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第 0 章 &nbsp; はじめに
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0.2 &nbsp; 本書の使い方
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第 1 章 &nbsp; アルゴリズムとの出会い
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6.1 &nbsp; ハッシュテーブル
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6.3 &nbsp; ハッシュアルゴリズム
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7.1 &nbsp; 二分木
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7.2 &nbsp; 二分木の走査
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7.3 &nbsp; 二分木の配列表現
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第 8 章 &nbsp; ヒープ
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8.1 &nbsp; ヒープ
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第 9 章 &nbsp; グラフ
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第 9 章 &nbsp; グラフ
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9.1 &nbsp; グラフ
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9.2 &nbsp; グラフの基本操作
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9.3 &nbsp; グラフの走査
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9.4 &nbsp; まとめ
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第 10 章 &nbsp; 探索
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第 10 章 &nbsp; 探索
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10.1 &nbsp; 二分探索
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10.2 &nbsp; 二分探索で挿入位置を探す
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10.3 &nbsp; 二分探索で境界を探す
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10.4 &nbsp; ハッシュを使った最適化
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10.5 &nbsp; 探索アルゴリズムを改めて考える
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10.6 &nbsp; まとめ
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10.7 &nbsp; 練習問題
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第 11 章 &nbsp; ソート
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第 11 章 &nbsp; ソート
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11.1 &nbsp; ソートアルゴリズム
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11.2 &nbsp; 選択ソート
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11.3 &nbsp; バブルソート
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11.4 &nbsp; 挿入ソート
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11.5 &nbsp; クイックソート
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11.6 &nbsp; マージソート
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11.7 &nbsp; ヒープソート
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11.8 &nbsp; バケットソート
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11.9 &nbsp; カウントソート
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11.10 &nbsp; 基数ソート
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11.11 &nbsp; まとめ
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11.12 &nbsp; 練習問題
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第 12 章 &nbsp; 分割統治
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12.1 &nbsp; 分割統治アルゴリズム
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12.2 &nbsp; 分割統治による探索戦略
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12.3 &nbsp; 二分木の構築問題
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12.4 &nbsp; ハノイの塔の問題
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12.5 &nbsp; まとめ
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第 13 章 &nbsp; バックトラッキング
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13.1 &nbsp; バックトラッキングアルゴリズム
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13.2 &nbsp; 順列列挙問題
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13.3 &nbsp; 部分集合和問題
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13.4 &nbsp; n クイーン問題
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13.5 &nbsp; まとめ
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13.6 &nbsp; 練習問題
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第 14 章 &nbsp; 動的計画法
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14.1 &nbsp; 動的計画法への第一歩
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14.2 &nbsp; 動的計画法の問題の特徴
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14.3 &nbsp; 動的計画法の解き方
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14.4 &nbsp; 0-1 ナップサック問題
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14.5 &nbsp; 個数制限なしナップサック問題
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14.6 &nbsp; 編集距離問題
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14.7 &nbsp; まとめ
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14.8 &nbsp; 練習問題
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第 15 章 &nbsp; 貪欲法
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15.1 &nbsp; 貪欲アルゴリズム
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15.2 &nbsp; 分割可能ナップサック問題
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15.3 &nbsp; 最大容量問題
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15.4 &nbsp; 整数を分割して積を最大にする問題
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15.5 &nbsp; まとめ
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<h1 id="_1">序文<a class="headerlink" href="#_1" title="この見出しへのリンク">&para;</a></h1>
<p>数年前、私は力扣で「剑指 Offer」シリーズの解説を公開し、多くの読者から励ましと支援をいただきました。読者との交流で最もよく尋ねられたのが、「アルゴリズムはどう学び始めればよいのか」という質問です。私は次第に、この問いに強い関心を持つようになりました。</p>
<p>手探りのまま問題演習に取り組む方法は、単純で直接的、しかも効果があるためか、最もよく選ばれているようです。ただ、問題演習は「マインスイーパ」に似ています。独学の力がある人は地雷を一つずつ取り除けますが、基礎が足りない人は何度も地雷を踏み、挫折するたびに後ずさりしてしまうかもしれません。教科書を通読する方法も一般的ですが、就職を目指す人は、卒業論文、履歴書の提出、筆記試験や面接の準備で精一杯です。分厚い本を読みこなすことは、大きな難題になりがちです。</p>
<p>あなたも同じような悩みを抱えているなら、幸いにもこの本があなたを「見つけて」くれました。本書はこの問いに対する私なりの答えであり、最適解ではなくても、少なくとも前向きな試みです。本書を読んだだけで内定を得られるわけではありませんが、データ構造とアルゴリズムの「知識の地図」を探り、さまざまな「地雷」の形、大きさ、分布を知り、多様な「地雷の取り除き方」を身に付ける手助けをします。それらを身に付ければ、より自在に問題演習や文献の読解に取り組み、体系的な知識を少しずつ築けるはずです。</p>
<p>私はファインマン教授の言葉、「知識は無料ではありません。注意を払わなければなりません。」に深く共感しています。この意味では、本書も完全に「無料」ではありません。あなたが本書に注いでくれる貴重な「注意」に応えるため、私も最大限の「注意」を払い、全力で執筆に取り組みます。</p>
<p>自分の学識や力がまだ十分でないことは承知しています。内容はしばらく推敲を重ねてきましたが、なお多くの誤りが残っているはずです。先生方や学習者の皆さんからのご批判、ご指摘をお願いいたします。</p>
<p><img alt="Hello Algo" class="cover-image" src="../assets/covers/chapter_hello_algo.jpg" /></p>
<div style="text-align: center;">
<h2 style="margin-top: 0.8em; margin-bottom: 0.8em;">Hello、アルゴリズム!</h2>
</div>
<p>コンピュータの登場は、世界に大きな変革をもたらしました。高速な計算能力と優れたプログラマビリティを備えたコンピュータは、アルゴリズムの実行とデータ処理に理想的な媒体となりました。ゲームの写実的な映像、自動運転の知的な判断、AlphaGo の見事な対局、ChatGPT の自然な対話などは、いずれもコンピュータ上でアルゴリズムが巧みに働く例です。</p>
<p>実際には、コンピュータが生まれる前から、アルゴリズムとデータ構造は世界の隅々に存在していました。初期のアルゴリズムは、古代の数え方や道具の製作手順など、比較的単純でした。文明が進むにつれ、アルゴリズムも精緻で複雑になりました。巧みな職人の技、生産力を解き放つ工業製品、宇宙の運行を説明する科学法則まで、平凡なものにも驚異的なものにも、その背後には巧妙なアルゴリズムの考え方が隠れています。</p>
<p>データ構造も同じく至るところにあります。大きくは社会的ネットワーク、小さくは地下鉄の路線まで、多くのシステムは「グラフ」でモデル化できます。国から家庭まで、社会の主な組織形態には「木」の特徴が見られます。冬の重ね着は「スタック」のように、最初に着た服を最後に脱ぎます。バドミントンのシャトルの筒は、一方から入れて他方から取り出す「キュー」です。辞書は「ハッシュテーブル」のように、目的の項目を素早く探せます。</p>
<p>本書は、分かりやすいアニメーション図解と実行できるコード例を通して、アルゴリズムとデータ構造の中心的な概念を理解し、プログラミングで実装できるようになることを目指しています。そのうえで、複雑な世界にアルゴリズムがどのように息づいているかを示し、その美しさを伝えたいと考えています。本書があなたの役に立つことを願っています。</p>
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