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krahets
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<meta charset="utf-8">
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<meta name="viewport" content="width=device-width,initial-scale=1">
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<meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
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<meta name="description" content="アニメーション図解とワンクリック実行コードで学べるデータ構造とアルゴリズムの入門書">
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<meta name="author" content="krahets">
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<path
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d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
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</svg>
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<span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
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<span>日本語版のレビュアーを募集しています。詳しくは <a href="/ja/chapter_appendix/contribution/">こちら</a> をご覧ください。</span>
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</div>
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</div>
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<span class="md-ellipsis">
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序
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はじめに
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<span class="md-nav__icon md-icon"></span>
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序
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はじめに
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</label>
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<span class="md-ellipsis">
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1.1 アルゴリズムはどこにでもある
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1.1 アルゴリズムは至るところにある
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<span class="md-ellipsis">
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1.2 アルゴリズムとは何か
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1.2 アルゴリズムとは
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<span class="md-ellipsis">
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2.1 アルゴリズムの効率評価
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2.1 アルゴリズム効率の評価
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<span class="md-ellipsis">
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3.3 数値の符号化 *
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3.3 数値エンコーディング *
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<span class="md-ellipsis">
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3.4 文字の符号化 *
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3.4 文字エンコーディング *
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<span class="md-ellipsis">
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第 6 章 ハッシュ表
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第 6 章 ハッシュテーブル
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<span class="md-nav__icon md-icon"></span>
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第 6 章 ハッシュ表
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第 6 章 ハッシュテーブル
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</label>
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<span class="md-ellipsis">
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6.1 ハッシュ表
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6.1 ハッシュテーブル
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<span class="md-ellipsis">
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7.5 AVL木 *
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7.5 AVL 木 *
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<span class="md-ellipsis">
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8.2 ヒープ構築操作
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8.2 ヒープ構築
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<span class="md-ellipsis">
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10.2 二分探索の挿入点
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10.2 二分探索の挿入位置
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<span class="md-ellipsis">
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10.4 ハッシュ最適化戦略
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10.4 ハッシュによる最適化戦略
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<span class="md-ellipsis">
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10.5 探索アルゴリズムの再認識
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10.5 探索アルゴリズム再考
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<span class="md-ellipsis">
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12.1 分割統治アルゴリズム
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12.1 分割統治法
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<span class="md-ellipsis">
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12.3 木の構築問題
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12.3 二分木の構築問題
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<span class="md-ellipsis">
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12.4 ハノイの塔問題
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12.4 ハノイの塔の問題
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<span class="md-ellipsis">
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13.3 部分集合和問題
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13.3 部分和問題
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<span class="md-ellipsis">
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13.4 Nクイーン問題
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13.4 n クイーン問題
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<span class="md-ellipsis">
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14.1 動的計画法の初歩
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14.1 動的計画法入門
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<span class="md-ellipsis">
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14.2 DP 問題の特性
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14.2 動的計画法の問題特性
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<span class="md-ellipsis">
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14.3 DP の解法の考え方
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14.3 動的計画法の問題解決の考え方
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<span class="md-ellipsis">
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14.4 0-1ナップサック問題
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14.4 0-1 ナップサック問題
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<span class="md-ellipsis">
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15.1 貪欲アルゴリズム
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15.1 貪欲法
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<a href="#2" class="md-nav__link">
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<span class="md-ellipsis">
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2. 実装
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2. コード実装
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</span>
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</a>
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<span class="md-ellipsis">
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16.2 一緒に創作に参加する
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16.2 一緒に制作に参加しましょう
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<a href="#2" class="md-nav__link">
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<span class="md-ellipsis">
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2. 実装
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2. コード実装
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</span>
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</a>
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<h1 id="153">15.3 最大容量問題<a class="headerlink" href="#153" title="Permanent link">¶</a></h1>
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<div class="admonition question">
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<p class="admonition-title">Question</p>
