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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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<title>12.3 二分木構築問題 - Hello アルゴリズム</title>
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<title>12.3 二分木の構築問題 - Hello アルゴリズム</title>
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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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<div class="md-header__topic" data-md-component="header-topic">
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<span class="md-ellipsis">
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12.3 二分木構築問題
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12.3 二分木の構築問題
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</span>
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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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12.3 木の構築問題
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12.3 二分木の構築問題
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<a href="#1" class="md-nav__link">
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<span class="md-ellipsis">
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1. 分割統治問題かどうかの判定
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1. 分割統治問題かどうかを判断する
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</span>
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</a>
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<a href="#2" class="md-nav__link">
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<span class="md-ellipsis">
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2. 部分木の分割方法
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2. 部分木をどのように分割するか
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</span>
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</a>
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<a href="#3" class="md-nav__link">
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<span class="md-ellipsis">
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3. 変数に基づく部分木範囲の記述
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3. 変数を用いて部分木区間を記述する
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</span>
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</a>
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<a href="#4" class="md-nav__link">
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<span class="md-ellipsis">
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4. コード実装
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4. コードの実装
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</span>
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</a>
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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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<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="#1" class="md-nav__link">
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<span class="md-ellipsis">
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1. 分割統治問題かどうかの判定
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1. 分割統治問題かどうかを判断する
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</span>
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</a>
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<a href="#2" class="md-nav__link">
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<span class="md-ellipsis">
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2. 部分木の分割方法
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2. 部分木をどのように分割するか
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</span>
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</a>
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<a href="#3" class="md-nav__link">
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<span class="md-ellipsis">
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3. 変数に基づく部分木範囲の記述
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3. 変数を用いて部分木区間を記述する
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</span>
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</a>
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<a href="#4" class="md-nav__link">
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<span class="md-ellipsis">
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4. コード実装
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4. コードの実装
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</span>
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</a>
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<!-- Page content -->
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<h1 id="123">12.3 二分木構築問題<a class="headerlink" href="#123" title="Permanent link">¶</a></h1>
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<h1 id="123">12.3 二分木の構築問題<a class="headerlink" href="#123" 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>二分木の前順走査 <code>preorder</code> シーケンスと中順走査 <code>inorder</code> シーケンスが与えられた場合、二分木を構築してそのルートノードを返してください。二分木に重複するノード値がないと仮定します（以下の図に示すように）。</p>
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<p>二分木の前順走査 <code>preorder</code> と中順走査 <code>inorder</code> が与えられたとき、これらから二分木を構築し、その根ノードを返してください。二分木には値が重複するノードが存在しないものとします（下図のとおり）。</p>
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</div>
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<p><img alt="二分木構築のサンプルデータ" class="animation-figure" src="../build_binary_tree_problem.assets/build_tree_example.png" /></p>
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<p align="center"> 図 12-5 二分木構築のサンプルデータ </p>
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<p><img alt="二分木を構築する例のデータ" class="animation-figure" src="../build_binary_tree_problem.assets/build_tree_example.png" /></p>
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<p align="center"> 図 12-5 二分木を構築する例のデータ </p>
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<h3 id="1">1. 分割統治問題かどうかの判定<a class="headerlink" href="#1" title="Permanent link">¶</a></h3>
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<p><code>preorder</code> と <code>inorder</code> シーケンスから二分木を構築する元の問題は、典型的な分割統治問題です。</p>
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<h3 id="1">1. 分割統治問題かどうかを判断する<a class="headerlink" href="#1" title="Permanent link">¶</a></h3>
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<p>元の問題は <code>preorder</code> と <code>inorder</code> から二分木を構築することであり、典型的な分割統治問題です。</p>
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<ul>
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<li><strong>問題を分解できる</strong>：分割統治の観点から、元の問題を2つの部分問題（左の部分木の構築と右の部分木の構築）とルートノードの初期化という1つの操作に分割できます。各部分木（部分問題）について、同じアプローチを継続的に適用し、より小さな部分木（部分問題）に分割し、最小の部分問題（空の部分木）に到達するまで続けます。</li>
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<li><strong>部分問題は独立している</strong>：左と右の部分木は重複しません。左の部分木を構築する際、左の部分木に対応する中順走査と前順走査のセグメントのみが必要です。右の部分木にも同じアプローチが適用されます。</li>
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<li><strong>部分問題の解を組み合わせることができる</strong>：左と右の部分木（部分問題の解）を構築したら、それらをルートノードに接続して元の問題の解を取得できます。</li>
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<li><strong>問題は分解できる</strong>：分割統治の観点から見ると、元の問題は 2 つの部分問題、すなわち左部分木の構築と右部分木の構築に分けられ、さらに根ノードを初期化する 1 ステップが加わります。各部分木（部分問題）に対しても、同じ分割方法を再利用してより小さな部分木（部分問題）へと分けていき、最小の部分問題（空部分木）に達した時点で終了します。</li>
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<li><strong>部分問題は独立している</strong>：左部分木と右部分木は互いに独立しており、両者の間に重なりはありません。左部分木を構築するときは、中順走査と前順走査のうち左部分木に対応する部分だけを見れば十分です。右部分木も同様です。</li>
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<li><strong>部分問題の解は統合できる</strong>：左部分木と右部分木（部分問題の解）が得られたら、それらを根ノードに接続することで元の問題の解を得られます。</li>
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</ul>
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<h3 id="2">2. 部分木の分割方法<a class="headerlink" href="#2" title="Permanent link">¶</a></h3>
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<p>上記の分析に基づいて、この問題は分割統治を使用して解決できます。<strong>しかし、前順走査 <code>preorder</code> シーケンスと中順走査 <code>inorder</code> シーケンスを使用して左と右の部分木をどのように分割すればよいでしょうか？</strong></p>
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<p>定義により、<code>preorder</code> と <code>inorder</code> シーケンスの両方を3つの部分に分割できます：</p>
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<h3 id="2">2. 部分木をどのように分割するか<a class="headerlink" href="#2" title="Permanent link">¶</a></h3>
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<p>以上の分析より、この問題は分割統治で解けます。<strong>では、前順走査 <code>preorder</code> と中順走査 <code>inorder</code> を使って左部分木と右部分木をどのように分割すればよいのでしょうか</strong>？</p>
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||||
