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12.4 ハノイの塔問題
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第 0 章 前書き
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0.2 本書の使い方
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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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第 2 章 計算量解析
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|
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|
||
|
||
第 2 章 計算量解析
|
||
|
||
|
||
</label>
|
||
<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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|
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|
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|
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|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
2.1 アルゴリズムの効率評価
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
2.2 反復と再帰
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
2.3 時間計算量
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
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|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
2.4 空間計算量
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
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|
||
|
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|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
2.5 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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<li class="md-nav__item md-nav__item--nested">
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
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<div class="md-nav__link md-nav__container">
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|
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|
||
<span class="md-ellipsis">
|
||
|
||
|
||
第 3 章 データ構造
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
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|
||
</a>
|
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<label class="md-nav__link " for="__nav_5" id="__nav_5_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_5_label" aria-expanded="false">
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<label class="md-nav__title" for="__nav_5">
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<span class="md-nav__icon md-icon"></span>
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|
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|
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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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|
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<li class="md-nav__item">
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<a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
|
||
|
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|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
3.1 データ構造の分類
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
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|
||
|
||
|
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|
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|
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|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
3.2 基本データ型
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
3.3 数値の符号化 *
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
3.4 文字の符号化 *
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_data_structure/summary/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
3.5 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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<li class="md-nav__item md-nav__item--nested">
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
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<div class="md-nav__link md-nav__container">
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<a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
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|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
第 4 章 配列と連結リスト
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
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|
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|
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<label class="md-nav__link " for="__nav_6" id="__nav_6_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_6_label" aria-expanded="false">
|
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<label class="md-nav__title" for="__nav_6">
|
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<span class="md-nav__icon md-icon"></span>
|
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|
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|
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第 4 章 配列と連結リスト
|
||
|
||
|
||
</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_array_and_linkedlist/array/" class="md-nav__link">
|
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|
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|
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|
||
<span class="md-ellipsis">
|
||
|
||
|
||
4.1 配列
|
||
|
||
|
||
|
||
</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/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">
|
||
|
||
|
||
4.2 連結リスト
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
4.3 リスト
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<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>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
4.5 まとめ
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
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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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|
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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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|
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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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|
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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>
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
第 5 章 スタックとキュー
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
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|
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|
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<label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
|
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<span class="md-nav__icon md-icon"></span>
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</label>
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</div>
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|