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<p>配列 <span class="arithmatex">\(ht\)</span> を入力します。各要素は垂直仕切りの高さを表します。配列内の任意の2つの仕切りと、それらの間のスペースによってコンテナを形成できます。</p>
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<p>コンテナの容量は高さと幅の積（面積）で、高さは短い方の仕切りによって決定され、幅は2つの仕切りの配列インデックスの差です。</p>
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<p>コンテナの容量を最大化する2つの仕切りを配列から選択し、この最大容量を返してください。例を下の図に示します。</p>
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<p>配列 <span class="arithmatex">\(ht\)</span> が与えられ、各要素は垂直な仕切り板の高さを表します。配列内の任意の 2 枚の仕切り板と、その間の空間で容器を構成できます。</p>
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<p>容器の容量は高さと幅の積（面積）に等しく、高さは短い方の仕切り板で決まり、幅は 2 枚の仕切り板の配列インデックスの差です。</p>
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<p>配列から 2 枚の仕切り板を選び、構成される容器の容量が最大となるようにしてください。最大容量を返します。例を以下の図に示します。</p>
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</div>
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<p><img alt="最大容量問題の例データ" class="animation-figure" src="../max_capacity_problem.assets/max_capacity_example.png" /></p>
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<p align="center"> 図 15-7 最大容量問題の例データ </p>
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<p><img alt="最大容量問題のサンプルデータ" class="animation-figure" src="../max_capacity_problem.assets/max_capacity_example.png" /></p>
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<p align="center"> 図 15-7 最大容量問題のサンプルデータ </p>
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<p>コンテナは任意の2つの仕切りによって形成されるため、<strong>この問題の状態は2つの仕切りのインデックスで表現され、<span class="arithmatex">\([i, j]\)</span> と表記されます</strong>。</p>
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<p>問題の記述によれば、容量は高さと幅の積に等しく、高さは短い方の仕切りによって決定され、幅は2つの仕切りの配列インデックスの差です。容量 <span class="arithmatex">\(cap[i, j]\)</span> の式は：</p>
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<p>容器は任意の 2 枚の仕切り板で囲まれるため、<strong>本問の状態は 2 枚の仕切り板のインデックスで表され、<span class="arithmatex">\([i, j]\)</span> と記します</strong>。</p>
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<p>問題の条件より、容量は高さと幅の積に等しく、高さは短い板で決まり、幅は 2 枚の仕切り板の配列インデックスの差です。容量を <span class="arithmatex">\(cap[i, j]\)</span> とすると、計算式は次のようになります。</p>
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<div class="arithmatex">\[
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cap[i, j] = \min(ht[i], ht[j]) \times (j - i)
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\]</div>
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<p>配列の長さを <span class="arithmatex">\(n\)</span> と仮定すると、2つの仕切りの組み合わせ数（状態の総数）は <span class="arithmatex">\(C_n^2 = \frac{n(n - 1)}{2}\)</span> です。最も直接的なアプローチは**すべての可能な状態を列挙する**ことで、時間計算量は <span class="arithmatex">\(O(n^2)\)</span> になります。</p>
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<p>配列の長さを <span class="arithmatex">\(n\)</span> とすると、2 枚の仕切り板の組合せ数（状態総数）は <span class="arithmatex">\(C_n^2 = \frac{n(n - 1)}{2}\)</span> 個です。最も直接的には、<strong>すべての状態を総当たりできます</strong>。これにより最大容量を求められ、時間計算量は <span class="arithmatex">\(O(n^2)\)</span> です。</p>
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<h3 id="1">1. 貪欲戦略の決定<a class="headerlink" href="#1" title="Permanent link">¶</a></h3>
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<p>この問題にはより効率的な解法があります。下の図に示すように、インデックス <span class="arithmatex">\(i < j\)</span> かつ高さ <span class="arithmatex">\(ht[i] < ht[j]\)</span> の状態 <span class="arithmatex">\([i, j]\)</span> を選択します。つまり、<span class="arithmatex">\(i\)</span> は短い仕切り、<span class="arithmatex">\(j\)</span> は高い仕切りです。</p>
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<p>この問題にはさらに効率的な解法があります。以下の図のように、状態 <span class="arithmatex">\([i, j]\)</span> を 1 つ選び、インデックスが <span class="arithmatex">\(i < j\)</span> かつ高さが <span class="arithmatex">\(ht[i] < ht[j]\)</span> を満たすとします。つまり、<span class="arithmatex">\(i\)</span> が短い板、<span class="arithmatex">\(j\)</span> が長い板です。</p>
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<p><img alt="初期状態" class="animation-figure" src="../max_capacity_problem.assets/max_capacity_initial_state.png" /></p>
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<p align="center"> 図 15-8 初期状態 </p>
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<p>下の図に示すように、<strong>高い仕切り <span class="arithmatex">\(j\)</span> を短い仕切り <span class="arithmatex">\(i\)</span> に近づけて移動すると、容量は確実に減少します</strong>。</p>
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<p>これは、高い仕切り <span class="arithmatex">\(j\)</span> を移動すると、幅 <span class="arithmatex">\(j-i\)</span> が確実に減少するためです。高さは短い仕切りによって決定されるため、高さは同じまま（<span class="arithmatex">\(i\)</span> が短い仕切りのまま）か減少（移動した <span class="arithmatex">\(j\)</span> が短い仕切りになる）しかありません。</p>
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<p><img alt="高い仕切りを内側に移動した後の状態" class="animation-figure" src="../max_capacity_problem.assets/max_capacity_moving_long_board.png" /></p>
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<p align="center"> 図 15-9 高い仕切りを内側に移動した後の状態 </p>
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<p>以下の図のように、<strong>このとき長い板 <span class="arithmatex">\(j\)</span> を短い板 <span class="arithmatex">\(i\)</span> に近づけると、容量は必ず小さくなります</strong>。</p>
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<p>これは、長い板 <span class="arithmatex">\(j\)</span> を動かした後は幅 <span class="arithmatex">\(j-i\)</span> が必ず小さくなるためです。また、高さは短い板で決まるので、高さは変わらない（ <span class="arithmatex">\(i\)</span> が依然として短い板）か、小さくなる（移動後の <span class="arithmatex">\(j\)</span> が短い板になる）ことしかありません。</p>
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<p><img alt="長い板を内側へ動かした後の状態" class="animation-figure" src="../max_capacity_problem.assets/max_capacity_moving_long_board.png" /></p>
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<p align="center"> 図 15-9 長い板を内側へ動かした後の状態 </p>
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<p>逆に、<strong>短い仕切り <span class="arithmatex">\(i\)</span> を内側に移動することによってのみ容量を増加させることが可能です</strong>。幅は確実に減少しますが、<strong>高さが増加する可能性があります</strong>（移動した短い仕切り <span class="arithmatex">\(i\)</span> が高くなる場合）。例えば、下の図では、短い仕切りを移動した後に面積が増加しています。</p>
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<p><img alt="短い仕切りを内側に移動した後の状態" class="animation-figure" src="../max_capacity_problem.assets/max_capacity_moving_short_board.png" /></p>
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<p align="center"> 図 15-10 短い仕切りを内側に移動した後の状態 </p>
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<p>逆に考えると、<strong>短い板 <span class="arithmatex">\(i\)</span> を内側へ縮めた場合にのみ、容量が大きくなる可能性があります</strong>。幅は必ず小さくなりますが、**高さは大きくなる可能性がある**からです（移動後の短い板 <span class="arithmatex">\(i\)</span> がより長くなる可能性があります）。たとえば次の図では、短い板を動かした後に面積が大きくなっています。</p>
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<p><img alt="短い板を内側へ動かした後の状態" class="animation-figure" src="../max_capacity_problem.assets/max_capacity_moving_short_board.png" /></p>
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<p align="center"> 図 15-10 短い板を内側へ動かした後の状態 </p>
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<p>これにより、この問題の貪欲戦略が導かれます：コンテナの両端に2つのポインタを初期化し、各ラウンドで短い仕切りに対応するポインタを内側に移動し、2つのポインタが出会うまで続けます。</p>
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<p>下の図は貪欲戦略の実行を示しています。</p>
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<p>以上から、本問の貪欲戦略を導けます。2 本のポインタを初期化して容器の両端に置き、各ラウンドで短い板に対応するポインタを内側へ縮め、2 本のポインタが出会うまで続けます。</p>
|
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<p>以下の図は、貪欲戦略の実行過程を示しています。</p>
|
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<ol>
|
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<li>最初に、ポインタ <span class="arithmatex">\(i\)</span> と <span class="arithmatex">\(j\)</span> が配列の両端に配置されます。</li>
|
||||
<li>初期状態では、ポインタ <span class="arithmatex">\(i\)</span> と <span class="arithmatex">\(j\)</span> は配列の両端にあります。</li>
|
||||
<li>現在の状態の容量 <span class="arithmatex">\(cap[i, j]\)</span> を計算し、最大容量を更新します。</li>
|
||||
<li>仕切り <span class="arithmatex">\(i\)</span> と <span class="arithmatex">\(j\)</span> の高さを比較し、短い仕切りを1ステップ内側に移動します。</li>
|
||||
<li><span class="arithmatex">\(i\)</span> と <span class="arithmatex">\(j\)</span> が出会うまでステップ <code>2.</code> と <code>3.</code> を繰り返します。</li>