<p>定義に従うと、<code>preorder</code> と <code>inorder</code> はいずれも 3 つの部分に分けられます。</p>
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<ul>
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||||
<li>前順走査：<code>[ ルート | 左の部分木 | 右の部分木 ]</code>。例えば、図では、木は <code>[ 3 | 9 | 2 1 7 ]</code> に対応します。</li>
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<li>中順走査：<code>[ 左の部分木 | ルート | 右の部分木 ]</code>。例えば、図では、木は <code>[ 9 | 3 | 1 2 7 ]</code> に対応します。</li>
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||||
<li>前順走査：<code>[ 根ノード | 左部分木 | 右部分木 ]</code> ，例えば上図の木は <code>[ 3 | 9 | 2 1 7 ]</code> に対応します。</li>
|
||||
<li>中順走査：<code>[ 左部分木 | 根ノード ｜ 右部分木 ]</code> ，例えば上図の木は <code>[ 9 | 3 | 1 2 7 ]</code> に対応します。</li>
|
||||
</ul>
|
||||
<p>前の図のデータを使用して、次の図に示すステップに従って分割結果を取得できます：</p>
|
||||
<p>上図のデータを例にすると、下図の手順によって分割結果を得られます。</p>
|
||||
<ol>
|
||||
<li>前順走査の最初の要素3がルートノードの値です。</li>
|
||||
<li><code>inorder</code> シーケンス内でルートノード3のインデックスを見つけ、このインデックスを使用して <code>inorder</code> を <code>[ 9 | 3 ｜ 1 2 7 ]</code> に分割します。</li>
|
||||
<li><code>inorder</code> シーケンスの分割に従って、左と右の部分木がそれぞれ1個と3個のノードを含むことが簡単に決定できるため、<code>preorder</code> シーケンスを <code>[ 3 | 9 | 2 1 7 ]</code> に対応して分割できます。</li>
|
||||
<li>前順走査の先頭要素 3 が根ノードの値です。</li>
|
||||
<li>根ノード 3 の <code>inorder</code> におけるインデックスを探すと、そのインデックスを用いて <code>inorder</code> を <code>[ 9 | 3 ｜ 1 2 7 ]</code> に分割できます。</li>
|
||||
<li><code>inorder</code> の分割結果から、左部分木と右部分木のノード数はそれぞれ 1 と 3 であることがわかり、したがって <code>preorder</code> を <code>[ 3 | 9 | 2 1 7 ]</code> に分割できます。</li>
|
||||
</ol>
|
||||
<p><img alt="前順走査と中順走査での部分木の分割" class="animation-figure" src="../build_binary_tree_problem.assets/build_tree_preorder_inorder_division.png" /></p>
|
||||
<p align="center"> 図 12-6 前順走査と中順走査での部分木の分割 </p>
|
||||
<p><img alt="前順走査と中順走査で部分木を分割する" class="animation-figure" src="../build_binary_tree_problem.assets/build_tree_preorder_inorder_division.png" /></p>
|
||||
<p align="center"> 図 12-6 前順走査と中順走査で部分木を分割する </p>
|
||||
|
||||
<h3 id="3">3. 変数に基づく部分木範囲の記述<a class="headerlink" href="#3" title="Permanent link">¶</a></h3>
|
||||
<p>上記の分割方法に基づいて、<strong><code>preorder</code> と <code>inorder</code> シーケンスにおけるルート、左の部分木、右の部分木のインデックス範囲を取得しました</strong>。これらのインデックス範囲を記述するために、いくつかのポインタ変数を使用します。</p>
|
||||
<h3 id="3">3. 変数を用いて部分木区間を記述する<a class="headerlink" href="#3" title="Permanent link">¶</a></h3>
|
||||
<p>以上の分割方法により、**根ノード、左部分木、右部分木が <code>preorder</code> と <code>inorder</code> の中で占めるインデックス区間**が得られました。これらのインデックス区間を表すために、いくつかのポインタ変数を導入します。</p>
|
||||
<ul>
|
||||
<li>現在の木のルートノードの <code>preorder</code> シーケンスでのインデックスを <span class="arithmatex">\(i\)</span> とします。</li>
|
||||
<li>現在の木のルートノードの <code>inorder</code> シーケンスでのインデックスを <span class="arithmatex">\(m\)</span> とします。</li>
|
||||
<li>現在の木の <code>inorder</code> シーケンスでのインデックス範囲を <span class="arithmatex">\([l, r]\)</span> とします。</li>
|
||||
<li>現在の木の根ノードが <code>preorder</code> に現れるインデックスを <span class="arithmatex">\(i\)</span> とします。</li>
|
||||
<li>現在の木の根ノードが <code>inorder</code> に現れるインデックスを <span class="arithmatex">\(m\)</span> とします。</li>
|
||||
<li>現在の木が <code>inorder</code> において占めるインデックス区間を <span class="arithmatex">\([l, r]\)</span> とします。</li>
|
||||
</ul>
|
||||
<p>以下の表に示すように、これらの変数は <code>preorder</code> シーケンスでのルートノードのインデックスと <code>inorder</code> シーケンスでの部分木のインデックス範囲を表します。</p>
|
||||
<p align="center"> 表 12-1 前順走査と中順走査でのルートノードと部分木のインデックス </p>
|
||||
<p>次の表のように、これらの変数を用いれば根ノードの <code>preorder</code> におけるインデックスと、部分木の <code>inorder</code> におけるインデックス区間を表せます。</p>
|
||||
<p align="center"> 表 12-1 根ノードと部分木の前順走査・中順走査におけるインデックス </p>
|
||||
|
||||
<div class="center-table">
|
||||
<table>
|
||||
<thead>
|
||||
<tr>
|
||||
<th></th>
|
||||
<th><code>preorder</code> でのルートノードインデックス</th>
|
||||
<th><code>inorder</code> での部分木インデックス範囲</th>
|
||||
<th>根ノードの <code>preorder</code> におけるインデックス</th>
|
||||
<th>部分木の <code>inorder</code> におけるインデックス区間</th>
|
||||
</tr>
|
||||
</thead>
|
||||
<tbody>
|
||||
@@ -4455,24 +4455,24 @@
|
||||
<td><span class="arithmatex">\([l, r]\)</span></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>左の部分木</td>
|
||||
<td>左部分木</td>
|
||||
<td><span class="arithmatex">\(i + 1\)</span></td>
|
||||
<td><span class="arithmatex">\([l, m-1]\)</span></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>右の部分木</td>
|
||||
<td>右部分木</td>
|
||||
<td><span class="arithmatex">\(i + 1 + (m - l)\)</span></td>
|
||||
<td><span class="arithmatex">\([m+1, r]\)</span></td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table>
|
||||
</div>
|
||||
<p>右の部分木のルートインデックスの <span class="arithmatex">\((m-l)\)</span> は「左の部分木のノード数」を表すことに注意してください。より明確な理解のために、以下の図を参照することが役立つ場合があります。</p>
|
||||
<p><img alt="ルートノードと左右の部分木のインデックス" class="animation-figure" src="../build_binary_tree_problem.assets/build_tree_division_pointers.png" /></p>
|
||||
<p align="center"> 図 12-7 ルートノードと左右の部分木のインデックス </p>
|
||||
<p>右部分木の根ノードのインデックスにある <span class="arithmatex">\((m-l)\)</span> は「左部分木のノード数」を意味します。下図と合わせて理解することを勧めます。</p>
|
||||
<p><img alt="根ノードと左右部分木のインデックス区間の表し方" class="animation-figure" src="../build_binary_tree_problem.assets/build_tree_division_pointers.png" /></p>
|
||||
<p align="center"> 図 12-7 根ノードと左右部分木のインデックス区間の表し方 </p>
|
||||
|
||||
<h3 id="4">4. コード実装<a class="headerlink" href="#4" title="Permanent link">¶</a></h3>
|
||||
<p><span class="arithmatex">\(m\)</span> の問い合わせの効率を向上させるために、ハッシュテーブル <code>hmap</code> を使用して <code>inorder</code> シーケンスの要素からそのインデックスへのマッピングを格納します：</p>
|
||||
<h3 id="4">4. コードの実装<a class="headerlink" href="#4" title="Permanent link">¶</a></h3>
|
||||
<p><span class="arithmatex">\(m\)</span> の検索効率を高めるために、ハッシュテーブル <code>hmap</code> を用いて配列 <code>inorder</code> の要素からインデックスへの対応を保存します。</p>
|
||||
<div class="tabbed-set tabbed-alternate" data-tabs="1:13"><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" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label></div>
|
||||
<div class="tabbed-content">
|
||||
<div class="tabbed-block">
|
||||
@@ -4483,50 +4483,50 @@
|
||||
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a> <span class="n">l</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span>
|
||||
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a> <span class="n">r</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span>
|
||||
<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a><span class="p">)</span> <span class="o">-></span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">:</span>
|
||||
<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a><span class="w"> </span><span class="sd">"""二分木の構築：分割統治"""</span>
|
||||
<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a> <span class="c1"># 部分木の区間が空のとき終了</span>
|
||||
<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a><span class="w"> </span><span class="sd">"""二分木を構築：分割統治"""</span>
|
||||
<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a> <span class="c1"># 部分木区間が空なら終了する</span>
|
||||
<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a> <span class="k">if</span> <span class="n">r</span> <span class="o">-</span> <span class="n">l</span> <span class="o"><</span> <span class="mi">0</span><span class="p">:</span>
|
||||
<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a> <span class="k">return</span> <span class="kc">None</span>
|
||||
<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a> <span class="c1"># ルートノードを初期化</span>
|
||||
<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a> <span class="c1"># ルートノードを初期化する</span>
|
||||
<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a> <span class="n">root</span> <span class="o">=</span> <span class="n">TreeNode</span><span class="p">(</span><span class="n">preorder</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
|
||||
<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a> <span class="c1"># m をクエリして左部分木と右部分木を分割</span>
|
||||
<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a> <span class="c1"># m を求めて左右部分木を分割する</span>
|
||||
<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a> <span class="n">m</span> <span class="o">=</span> <span class="n">inorder_map</span><span class="p">[</span><span class="n">preorder</span><span class="p">[</span><span class="n">i</span><span class="p">]]</span>
|
||||
<a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a> <span class="c1"># 部分問題：左部分木を構築</span>
|
||||
<a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a> <span class="c1"># 部分問題：左部分木を構築する</span>
|
||||
<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a> <span class="n">root</span><span class="o">.</span><span class="n">left</span> <span class="o">=</span> <span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span> <span class="n">inorder_map</span><span class="p">,</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">l</span><span class="p">,</span> <span class="n">m</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a> <span class="c1"># 部分問題：右部分木を構築</span>