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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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|
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|
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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">
|
||
|
||
|
||
5.1 スタック
|
||
|
||
|
||
|
||
</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/queue/" class="md-nav__link">
|
||
|
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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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|
||
<li class="md-nav__item">
|
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<a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
|
||
|
||
|
||
|
||
<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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|
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|
||
<li class="md-nav__item">
|
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<a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
5.4 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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|
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<li class="md-nav__item md-nav__item--nested">
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
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<div class="md-nav__link md-nav__container">
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|
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|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21zm-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54zM19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2"/></svg>
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
第 6 章 ハッシュ表
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
|
||
|
||
<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>
|
||
</label>
|
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|
||
</div>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_8">
|
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<span class="md-nav__icon md-icon"></span>
|
||
|
||
|
||
第 6 章 ハッシュ表
|
||
|
||
|
||
</label>
|
||
<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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|
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|
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|
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|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_hashing/hash_map/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
6.1 ハッシュ表
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
6.2 ハッシュ衝突
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<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>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<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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<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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|
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|
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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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|
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|
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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>
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
第 7 章 木
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
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|
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|
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<label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
|
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<span class="md-nav__icon md-icon"></span>
|
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</label>
|
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|
||
</div>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_9">
|
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<span class="md-nav__icon md-icon"></span>
|
||
|
||
|
||
第 7 章 木
|
||
|
||
|
||
</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_tree/binary_tree/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
7.1 二分木
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<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>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<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>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<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>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
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|
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|
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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">
|
||
<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>
|
||
|
||
|
||
<label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
|
||
<span class="md-nav__icon md-icon"></span>
|
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</label>
|
||
|
||
</div>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_10">
|
||
<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>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<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>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<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>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_heap/summary/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
8.4 まとめ
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
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|
||
<li class="md-nav__item md-nav__item--nested">
|
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|
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
|
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|
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|
||
<div class="md-nav__link md-nav__container">
|
||
<a href="../../chapter_graph/" class="md-nav__link ">
|
||
|
||
|
||
|
||
<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>
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
第 9 章 グラフ
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
|
||
|
||
<label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
</div>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_11">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
|
||
|
||
第 9 章 グラフ
|
||
|
||
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_graph/graph/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
9.1 グラフ
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_graph/graph_operations/" class="md-nav__link">
|
||
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
|
||
|
||
9.2 グラフの基本操作