|
||||
<li>板 <span class="arithmatex">\(i\)</span> と板 <span class="arithmatex">\(j\)</span> の高さを比較し、短い板を内側へ 1 マス移動します。</li>
|
||||
<li><code>2.</code> と <code>3.</code> を繰り返し実行し、<span class="arithmatex">\(i\)</span> と <span class="arithmatex">\(j\)</span> が出会ったら終了します。</li>
|
||||
</ol>
|
||||
<div class="tabbed-set tabbed-alternate" data-tabs="1:9"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1"><1></label><label for="__tabbed_1_2"><2></label><label for="__tabbed_1_3"><3></label><label for="__tabbed_1_4"><4></label><label for="__tabbed_1_5"><5></label><label for="__tabbed_1_6"><6></label><label for="__tabbed_1_7"><7></label><label for="__tabbed_1_8"><8></label><label for="__tabbed_1_9"><9></label></div>
|
||||
<div class="tabbed-content">
|
||||
<div class="tabbed-block">
|
||||
<p><img alt="最大容量問題の貪欲プロセス" class="animation-figure" src="../max_capacity_problem.assets/max_capacity_greedy_step1.png" /></p>
|
||||
<p><img alt="最大容量問題の貪欲な過程" class="animation-figure" src="../max_capacity_problem.assets/max_capacity_greedy_step1.png" /></p>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<p><img alt="max_capacity_greedy_step2" class="animation-figure" src="../max_capacity_problem.assets/max_capacity_greedy_step2.png" /></p>
|
||||
@@ -4445,26 +4445,26 @@ cap[i, j] = \min(ht[i], ht[j]) \times (j - i)
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<p align="center"> 図 15-11 最大容量問題の貪欲プロセス </p>
|
||||
<p align="center"> 図 15-11 最大容量問題の貪欲な過程 </p>
|
||||
|
||||
<h3 id="2">2. 実装<a class="headerlink" href="#2" title="Permanent link">¶</a></h3>
|
||||
<p>コードは最大 <span class="arithmatex">\(n\)</span> 回ループするため、<strong>時間計算量は <span class="arithmatex">\(O(n)\)</span></strong> です。</p>
|
||||
<p>変数 <span class="arithmatex">\(i\)</span>、<span class="arithmatex">\(j\)</span>、<span class="arithmatex">\(res\)</span> は一定量の追加スペースを使用するため、<strong>空間計算量は <span class="arithmatex">\(O(1)\)</span></strong> です。</p>
|
||||
<h3 id="2">2. コード実装<a class="headerlink" href="#2" title="Permanent link">¶</a></h3>
|
||||
<p>コードのループ回数は最大でも <span class="arithmatex">\(n\)</span> 回であるため、<strong>時間計算量は <span class="arithmatex">\(O(n)\)</span></strong> です。</p>
|
||||
<p>変数 <span class="arithmatex">\(i\)</span>、<span class="arithmatex">\(j\)</span>、<span class="arithmatex">\(res\)</span> が使う追加領域は定数サイズなので、<strong>空間計算量は <span class="arithmatex">\(O(1)\)</span></strong> です。</p>
|
||||
<div class="tabbed-set tabbed-alternate" data-tabs="2:13"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Ruby</label></div>
|
||||
<div class="tabbed-content">
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">max_capacity.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">max_capacity</span><span class="p">(</span><span class="n">ht</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">])</span> <span class="o">-></span> <span class="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">"""最大容量：貪欲法"""</span>
|
||||
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a> <span class="c1"># i、j を初期化、配列の両端で分割させる</span>
|
||||
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a> <span class="c1"># i, j を初期化し、それぞれ配列の両端に置く</span>
|
||||
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a> <span class="n">i</span><span class="p">,</span> <span class="n">j</span> <span class="o">=</span> <span class="mi">0</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">ht</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span>
|
||||
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a> <span class="c1"># 初期最大容量は 0</span>
|
||||
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a> <span class="c1"># 初期の最大容量は 0</span>
|
||||
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a> <span class="n">res</span> <span class="o">=</span> <span class="mi">0</span>
|
||||
<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a> <span class="c1"># 2 つの板が出会うまで貪欲選択をループ</span>
|
||||
<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a> <span class="c1"># 2 枚の板が出会うまで貪欲選択を繰り返す</span>
|
||||
<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a> <span class="k">while</span> <span class="n">i</span> <span class="o"><</span> <span class="n">j</span><span class="p">:</span>
|
||||
<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a> <span class="c1"># 最大容量を更新</span>
|
||||
<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a> <span class="c1"># 最大容量を更新する</span>
|
||||
<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a> <span class="n">cap</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="n">ht</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">ht</span><span class="p">[</span><span class="n">j</span><span class="p">])</span> <span class="o">*</span> <span class="p">(</span><span class="n">j</span> <span class="o">-</span> <span class="n">i</span><span class="p">)</span>
|
||||
<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a> <span class="n">res</span> <span class="o">=</span> <span class="nb">max</span><span class="p">(</span><span class="n">res</span><span class="p">,</span> <span class="n">cap</span><span class="p">)</span>
|
||||
<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a> <span class="c1"># 短い板を内側に移動</span>
|
||||
<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a> <span class="c1"># 短い方を内側へ動かす</span>
|
||||
<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a> <span class="k">if</span> <span class="n">ht</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o"><</span> <span class="n">ht</span><span class="p">[</span><span class="n">j</span><span class="p">]:</span>
|
||||
<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a> <span class="n">i</span> <span class="o">+=</span> <span class="mi">1</span>
|
||||
<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a> <span class="k">else</span><span class="p">:</span>
|
||||
@@ -4475,16 +4475,16 @@ cap[i, j] = \min(ht[i], ht[j]) \times (j - i)
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">max_capacity.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 最大容量：貪欲法 */</span>
|
||||
<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">maxCapacity</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">ht</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">// i、j を初期化し、配列の両端で分割させる</span>
|
||||
<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w"> </span><span class="c1">// i, j を初期化し、それぞれ配列の両端に置く</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">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ht</span><span class="p">.</span><span class="n">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-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w"> </span><span class="c1">// 初期最大容量は 0</span>
|
||||
<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w"> </span><span class="c1">// 初期の最大容量は 0</span>
|
||||
<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||||
<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w"> </span><span class="c1">// 2つの板が出会うまで貪欲選択をループ</span>
|
||||
<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w"> </span><span class="c1">// 2 枚の板が出会うまで貪欲選択を繰り返す</span>
|
||||
<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w"> </span><span class="k">while</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="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w"> </span><span class="c1">// 最大容量を更新</span>
|
||||
<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w"> </span><span class="c1">// 最大容量を更新する</span>
|
||||
<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">cap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">min</span><span class="p">(</span><span class="n">ht</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">ht</span><span class="p">[</span><span class="n">j</span><span class="p">])</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
|
||||
<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max</span><span class="p">(</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">cap</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">// より短い板を内側に移動</span>