|
||||
<a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a> <span class="c1"># 部分問題：右部分木を構築する</span>
|
||||
<a id="__codelineno-0-19" name="__codelineno-0-19" href="#__codelineno-0-19"></a> <span class="n">root</span><span class="o">.</span><span class="n">right</span> <span class="o">=</span> <span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span> <span class="n">inorder_map</span><span class="p">,</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">1</span> <span class="o">+</span> <span class="n">m</span> <span class="o">-</span> <span class="n">l</span><span class="p">,</span> <span class="n">m</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">r</span><span class="p">)</span>
|
||||
<a id="__codelineno-0-20" name="__codelineno-0-20" href="#__codelineno-0-20"></a> <span class="c1"># ルートノードを返す</span>
|
||||
<a id="__codelineno-0-20" name="__codelineno-0-20" href="#__codelineno-0-20"></a> <span class="c1"># 根ノードを返す</span>
|
||||
<a id="__codelineno-0-21" name="__codelineno-0-21" href="#__codelineno-0-21"></a> <span class="k">return</span> <span class="n">root</span>
|
||||
<a id="__codelineno-0-22" name="__codelineno-0-22" href="#__codelineno-0-22"></a>
|
||||
<a id="__codelineno-0-23" name="__codelineno-0-23" href="#__codelineno-0-23"></a><span class="k">def</span><span class="w"> </span><span class="nf">build_tree</span><span class="p">(</span><span class="n">preorder</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">inorder</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="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">:</span>
|
||||
<a id="__codelineno-0-24" name="__codelineno-0-24" href="#__codelineno-0-24"></a><span class="w"> </span><span class="sd">"""二分木を構築"""</span>
|
||||
<a id="__codelineno-0-25" name="__codelineno-0-25" href="#__codelineno-0-25"></a> <span class="c1"># ハッシュテーブルを初期化、中順走査の要素からインデックスへのマッピングを保存</span>
|
||||
<a id="__codelineno-0-25" name="__codelineno-0-25" href="#__codelineno-0-25"></a> <span class="c1"># inorder の要素からインデックスへの対応を格納するハッシュテーブルを初期化する</span>
|
||||
<a id="__codelineno-0-26" name="__codelineno-0-26" href="#__codelineno-0-26"></a> <span class="n">inorder_map</span> <span class="o">=</span> <span class="p">{</span><span class="n">val</span><span class="p">:</span> <span class="n">i</span> <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">val</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">inorder</span><span class="p">)}</span>
|
||||
<a id="__codelineno-0-27" name="__codelineno-0-27" href="#__codelineno-0-27"></a> <span class="n">root</span> <span class="o">=</span> <span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span> <span class="n">inorder_map</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">inorder</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-0-28" name="__codelineno-0-28" href="#__codelineno-0-28"></a> <span class="k">return</span> <span class="n">root</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">build_tree.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 二分木の構築：分割統治 */</span>
|
||||
<div class="highlight"><span class="filename">build_tree.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 二分木を構築：分割統治 */</span>
|
||||
<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="nf">dfs</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">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">unordered_map</span><span class="o"><</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">></span><span class="w"> </span><span class="o">&</span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">r</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">// 部分木の区間が空の場合に終了</span>
|
||||
<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w"> </span><span class="c1">// 部分木区間が空なら終了する</span>
|
||||
<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</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-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nb">NULL</span><span class="p">;</span>
|
||||
<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w"> </span><span class="c1">// ルートノードを初期化</span>
|
||||
<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w"> </span><span class="c1">// ルートノードを初期化する</span>
|
||||
<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="n">preorder</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
|
||||
<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w"> </span><span class="c1">// m を問い合わせて左右の部分木を分割</span>
|
||||
<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w"> </span><span class="c1">// m を求めて左右部分木を分割する</span>
|
||||
<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">[</span><span class="n">preorder</span><span class="p">[</span><span class="n">i</span><span class="p">]];</span>
|
||||
<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w"> </span><span class="c1">// 部分問題：左の部分木を構築</span>
|
||||
<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w"> </span><span class="c1">// 部分問題：左部分木を構築する</span>
|
||||
<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w"> </span><span class="n">root</span><span class="o">-></span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">m</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-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w"> </span><span class="c1">// 部分問題：右の部分木を構築</span>
|
||||
<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w"> </span><span class="c1">// 部分問題：右部分木を構築する</span>
|
||||
<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w"> </span><span class="n">root</span><span class="o">-></span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">r</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="c1">// ルートノードを返す</span>
|
||||
<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w"> </span><span class="c1">// 根ノードを返す</span>
|
||||
<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
|
||||
<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="p">}</span>
|
||||
<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a>
|
||||
<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="cm">/* 二分木の構築 */</span>
|
||||
<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="cm">/* 二分木を構築 */</span>
|
||||
<a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="nf">buildTree</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">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o"><</span><span class="kt">int</span><span class="o">></span><span class="w"> </span><span class="o">&</span><span class="n">inorder</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="w"> </span><span class="c1">// ハッシュテーブルを初期化し、中間順序の要素からインデックスへのマッピングを格納</span>
|
||||
<a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="w"> </span><span class="c1">// inorder の要素からインデックスへの対応を格納するハッシュテーブルを初期化する</span>
|
||||
<a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a><span class="w"> </span><span class="n">unordered_map</span><span class="o"><</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">></span><span class="w"> </span><span class="n">inorderMap</span><span class="p">;</span>
|
||||
<a id="__codelineno-1-22" name="__codelineno-1-22" href="#__codelineno-1-22"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">inorder</span><span class="p">.</span><span class="n">size</span><span class="p">();</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-1-23" name="__codelineno-1-23" href="#__codelineno-1-23"></a><span class="w"> </span><span class="n">inorderMap</span><span class="p">[</span><span class="n">inorder</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">i</span><span class="p">;</span>
|
||||
@@ -4537,26 +4537,26 @@
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">build_tree.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 二分木の構築：分割統治 */</span>
|
||||
<div class="highlight"><span class="filename">build_tree.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 二分木を構築：分割統治 */</span>
|
||||
<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="n">TreeNode</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">Map</span><span class="o"><</span><span class="n">Integer</span><span class="p">,</span><span class="w"> </span><span class="n">Integer</span><span class="o">></span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">r</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">// 部分木の区間が空の場合に終了</span>
|
||||
