隣接行列のようにリストインデックスを使用して異なる頂点を区別する場合、インデックス<span class="arithmatex">\(i\)</span>の頂点を削除したい場合、隣接リスト全体を走査し、<span class="arithmatex">\(i\)</span>より大きいすべてのインデックスを1つずつ減少させる必要があり、これは非常に非効率的です。しかし、各頂点が一意の<code>Vertex</code>インスタンスである場合、頂点を削除しても他の頂点に変更を加える必要がありません。</p>
|
||
<div class="tabbed-set tabbed-alternate" data-tabs="4:13"><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" /><input id="__tabbed_4_11" name="__tabbed_4" type="radio" /><input id="__tabbed_4_12" name="__tabbed_4" type="radio" /><input id="__tabbed_4_13" name="__tabbed_4" type="radio" /><div class="tabbed-labels"><label for="__tabbed_4_1">Python</label><label for="__tabbed_4_2">C++</label><label for="__tabbed_4_3">Java</label><label for="__tabbed_4_4">C#</label><label for="__tabbed_4_5">Go</label><label for="__tabbed_4_6">Swift</label><label for="__tabbed_4_7">JS</label><label for="__tabbed_4_8">TS</label><label for="__tabbed_4_9">Dart</label><label for="__tabbed_4_10">Rust</label><label for="__tabbed_4_11">C</label><label for="__tabbed_4_12">Kotlin</label><label for="__tabbed_4_13">Ruby</label></div>
|
||
<div class="tabbed-content">
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">graph_adjacency_list.py</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="k">class</span><span class="w"> </span><span class="nc">GraphAdjList</span><span class="p">:</span>
|
||
<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="w"> </span><span class="sd">"""隣接リストに基づく無向グラフクラス"""</span>
|
||
<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a>
|
||
<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a> <span class="k">def</span><span class="w"> </span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">edges</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">list</span><span class="p">[</span><span class="n">Vertex</span><span class="p">]]):</span>
|
||
<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a><span class="w"> </span><span class="sd">"""コンストラクタ"""</span>
|
||
<a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a> <span class="c1"># 隣接リスト、キー: 頂点、値: その頂点の隣接する全頂点</span>
|
||
<a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a> <span class="bp">self</span><span class="o">.</span><span class="n">adj_list</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">[</span><span class="n">Vertex</span><span class="p">,</span> <span class="nb">list</span><span class="p">[</span><span class="n">Vertex</span><span class="p">]]()</span>
|
||
<a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a> <span class="c1"># すべての頂点と辺を追加</span>
|
||
<a id="__codelineno-13-9" name="__codelineno-13-9" href="#__codelineno-13-9"></a> <span class="k">for</span> <span class="n">edge</span> <span class="ow">in</span> <span class="n">edges</span><span class="p">:</span>
|
||
<a id="__codelineno-13-10" name="__codelineno-13-10" href="#__codelineno-13-10"></a> <span class="bp">self</span><span class="o">.</span><span class="n">add_vertex</span><span class="p">(</span><span class="n">edge</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
|
||
<a id="__codelineno-13-11" name="__codelineno-13-11" href="#__codelineno-13-11"></a> <span class="bp">self</span><span class="o">.</span><span class="n">add_vertex</span><span class="p">(</span><span class="n">edge</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
|
||
<a id="__codelineno-13-12" name="__codelineno-13-12" href="#__codelineno-13-12"></a> <span class="bp">self</span><span class="o">.</span><span class="n">add_edge</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">edge</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
|
||
<a id="__codelineno-13-13" name="__codelineno-13-13" href="#__codelineno-13-13"></a>
|
||
<a id="__codelineno-13-14" name="__codelineno-13-14" href="#__codelineno-13-14"></a> <span class="k">def</span><span class="w"> </span><span class="nf">size</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-></span> <span class="nb">int</span><span class="p">:</span>
|
||
<a id="__codelineno-13-15" name="__codelineno-13-15" href="#__codelineno-13-15"></a><span class="w"> </span><span class="sd">"""頂点数を取得"""</span>
|
||
<a id="__codelineno-13-16" name="__codelineno-13-16" href="#__codelineno-13-16"></a> <span class="k">return</span> <span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">adj_list</span><span class="p">)</span>
|
||
<a id="__codelineno-13-17" name="__codelineno-13-17" href="#__codelineno-13-17"></a>
|
||
<a id="__codelineno-13-18" name="__codelineno-13-18" href="#__codelineno-13-18"></a> <span class="k">def</span><span class="w"> </span><span class="nf">add_edge</span><span class="p">(</span><span class="bp">self</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>
|
||
<a id="__codelineno-13-19" name="__codelineno-13-19" href="#__codelineno-13-19"></a><span class="w"> </span><span class="sd">"""辺を追加"""</span>
|
||
<a id="__codelineno-13-20" name="__codelineno-13-20" href="#__codelineno-13-20"></a> <span class="k">if</span> <span class="n">vet1</span> <span class="ow">not</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">adj_list</span> <span class="ow">or</span> <span class="n">vet2</span> <span class="ow">not</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">adj_list</span> <span class="ow">or</span> <span class="n">vet1</span> <span class="o">==</span> <span class="n">vet2</span><span class="p">:</span>
|
||
<a id="__codelineno-13-21" name="__codelineno-13-21" href="#__codelineno-13-21"></a> <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">()</span>