|
||||
<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w"> </span><span class="c1">// 短い方を内側へ動かす</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">ht</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">ht</span><span class="p">[</span><span class="n">j</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">i</span><span class="o">++</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="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||||
@@ -4498,16 +4498,16 @@ cap[i, j] = \min(ht[i], ht[j]) \times (j - i)
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">max_capacity.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 最大容量：貪欲法 */</span>
|
||||
<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">maxCapacity</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">ht</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">// i、j を初期化し、配列の両端で分割させる</span>
|
||||
<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w"> </span><span class="c1">// i, j を初期化し、それぞれ配列の両端に置く</span>
|
||||
<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ht</span><span class="p">.</span><span class="na">length</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">// 初期最大容量は 0</span>
|
||||
<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w"> </span><span class="c1">// 初期の最大容量は 0</span>
|
||||
<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||||
<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w"> </span><span class="c1">// 2つの板が出会うまで貪欲選択をループ</span>
|
||||
<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w"> </span><span class="c1">// 2 枚の板が出会うまで貪欲選択を繰り返す</span>
|
||||
<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w"> </span><span class="k">while</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="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w"> </span><span class="c1">// 最大容量を更新</span>
|
||||
<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w"> </span><span class="c1">// 最大容量を更新する</span>
|
||||
<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">cap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="na">min</span><span class="p">(</span><span class="n">ht</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">ht</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
|
||||
<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="na">max</span><span class="p">(</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">cap</span><span class="p">);</span>
|
||||
<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w"> </span><span class="c1">// より短い板を内側に移動</span>
|
||||
<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w"> </span><span class="c1">// 短い方を内側へ動かす</span>
|
||||
<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">ht</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">ht</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w"> </span><span class="n">i</span><span class="o">++</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><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||||
@@ -4519,58 +4519,260 @@ cap[i, j] = \min(ht[i], ht[j]) \times (j - i)
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">max_capacity.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">max_capacity</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">MaxCapacity</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">max_capacity.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 最大容量：貪欲法 */</span>
|
||||
<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">MaxCapacity</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">ht</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w"> </span><span class="c1">// i, j を初期化し、それぞれ配列の両端に置く</span>
|
||||
<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ht</span><span class="p">.</span><span class="n">Length</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-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w"> </span><span class="c1">// 初期の最大容量は 0</span>
|
||||
<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||||
<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w"> </span><span class="c1">// 2 枚の板が出会うまで貪欲選択を繰り返す</span>
|
||||
<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w"> </span><span class="k">while</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="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w"> </span><span class="c1">// 最大容量を更新する</span>
|
||||
<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">cap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="n">Min</span><span class="p">(</span><span class="n">ht</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">ht</span><span class="p">[</span><span class="n">j</span><span class="p">])</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
|
||||
<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="n">Max</span><span class="p">(</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">cap</span><span class="p">);</span>
|
||||
<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="w"> </span><span class="c1">// 短い方を内側へ動かす</span>
|
||||
<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">ht</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">ht</span><span class="p">[</span><span class="n">j</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">;</span>
|
||||
<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="w"> </span><span class="n">j</span><span class="o">--</span><span class="p">;</span>
|
||||
<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-3-19" name="__codelineno-3-19" href="#__codelineno-3-19"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
|
||||
<a id="__codelineno-3-20" name="__codelineno-3-20" href="#__codelineno-3-20"></a><span class="p">}</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">max_capacity.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">maxCapacity</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">max_capacity.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* 最大容量：貪欲法 */</span>
|
||||
<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">maxCapacity</span><span class="p">(</span><span class="nx">ht</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="w"> </span><span class="c1">// i, j を初期化し、それぞれ配列の両端に置く</span>
|
||||
<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w"> </span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">ht</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span>
|
||||
<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w"> </span><span class="c1">// 初期の最大容量は 0</span>
|
||||
<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span>
|
||||
<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w"> </span><span class="c1">// 2 枚の板が出会うまで貪欲選択を繰り返す</span>
|
||||
<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p"><</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w"> </span><span class="c1">// 最大容量を更新する</span>
|
||||
<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="w"> </span><span class="nx">capacity</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">int</span><span class="p">(</span><span class="nx">math</span><span class="p">.</span><span class="nx">Min</span><span class="p">(</span><span class="nb">float64</span><span class="p">(</span><span class="nx">ht</span><span class="p">[</span><span class="nx">i</span><span class="p">]),</span><span class="w"> </span><span class="nb">float64</span><span class="p">(</span><span class="nx">ht</span><span class="p">[</span><span class="nx">j</span><span class="p">])))</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="nx">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">i</span><span class="p">)</span>
|
||||
<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">int</span><span class="p">(</span><span class="nx">math</span><span class="p">.</span><span class="nx">Max</span><span class="p">(</span><span class="nb">float64</span><span class="p">(</span><span class="nx">res</span><span class="p">),</span><span class="w"> </span><span class="nb">float64</span><span class="p">(</span><span class="nx">capacity</span><span class="p">)))</span>
