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第 8 章 &nbsp; ヒープ
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8.2 &nbsp; ヒープ構築
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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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第 10 章 &nbsp; 探索
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10.1 &nbsp; 二分探索
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10.2 &nbsp; 二分探索の挿入位置
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10.3 &nbsp; 二分探索の境界
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10.4 &nbsp; ハッシュによる最適化戦略
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10.5 &nbsp; 探索アルゴリズム再考
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第 11 章 &nbsp; 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; 計数ソート
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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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第 12 章 &nbsp; 分割統治
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12.1 &nbsp; 分割統治法
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12.2 &nbsp; 分割統治探索戦略
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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; 全順列問題
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13.3 &nbsp; 部分和問題
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13.4 &nbsp; n クイーン問題
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第 14 章 &nbsp; 動的計画法
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14.1 &nbsp; 動的計画法入門
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14.2 &nbsp; 動的計画法の問題特性
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14.4 &nbsp; 0-1 ナップサック問題
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<h1 id="36">3.6 &nbsp; 演習<a class="headerlink" href="#36" title="Permanent link">&para;</a></h1>
<h2 id="361">3.6.1 &nbsp; 確認問題<a class="headerlink" href="#361" title="Permanent link">&para;</a></h2>
<h3 id="1">1. &nbsp; 身近な場面にあるデータの関係<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
<p>データ同士の関係に基づいて、次の 3 つの場面に「線形構造、木構造、網状構造」のいずれかを選び、理由を説明してください。</p>
<!-- numbered-subquestions -->
<ol>
<li>生徒が一列に並び、それぞれが自分の前と後ろにいる人だけに注目する。</li>
<li>学校が「学校 → 学年 → クラス」という階層で管理されている。</li>
<li>都市の道路が複数の交差点を結び、1 つの交差点から複数の別の交差点へ行けるほか、道路が環状につながることもある。</li>
</ol>
<details class="success">
<summary>解答</summary>
<ol>
<li>
<p>線形構造です。列の先頭と最後にいる人を除き、それぞれの人は前後の 1 人ずつとだけ隣り合い、関係が一本の線に沿って並んでいます。</p>
</li>
<li>
<p>木構造です。各クラスはいずれか 1 つの学年に属し、各学年はさらに学校に属しており、関係が上から下へ階層的に広がっています。</p>
</li>
<li>
<p>網状構造です。1 つの交差点を複数の交差点と結ぶことができ、経路が環状につながる場合もあるため、1 つの順序や厳密な階層では表せません。</p>
<p>構造を判断するときは、メモリをどれだけ使うかを先に考えるのではなく、まず要素同士の関係を観察します。</p>
</li>
</ol>
</details>
<h3 id="2">2. &nbsp; 論理的な順序をメモリに保存する方法<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
<p>論理的な順序 <code>A → B → C</code> を保存するために、次の 2 つの簡略化したメモリ配置を考えます。</p>
<ul>
<li>方法 A：<code>A、B、C</code> を、それぞれ番号 <code>20、21、22</code> のメモリ領域に置く。</li>
<li>方法 B：<code>A、B、C</code> を、それぞれ番号 <code>20、7、31</code> のメモリ領域に置き、<code>A</code> に <code>B</code> の位置、<code>B</code> に <code>C</code> の位置を記録する。</li>
</ul>
<!-- numbered-subquestions -->
<ol>
<li>どちらが連続した領域への保存で、どちらが分散した領域への保存ですか？</li>
<li>2 つの方法は、それぞれ配列と連結リストのどちらに近いですか？</li>
<li>方法 B のメモリ領域の番号は大きさの順に並んでいません。それでも <code>A → B → C</code> という論理的な順序を表せるのはなぜですか？</li>
</ol>
<details class="success">
<summary>解答</summary>
<ol>
<li>
<p>方法 A は連続したメモリ領域を使っているため、連続した領域への保存です。方法 B のノードは別々の場所に分散しているため、分散した領域への保存です。</p>
</li>
<li>
<p>方法 A は配列に、方法 B は連結リストに近いです。</p>
</li>
<li>
<p>論理的な順序を決めるのはノード間に記録された接続関係であり、メモリ領域の番号の大小ではありません。
<code>A</code> に記録された位置から <code>B</code> を見つけ、さらに <code>B</code> に記録された位置から <code>C</code> を見つけられるため、<code>A、B、C</code> の順にアクセスできます。</p>
<p>このことからも、論理構造と物理構造は、同じデータを異なる視点から捉えたものだと分かります。</p>
</li>
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</details>
<h3 id="3">3. &nbsp; 宿題の記録におけるデータ型と構造<a class="headerlink" href="#3" title="Permanent link">&para;</a></h3>
<p>ある学習グループが、座席順に 4 人の生徒が宿題を提出したかどうかを記録したところ、次の結果になりました。</p>
<p><code>[true, false, true, true]</code></p>
<!-- numbered-subquestions -->
<ol>
<li>各要素には、どの基本データ型が適していますか？</li>
<li>この 4 つの要素は座席順に一列に並んでいます。どのような論理構造を使っていますか？</li>
<li>今後、各生徒の宿題の点数を <code>[90, 0, 85, 100]</code> と記録するように変えた場合、変わるのはデータの「内容の型」と「構成方法」のどちらですか？理由も説明してください。</li>
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<summary>解答</summary>
<ol>
<li>
<p>各要素は「はい」か「いいえ」だけを表すため、ブール型 <code>bool</code> が適しています。</p>
</li>
<li>
<p>これらの要素は座席順に並んで線形構造を作っており、配列で保存できます。</p>
</li>
<li>
<p>変わるのは内容の型です。要素がブール値から整数に変わります。一方、構成方法は変わりません。
データは引き続き座席順に一列に並び、配列という線形構造を使えます。</p>
<p>基本データ型は「何を保存するか」を、データ構造は「データをどのように構成するか」を表します。</p>
</li>
</ol>
</details>
<h2 id="362">3.6.2 &nbsp; プログラミング演習<a class="headerlink" href="#362" title="Permanent link">&para;</a></h2>
<h3 id="1-1">1. &nbsp; 二進表現に含まれる 1 の個数<a class="headerlink" href="#1-1" title="Permanent link">&para;</a></h3>
<p>0 以上の整数 <code>n</code> が与えられます。その二進表現に 1 がいくつ含まれるかを数えてください。</p>
<p>ビット演算を使って求めてください。二進表現を文字列に変換したり、1 を直接数える組み込み関数を使ったりしてはいけません。</p>
<details class="tip">
<summary>解法のヒント</summary>
<ol>
<li>n &amp; 1 で n の最下位ビットを取り出し、そのビットが 1 かどうかを判定できます</li>
<li>1 ビット右へシフトすると、現在の最下位ビットが取り除かれます。多くの言語では演算子 &gt;&gt; を使います</li>
<li>各ビットを調べて右へシフトする方法を完成させたら、n &amp; (n - 1) が n の最も右にある 1 を 0 に変えることも確認してみましょう</li>
</ol>
</details>
<p><a class="rounded-button exercise-button" href="https://leetcode.com/problems/number-of-1-bits/" rel="noopener noreferrer" target="_blank">LeetCode</a></p>
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