|
||
<a id="__codelineno-13-22" name="__codelineno-13-22" href="#__codelineno-13-22"></a> <span class="c1"># 辺 vet1 - vet2 を追加</span>
|
||
<a id="__codelineno-13-23" name="__codelineno-13-23" href="#__codelineno-13-23"></a> <span class="bp">self</span><span class="o">.</span><span class="n">adj_list</span><span class="p">[</span><span class="n">vet1</span><span class="p">]</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">vet2</span><span class="p">)</span>
|
||
<a id="__codelineno-13-24" name="__codelineno-13-24" href="#__codelineno-13-24"></a> <span class="bp">self</span><span class="o">.</span><span class="n">adj_list</span><span class="p">[</span><span class="n">vet2</span><span class="p">]</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">vet1</span><span class="p">)</span>
|
||
<a id="__codelineno-13-25" name="__codelineno-13-25" href="#__codelineno-13-25"></a>
|
||
<a id="__codelineno-13-26" name="__codelineno-13-26" href="#__codelineno-13-26"></a> <span class="k">def</span><span class="w"> </span><span class="nf">remove_edge</span><span class="p">(</span><span class="bp">self</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>
|
||
<a id="__codelineno-13-27" name="__codelineno-13-27" href="#__codelineno-13-27"></a><span class="w"> </span><span class="sd">"""辺を削除"""</span>
|
||
<a id="__codelineno-13-28" name="__codelineno-13-28" href="#__codelineno-13-28"></a> <span class="k">if</span> <span class="n">vet1</span> <span class="ow">not</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">adj_list</span> <span class="ow">or</span> <span class="n">vet2</span> <span class="ow">not</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">adj_list</span> <span class="ow">or</span> <span class="n">vet1</span> <span class="o">==</span> <span class="n">vet2</span><span class="p">:</span>
|
||
<a id="__codelineno-13-29" name="__codelineno-13-29" href="#__codelineno-13-29"></a> <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">()</span>
|
||
<a id="__codelineno-13-30" name="__codelineno-13-30" href="#__codelineno-13-30"></a> <span class="c1"># 辺 vet1 - vet2 を削除</span>
|
||
<a id="__codelineno-13-31" name="__codelineno-13-31" href="#__codelineno-13-31"></a> <span class="bp">self</span><span class="o">.</span><span class="n">adj_list</span><span class="p">[</span><span class="n">vet1</span><span class="p">]</span><span class="o">.</span><span class="n">remove</span><span class="p">(</span><span class="n">vet2</span><span class="p">)</span>
|
||
<a id="__codelineno-13-32" name="__codelineno-13-32" href="#__codelineno-13-32"></a> <span class="bp">self</span><span class="o">.</span><span class="n">adj_list</span><span class="p">[</span><span class="n">vet2</span><span class="p">]</span><span class="o">.</span><span class="n">remove</span><span class="p">(</span><span class="n">vet1</span><span class="p">)</span>
|
||
<a id="__codelineno-13-33" name="__codelineno-13-33" href="#__codelineno-13-33"></a>
|
||
<a id="__codelineno-13-34" name="__codelineno-13-34" href="#__codelineno-13-34"></a> <span class="k">def</span><span class="w"> </span><span class="nf">add_vertex</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">vet</span><span class="p">:</span> <span class="n">Vertex</span><span class="p">):</span>
|
||
<a id="__codelineno-13-35" name="__codelineno-13-35" href="#__codelineno-13-35"></a><span class="w"> </span><span class="sd">"""頂点を追加"""</span>
|
||
<a id="__codelineno-13-36" name="__codelineno-13-36" href="#__codelineno-13-36"></a> <span class="k">if</span> <span class="n">vet</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">adj_list</span><span class="p">:</span>
|
||
<a id="__codelineno-13-37" name="__codelineno-13-37" href="#__codelineno-13-37"></a> <span class="k">return</span>
|
||
<a id="__codelineno-13-38" name="__codelineno-13-38" href="#__codelineno-13-38"></a> <span class="c1"># 隣接リストに新しい連結リストを追加</span>
|
||
<a id="__codelineno-13-39" name="__codelineno-13-39" href="#__codelineno-13-39"></a> <span class="bp">self</span><span class="o">.</span><span class="n">adj_list</span><span class="p">[</span><span class="n">vet</span><span class="p">]</span> <span class="o">=</span> <span class="p">[]</span>
|
||
<a id="__codelineno-13-40" name="__codelineno-13-40" href="#__codelineno-13-40"></a>
|
||
<a id="__codelineno-13-41" name="__codelineno-13-41" href="#__codelineno-13-41"></a> <span class="k">def</span><span class="w"> </span><span class="nf">remove_vertex</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">vet</span><span class="p">:</span> <span class="n">Vertex</span><span class="p">):</span>
|
||
<a id="__codelineno-13-42" name="__codelineno-13-42" href="#__codelineno-13-42"></a><span class="w"> </span><span class="sd">"""頂点を削除"""</span>
|
||
<a id="__codelineno-13-43" name="__codelineno-13-43" href="#__codelineno-13-43"></a> <span class="k">if</span> <span class="n">vet</span> <span class="ow">not</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">adj_list</span><span class="p">:</span>
|
||
<a id="__codelineno-13-44" name="__codelineno-13-44" href="#__codelineno-13-44"></a> <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">()</span>
|
||
<a id="__codelineno-13-45" name="__codelineno-13-45" href="#__codelineno-13-45"></a> <span class="c1"># 隣接リストから頂点vetに対応する連結リストを削除</span>
|
||