|
||||
<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="w"> </span><span class="c1">// 短い方を内側へ動かす</span>
|
||||
<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">ht</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p"><</span><span class="w"> </span><span class="nx">ht</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="w"> </span><span class="nx">i</span><span class="o">++</span>
|
||||
<a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-4-16" name="__codelineno-4-16" href="#__codelineno-4-16"></a><span class="w"> </span><span class="nx">j</span><span class="o">--</span>
|
||||
<a id="__codelineno-4-17" name="__codelineno-4-17" href="#__codelineno-4-17"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-4-18" name="__codelineno-4-18" href="#__codelineno-4-18"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-4-19" name="__codelineno-4-19" href="#__codelineno-4-19"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span>
|
||||
<a id="__codelineno-4-20" name="__codelineno-4-20" href="#__codelineno-4-20"></a><span class="p">}</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">max_capacity.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">maxCapacity</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">max_capacity.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* 最大容量：貪欲法 */</span>
|
||||
<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">maxCapacity</span><span class="p">(</span><span class="n">ht</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">])</span><span class="w"> </span><span class="p">-></span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="w"> </span><span class="c1">// i, j を初期化し、それぞれ配列の両端に置く</span>
|
||||
<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">i</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">ht</span><span class="p">.</span><span class="n">startIndex</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">ht</span><span class="p">.</span><span class="n">endIndex</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span>
|
||||
<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="w"> </span><span class="c1">// 初期の最大容量は 0</span>
|
||||
<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">res</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
|
||||
<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="w"> </span><span class="c1">// 2 枚の板が出会うまで貪欲選択を繰り返す</span>
|
||||
<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="w"> </span><span class="c1">// 最大容量を更新する</span>
|
||||
<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nv">cap</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="bp">min</span><span class="p">(</span><span class="n">ht</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">ht</span><span class="p">[</span><span class="n">j</span><span class="p">])</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">)</span>
|
||||
<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="bp">max</span><span class="p">(</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">cap</span><span class="p">)</span>
|
||||
<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="w"> </span><span class="c1">// 短い方を内側へ動かす</span>
|
||||
<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">ht</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">ht</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
|
||||
<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mi">1</span>
|
||||
<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-5-19" name="__codelineno-5-19" href="#__codelineno-5-19"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
|
||||
<a id="__codelineno-5-20" name="__codelineno-5-20" href="#__codelineno-5-20"></a><span class="p">}</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">max_capacity.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">maxCapacity</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">max_capacity.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* 最大容量：貪欲法 */</span>
|
||||
<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">maxCapacity</span><span class="p">(</span><span class="nx">ht</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="w"> </span><span class="c1">// i, j を初期化し、それぞれ配列の両端に置く</span>
|
||||
<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">,</span>
|
||||
<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">ht</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
|
||||
<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w"> </span><span class="c1">// 初期の最大容量は 0</span>
|
||||
<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
|
||||
<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="w"> </span><span class="c1">// 2 枚の板が出会うまで貪欲選択を繰り返す</span>
|
||||
<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a><span class="w"> </span><span class="c1">// 最大容量を更新する</span>
|
||||
<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">cap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">min</span><span class="p">(</span><span class="nx">ht</span><span class="p">[</span><span class="nx">i</span><span class="p">],</span><span class="w"> </span><span class="nx">ht</span><span class="p">[</span><span class="nx">j</span><span class="p">])</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="nx">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">i</span><span class="p">);</span>
|
||||
<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">max</span><span class="p">(</span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nx">cap</span><span class="p">);</span>
|
||||
<a id="__codelineno-6-13" name="__codelineno-6-13" href="#__codelineno-6-13"></a><span class="w"> </span><span class="c1">// 短い方を内側へ動かす</span>
|
||||
<a id="__codelineno-6-14" name="__codelineno-6-14" href="#__codelineno-6-14"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">ht</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">ht</span><span class="p">[</span><span class="nx">j</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-6-15" name="__codelineno-6-15" href="#__codelineno-6-15"></a><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
|
||||
<a id="__codelineno-6-16" name="__codelineno-6-16" href="#__codelineno-6-16"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-6-17" name="__codelineno-6-17" href="#__codelineno-6-17"></a><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
|
||||
<a id="__codelineno-6-18" name="__codelineno-6-18" href="#__codelineno-6-18"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-6-19" name="__codelineno-6-19" href="#__codelineno-6-19"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-6-20" name="__codelineno-6-20" href="#__codelineno-6-20"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
|
||||
<a id="__codelineno-6-21" name="__codelineno-6-21" href="#__codelineno-6-21"></a><span class="p">}</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">max_capacity.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">maxCapacity</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">max_capacity.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* 最大容量：貪欲法 */</span>
|
||||
<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">maxCapacity</span><span class="p">(</span><span class="nx">ht</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[])</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="w"> </span><span class="c1">// i, j を初期化し、それぞれ配列の両端に置く</span>
|
||||
<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">,</span>
|
||||
<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">ht</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
|
||||
<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w"> </span><span class="c1">// 初期の最大容量は 0</span>
|
||||
<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
|
||||
<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="w"> </span><span class="c1">// 2 枚の板が出会うまで貪欲選択を繰り返す</span>