<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w"> </span><span class="c1">// 部分木区間が空なら終了する</span>
|
||||
<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</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-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
|
||||
<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w"> </span><span class="c1">// ルートノードを初期化</span>
|
||||
<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w"> </span><span class="c1">// ルートノードを初期化する</span>
|
||||
<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="n">preorder</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">);</span>
|
||||
<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w"> </span><span class="c1">// m を問い合わせて左右の部分木を分割</span>
|
||||
<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w"> </span><span class="c1">// m を求めて左右部分木を分割する</span>
|
||||
<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">preorder</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">);</span>
|
||||
<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w"> </span><span class="c1">// 部分問題：左の部分木を構築</span>
|
||||
<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w"> </span><span class="c1">// 部分問題：左部分木を構築する</span>
|
||||
<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w"> </span><span class="n">root</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">m</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-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w"> </span><span class="c1">// 部分問題：右の部分木を構築</span>
|
||||
<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w"> </span><span class="c1">// 部分問題：右部分木を構築する</span>
|
||||
<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w"> </span><span class="n">root</span><span class="p">.</span><span class="na">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">r</span><span class="p">);</span>
|
||||
<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w"> </span><span class="c1">// ルートノードを返す</span>
|
||||
<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w"> </span><span class="c1">// 根ノードを返す</span>
|
||||
<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
|
||||
<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="p">}</span>
|
||||
<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a>
|
||||
<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="cm">/* 二分木の構築 */</span>
|
||||
<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="cm">/* 二分木を構築 */</span>
|
||||
<a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="n">TreeNode</span><span class="w"> </span><span class="nf">buildTree</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">inorder</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a><span class="w"> </span><span class="c1">// ハッシュテーブルを初期化し、中間順序の要素からインデックスへのマッピングを格納</span>
|
||||
<a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a><span class="w"> </span><span class="c1">// inorder の要素からインデックスへの対応を格納するハッシュテーブルを初期化する</span>
|
||||
<a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a><span class="w"> </span><span class="n">Map</span><span class="o"><</span><span class="n">Integer</span><span class="p">,</span><span class="w"> </span><span class="n">Integer</span><span class="o">></span><span class="w"> </span><span class="n">inorderMap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">HashMap</span><span class="o"><></span><span class="p">();</span>
|
||||
<a id="__codelineno-2-22" name="__codelineno-2-22" href="#__codelineno-2-22"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">inorder</span><span class="p">.</span><span class="na">length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-2-23" name="__codelineno-2-23" href="#__codelineno-2-23"></a><span class="w"> </span><span class="n">inorderMap</span><span class="p">.</span><span class="na">put</span><span class="p">(</span><span class="n">inorder</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">i</span><span class="p">);</span>
|
||||
@@ -4567,72 +4567,341 @@
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">build_tree.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">build_tree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">DFS</span><span class="p">}</span>
|
||||
<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a>
|
||||
<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">build_tree</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">BuildTree</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">build_tree.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 二分木を構築：分割統治 */</span>
|
||||
<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">DFS</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">Dictionary</span><span class="o"><</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">></span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">r</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">// 部分木区間が空なら終了する</span>
|
||||
<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</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-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">null</span><span class="p">;</span>
|
||||
<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w"> </span><span class="c1">// ルートノードを初期化する</span>
|
||||
<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">(</span><span class="n">preorder</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
|
||||
<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w"> </span><span class="c1">// m を求めて左右部分木を分割する</span>
|
||||
<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">[</span><span class="n">preorder</span><span class="p">[</span><span class="n">i</span><span class="p">]];</span>
|
||||
<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="w"> </span><span class="c1">// 部分問題：左部分木を構築する</span>
|
||||
<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w"> </span><span class="n">root</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">DFS</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">m</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-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="w"> </span><span class="c1">// 部分問題：右部分木を構築する</span>
|
||||
<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="w"> </span><span class="n">root</span><span class="p">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">DFS</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">r</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="c1">// 根ノードを返す</span>
|
||||
<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
|
||||
<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="p">}</span>
|
||||
<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a>
|
||||
<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="cm">/* 二分木を構築 */</span>
|
||||
<a id="__codelineno-3-19" name="__codelineno-3-19" href="#__codelineno-3-19"></a><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">BuildTree</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">inorder</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-3-20" name="__codelineno-3-20" href="#__codelineno-3-20"></a><span class="w"> </span><span class="c1">// inorder の要素からインデックスへの対応を格納するハッシュテーブルを初期化する</span>
|
||||
<a id="__codelineno-3-21" name="__codelineno-3-21" href="#__codelineno-3-21"></a><span class="w"> </span><span class="n">Dictionary</span><span class="o"><</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">></span><span class="w"> </span><span class="n">inorderMap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
|
||||
<a id="__codelineno-3-22" name="__codelineno-3-22" href="#__codelineno-3-22"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">inorder</span><span class="p">.</span><span class="n">Length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-3-23" name="__codelineno-3-23" href="#__codelineno-3-23"></a><span class="w"> </span><span class="n">inorderMap</span><span class="p">.</span><span class="n">TryAdd</span><span class="p">(</span><span class="n">inorder</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
|
||||
<a id="__codelineno-3-24" name="__codelineno-3-24" href="#__codelineno-3-24"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-3-25" name="__codelineno-3-25" href="#__codelineno-3-25"></a><span class="w"> </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">DFS</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">inorder</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-3-26" name="__codelineno-3-26" href="#__codelineno-3-26"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
|
||||