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_graph/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="../../chapter_graph/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--active md-nav__item--nested">
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" checked>
|
||
|
||
|
||
<div class="md-nav__link md-nav__container">
|
||
<a href="../" 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="true">
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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 12 章 分割統治
|
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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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|
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|
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|
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<li class="md-nav__item">
|
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<a href="../divide_and_conquer/" class="md-nav__link">
|
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|
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|
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|
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<span class="md-ellipsis">
|
||
|
||
|
||
12.1 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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|
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|
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|
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<li class="md-nav__item">
|
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<a href="../binary_search_recur/" class="md-nav__link">
|
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|
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|
||
|
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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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|
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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="../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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|
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|
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|
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<span class="md-ellipsis">
|
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|
||
|
||
12.4 ハノイの塔問題
|
||
|
||
|
||
|
||
</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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|
||
<span class="md-ellipsis">
|
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|
||
|
||
12.4 ハノイの塔問題
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
|
||
|
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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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|
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|
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|
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<label class="md-nav__title" for="__toc">
|
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<span class="md-nav__icon md-icon"></span>
|
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目次
|
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<ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
|
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|
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<li class="md-nav__item">
|
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<a href="#1" class="md-nav__link">
|
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<span class="md-ellipsis">
|
||
|
||
1. 基本ケースを考える
|
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|
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</span>
|
||
</a>
|
||
|
||
</li>
|
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|
||
<li class="md-nav__item">
|
||
<a href="#2" class="md-nav__link">
|
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<span class="md-ellipsis">
|
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|
||
2. 部分問題の分解
|
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|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
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|
||
<li class="md-nav__item">
|
||
<a href="#3" class="md-nav__link">
|
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<span class="md-ellipsis">
|
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|
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3. コード実装
|
||
|
||
</span>
|
||
</a>
|
||
|
||
</li>
|
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|
||
</ul>
|
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|
||
</nav>
|
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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="../summary/" class="md-nav__link">
|
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|
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|
||
|
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<span class="md-ellipsis">
|
||
|
||
|
||
12.5 まとめ
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
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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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|
||
|
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|
||
|
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|
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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="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2zm-4-6H5v-2h2z"/></svg>
|
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|
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<span class="md-ellipsis">
|
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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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</span>
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</a>
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<span class="md-nav__icon md-icon"></span>
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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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<ul class="md-nav__list" data-md-scrollfix>
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<li class="md-nav__item">
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<a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
|
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<span class="md-ellipsis">
|
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|
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|
||
13.1 バックトラッキングアルゴリズム
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
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|
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|
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|