<a id="__codelineno-13-46" name="__codelineno-13-46" href="#__codelineno-13-46"></a> <span class="bp">self</span><span class="o">.</span><span class="n">adj_list</span><span class="o">.</span><span class="n">pop</span><span class="p">(</span><span class="n">vet</span><span class="p">)</span>
|
||
<a id="__codelineno-13-47" name="__codelineno-13-47" href="#__codelineno-13-47"></a> <span class="c1"># 他の頂点の連結リストを走査し、vetを含むすべての辺を削除</span>
|
||
<a id="__codelineno-13-48" name="__codelineno-13-48" href="#__codelineno-13-48"></a> <span class="k">for</span> <span class="n">vertex</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">adj_list</span><span class="p">:</span>
|
||
<a id="__codelineno-13-49" name="__codelineno-13-49" href="#__codelineno-13-49"></a> <span class="k">if</span> <span class="n">vet</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">adj_list</span><span class="p">[</span><span class="n">vertex</span><span class="p">]:</span>
|
||
<a id="__codelineno-13-50" name="__codelineno-13-50" href="#__codelineno-13-50"></a> <span class="bp">self</span><span class="o">.</span><span class="n">adj_list</span><span class="p">[</span><span class="n">vertex</span><span class="p">]</span><span class="o">.</span><span class="n">remove</span><span class="p">(</span><span class="n">vet</span><span class="p">)</span>
|
||
<a id="__codelineno-13-51" name="__codelineno-13-51" href="#__codelineno-13-51"></a>
|
||
<a id="__codelineno-13-52" name="__codelineno-13-52" href="#__codelineno-13-52"></a> <span class="k">def</span><span class="w"> </span><span class="nf">print</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
|
||
<a id="__codelineno-13-53" name="__codelineno-13-53" href="#__codelineno-13-53"></a><span class="w"> </span><span class="sd">"""隣接リストを出力"""</span>
|
||
<a id="__codelineno-13-54" name="__codelineno-13-54" href="#__codelineno-13-54"></a> <span class="nb">print</span><span class="p">(</span><span class="s2">"隣接リスト ="</span><span class="p">)</span>
|
||
<a id="__codelineno-13-55" name="__codelineno-13-55" href="#__codelineno-13-55"></a> <span class="k">for</span> <span class="n">vertex</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">adj_list</span><span class="p">:</span>
|
||
<a id="__codelineno-13-56" name="__codelineno-13-56" href="#__codelineno-13-56"></a> <span class="n">tmp</span> <span class="o">=</span> <span class="p">[</span><span class="n">v</span><span class="o">.</span><span class="n">val</span> <span class="k">for</span> <span class="n">v</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">adj_list</span><span class="p">[</span><span class="n">vertex</span><span class="p">]]</span>
|
||
<a id="__codelineno-13-57" name="__codelineno-13-57" href="#__codelineno-13-57"></a> <span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"</span><span class="si">{</span><span class="n">vertex</span><span class="o">.</span><span class="n">val</span><span class="si">}</span><span class="s2">: </span><span class="si">{</span><span class="n">tmp</span><span class="si">}</span><span class="s2">,"</span><span class="p">)</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">graph_adjacency_list.cpp</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* 隣接リストに基づく無向グラフクラス */</span>
|
||
<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">GraphAdjList</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w"> </span><span class="k">public</span><span class="o">:</span>
|
||
<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="w"> </span><span class="c1">// 隣接リスト、キー：頂点、値：その頂点のすべての隣接頂点</span>
|
||
<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="w"> </span><span class="n">unordered_map</span><span class="o"><</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o"><</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*>></span><span class="w"> </span><span class="n">adjList</span><span class="p">;</span>
|
||
<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a>
|
||
<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="w"> </span><span class="cm">/* ベクターから指定されたノードを削除 */</span>
|
||
<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="n">vector</span><span class="o"><</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*></span><span class="w"> </span><span class="o">&</span><span class="n">vec</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="n">vet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></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">i</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">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">vec</span><span class="p">.</span><span class="n">size</span><span class="p">();</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">vec</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">vet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a><span class="w"> </span><span class="n">vec</span><span class="p">.</span><span class="n">erase</span><span class="p">(</span><span class="n">vec</span><span class="p">.</span><span class="n">begin</span><span class="p">()</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
|
||
<a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a><span class="w"> </span><span class="k">break</span><span class="p">;</span>
|
||
<a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-14-16" name="__codelineno-14-16" href="#__codelineno-14-16"></a>
|
||
<a id="__codelineno-14-17" name="__codelineno-14-17" href="#__codelineno-14-17"></a><span class="w"> </span><span class="cm">/* コンストラクタ */</span>
|
||