<a id="__codelineno-3-27" name="__codelineno-3-27" href="#__codelineno-3-27"></a><span class="p">}</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">build_tree.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">dfsBuildTree</span><span class="p">}</span>
|
||||
<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a>
|
||||
<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">buildTree</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">build_tree.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* 二分木を構築：分割統治 */</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">dfsBuildTree</span><span class="p">(</span><span class="nx">preorder</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">inorderMap</span><span class="w"> </span><span class="kd">map</span><span class="p">[</span><span class="kt">int</span><span class="p">]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">l</span><span class="p">,</span><span class="w"> </span><span class="nx">r</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="nx">TreeNode</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">// 部分木区間が空なら終了する</span>
|
||||
<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">r</span><span class="o">-</span><span class="nx">l</span><span class="w"> </span><span class="p"><</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="kc">nil</span>
|
||||
<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w"> </span><span class="c1">// ルートノードを初期化する</span>
|
||||
<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w"> </span><span class="nx">root</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">NewTreeNode</span><span class="p">(</span><span class="nx">preorder</span><span class="p">[</span><span class="nx">i</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">// m を求めて左右部分木を分割する</span>
|
||||
<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">inorderMap</span><span class="p">[</span><span class="nx">preorder</span><span class="p">[</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="c1">// 部分問題：左部分木を構築する</span>
|
||||
<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="w"> </span><span class="nx">root</span><span class="p">.</span><span class="nx">Left</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">dfsBuildTree</span><span class="p">(</span><span class="nx">preorder</span><span class="p">,</span><span class="w"> </span><span class="nx">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="o">+</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="nx">l</span><span class="p">,</span><span class="w"> </span><span class="nx">m</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="w"> </span><span class="c1">// 部分問題：右部分木を構築する</span>
|
||||
<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="w"> </span><span class="nx">root</span><span class="p">.</span><span class="nx">Right</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">dfsBuildTree</span><span class="p">(</span><span class="nx">preorder</span><span class="p">,</span><span class="w"> </span><span class="nx">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="o">+</span><span class="mi">1</span><span class="o">+</span><span class="nx">m</span><span class="o">-</span><span class="nx">l</span><span class="p">,</span><span class="w"> </span><span class="nx">m</span><span class="o">+</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="nx">r</span><span class="p">)</span>
|
||||
<a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a><span class="w"> </span><span class="c1">// 根ノードを返す</span>
|
||||
<a id="__codelineno-4-16" name="__codelineno-4-16" href="#__codelineno-4-16"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">root</span>
|
||||
<a id="__codelineno-4-17" name="__codelineno-4-17" href="#__codelineno-4-17"></a><span class="p">}</span>
|
||||
<a id="__codelineno-4-18" name="__codelineno-4-18" href="#__codelineno-4-18"></a>
|
||||
<a id="__codelineno-4-19" name="__codelineno-4-19" href="#__codelineno-4-19"></a><span class="cm">/* 二分木を構築 */</span>
|
||||
<a id="__codelineno-4-20" name="__codelineno-4-20" href="#__codelineno-4-20"></a><span class="kd">func</span><span class="w"> </span><span class="nx">buildTree</span><span class="p">(</span><span class="nx">preorder</span><span class="p">,</span><span class="w"> </span><span class="nx">inorder</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="nx">TreeNode</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-4-21" name="__codelineno-4-21" href="#__codelineno-4-21"></a><span class="w"> </span><span class="c1">// inorder の要素からインデックスへの対応を格納するハッシュテーブルを初期化する</span>
|
||||
<a id="__codelineno-4-22" name="__codelineno-4-22" href="#__codelineno-4-22"></a><span class="w"> </span><span class="nx">inorderMap</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">(</span><span class="kd">map</span><span class="p">[</span><span class="kt">int</span><span class="p">]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">inorder</span><span class="p">))</span>
|
||||
<a id="__codelineno-4-23" name="__codelineno-4-23" href="#__codelineno-4-23"></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="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p"><</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">inorder</span><span class="p">);</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-4-24" name="__codelineno-4-24" href="#__codelineno-4-24"></a><span class="w"> </span><span class="nx">inorderMap</span><span class="p">[</span><span class="nx">inorder</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">i</span>
|
||||
<a id="__codelineno-4-25" name="__codelineno-4-25" href="#__codelineno-4-25"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-4-26" name="__codelineno-4-26" href="#__codelineno-4-26"></a>
|
||||
<a id="__codelineno-4-27" name="__codelineno-4-27" href="#__codelineno-4-27"></a><span class="w"> </span><span class="nx">root</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">dfsBuildTree</span><span class="p">(</span><span class="nx">preorder</span><span class="p">,</span><span class="w"> </span><span class="nx">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</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">inorder</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-4-28" name="__codelineno-4-28" href="#__codelineno-4-28"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">root</span>
|
||||
<a id="__codelineno-4-29" name="__codelineno-4-29" href="#__codelineno-4-29"></a><span class="p">}</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">build_tree.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">dfs</span><span class="p">}</span>
|
||||
<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a>
|
||||
<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">buildTree</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">build_tree.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* 二分木を構築：分割統治 */</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">dfs</span><span class="p">(</span><span class="n">preorder</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="n">inorderMap</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="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">,</span><span class="w"> </span><span class="n">l</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">,</span><span class="w"> </span><span class="n">r</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-></span><span class="w"> </span><span class="n">TreeNode</span><span class="p">?</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">// 部分木区間が空なら終了する</span>
|
||||
<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="kc">nil</span>
|
||||
<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="w"> </span><span class="c1">// ルートノードを初期化する</span>
|
||||
<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nv">root</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="n">x</span><span class="p">:</span><span class="w"> </span><span class="n">preorder</span><span class="p">[</span><span class="n">i</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">// m を求めて左右部分木を分割する</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">m</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">[</span><span class="n">preorder</span><span class="p">[</span><span class="n">i</span><span class="p">]]</span><span class="o">!</span>
|
||||
<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a><span class="w"> </span><span class="c1">// 部分問題：左部分木を構築する</span>
|
||||