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|
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<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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|
||
|
||
13.2 全順列問題
|
||
|
||
|
||
|
||
</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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|
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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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|
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<span class="md-ellipsis">
|
||
|
||
|
||
13.3 部分集合和問題
|
||
|
||
|
||
|
||
</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_backtracking/n_queens_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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|
||
|
||
13.4 Nクイーン問題
|
||
|
||
|
||
|
||
</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_backtracking/summary/" class="md-nav__link">
|
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|
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|
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|
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<span class="md-ellipsis">
|
||
|
||
|
||
13.5 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>
|
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</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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<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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|
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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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<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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<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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<li class="md-nav__item">
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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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<span class="md-ellipsis">
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|
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|
||
14.4 0-1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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|
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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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|
||
14.5 完全ナップサック問題
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
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</li>
|
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|
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<li class="md-nav__item">
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<span class="md-ellipsis">
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|
||
|
||
14.6 編集距離問題
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
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|
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|
||
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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|
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第 15 章 貪欲法
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第 15 章 貪欲法
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15.1 貪欲アルゴリズム
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15.2 分数ナップサック問題
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15.3 最大容量問題
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15.4 最大積分割問題
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15.5 まとめ
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|
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第 16 章 付録
|
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|
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16.1 プログラミング環境のインストール
|
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|
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|
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|
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|
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16.2 一緒に創作に参加する
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|
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16.3 用語集
|
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|
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参考文献
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目次
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1. 基本ケースを考える
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2. 部分問題の分解
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3. コード実装
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<h1 id="124">12.4 ハノイの塔問題<a class="headerlink" href="#124" title="Permanent link">¶</a></h1>
|
||
<p>マージソートと二分木構築の両方で、元の問題を2つの部分問題に分解し、それぞれが元の問題のサイズの半分でした。しかし、ハノイの塔では、異なる分解戦略を採用します。</p>
|
||
<div class="admonition question">
|
||
<p class="admonition-title">Question</p>
|
||
<p>3つの柱があり、それぞれ <code>A</code>、<code>B</code>、<code>C</code> と表記されます。最初、柱 <code>A</code> には <span class="arithmatex">\(n\)</span> 枚の円盤があり、上から下に向かって昇順のサイズで配置されています。私たちのタスクは、これらの <span class="arithmatex">\(n\)</span> 枚の円盤を柱 <code>C</code> に移動し、元の順序を維持することです（以下の図に示すように）。移動中には以下のルールが適用されます：</p>
|
||
<ol>
|
||
<li>円盤は柱の上部からのみ取り除くことができ、別の柱の上部に置く必要があります。</li>
|
||
<li>一度に移動できるのは1枚の円盤のみです。</li>
|
||
<li>小さい円盤は常に大きい円盤の上にある必要があります。</li>
|
||
</ol>
|
||
</div>
|
||
<p><a class="glightbox" href="../hanota_problem.assets/hanota_example.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="ハノイの塔の例" class="animation-figure" src="../hanota_problem.assets/hanota_example.png" /></a></p>
|
||
<p align="center"> 図 12-10 ハノイの塔の例 </p>
|
||
|
||
<p><strong>サイズ <span class="arithmatex">\(i\)</span> のハノイの塔問題を <span class="arithmatex">\(f(i)\)</span> と表記します</strong>。例えば、<span class="arithmatex">\(f(3)\)</span> は3枚の円盤を柱 <code>A</code> から柱 <code>C</code> に移動することを表します。</p>
|
||
<h3 id="1">1. 基本ケースを考える<a class="headerlink" href="#1" title="Permanent link">¶</a></h3>
|
||
<p>以下の図に示すように、問題 <span class="arithmatex">\(f(1)\)</span>（円盤が1枚のみ）については、<code>A</code> から <code>C</code> に直接移動できます。</p>
|
||
<div class="tabbed-set tabbed-alternate" data-tabs="1:2"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1"><1></label><label for="__tabbed_1_2"><2></label></div>
|
||
<div class="tabbed-content">
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../hanota_problem.assets/hanota_f1_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="サイズ1の問題の解" class="animation-figure" src="../hanota_problem.assets/hanota_f1_step1.png" /></a></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../hanota_problem.assets/hanota_f1_step2.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="hanota_f1_step2" class="animation-figure" src="../hanota_problem.assets/hanota_f1_step2.png" /></a></p>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<p align="center"> 図 12-11 サイズ1の問題の解 </p>