<a id="__codelineno-14-18" name="__codelineno-14-18" href="#__codelineno-14-18"></a><span class="w"> </span><span class="n">GraphAdjList</span><span class="p">(</span><span class="k">const</span><span class="w"> </span><span class="n">vector</span><span class="o"><</span><span class="n">vector</span><span class="o"><</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*>></span><span class="w"> </span><span class="o">&</span><span class="n">edges</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-14-19" name="__codelineno-14-19" href="#__codelineno-14-19"></a><span class="w"> </span><span class="c1">// すべての頂点と辺を追加</span>
|
||
<a id="__codelineno-14-20" name="__codelineno-14-20" href="#__codelineno-14-20"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="k">const</span><span class="w"> </span><span class="n">vector</span><span class="o"><</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*></span><span class="w"> </span><span class="o">&</span><span class="n">edge</span><span class="w"> </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>
|
||
<a id="__codelineno-14-21" name="__codelineno-14-21" href="#__codelineno-14-21"></a><span class="w"> </span><span class="n">addVertex</span><span class="p">(</span><span class="n">edge</span><span class="p">[</span><span class="mi">0</span><span class="p">]);</span>
|
||
<a id="__codelineno-14-22" name="__codelineno-14-22" href="#__codelineno-14-22"></a><span class="w"> </span><span class="n">addVertex</span><span class="p">(</span><span class="n">edge</span><span class="p">[</span><span class="mi">1</span><span class="p">]);</span>
|
||
<a id="__codelineno-14-23" name="__codelineno-14-23" href="#__codelineno-14-23"></a><span class="w"> </span><span class="n">addEdge</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="w"> </span><span class="n">edge</span><span class="p">[</span><span class="mi">1</span><span class="p">]);</span>
|
||
<a id="__codelineno-14-24" name="__codelineno-14-24" href="#__codelineno-14-24"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-14-25" name="__codelineno-14-25" href="#__codelineno-14-25"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-14-26" name="__codelineno-14-26" href="#__codelineno-14-26"></a>
|
||
<a id="__codelineno-14-27" name="__codelineno-14-27" href="#__codelineno-14-27"></a><span class="w"> </span><span class="cm">/* 頂点数を取得 */</span>
|
||
<a id="__codelineno-14-28" name="__codelineno-14-28" href="#__codelineno-14-28"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-14-29" name="__codelineno-14-29" href="#__codelineno-14-29"></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="n">size</span><span class="p">();</span>
|
||
<a id="__codelineno-14-30" name="__codelineno-14-30" href="#__codelineno-14-30"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-14-31" name="__codelineno-14-31" href="#__codelineno-14-31"></a>
|
||
<a id="__codelineno-14-32" name="__codelineno-14-32" href="#__codelineno-14-32"></a><span class="w"> </span><span class="cm">/* 辺を追加 */</span>
|
||
<a id="__codelineno-14-33" name="__codelineno-14-33" href="#__codelineno-14-33"></a><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="n">addEdge</span><span class="p">(</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</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="o">*</span><span class="n">vet2</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-14-34" name="__codelineno-14-34" href="#__codelineno-14-34"></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="n">count</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="n">count</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>
|
||
<a id="__codelineno-14-35" name="__codelineno-14-35" href="#__codelineno-14-35"></a><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="n">invalid_argument</span><span class="p">(</span><span class="s">"Vertex does not exist"</span><span class="p">);</span>
|
||
<a id="__codelineno-14-36" name="__codelineno-14-36" href="#__codelineno-14-36"></a><span class="w"> </span><span class="c1">// 辺 vet1 - vet2 を追加</span>
|
||
<a id="__codelineno-14-37" name="__codelineno-14-37" href="#__codelineno-14-37"></a><span class="w"> </span><span class="n">adjList</span><span class="p">[</span><span class="n">vet1</span><span class="p">].</span><span class="n">push_back</span><span class="p">(</span><span class="n">vet2</span><span class="p">);</span>
|
||
<a id="__codelineno-14-38" name="__codelineno-14-38" href="#__codelineno-14-38"></a><span class="w"> </span><span class="n">adjList</span><span class="p">[</span><span class="n">vet2</span><span class="p">].</span><span class="n">push_back</span><span class="p">(</span><span class="n">vet1</span><span class="p">);</span>
|
||
<a id="__codelineno-14-39" name="__codelineno-14-39" href="#__codelineno-14-39"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-14-40" name="__codelineno-14-40" href="#__codelineno-14-40"></a>
|
||
<a id="__codelineno-14-41" name="__codelineno-14-41" href="#__codelineno-14-41"></a><span class="w"> </span><span class="cm">/* 辺を削除 */</span>
|
||
<a id="__codelineno-14-42" name="__codelineno-14-42" href="#__codelineno-14-42"></a><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="n">removeEdge</span><span class="p">(</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</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="o">*</span><span class="n">vet2</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-14-43" name="__codelineno-14-43" href="#__codelineno-14-43"></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="n">count</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="n">count</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>