|
||||
<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="w"> </span><span class="c1">// 最大容量を更新する</span>
|
||||
<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">cap</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">min</span><span class="p">(</span><span class="nx">ht</span><span class="p">[</span><span class="nx">i</span><span class="p">],</span><span class="w"> </span><span class="nx">ht</span><span class="p">[</span><span class="nx">j</span><span class="p">])</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="nx">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">i</span><span class="p">);</span>
|
||||
<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">max</span><span class="p">(</span><span class="nx">res</span><span class="p">,</span><span class="w"> </span><span class="nx">cap</span><span class="p">);</span>
|
||||
<a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="w"> </span><span class="c1">// 短い方を内側へ動かす</span>
|
||||
<a id="__codelineno-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">ht</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">ht</span><span class="p">[</span><span class="nx">j</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-7-15" name="__codelineno-7-15" href="#__codelineno-7-15"></a><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
|
||||
<a id="__codelineno-7-16" name="__codelineno-7-16" href="#__codelineno-7-16"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-7-17" name="__codelineno-7-17" href="#__codelineno-7-17"></a><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
|
||||
<a id="__codelineno-7-18" name="__codelineno-7-18" href="#__codelineno-7-18"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-7-19" name="__codelineno-7-19" href="#__codelineno-7-19"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-7-20" name="__codelineno-7-20" href="#__codelineno-7-20"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">res</span><span class="p">;</span>
|
||||
<a id="__codelineno-7-21" name="__codelineno-7-21" href="#__codelineno-7-21"></a><span class="p">}</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">max_capacity.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">maxCapacity</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">max_capacity.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 最大容量：貪欲法 */</span>
|
||||
<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">maxCapacity</span><span class="p">(</span><span class="n">List</span><span class="o"><</span><span class="kt">int</span><span class="o">></span><span class="w"> </span><span class="n">ht</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="w"> </span><span class="c1">// i, j を初期化し、それぞれ配列の両端に置く</span>
|
||||
<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ht</span><span class="p">.</span><span class="n">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
|
||||
<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="w"> </span><span class="c1">// 初期の最大容量は 0</span>
|
||||
<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
|
||||
<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="w"> </span><span class="c1">// 2 枚の板が出会うまで貪欲選択を繰り返す</span>
|
||||
<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="w"> </span><span class="k">while</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="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="w"> </span><span class="c1">// 最大容量を更新する</span>
|
||||
<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">cap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">min</span><span class="p">(</span><span class="n">ht</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">ht</span><span class="p">[</span><span class="n">j</span><span class="p">])</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
|
||||
<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max</span><span class="p">(</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">cap</span><span class="p">);</span>
|
||||
<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a><span class="w"> </span><span class="c1">// 短い方を内側へ動かす</span>
|
||||
<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">ht</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">ht</span><span class="p">[</span><span class="n">j</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">;</span>
|
||||
<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-8-16" name="__codelineno-8-16" href="#__codelineno-8-16"></a><span class="w"> </span><span class="n">j</span><span class="o">--</span><span class="p">;</span>
|
||||
<a id="__codelineno-8-17" name="__codelineno-8-17" href="#__codelineno-8-17"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-8-18" name="__codelineno-8-18" href="#__codelineno-8-18"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-8-19" name="__codelineno-8-19" href="#__codelineno-8-19"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
|
||||
<a id="__codelineno-8-20" name="__codelineno-8-20" href="#__codelineno-8-20"></a><span class="p">}</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">max_capacity.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">max_capacity</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">max_capacity.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* 最大容量：貪欲法 */</span>
|
||||
<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">max_capacity</span><span class="p">(</span><span class="n">ht</span><span class="p">:</span><span class="w"> </span><span class="kp">&</span><span class="p">[</span><span class="kt">i32</span><span class="p">])</span><span class="w"> </span><span class="p">-></span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="w"> </span><span class="c1">// i, j を初期化し、それぞれ配列の両端に置く</span>
|
||||
<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||||
<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ht</span><span class="p">.</span><span class="n">len</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-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w"> </span><span class="c1">// 初期の最大容量は 0</span>
|
||||
<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||||
<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="w"> </span><span class="c1">// 2 枚の板が出会うまで貪欲選択を繰り返す</span>
|
||||
<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="w"> </span><span class="c1">// 最大容量を更新する</span>
|
||||
<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">cap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">std</span><span class="p">::</span><span class="n">cmp</span><span class="p">::</span><span class="n">min</span><span class="p">(</span><span class="n">ht</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">ht</span><span class="p">[</span><span class="n">j</span><span class="p">])</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span><span class="p">;</span>
|
||||
<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">std</span><span class="p">::</span><span class="n">cmp</span><span class="p">::</span><span class="n">max</span><span class="p">(</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">cap</span><span class="p">);</span>
|
||||
<a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="w"> </span><span class="c1">// 短い方を内側へ動かす</span>
|
||||
<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">ht</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">ht</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-9-15" name="__codelineno-9-15" href="#__codelineno-9-15"></a><span class="w"> </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>
|
||||
<a id="__codelineno-9-16" name="__codelineno-9-16" href="#__codelineno-9-16"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-9-17" name="__codelineno-9-17" href="#__codelineno-9-17"></a><span class="w"> </span><span class="n">j</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-9-18" name="__codelineno-9-18" href="#__codelineno-9-18"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-9-19" name="__codelineno-9-19" href="#__codelineno-9-19"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-9-20" name="__codelineno-9-20" href="#__codelineno-9-20"></a><span class="w"> </span><span class="n">res</span>