|
||
|
||
<p><span class="arithmatex">\(f(2)\)</span>（円盤が2枚）については、**柱 <code>B</code> の助けを借りて小さい円盤を大きい円盤の上に保つ**必要があります。以下の図に示すように：</p>
|
||
<ol>
|
||
<li>まず、小さい円盤を <code>A</code> から <code>B</code> に移動します。</li>
|
||
<li>次に、大きい円盤を <code>A</code> から <code>C</code> に移動します。</li>
|
||
<li>最後に、小さい円盤を <code>B</code> から <code>C</code> に移動します。</li>
|
||
</ol>
|
||
<div class="tabbed-set tabbed-alternate" data-tabs="2:4"><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" /><div class="tabbed-labels"><label for="__tabbed_2_1"><1></label><label for="__tabbed_2_2"><2></label><label for="__tabbed_2_3"><3></label><label for="__tabbed_2_4"><4></label></div>
|
||
<div class="tabbed-content">
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../hanota_problem.assets/hanota_f2_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="サイズ2の問題の解" class="animation-figure" src="../hanota_problem.assets/hanota_f2_step1.png" /></a></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../hanota_problem.assets/hanota_f2_step2.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="hanota_f2_step2" class="animation-figure" src="../hanota_problem.assets/hanota_f2_step2.png" /></a></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../hanota_problem.assets/hanota_f2_step3.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="hanota_f2_step3" class="animation-figure" src="../hanota_problem.assets/hanota_f2_step3.png" /></a></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../hanota_problem.assets/hanota_f2_step4.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="hanota_f2_step4" class="animation-figure" src="../hanota_problem.assets/hanota_f2_step4.png" /></a></p>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<p align="center"> 図 12-12 サイズ2の問題の解 </p>
|
||
|
||
<p><span class="arithmatex">\(f(2)\)</span> を解決する過程は次のように要約できます：<strong><code>B</code> の助けを借りて2枚の円盤を <code>A</code> から <code>C</code> に移動する</strong>。ここで、<code>C</code> をターゲット柱、<code>B</code> をバッファ柱と呼びます。</p>
|
||
<h3 id="2">2. 部分問題の分解<a class="headerlink" href="#2" title="Permanent link">¶</a></h3>
|
||
<p>問題 <span class="arithmatex">\(f(3)\)</span>（つまり、円盤が3枚の場合）については、状況がやや複雑になります。</p>
|
||
<p>すでに <span class="arithmatex">\(f(1)\)</span> と <span class="arithmatex">\(f(2)\)</span> の解が分かっているので、分割統治の観点を採用し、<strong><code>A</code> の上の2枚の円盤を1つの単位として扱い</strong>、以下の図に示すステップを実行できます。これにより、3枚の円盤を <code>A</code> から <code>C</code> に正常に移動できます。</p>
|
||
<ol>
|
||
<li><code>B</code> をターゲット柱、<code>C</code> をバッファ柱として、2枚の円盤を <code>A</code> から <code>B</code> に移動します。</li>
|
||
<li>残りの円盤を <code>A</code> から直接 <code>C</code> に移動します。</li>
|
||
<li><code>C</code> をターゲット柱、<code>A</code> をバッファ柱として、2枚の円盤を <code>B</code> から <code>C</code> に移動します。</li>
|
||
</ol>
|
||
<div class="tabbed-set tabbed-alternate" data-tabs="3:4"><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" /><div class="tabbed-labels"><label for="__tabbed_3_1"><1></label><label for="__tabbed_3_2"><2></label><label for="__tabbed_3_3"><3></label><label for="__tabbed_3_4"><4></label></div>
|
||
<div class="tabbed-content">
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../hanota_problem.assets/hanota_f3_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="サイズ3の問題の解" class="animation-figure" src="../hanota_problem.assets/hanota_f3_step1.png" /></a></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../hanota_problem.assets/hanota_f3_step2.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="hanota_f3_step2" class="animation-figure" src="../hanota_problem.assets/hanota_f3_step2.png" /></a></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../hanota_problem.assets/hanota_f3_step3.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="hanota_f3_step3" class="animation-figure" src="../hanota_problem.assets/hanota_f3_step3.png" /></a></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><a class="glightbox" href="../hanota_problem.assets/hanota_f3_step4.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="hanota_f3_step4" class="animation-figure" src="../hanota_problem.assets/hanota_f3_step4.png" /></a></p>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<p align="center"> 図 12-13 サイズ3の問題の解 </p>
|
||
|
||
<p>本質的に、<strong><span class="arithmatex">\(f(3)\)</span> を2つの <span class="arithmatex">\(f(2)\)</span> 部分問題と1つの <span class="arithmatex">\(f(1)\)</span> 部分問題に分解します</strong>。これら3つの部分問題を順次解決することで、元の問題が解決され、部分問題が独立しており、それらの解をマージできることを示しています。</p>
|
||
<p>ここから、以下の図に示すハノイの塔の分割統治戦略を要約できます。元の問題 <span class="arithmatex">\(f(n)\)</span> を2つの部分問題 <span class="arithmatex">\(f(n-1)\)</span> と1つの部分問題 <span class="arithmatex">\(f(1)\)</span> に分割し、以下の順序でこれら3つの部分問題を解決します：</p>
|
||
<ol>
|
||
<li><code>C</code> をバッファとして使用し、<span class="arithmatex">\(n-1\)</span> 枚の円盤を <code>A</code> から <code>B</code> に移動します。</li>
|
||
<li>残りの円盤を <code>A</code> から直接 <code>C</code> に移動します。</li>
|
||
<li><code>A</code> をバッファとして使用し、<span class="arithmatex">\(n-1\)</span> 枚の円盤を <code>B</code> から <code>C</code> に移動します。</li>
|
||
</ol>
|
||
<p>各 <span class="arithmatex">\(f(n-1)\)</span> 部分問題について、<strong>同じ再帰分割を適用でき</strong>、最小の部分問題 <span class="arithmatex">\(f(1)\)</span> に到達するまで続けます。<span class="arithmatex">\(f(1)\)</span> は単一の移動のみが必要であることがすでに分かっているため、解決するのは簡単です。</p>
|
||
<p><a class="glightbox" href="../hanota_problem.assets/hanota_divide_and_conquer.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="ハノイの塔を解決するための分割統治戦略" class="animation-figure" src="../hanota_problem.assets/hanota_divide_and_conquer.png" /></a></p>
|
||
<p align="center"> 図 12-14 ハノイの塔を解決するための分割統治戦略 </p>
|
||
|
||
<h3 id="3">3. コード実装<a class="headerlink" href="#3" title="Permanent link">¶</a></h3>
|
||
<p>コードでは、再帰関数 <code>dfs(i, src, buf, tar)</code> を定義します。これは柱 <code>src</code> から上の <span class="arithmatex">\(i\)</span> 枚の円盤を柱 <code>tar</code> に移動し、柱 <code>buf</code> をバッファとして使用します：</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">hanota.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">move</span><span class="p">(</span><span class="n">src</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">tar</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-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w"> </span><span class="sd">"""円盤を移動"""</span>
|
||
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a> <span class="c1"># src の上から円盤を取り出す</span>
|
||
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a> <span class="n">pan</span> <span class="o">=</span> <span class="n">src</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>
|
||
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a> <span class="c1"># 円盤を tar の上に置く</span>
|
||
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a> <span class="n">tar</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">pan</span><span class="p">)</span>