|
||
<a id="__codelineno-14-44" name="__codelineno-14-44" href="#__codelineno-14-44"></a><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="n">invalid_argument</span><span class="p">(</span><span class="s">"Vertex does not exist"</span><span class="p">);</span>
|
||
<a id="__codelineno-14-45" name="__codelineno-14-45" href="#__codelineno-14-45"></a><span class="w"> </span><span class="c1">// 辺 vet1 - vet2 を削除</span>
|
||
<a id="__codelineno-14-46" name="__codelineno-14-46" href="#__codelineno-14-46"></a><span class="w"> </span><span class="n">remove</span><span class="p">(</span><span class="n">adjList</span><span class="p">[</span><span class="n">vet1</span><span class="p">],</span><span class="w"> </span><span class="n">vet2</span><span class="p">);</span>
|
||
<a id="__codelineno-14-47" name="__codelineno-14-47" href="#__codelineno-14-47"></a><span class="w"> </span><span class="n">remove</span><span class="p">(</span><span class="n">adjList</span><span class="p">[</span><span class="n">vet2</span><span class="p">],</span><span class="w"> </span><span class="n">vet1</span><span class="p">);</span>
|
||
<a id="__codelineno-14-48" name="__codelineno-14-48" href="#__codelineno-14-48"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-14-49" name="__codelineno-14-49" href="#__codelineno-14-49"></a>
|
||
<a id="__codelineno-14-50" name="__codelineno-14-50" href="#__codelineno-14-50"></a><span class="w"> </span><span class="cm">/* 頂点を追加 */</span>
|
||
<a id="__codelineno-14-51" name="__codelineno-14-51" href="#__codelineno-14-51"></a><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="n">addVertex</span><span class="p">(</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="n">vet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-14-52" name="__codelineno-14-52" href="#__codelineno-14-52"></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="n">count</span><span class="p">(</span><span class="n">vet</span><span class="p">))</span>
|
||
<a id="__codelineno-14-53" name="__codelineno-14-53" href="#__codelineno-14-53"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
|
||
<a id="__codelineno-14-54" name="__codelineno-14-54" href="#__codelineno-14-54"></a><span class="w"> </span><span class="c1">// 隣接リストに新しい連結リストを追加</span>
|
||
<a id="__codelineno-14-55" name="__codelineno-14-55" href="#__codelineno-14-55"></a><span class="w"> </span><span class="n">adjList</span><span class="p">[</span><span class="n">vet</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">vector</span><span class="o"><</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*></span><span class="p">();</span>
|
||
<a id="__codelineno-14-56" name="__codelineno-14-56" href="#__codelineno-14-56"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-14-57" name="__codelineno-14-57" href="#__codelineno-14-57"></a>
|
||
<a id="__codelineno-14-58" name="__codelineno-14-58" href="#__codelineno-14-58"></a><span class="w"> </span><span class="cm">/* 頂点を削除 */</span>
|
||
<a id="__codelineno-14-59" name="__codelineno-14-59" href="#__codelineno-14-59"></a><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="n">removeVertex</span><span class="p">(</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="n">vet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-14-60" name="__codelineno-14-60" href="#__codelineno-14-60"></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="n">count</span><span class="p">(</span><span class="n">vet</span><span class="p">))</span>
|
||
<a id="__codelineno-14-61" name="__codelineno-14-61" href="#__codelineno-14-61"></a><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="n">invalid_argument</span><span class="p">(</span><span class="s">"Vertex does not exist"</span><span class="p">);</span>
|
||
<a id="__codelineno-14-62" name="__codelineno-14-62" href="#__codelineno-14-62"></a><span class="w"> </span><span class="c1">// 隣接リストから頂点vetに対応する連結リストを削除</span>
|
||
<a id="__codelineno-14-63" name="__codelineno-14-63" href="#__codelineno-14-63"></a><span class="w"> </span><span class="n">adjList</span><span class="p">.</span><span class="n">erase</span><span class="p">(</span><span class="n">vet</span><span class="p">);</span>
|
||
<a id="__codelineno-14-64" name="__codelineno-14-64" href="#__codelineno-14-64"></a><span class="w"> </span><span class="c1">// 他の頂点の連結リストを走査し、vetを含むすべての辺を削除</span>
|
||
<a id="__codelineno-14-65" name="__codelineno-14-65" href="#__codelineno-14-65"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="k">auto</span><span class="w"> </span><span class="o">&</span><span class="n">adj</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">adjList</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-14-66" name="__codelineno-14-66" href="#__codelineno-14-66"></a><span class="w"> </span><span class="n">remove</span><span class="p">(</span><span class="n">adj</span><span class="p">.</span><span class="n">second</span><span class="p">,</span><span class="w"> </span><span class="n">vet</span><span class="p">);</span>
|
||
<a id="__codelineno-14-67" name="__codelineno-14-67" href="#__codelineno-14-67"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-14-68" name="__codelineno-14-68" href="#__codelineno-14-68"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-14-69" name="__codelineno-14-69" href="#__codelineno-14-69"></a>