<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="w"> </span><span class="n">root</span><span class="p">.</span><span class="kr">left</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">:</span><span class="w"> </span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">:</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">l</span><span class="p">:</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">r</span><span class="p">:</span><span class="w"> </span><span class="n">m</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-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="w"> </span><span class="c1">// 部分問題：右部分木を構築する</span>
|
||||
<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a><span class="w"> </span><span class="n">root</span><span class="p">.</span><span class="kr">right</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">:</span><span class="w"> </span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">:</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">l</span><span class="p">:</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">r</span><span class="p">:</span><span class="w"> </span><span class="n">r</span><span class="p">)</span>
|
||||
<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a><span class="w"> </span><span class="c1">// 根ノードを返す</span>
|
||||
<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">root</span>
|
||||
<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a><span class="p">}</span>
|
||||
<a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a>
|
||||
<a id="__codelineno-5-19" name="__codelineno-5-19" href="#__codelineno-5-19"></a><span class="cm">/* 二分木を構築 */</span>
|
||||
<a id="__codelineno-5-20" name="__codelineno-5-20" href="#__codelineno-5-20"></a><span class="kd">func</span><span class="w"> </span><span class="nf">buildTree</span><span class="p">(</span><span class="n">preorder</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="n">inorder</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="n">TreeNode</span><span class="p">?</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-5-21" name="__codelineno-5-21" href="#__codelineno-5-21"></a><span class="w"> </span><span class="c1">// inorder の要素からインデックスへの対応を格納するハッシュテーブルを初期化する</span>
|
||||
<a id="__codelineno-5-22" name="__codelineno-5-22" href="#__codelineno-5-22"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nv">inorderMap</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">inorder</span><span class="p">.</span><span class="n">enumerated</span><span class="p">().</span><span class="bp">reduce</span><span class="p">(</span><span class="n">into</span><span class="p">:</span><span class="w"> </span><span class="p">[:])</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nv">$0</span><span class="p">[</span><span class="nv">$1</span><span class="p">.</span><span class="n">element</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nv">$1</span><span class="p">.</span><span class="n">offset</span><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-5-23" name="__codelineno-5-23" href="#__codelineno-5-23"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">:</span><span class="w"> </span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">:</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="n">inorder</span><span class="p">.</span><span class="n">startIndex</span><span class="p">,</span><span class="w"> </span><span class="n">l</span><span class="p">:</span><span class="w"> </span><span class="n">inorder</span><span class="p">.</span><span class="n">startIndex</span><span class="p">,</span><span class="w"> </span><span class="n">r</span><span class="p">:</span><span class="w"> </span><span class="n">inorder</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><span class="p">)</span>
|
||||
<a id="__codelineno-5-24" name="__codelineno-5-24" href="#__codelineno-5-24"></a><span class="p">}</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">build_tree.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">dfs</span><span class="p">}</span>
|
||||
<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a>
|
||||
<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">buildTree</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">build_tree.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* 二分木を構築：分割統治 */</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">dfs</span><span class="p">(</span><span class="nx">preorder</span><span class="p">,</span><span class="w"> </span><span class="nx">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">l</span><span class="p">,</span><span class="w"> </span><span class="nx">r</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">// 部分木区間が空なら終了する</span>
|
||||
<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">r</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">l</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="kc">null</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="c1">// ルートノードを初期化する</span>
|
||||
<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">TreeNode</span><span class="p">(</span><span class="nx">preorder</span><span class="p">[</span><span class="nx">i</span><span class="p">]);</span>
|
||||
<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="w"> </span><span class="c1">// m を求めて左右部分木を分割する</span>
|
||||
<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">inorderMap</span><span class="p">.</span><span class="nx">get</span><span class="p">(</span><span class="nx">preorder</span><span class="p">[</span><span class="nx">i</span><span class="p">]);</span>
|
||||
<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="w"> </span><span class="c1">// 部分問題：左部分木を構築する</span>
|
||||
<a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a><span class="w"> </span><span class="nx">root</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">preorder</span><span class="p">,</span><span class="w"> </span><span class="nx">inorderMap</span><span class="p">,</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">1</span><span class="p">,</span><span class="w"> </span><span class="nx">l</span><span class="p">,</span><span class="w"> </span><span class="nx">m</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-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a><span class="w"> </span><span class="c1">// 部分問題：右部分木を構築する</span>
|
||||
<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="w"> </span><span class="nx">root</span><span class="p">.</span><span class="nx">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">preorder</span><span class="p">,</span><span class="w"> </span><span class="nx">inorderMap</span><span class="p">,</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">1</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">l</span><span class="p">,</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="nx">r</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">// 根ノードを返す</span>
|
||||
<a id="__codelineno-6-14" name="__codelineno-6-14" href="#__codelineno-6-14"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">root</span><span class="p">;</span>
|
||||
<a id="__codelineno-6-15" name="__codelineno-6-15" href="#__codelineno-6-15"></a><span class="p">}</span>
|
||||
<a id="__codelineno-6-16" name="__codelineno-6-16" href="#__codelineno-6-16"></a>
|
||||
<a id="__codelineno-6-17" name="__codelineno-6-17" href="#__codelineno-6-17"></a><span class="cm">/* 二分木を構築 */</span>
|
||||
<a id="__codelineno-6-18" name="__codelineno-6-18" href="#__codelineno-6-18"></a><span class="kd">function</span><span class="w"> </span><span class="nx">buildTree</span><span class="p">(</span><span class="nx">preorder</span><span class="p">,</span><span class="w"> </span><span class="nx">inorder</span><span class="p">)</span><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="c1">// inorder の要素からインデックスへの対応を格納するハッシュテーブルを初期化する</span>
|
||||
<a id="__codelineno-6-20" name="__codelineno-6-20" href="#__codelineno-6-20"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">inorderMap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Map</span><span class="p">();</span>
|
||||
<a id="__codelineno-6-21" name="__codelineno-6-21" href="#__codelineno-6-21"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</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><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">inorder</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-6-22" name="__codelineno-6-22" href="#__codelineno-6-22"></a><span class="w"> </span><span class="nx">inorderMap</span><span class="p">.</span><span class="nx">set</span><span class="p">(</span><span class="nx">inorder</span><span class="p">[</span><span class="nx">i</span><span class="p">],</span><span class="w"> </span><span class="nx">i</span><span class="p">);</span>