|
||
<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>
|
||
<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a><span class="k">def</span><span class="w"> </span><span class="nf">dfs</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">src</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">buf</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">tar</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-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a><span class="w"> </span><span class="sd">"""ハノイの塔問題 f(i) を解く"""</span>
|
||
<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a> <span class="c1"># src に円盤が 1 つだけ残っている場合、それを tar に移動</span>
|
||
<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a> <span class="k">if</span> <span class="n">i</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
|
||
<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a> <span class="n">move</span><span class="p">(</span><span class="n">src</span><span class="p">,</span> <span class="n">tar</span><span class="p">)</span>
|
||
<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a> <span class="k">return</span>
|
||
<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a> <span class="c1"># 部分問題 f(i-1)：tar の助けを借りて src の上の i-1 個の円盤を buf に移動</span>
|
||
<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a> <span class="n">dfs</span><span class="p">(</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">src</span><span class="p">,</span> <span class="n">tar</span><span class="p">,</span> <span class="n">buf</span><span class="p">)</span>
|
||
<a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a> <span class="c1"># 部分問題 f(1)：残りの 1 個の円盤を src から tar に移動</span>
|
||
<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a> <span class="n">move</span><span class="p">(</span><span class="n">src</span><span class="p">,</span> <span class="n">tar</span><span class="p">)</span>
|
||
<a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a> <span class="c1"># 部分問題 f(i-1)：src の助けを借りて buf の上の i-1 個の円盤を tar に移動</span>
|
||
<a id="__codelineno-0-19" name="__codelineno-0-19" href="#__codelineno-0-19"></a> <span class="n">dfs</span><span class="p">(</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">buf</span><span class="p">,</span> <span class="n">src</span><span class="p">,</span> <span class="n">tar</span><span class="p">)</span>
|
||
<a id="__codelineno-0-20" name="__codelineno-0-20" href="#__codelineno-0-20"></a>
|
||
<a id="__codelineno-0-21" name="__codelineno-0-21" href="#__codelineno-0-21"></a><span class="k">def</span><span class="w"> </span><span class="nf">solve_hanota</span><span class="p">(</span><span class="n">A</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">B</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">C</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-0-22" name="__codelineno-0-22" href="#__codelineno-0-22"></a><span class="w"> </span><span class="sd">"""ハノイの塔問題を解く"""</span>
|
||
<a id="__codelineno-0-23" name="__codelineno-0-23" href="#__codelineno-0-23"></a> <span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">A</span><span class="p">)</span>
|
||
<a id="__codelineno-0-24" name="__codelineno-0-24" href="#__codelineno-0-24"></a> <span class="c1"># B の助けを借りて A の上の n 個の円盤を C に移動</span>
|
||
<a id="__codelineno-0-25" name="__codelineno-0-25" href="#__codelineno-0-25"></a> <span class="n">dfs</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">A</span><span class="p">,</span> <span class="n">B</span><span class="p">,</span> <span class="n">C</span><span class="p">)</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">hanota.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 円盤を移動 */</span>
|
||
<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">move</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">src</span><span class="p">,</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">tar</span><span class="p">)</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="c1">// src の最上部から円盤を取り出す</span>
|
||
<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">pan</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">src</span><span class="p">.</span><span class="n">back</span><span class="p">();</span>
|
||
<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w"> </span><span class="n">src</span><span class="p">.</span><span class="n">pop_back</span><span class="p">();</span>
|
||
<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w"> </span><span class="c1">// 円盤を tar の最上部に配置</span>
|
||
<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w"> </span><span class="n">tar</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">pan</span><span class="p">);</span>
|
||
<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="p">}</span>
|
||
<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a>
|
||
<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="cm">/* ハノイの塔問題 f(i) を解く */</span>
|
||
<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="kt">void</span><span class="w"> </span><span class="nf">dfs</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="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">src</span><span class="p">,</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">buf</span><span class="p">,</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">tar</span><span class="p">)</span><span class="w"> </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="c1">// src に円盤が1つだけ残っている場合、それを tar に移動</span>
|
||
<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></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">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w"> </span><span class="n">move</span><span class="p">(</span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">);</span>
|
||
<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w"> </span><span class="k">return</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="p">}</span>
|
||
<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="w"> </span><span class="c1">// 部分問題 f(i-1)：tar の助けを借りて、上位 i-1 個の円盤を src から buf に移動</span>
|
||
<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="w"> </span><span class="n">dfs</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">1</span><span class="p">,</span><span class="w"> </span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">,</span><span class="w"> </span><span class="n">buf</span><span class="p">);</span>
|
||
<a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a><span class="w"> </span><span class="c1">// 部分問題 f(1)：残りの1つの円盤を src から tar に移動</span>
|
||
<a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="w"> </span><span class="n">move</span><span class="p">(</span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">);</span>
|
||