|
||
<a id="__codelineno-14-70" name="__codelineno-14-70" href="#__codelineno-14-70"></a><span class="w"> </span><span class="cm">/* 隣接リストを印刷 */</span>
|
||
<a id="__codelineno-14-71" name="__codelineno-14-71" href="#__codelineno-14-71"></a><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="n">print</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-14-72" name="__codelineno-14-72" href="#__codelineno-14-72"></a><span class="w"> </span><span class="n">cout</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="s">"隣接リスト ="</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span>
|
||
<a id="__codelineno-14-73" name="__codelineno-14-73" href="#__codelineno-14-73"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="k">auto</span><span class="w"> </span><span class="o">&</span><span class="n">adj</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">adjList</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-14-74" name="__codelineno-14-74" href="#__codelineno-14-74"></a><span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="k">auto</span><span class="w"> </span><span class="o">&</span><span class="n">key</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">adj</span><span class="p">.</span><span class="n">first</span><span class="p">;</span>
|
||
<a id="__codelineno-14-75" name="__codelineno-14-75" href="#__codelineno-14-75"></a><span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="k">auto</span><span class="w"> </span><span class="o">&</span><span class="n">vec</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">adj</span><span class="p">.</span><span class="n">second</span><span class="p">;</span>
|
||
<a id="__codelineno-14-76" name="__codelineno-14-76" href="#__codelineno-14-76"></a><span class="w"> </span><span class="n">cout</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">key</span><span class="o">-></span><span class="n">val</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="s">": "</span><span class="p">;</span>
|
||
<a id="__codelineno-14-77" name="__codelineno-14-77" href="#__codelineno-14-77"></a><span class="w"> </span><span class="n">printVector</span><span class="p">(</span><span class="n">vetsToVals</span><span class="p">(</span><span class="n">vec</span><span class="p">));</span>
|
||
<a id="__codelineno-14-78" name="__codelineno-14-78" href="#__codelineno-14-78"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-14-79" name="__codelineno-14-79" href="#__codelineno-14-79"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-14-80" name="__codelineno-14-80" href="#__codelineno-14-80"></a><span class="p">};</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">graph_adjacency_list.java</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* 隣接リストに基づく無向グラフクラス */</span>
|
||
<a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="kd">class</span> <span class="nc">GraphAdjList</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w"> </span><span class="c1">// 隣接リスト、キー: 頂点、値: その頂点のすべての隣接頂点</span>
|
||
<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></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">List</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>
|
||
<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a>
|
||
<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="w"> </span><span class="cm">/* コンストラクタ */</span>
|
||
<a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></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>
|
||
<a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></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>
|
||
<a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="w"> </span><span class="c1">// すべての頂点と辺を追加</span>
|
||
<a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></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>
|
||
<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></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>
|
||
<a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></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>
|
||
<a id="__codelineno-15-13" name="__codelineno-15-13" href="#__codelineno-15-13"></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>
|
||
<a id="__codelineno-15-14" name="__codelineno-15-14" href="#__codelineno-15-14"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-15-15" name="__codelineno-15-15" href="#__codelineno-15-15"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-15-16" name="__codelineno-15-16" href="#__codelineno-15-16"></a>
|
||
<a id="__codelineno-15-17" name="__codelineno-15-17" href="#__codelineno-15-17"></a><span class="w"> </span><span class="cm">/* 頂点数を取得 */</span>
|
||
<a id="__codelineno-15-18" name="__codelineno-15-18" href="#__codelineno-15-18"></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>
|
||
<a id="__codelineno-15-19" name="__codelineno-15-19" href="#__codelineno-15-19"></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>
|
||
<a id="__codelineno-15-20" name="__codelineno-15-20" href="#__codelineno-15-20"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-15-21" name="__codelineno-15-21" href="#__codelineno-15-21"></a>
|
||
<a id="__codelineno-15-22" name="__codelineno-15-22" href="#__codelineno-15-22"></a><span class="w"> </span><span class="cm">/* 辺を追加 */</span>
|
||
<a id="__codelineno-15-23" name="__codelineno-15-23" href="#__codelineno-15-23"></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>