|
||||
<a id="__codelineno-9-21" name="__codelineno-9-21" href="#__codelineno-9-21"></a><span class="p">}</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">max_capacity.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">maxCapacity</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">max_capacity.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* 最大容量：貪欲法 */</span>
|
||||
<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">maxCapacity</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">ht</span><span class="p">[],</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">htLength</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w"> </span><span class="c1">// i, j を初期化し、それぞれ配列の両端に置く</span>
|
||||
<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||||
<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">htLength</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-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a><span class="w"> </span><span class="c1">// 初期の最大容量は 0</span>
|
||||
<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||||
<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="w"> </span><span class="c1">// 2 枚の板が出会うまで貪欲選択を繰り返す</span>
|
||||
<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="w"> </span><span class="k">while</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="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="w"> </span><span class="c1">// 最大容量を更新する</span>
|
||||
<a id="__codelineno-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">capacity</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">myMin</span><span class="p">(</span><span class="n">ht</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">ht</span><span class="p">[</span><span class="n">j</span><span class="p">])</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
|
||||
<a id="__codelineno-10-12" name="__codelineno-10-12" href="#__codelineno-10-12"></a><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">myMax</span><span class="p">(</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">capacity</span><span class="p">);</span>
|
||||
<a id="__codelineno-10-13" name="__codelineno-10-13" href="#__codelineno-10-13"></a><span class="w"> </span><span class="c1">// 短い方を内側へ動かす</span>
|
||||
<a id="__codelineno-10-14" name="__codelineno-10-14" href="#__codelineno-10-14"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">ht</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">ht</span><span class="p">[</span><span class="n">j</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-10-15" name="__codelineno-10-15" href="#__codelineno-10-15"></a><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">;</span>
|
||||
<a id="__codelineno-10-16" name="__codelineno-10-16" href="#__codelineno-10-16"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-10-17" name="__codelineno-10-17" href="#__codelineno-10-17"></a><span class="w"> </span><span class="n">j</span><span class="o">--</span><span class="p">;</span>
|
||||
<a id="__codelineno-10-18" name="__codelineno-10-18" href="#__codelineno-10-18"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-10-19" name="__codelineno-10-19" href="#__codelineno-10-19"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-10-20" name="__codelineno-10-20" href="#__codelineno-10-20"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
|
||||
<a id="__codelineno-10-21" name="__codelineno-10-21" href="#__codelineno-10-21"></a><span class="p">}</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">max_capacity.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">maxCapacity</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">max_capacity.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* 最大容量：貪欲法 */</span>
|
||||
<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">maxCapacity</span><span class="p">(</span><span class="n">ht</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="w"> </span><span class="c1">// i, j を初期化し、それぞれ配列の両端に置く</span>
|
||||
<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span>
|
||||
<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ht</span><span class="p">.</span><span class="na">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span>
|
||||
<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="w"> </span><span class="c1">// 初期の最大容量は 0</span>
|
||||
<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span>
|
||||
<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="w"> </span><span class="c1">// 2 枚の板が出会うまで貪欲選択を繰り返す</span>
|
||||
<a id="__codelineno-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></a><span class="w"> </span><span class="k">while</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="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a><span class="w"> </span><span class="c1">// 最大容量を更新する</span>
|
||||
<a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">cap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">min</span><span class="p">(</span><span class="n">ht</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">ht</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">)</span>
|
||||
<a id="__codelineno-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></a><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max</span><span class="p">(</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">cap</span><span class="p">)</span>
|
||||
<a id="__codelineno-11-13" name="__codelineno-11-13" href="#__codelineno-11-13"></a><span class="w"> </span><span class="c1">// 短い方を内側へ動かす</span>
|
||||
<a id="__codelineno-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">ht</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">ht</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-11-15" name="__codelineno-11-15" href="#__codelineno-11-15"></a><span class="w"> </span><span class="n">i</span><span class="o">++</span>
|
||||
<a id="__codelineno-11-16" name="__codelineno-11-16" href="#__codelineno-11-16"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-11-17" name="__codelineno-11-17" href="#__codelineno-11-17"></a><span class="w"> </span><span class="n">j</span><span class="o">--</span>
|
||||
<a id="__codelineno-11-18" name="__codelineno-11-18" href="#__codelineno-11-18"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-11-19" name="__codelineno-11-19" href="#__codelineno-11-19"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-11-20" name="__codelineno-11-20" href="#__codelineno-11-20"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span>
|
||||
<a id="__codelineno-11-21" name="__codelineno-11-21" href="#__codelineno-11-21"></a><span class="p">}</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">max_capacity.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">max_capacity</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">max_capacity.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### 最大容量：貪欲法 ###</span>
|
||||
<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">max_capacity</span><span class="p">(</span><span class="n">ht</span><span class="p">)</span>
|
||||
<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w"> </span><span class="c1"># i, j を初期化し、それぞれ配列の両端に置く</span>
|
||||
<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">ht</span><span class="o">.</span><span class="n">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span>
|
||||
<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w"> </span><span class="c1"># 初期の最大容量は 0</span>
|
||||
<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
|
||||
<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a>
|
||||
<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w"> </span><span class="c1"># 2 枚の板が出会うまで貪欲選択を繰り返す</span>
|
||||