<a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a><span class="w"> </span><span class="c1">// 部分問題 f(i-1)：src の助けを借りて、上位 i-1 個の円盤を buf から tar に移動</span>
|
||
<a id="__codelineno-1-22" name="__codelineno-1-22" href="#__codelineno-1-22"></a><span class="w"> </span><span class="n">dfs</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">1</span><span class="p">,</span><span class="w"> </span><span class="n">buf</span><span class="p">,</span><span class="w"> </span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">);</span>
|
||
<a id="__codelineno-1-23" name="__codelineno-1-23" href="#__codelineno-1-23"></a><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="cm">/* ハノイの塔問題を解く */</span>
|
||
<a id="__codelineno-1-26" name="__codelineno-1-26" href="#__codelineno-1-26"></a><span class="kt">void</span><span class="w"> </span><span class="nf">solveHanota</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">A</span><span class="p">,</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">B</span><span class="p">,</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">C</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">A</span><span class="p">.</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">// B の助けを借りて、上位 n 個の円盤を A から C に移動</span>
|
||
<a id="__codelineno-1-29" name="__codelineno-1-29" href="#__codelineno-1-29"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">A</span><span class="p">,</span><span class="w"> </span><span class="n">B</span><span class="p">,</span><span class="w"> </span><span class="n">C</span><span class="p">);</span>
|
||
<a id="__codelineno-1-30" name="__codelineno-1-30" href="#__codelineno-1-30"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">hanota.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 円盤を移動 */</span>
|
||
<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">move</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">src</span><span class="p">,</span><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">tar</span><span class="p">)</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="c1">// src の最上部から円盤を取り出す</span>
|
||
<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w"> </span><span class="n">Integer</span><span class="w"> </span><span class="n">pan</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">src</span><span class="p">.</span><span class="na">remove</span><span class="p">(</span><span class="n">src</span><span class="p">.</span><span class="na">size</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-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w"> </span><span class="c1">// 円盤を tar の最上部に配置</span>
|
||
<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w"> </span><span class="n">tar</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">pan</span><span class="p">);</span>
|
||
<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="p">}</span>
|
||
<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a>
|
||
<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="cm">/* ハノイの塔問題 f(i) を解く */</span>
|
||
<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="kt">void</span><span class="w"> </span><span class="nf">dfs</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="n">List</span><span class="o"><</span><span class="n">Integer</span><span class="o">></span><span class="w"> </span><span class="n">src</span><span class="p">,</span><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">buf</span><span class="p">,</span><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">tar</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w"> </span><span class="c1">// src に円盤が1つだけ残っている場合、それを tar に移動</span>
|
||
<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></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">1</span><span class="p">)</span><span class="w"> </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="n">move</span><span class="p">(</span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</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="k">return</span><span class="p">;</span>
|
||
<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w"> </span><span class="c1">// 部分問題 f(i-1)：tar の助けを借りて、上位 i-1 個の円盤を src から buf に移動</span>
|
||
<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="w"> </span><span class="n">dfs</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">1</span><span class="p">,</span><span class="w"> </span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">,</span><span class="w"> </span><span class="n">buf</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="c1">// 部分問題 f(1)：残りの1つの円盤を src から tar に移動</span>
|
||
<a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="w"> </span><span class="n">move</span><span class="p">(</span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">);</span>
|
||
<a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a><span class="w"> </span><span class="c1">// 部分問題 f(i-1)：src の助けを借りて、上位 i-1 個の円盤を buf から tar に移動</span>
|
||
<a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a><span class="w"> </span><span class="n">dfs</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">1</span><span class="p">,</span><span class="w"> </span><span class="n">buf</span><span class="p">,</span><span class="w"> </span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">);</span>
|
||
<a id="__codelineno-2-22" name="__codelineno-2-22" href="#__codelineno-2-22"></a><span class="p">}</span>
|
||
<a id="__codelineno-2-23" name="__codelineno-2-23" href="#__codelineno-2-23"></a>
|
||
<a id="__codelineno-2-24" name="__codelineno-2-24" href="#__codelineno-2-24"></a><span class="cm">/* ハノイの塔問題を解く */</span>
|
||
<a id="__codelineno-2-25" name="__codelineno-2-25" href="#__codelineno-2-25"></a><span class="kt">void</span><span class="w"> </span><span class="nf">solveHanota</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">A</span><span class="p">,</span><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">B</span><span class="p">,</span><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">C</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-2-26" name="__codelineno-2-26" href="#__codelineno-2-26"></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">A</span><span class="p">.</span><span class="na">size</span><span class="p">();</span>
|
||
<a id="__codelineno-2-27" name="__codelineno-2-27" href="#__codelineno-2-27"></a><span class="w"> </span><span class="c1">// B の助けを借りて、上位 n 個の円盤を A から C に移動</span>
|
||
<a id="__codelineno-2-28" name="__codelineno-2-28" href="#__codelineno-2-28"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">A</span><span class="p">,</span><span class="w"> </span><span class="n">B</span><span class="p">,</span><span class="w"> </span><span class="n">C</span><span class="p">);</span>
|
||