|
||||
<a id="__codelineno-6-23" name="__codelineno-6-23" href="#__codelineno-6-23"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-6-24" name="__codelineno-6-24" href="#__codelineno-6-24"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">preorder</span><span class="p">,</span><span class="w"> </span><span class="nx">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="nx">inorder</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-6-25" name="__codelineno-6-25" href="#__codelineno-6-25"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">root</span><span class="p">;</span>
|
||||
<a id="__codelineno-6-26" name="__codelineno-6-26" href="#__codelineno-6-26"></a><span class="p">}</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">build_tree.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">dfs</span><span class="p">}</span>
|
||||
<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a>
|
||||
<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">buildTree</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">build_tree.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* 二分木を構築：分割統治 */</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">dfs</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="nx">preorder</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[],</span>
|
||||
<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w"> </span><span class="nx">inorderMap</span><span class="o">:</span><span class="w"> </span><span class="kt">Map</span><span class="o"><</span><span class="kt">number</span><span class="p">,</span><span class="w"> </span><span class="kt">number</span><span class="o">></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">i</span><span class="o">:</span><span class="w"> </span><span class="kt">number</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="nx">l</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span>
|
||||
<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="w"> </span><span class="nx">r</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span>
|
||||
<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="nx">TreeNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="w"> </span><span class="c1">// 部分木区間が空なら終了する</span>
|
||||
<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">r</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">l</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
|
||||
<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="w"> </span><span class="c1">// ルートノードを初期化する</span>
|
||||
<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">root</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">TreeNode</span><span class="p">(</span><span class="nx">preorder</span><span class="p">[</span><span class="nx">i</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">// m を求めて左右部分木を分割する</span>
|
||||
<a id="__codelineno-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">inorderMap</span><span class="p">.</span><span class="nx">get</span><span class="p">(</span><span class="nx">preorder</span><span class="p">[</span><span class="nx">i</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="c1">// 部分問題：左部分木を構築する</span>
|
||||
<a id="__codelineno-7-16" name="__codelineno-7-16" href="#__codelineno-7-16"></a><span class="w"> </span><span class="nx">root</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">preorder</span><span class="p">,</span><span class="w"> </span><span class="nx">inorderMap</span><span class="p">,</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">1</span><span class="p">,</span><span class="w"> </span><span class="nx">l</span><span class="p">,</span><span class="w"> </span><span class="nx">m</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-7-17" name="__codelineno-7-17" href="#__codelineno-7-17"></a><span class="w"> </span><span class="c1">// 部分問題：右部分木を構築する</span>
|
||||
<a id="__codelineno-7-18" name="__codelineno-7-18" href="#__codelineno-7-18"></a><span class="w"> </span><span class="nx">root</span><span class="p">.</span><span class="nx">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">preorder</span><span class="p">,</span><span class="w"> </span><span class="nx">inorderMap</span><span class="p">,</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">1</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">l</span><span class="p">,</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="nx">r</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="c1">// 根ノードを返す</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">root</span><span class="p">;</span>
|
||||
<a id="__codelineno-7-21" name="__codelineno-7-21" href="#__codelineno-7-21"></a><span class="p">}</span>
|
||||
<a id="__codelineno-7-22" name="__codelineno-7-22" href="#__codelineno-7-22"></a>
|
||||
<a id="__codelineno-7-23" name="__codelineno-7-23" href="#__codelineno-7-23"></a><span class="cm">/* 二分木を構築 */</span>
|
||||
<a id="__codelineno-7-24" name="__codelineno-7-24" href="#__codelineno-7-24"></a><span class="kd">function</span><span class="w"> </span><span class="nx">buildTree</span><span class="p">(</span><span class="nx">preorder</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[],</span><span class="w"> </span><span class="nx">inorder</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="nx">TreeNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-7-25" name="__codelineno-7-25" href="#__codelineno-7-25"></a><span class="w"> </span><span class="c1">// inorder の要素からインデックスへの対応を格納するハッシュテーブルを初期化する</span>
|
||||
<a id="__codelineno-7-26" name="__codelineno-7-26" href="#__codelineno-7-26"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">inorderMap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Map</span><span class="o"><</span><span class="kt">number</span><span class="p">,</span><span class="w"> </span><span class="kt">number</span><span class="o">></span><span class="p">();</span>
|
||||
<a id="__codelineno-7-27" name="__codelineno-7-27" href="#__codelineno-7-27"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</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><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">inorder</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-7-28" name="__codelineno-7-28" href="#__codelineno-7-28"></a><span class="w"> </span><span class="nx">inorderMap</span><span class="p">.</span><span class="nx">set</span><span class="p">(</span><span class="nx">inorder</span><span class="p">[</span><span class="nx">i</span><span class="p">],</span><span class="w"> </span><span class="nx">i</span><span class="p">);</span>
|
||||
<a id="__codelineno-7-29" name="__codelineno-7-29" href="#__codelineno-7-29"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-7-30" name="__codelineno-7-30" href="#__codelineno-7-30"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">preorder</span><span class="p">,</span><span class="w"> </span><span class="nx">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="nx">inorder</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-7-31" name="__codelineno-7-31" href="#__codelineno-7-31"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">root</span><span class="p">;</span>
|
||||
<a id="__codelineno-7-32" name="__codelineno-7-32" href="#__codelineno-7-32"></a><span class="p">}</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">build_tree.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">dfs</span><span class="p">}</span>
|
||||
<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a>
|
||||
<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">buildTree</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">build_tree.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 二分木を構築：分割統治 */</span>
|
||||
<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">dfs</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="n">List</span><span class="o"><</span><span class="kt">int</span><span class="o">></span><span class="w"> </span><span class="n">preorder</span><span class="p">,</span>
|
||||
<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w"> </span><span class="n">Map</span><span class="o"><</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">></span><span class="w"> </span><span class="n">inorderMap</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="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</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">l</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="kt">int</span><span class="w"> </span><span class="n">r</span><span class="p">,</span>