|
||
<a id="__codelineno-15-24" name="__codelineno-15-24" href="#__codelineno-15-24"></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>
|
||
<a id="__codelineno-15-25" name="__codelineno-15-25" href="#__codelineno-15-25"></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>
|
||
<a id="__codelineno-15-26" name="__codelineno-15-26" href="#__codelineno-15-26"></a><span class="w"> </span><span class="c1">// 辺 vet1 - vet2 を追加</span>
|
||
<a id="__codelineno-15-27" name="__codelineno-15-27" href="#__codelineno-15-27"></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>
|
||
<a id="__codelineno-15-28" name="__codelineno-15-28" href="#__codelineno-15-28"></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>
|
||
<a id="__codelineno-15-29" name="__codelineno-15-29" href="#__codelineno-15-29"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-15-30" name="__codelineno-15-30" href="#__codelineno-15-30"></a>
|
||
<a id="__codelineno-15-31" name="__codelineno-15-31" href="#__codelineno-15-31"></a><span class="w"> </span><span class="cm">/* 辺を削除 */</span>
|
||
<a id="__codelineno-15-32" name="__codelineno-15-32" href="#__codelineno-15-32"></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>
|
||
<a id="__codelineno-15-33" name="__codelineno-15-33" href="#__codelineno-15-33"></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>
|
||
<a id="__codelineno-15-34" name="__codelineno-15-34" href="#__codelineno-15-34"></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>
|
||
<a id="__codelineno-15-35" name="__codelineno-15-35" href="#__codelineno-15-35"></a><span class="w"> </span><span class="c1">// 辺 vet1 - vet2 を削除</span>
|
||
<a id="__codelineno-15-36" name="__codelineno-15-36" href="#__codelineno-15-36"></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">vet1</span><span class="p">).</span><span class="na">remove</span><span class="p">(</span><span class="n">vet2</span><span class="p">);</span>
|
||
<a id="__codelineno-15-37" name="__codelineno-15-37" href="#__codelineno-15-37"></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>
|
||
<a id="__codelineno-15-38" name="__codelineno-15-38" href="#__codelineno-15-38"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-15-39" name="__codelineno-15-39" href="#__codelineno-15-39"></a>
|
||
<a id="__codelineno-15-40" name="__codelineno-15-40" href="#__codelineno-15-40"></a><span class="w"> </span><span class="cm">/* 頂点を追加 */</span>
|
||
<a id="__codelineno-15-41" name="__codelineno-15-41" href="#__codelineno-15-41"></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>
|
||
<a id="__codelineno-15-42" name="__codelineno-15-42" href="#__codelineno-15-42"></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>
|
||
<a id="__codelineno-15-43" name="__codelineno-15-43" href="#__codelineno-15-43"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
|
||
<a id="__codelineno-15-44" name="__codelineno-15-44" href="#__codelineno-15-44"></a><span class="w"> </span><span class="c1">// 隣接リストに新しい連結リストを追加</span>
|
||
<a id="__codelineno-15-45" name="__codelineno-15-45" href="#__codelineno-15-45"></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">ArrayList</span><span class="o"><></span><span class="p">());</span>
|
||
<a id="__codelineno-15-46" name="__codelineno-15-46" href="#__codelineno-15-46"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-15-47" name="__codelineno-15-47" href="#__codelineno-15-47"></a>
|
||
<a id="__codelineno-15-48" name="__codelineno-15-48" href="#__codelineno-15-48"></a><span class="w"> </span><span class="cm">/* 頂点を削除 */</span>
|
||
<a id="__codelineno-15-49" name="__codelineno-15-49" href="#__codelineno-15-49"></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">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>
|
||
<a id="__codelineno-15-50" name="__codelineno-15-50" href="#__codelineno-15-50"></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>
|
||
<a id="__codelineno-15-51" name="__codelineno-15-51" href="#__codelineno-15-51"></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>
|
||
<a id="__codelineno-15-52" name="__codelineno-15-52" href="#__codelineno-15-52"></a><span class="w"> </span><span class="c1">// 隣接リストから頂点 vet に対応する連結リストを削除</span>
|
||
<a id="__codelineno-15-53" name="__codelineno-15-53" href="#__codelineno-15-53"></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>
|
||
<a id="__codelineno-15-54" name="__codelineno-15-54" href="#__codelineno-15-54"></a><span class="w"> </span><span class="c1">// 他の頂点の連結リストを走査し、vet を含むすべての辺を削除</span>
|
||
<a id="__codelineno-15-55" name="__codelineno-15-55" href="#__codelineno-15-55"></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">Vertex</span><span class="o">></span><span class="w"> </span><span class="n">list</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>
|
||
<a id="__codelineno-15-56" name="__codelineno-15-56" href="#__codelineno-15-56"></a><span class="w"> </span><span class="n">list</span><span class="p">.</span><span class="na">remove</span><span class="p">(</span><span class="n">vet</span><span class="p">);</span>
|
||
<a id="__codelineno-15-57" name="__codelineno-15-57" href="#__codelineno-15-57"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-15-58" name="__codelineno-15-58" href="#__codelineno-15-58"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-15-59" name="__codelineno-15-59" href="#__codelineno-15-59"></a>
|
||