<a id="__codelineno-2-29" name="__codelineno-2-29" href="#__codelineno-2-29"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">hanota.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">hanota</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Move</span><span class="p">}</span>
|
||
<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a>
|
||
<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">hanota</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">DFS</span><span class="p">}</span>
|
||
<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a>
|
||
<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="na">[class]</span><span class="p">{</span><span class="n">hanota</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">SolveHanota</span><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">hanota.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="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">move</span><span class="p">}</span>
|
||
<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a>
|
||
<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">dfsHanota</span><span class="p">}</span>
|
||
<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a>
|
||
<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">solveHanota</span><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">hanota.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="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">move</span><span class="p">}</span>
|
||
<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a>
|
||
<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">dfs</span><span class="p">}</span>
|
||
<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a>
|
||
<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">solveHanota</span><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">hanota.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="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">move</span><span class="p">}</span>
|
||
<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a>
|
||
<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">dfs</span><span class="p">}</span>
|
||
<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a>
|
||
<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">solveHanota</span><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
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<div class="highlight"><span class="filename">hanota.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="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">move</span><span class="p">}</span>
|
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<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a>
|
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<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">dfs</span><span class="p">}</span>
|
||
<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a>
|
||
<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">solveHanota</span><span class="p">}</span>
|
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</code></pre></div>
|
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</div>
|
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<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">hanota.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="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">move</span><span class="p">}</span>
|
||
<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a>
|
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<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">dfs</span><span class="p">}</span>
|
||
<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a>
|
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<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">solveHanota</span><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">hanota.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="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">move_pan</span><span class="p">}</span>
|
||
<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a>
|
||
<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">dfs</span><span class="p">}</span>
|
||
<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a>
|
||
<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">solve_hanota</span><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">hanota.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="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">move</span><span class="p">}</span>
|
||
<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a>
|
||
<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">dfs</span><span class="p">}</span>
|
||
<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a>
|
||
<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">solveHanota</span><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">hanota.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="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">move</span><span class="p">}</span>
|
||
<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a>
|
||
<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">dfs</span><span class="p">}</span>
|
||
<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a>
|
||
<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">solveHanota</span><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">hanota.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="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">move</span><span class="p">}</span>
|
||
<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a>
|
||
<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">dfs</span><span class="p">}</span>
|
||
<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a>
|
||
<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">solve_hanota</span><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<p>以下の図に示すように、ハノイの塔問題は高さ <span class="arithmatex">\(n\)</span> の再帰木として視覚化できます。各ノードは部分問題を表し、<code>dfs()</code> の呼び出しに対応します。<strong>したがって、時間計算量は <span class="arithmatex">\(O(2^n)\)</span>、空間計算量は <span class="arithmatex">\(O(n)\)</span> です。</strong></p>
|
||
<p><a class="glightbox" href="../hanota_problem.assets/hanota_recursive_tree.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="ハノイの塔の再帰木" class="animation-figure" src="../hanota_problem.assets/hanota_recursive_tree.png" /></a></p>
|
||
<p align="center"> 図 12-15 ハノイの塔の再帰木 </p>
|
||
|
||
<div class="admonition quote">
|
||
<p class="admonition-title">Quote</p>
|
||
<p>ハノイの塔は古代の伝説に由来します。古代インドの寺院で、僧侶たちは3本の高いダイヤモンドの柱と、異なるサイズの <span class="arithmatex">\(64\)</span> 枚の金の円盤を持っていました。彼らは、最後の円盤が正しく置かれたとき、世界が終わると信じていました。</p>
|
||
<p>しかし、僧侶たちが1秒に1枚の円盤を移動したとしても、約 <span class="arithmatex">\(2^{64} \approx 1.84×10^{19}\)</span> —約5850億年—かかり、宇宙の年齢の現在の推定をはるかに超えています。したがって、この伝説が真実であれば、世界の終わりについて心配する必要はおそらくないでしょう。</p>
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