<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">j</span>
|
||||
<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w"> </span><span class="c1"># 最大容量を更新する</span>
|
||||
<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="w"> </span><span class="n">cap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="n">ht</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">ht</span><span class="o">[</span><span class="n">j</span><span class="o">]].</span><span class="n">min</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">)</span>
|
||||
<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">cap</span><span class="o">].</span><span class="n">max</span>
|
||||
<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a><span class="w"> </span><span class="c1"># 短い方を内側へ動かす</span>
|
||||
<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">ht</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">ht</span><span class="o">[</span><span class="n">j</span><span class="o">]</span>
|
||||
<a id="__codelineno-12-15" name="__codelineno-12-15" href="#__codelineno-12-15"></a><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
|
||||
<a id="__codelineno-12-16" name="__codelineno-12-16" href="#__codelineno-12-16"></a><span class="w"> </span><span class="k">else</span>
|
||||
<a id="__codelineno-12-17" name="__codelineno-12-17" href="#__codelineno-12-17"></a><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mi">1</span>
|
||||
<a id="__codelineno-12-18" name="__codelineno-12-18" href="#__codelineno-12-18"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-12-19" name="__codelineno-12-19" href="#__codelineno-12-19"></a><span class="w"> </span><span class="k">end</span>
|
||||
<a id="__codelineno-12-20" name="__codelineno-12-20" href="#__codelineno-12-20"></a>
|
||||
<a id="__codelineno-12-21" name="__codelineno-12-21" href="#__codelineno-12-21"></a><span class="w"> </span><span class="n">res</span>
|
||||
<a id="__codelineno-12-22" name="__codelineno-12-22" href="#__codelineno-12-22"></a><span class="k">end</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<details class="pythontutor">
|
||||
<summary>コードの可視化</summary>
|
||||
<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20max_capacity%28ht%3A%20list%5Bint%5D%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E6%9C%80%E5%A4%A7%E5%AE%B9%E9%87%8F%EF%BC%9A%E8%B2%AA%E6%AC%B2%E6%B3%95%22%22%22%0A%20%20%20%20%23%20i%2C%20j%20%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%E3%81%97%E3%80%81%E3%81%9D%E3%82%8C%E3%81%9E%E3%82%8C%E9%85%8D%E5%88%97%E3%81%AE%E4%B8%A1%E7%AB%AF%E3%81%AB%E7%BD%AE%E3%81%8F%0A%20%20%20%20i%2C%20j%20%3D%200%2C%20len%28ht%29%20-%201%0A%20%20%20%20%23%20%E5%88%9D%E6%9C%9F%E3%81%AE%E6%9C%80%E5%A4%A7%E5%AE%B9%E9%87%8F%E3%81%AF%200%0A%20%20%20%20res%20%3D%200%0A%20%20%20%20%23%202%20%E6%9E%9A%E3%81%AE%E6%9D%BF%E3%81%8C%E5%87%BA%E4%BC%9A%E3%81%86%E3%81%BE%E3%81%A7%E8%B2%AA%E6%AC%B2%E9%81%B8%E6%8A%9E%E3%82%92%E7%B9%B0%E3%82%8A%E8%BF%94%E3%81%99%0A%20%20%20%20while%20i%20%3C%20j%3A%0A%20%20%20%20%20%20%20%20%23%20%E6%9C%80%E5%A4%A7%E5%AE%B9%E9%87%8F%E3%82%92%E6%9B%B4%E6%96%B0%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20cap%20%3D%20min%28ht%5Bi%5D%2C%20ht%5Bj%5D%29%20%2A%20%28j%20-%20i%29%0A%20%20%20%20%20%20%20%20res%20%3D%20max%28res%2C%20cap%29%0A%20%20%20%20%20%20%20%20%23%20%E7%9F%AD%E3%81%84%E6%96%B9%E3%82%92%E5%86%85%E5%81%B4%E3%81%B8%E5%8B%95%E3%81%8B%E3%81%99%0A%20%20%20%20%20%20%20%20if%20ht%5Bi%5D%20%3C%20ht%5Bj%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20i%20%2B%3D%201%0A%20%20%20%20%20%20%20%20else%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20j%20-%3D%201%0A%20%20%20%20return%20res%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20ht%20%3D%20%5B3%2C%208%2C%205%2C%202%2C%207%2C%207%2C%203%2C%204%5D%0A%0A%20%20%20%20%23%20%E8%B2%AA%E6%AC%B2%E6%B3%95%0A%20%20%20%20res%20%3D%20max_capacity%28ht%29%0A%20%20%20%20print%28f%22%E6%9C%80%E5%A4%A7%E5%AE%B9%E9%87%8F%E3%81%AF%20%7Bres%7D%22%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=4&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
|
||||
<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20max_capacity%28ht%3A%20list%5Bint%5D%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E6%9C%80%E5%A4%A7%E5%AE%B9%E9%87%8F%EF%BC%9A%E8%B2%AA%E6%AC%B2%E6%B3%95%22%22%22%0A%20%20%20%20%23%20i%2C%20j%20%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%E3%81%97%E3%80%81%E3%81%9D%E3%82%8C%E3%81%9E%E3%82%8C%E9%85%8D%E5%88%97%E3%81%AE%E4%B8%A1%E7%AB%AF%E3%81%AB%E7%BD%AE%E3%81%8F%0A%20%20%20%20i%2C%20j%20%3D%200%2C%20len%28ht%29%20-%201%0A%20%20%20%20%23%20%E5%88%9D%E6%9C%9F%E3%81%AE%E6%9C%80%E5%A4%A7%E5%AE%B9%E9%87%8F%E3%81%AF%200%0A%20%20%20%20res%20%3D%200%0A%20%20%20%20%23%202%20%E6%9E%9A%E3%81%AE%E6%9D%BF%E3%81%8C%E5%87%BA%E4%BC%9A%E3%81%86%E3%81%BE%E3%81%A7%E8%B2%AA%E6%AC%B2%E9%81%B8%E6%8A%9E%E3%82%92%E7%B9%B0%E3%82%8A%E8%BF%94%E3%81%99%0A%20%20%20%20while%20i%20%3C%20j%3A%0A%20%20%20%20%20%20%20%20%23%20%E6%9C%80%E5%A4%A7%E5%AE%B9%E9%87%8F%E3%82%92%E6%9B%B4%E6%96%B0%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20cap%20%3D%20min%28ht%5Bi%5D%2C%20ht%5Bj%5D%29%20%2A%20%28j%20-%20i%29%0A%20%20%20%20%20%20%20%20res%20%3D%20max%28res%2C%20cap%29%0A%20%20%20%20%20%20%20%20%23%20%E7%9F%AD%E3%81%84%E6%96%B9%E3%82%92%E5%86%85%E5%81%B4%E3%81%B8%E5%8B%95%E3%81%8B%E3%81%99%0A%20%20%20%20%20%20%20%20if%20ht%5Bi%5D%20%3C%20ht%5Bj%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20i%20%2B%3D%201%0A%20%20%20%20%20%20%20%20else%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20j%20-%3D%201%0A%20%20%20%20return%20res%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20ht%20%3D%20%5B3%2C%208%2C%205%2C%202%2C%207%2C%207%2C%203%2C%204%5D%0A%0A%20%20%20%20%23%20%E8%B2%AA%E6%AC%B2%E6%B3%95%0A%20%20%20%20res%20%3D%20max_capacity%28ht%29%0A%20%20%20%20print%28f%22%E6%9C%80%E5%A4%A7%E5%AE%B9%E9%87%8F%E3%81%AF%20%7Bres%7D%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=4&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全画面で見る ></a></div></p>
|
||||
</details>
|
||||
<h3 id="3">3. 正しさの証明<a class="headerlink" href="#3" title="Permanent link">¶</a></h3>
|
||||
<p>貪欲法が列挙よりも高速である理由は、各ラウンドの貪欲選択が一部の状態を「スキップ」するからです。</p>
|
||||
<p>例えば、<span class="arithmatex">\(i\)</span> が短い仕切りで <span class="arithmatex">\(j\)</span> が高い仕切りである状態 <span class="arithmatex">\(cap[i, j]\)</span> の下で、短い仕切り <span class="arithmatex">\(i\)</span> を貪欲に1ステップ内側に移動すると、下の図に示す「スキップされた」状態につながります。<strong>これは、これらの状態の容量を後で検証できないことを意味します</strong>。</p>
|
||||
<p>貪欲法が総当たりより速いのは、各ラウンドの貪欲な選択がいくつかの状態を「スキップ」するためです。</p>
|
||||
<p>たとえば状態 <span class="arithmatex">\(cap[i, j]\)</span> において、<span class="arithmatex">\(i\)</span> が短い板、<span class="arithmatex">\(j\)</span> が長い板だとします。貪欲に短い板 <span class="arithmatex">\(i\)</span> を内側へ 1 マス動かすと、次の図に示す状態が「スキップ」されます。<strong>これは、その後それらの状態の容量を検証できないことを意味します</strong>。</p>
|
||||
<div class="arithmatex">\[
|
||||
cap[i, i+1], cap[i, i+2], \dots, cap[i, j-2], cap[i, j-1]
|
||||
\]</div>
|
||||
<p><img alt="短い仕切りの移動によってスキップされる状態" class="animation-figure" src="../max_capacity_problem.assets/max_capacity_skipped_states.png" /></p>
|
||||
<p align="center"> 図 15-12 短い仕切りの移動によってスキップされる状態 </p>
|
||||
<p><img alt="短い板の移動によってスキップされる状態" class="animation-figure" src="../max_capacity_problem.assets/max_capacity_skipped_states.png" /></p>
|
||||
<p align="center"> 図 15-12 短い板の移動によってスキップされる状態 </p>
|
||||
|
||||
<p>観察すると、<strong>これらのスキップされた状態は実際には高い仕切り <span class="arithmatex">\(j\)</span> が内側に移動したすべての状態**です。高い仕切りを内側に移動すると容量が確実に減少することをすでに証明しました。したがって、スキップされた状態は最適解である可能性がなく、**それらをスキップしても最適解を見逃すことはありません</strong>。</p>
|
||||
<p>分析により、短い仕切りを移動する操作は「安全」であり、貪欲戦略が効果的であることが示されます。</p>
|
||||
<p>観察すると、<strong>これらのスキップされた状態は、実際には長い板 <span class="arithmatex">\(j\)</span> を内側へ動かしたすべての状態そのものです</strong>。前述のとおり、長い板を内側へ動かすと容量は必ず小さくなります。つまり、スキップされた状態はいずれも最適解にはなりえず、<strong>それらを飛ばしても最適解を逃すことはありません</strong>。</p>
|
||||
<p>以上の分析から、短い板を動かす操作は「安全」であり、貪欲戦略は有効であると分かります。</p>
|
||||
|
||||
<!-- Source file information -->
|
||||
|
||||
|
||||
Reference in New Issue
Block a user