<a id="__codelineno-15-60" name="__codelineno-15-60" href="#__codelineno-15-60"></a><span class="w"> </span><span class="cm">/* 隣接リストを出力 */</span>
|
||
<a id="__codelineno-15-61" name="__codelineno-15-61" href="#__codelineno-15-61"></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>
|
||
<a id="__codelineno-15-62" name="__codelineno-15-62" href="#__codelineno-15-62"></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">"隣接リスト ="</span><span class="p">);</span>
|
||
<a id="__codelineno-15-63" name="__codelineno-15-63" href="#__codelineno-15-63"></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">List</span><span class="o"><</span><span class="n">Vertex</span><span class="o">>></span><span class="w"> </span><span class="n">pair</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>
|
||
<a id="__codelineno-15-64" name="__codelineno-15-64" href="#__codelineno-15-64"></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>
|
||
<a id="__codelineno-15-65" name="__codelineno-15-65" href="#__codelineno-15-65"></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">pair</span><span class="p">.</span><span class="na">getValue</span><span class="p">())</span>
|
||
<a id="__codelineno-15-66" name="__codelineno-15-66" href="#__codelineno-15-66"></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>
|
||
<a id="__codelineno-15-67" name="__codelineno-15-67" href="#__codelineno-15-67"></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">pair</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>
|
||
<a id="__codelineno-15-68" name="__codelineno-15-68" href="#__codelineno-15-68"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-15-69" name="__codelineno-15-69" href="#__codelineno-15-69"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-15-70" name="__codelineno-15-70" href="#__codelineno-15-70"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">graph_adjacency_list.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">GraphAdjList</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">graph_adjacency_list.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">graphAdjList</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<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="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">GraphAdjList</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">graph_adjacency_list.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">GraphAdjList</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">graph_adjacency_list.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">GraphAdjList</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">graph_adjacency_list.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">GraphAdjList</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">graph_adjacency_list.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">GraphAdjList</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">graph_adjacency_list.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">AdjListNode</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
|
||
<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a>
|
||
<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">GraphAdjList</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">graph_adjacency_list.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">GraphAdjList</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">graph_adjacency_list.rb</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">GraphAdjList</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<h2 id="923">9.2.3 効率の比較<a class="headerlink" href="#923" title="Permanent link">¶</a></h2>
|
||
<p>グラフに<span class="arithmatex">\(n\)</span>個の頂点と<span class="arithmatex">\(m\)</span>個の辺があると仮定すると、下表は隣接行列と隣接リストの時間効率と空間効率を比較しています。</p>
|
||
<p align="center"> 表 9-2 隣接行列と隣接リストの比較 </p>
|
||
|
||
<div class="center-table">
|
||
<table>
|
||
<thead>
|
||
<tr>
|
||
<th></th>
|
||
<th>隣接行列</th>
|
||
<th>隣接リスト（連結リスト）</th>
|
||
<th>隣接リスト（ハッシュテーブル）</th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr>
|
||
<td>隣接性の判定</td>
|
||
<td><span class="arithmatex">\(O(1)\)</span></td>
|
||
<td><span class="arithmatex">\(O(m)\)</span></td>
|
||
<td><span class="arithmatex">\(O(1)\)</span></td>
|
||
</tr>
|
||
<tr>
|
||
<td>辺の追加</td>
|
||
<td><span class="arithmatex">\(O(1)\)</span></td>
|
||
<td><span class="arithmatex">\(O(1)\)</span></td>
|
||
<td><span class="arithmatex">\(O(1)\)</span></td>
|
||
</tr>
|
||
<tr>
|
||
<td>辺の削除</td>
|
||
<td><span class="arithmatex">\(O(1)\)</span></td>
|
||
<td><span class="arithmatex">\(O(m)\)</span></td>
|
||
<td><span class="arithmatex">\(O(1)\)</span></td>
|
||
</tr>
|
||
<tr>
|
||
<td>頂点の追加</td>
|
||
<td><span class="arithmatex">\(O(n)\)</span></td>
|
||
<td><span class="arithmatex">\(O(1)\)</span></td>
|
||
<td><span class="arithmatex">\(O(1)\)</span></td>
|
||
</tr>
|
||
<tr>
|
||
<td>頂点の削除</td>
|
||
<td><span class="arithmatex">\(O(n^2)\)</span></td>
|
||
<td><span class="arithmatex">\(O(n + m)\)</span></td>
|
||
<td><span class="arithmatex">\(O(n)\)</span></td>
|
||
</tr>
|
||
<tr>
|
||
<td>メモリ空間使用量</td>
|
||
<td><span class="arithmatex">\(O(n^2)\)</span></td>
|
||
<td><span class="arithmatex">\(O(n + m)\)</span></td>
|
||
<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>上表を観察すると、隣接リスト（ハッシュテーブル）が最高の時間効率と空間効率を持っているように見えます。しかし、実際には、隣接行列での辺に対する操作がより効率的で、単一の配列アクセスまたは代入操作のみが必要です。全体的に、隣接行列は「空間と時間のトレードオフ」の原則を例示し、隣接リストは「時間と空間のトレードオフ」を例示しています。</p>
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