|
||||
<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><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">// 部分木区間が空なら終了する</span>
|
||||
<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</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="p">{</span>
|
||||
<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="kc">null</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="p">}</span>
|
||||
<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a><span class="w"> </span><span class="c1">// ルートノードを初期化する</span>
|
||||
<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a><span class="w"> </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="n">preorder</span><span class="p">[</span><span class="n">i</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="c1">// m を求めて左右部分木を分割する</span>
|
||||
<a id="__codelineno-8-16" name="__codelineno-8-16" href="#__codelineno-8-16"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">[</span><span class="n">preorder</span><span class="p">[</span><span class="n">i</span><span class="p">]]</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="c1">// 部分問題：左部分木を構築する</span>
|
||||
<a id="__codelineno-8-18" name="__codelineno-8-18" href="#__codelineno-8-18"></a><span class="w"> </span><span class="n">root</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">m</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-8-19" name="__codelineno-8-19" href="#__codelineno-8-19"></a><span class="w"> </span><span class="c1">// 部分問題：右部分木を構築する</span>
|
||||
<a id="__codelineno-8-20" name="__codelineno-8-20" href="#__codelineno-8-20"></a><span class="w"> </span><span class="n">root</span><span class="p">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">r</span><span class="p">);</span>
|
||||
<a id="__codelineno-8-21" name="__codelineno-8-21" href="#__codelineno-8-21"></a><span class="w"> </span><span class="c1">// 根ノードを返す</span>
|
||||
<a id="__codelineno-8-22" name="__codelineno-8-22" href="#__codelineno-8-22"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
|
||||
<a id="__codelineno-8-23" name="__codelineno-8-23" href="#__codelineno-8-23"></a><span class="p">}</span>
|
||||
<a id="__codelineno-8-24" name="__codelineno-8-24" href="#__codelineno-8-24"></a>
|
||||
<a id="__codelineno-8-25" name="__codelineno-8-25" href="#__codelineno-8-25"></a><span class="cm">/* 二分木を構築 */</span>
|
||||
<a id="__codelineno-8-26" name="__codelineno-8-26" href="#__codelineno-8-26"></a><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">buildTree</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">preorder</span><span class="p">,</span><span class="w"> </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">inorder</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-8-27" name="__codelineno-8-27" href="#__codelineno-8-27"></a><span class="w"> </span><span class="c1">// inorder の要素からインデックスへの対応を格納するハッシュテーブルを初期化する</span>
|
||||
<a id="__codelineno-8-28" name="__codelineno-8-28" href="#__codelineno-8-28"></a><span class="w"> </span><span class="n">Map</span><span class="o"><</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">></span><span class="w"> </span><span class="n">inorderMap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{};</span>
|
||||
<a id="__codelineno-8-29" name="__codelineno-8-29" href="#__codelineno-8-29"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">inorder</span><span class="p">.</span><span class="n">length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-8-30" name="__codelineno-8-30" href="#__codelineno-8-30"></a><span class="w"> </span><span class="n">inorderMap</span><span class="p">[</span><span class="n">inorder</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">i</span><span class="p">;</span>
|
||||
<a id="__codelineno-8-31" name="__codelineno-8-31" href="#__codelineno-8-31"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-8-32" name="__codelineno-8-32" href="#__codelineno-8-32"></a><span class="w"> </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="n">inorder</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-8-33" name="__codelineno-8-33" href="#__codelineno-8-33"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
|
||||
<a id="__codelineno-8-34" name="__codelineno-8-34" href="#__codelineno-8-34"></a><span class="p">}</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">build_tree.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">dfs</span><span class="p">}</span>
|
||||
<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a>
|
||||
<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">build_tree</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">build_tree.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* 二分木を構築：分割統治 */</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">dfs</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="n">preorder</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>
|
||||
<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="w"> </span><span class="n">inorder_map</span><span class="p">:</span><span class="w"> </span><span class="kp">&</span><span class="nc">HashMap</span><span class="o"><</span><span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="kt">i32</span><span class="o">></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="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</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="n">l</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">,</span>
|
||||
<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="w"> </span><span class="n">r</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">,</span>
|
||||
<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="p">)</span><span class="w"> </span><span class="p">-></span><span class="w"> </span><span class="nb">Option</span><span class="o"><</span><span class="n">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>>></span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="w"> </span><span class="c1">// 部分木区間が空なら終了する</span>
|
||||
<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nb">None</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="p">}</span>
|
||||
<a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="w"> </span><span class="c1">// ルートノードを初期化する</span>
|
||||
<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">::</span><span class="n">new</span><span class="p">(</span><span class="n">preorder</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</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="c1">// m を求めて左右部分木を分割する</span>
|
||||
<a id="__codelineno-9-16" name="__codelineno-9-16" href="#__codelineno-9-16"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">inorder_map</span><span class="p">.</span><span class="n">get</span><span class="p">(</span><span class="o">&</span><span class="n">preorder</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">]).</span><span class="n">unwrap</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="c1">// 部分問題：左部分木を構築する</span>
|
||||
<a id="__codelineno-9-18" name="__codelineno-9-18" href="#__codelineno-9-18"></a><span class="w"> </span><span class="n">root</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorder_map</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">m</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-9-19" name="__codelineno-9-19" href="#__codelineno-9-19"></a><span class="w"> </span><span class="c1">// 部分問題：右部分木を構築する</span>
|
||||
<a id="__codelineno-9-20" name="__codelineno-9-20" href="#__codelineno-9-20"></a><span class="w"> </span><span class="n">root</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorder_map</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">r</span><span class="p">);</span>
|
||||
<a id="__codelineno-9-21" name="__codelineno-9-21" href="#__codelineno-9-21"></a><span class="w"> </span><span class="c1">// 根ノードを返す</span>
|
||||
<a id="__codelineno-9-22" name="__codelineno-9-22" href="#__codelineno-9-22"></a><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">root</span><span class="p">)</span>
|
||||
<a id="__codelineno-9-23" name="__codelineno-9-23" href="#__codelineno-9-23"></a><span class="p">}</span>
|
||||
<a id="__codelineno-9-24" name="__codelineno-9-24" href="#__codelineno-9-24"></a>
|
||||
<a id="__codelineno-9-25" name="__codelineno-9-25" href="#__codelineno-9-25"></a><span class="cm">/* 二分木を構築 */</span>
|
||||
<a id="__codelineno-9-26" name="__codelineno-9-26" href="#__codelineno-9-26"></a><span class="k">fn</span><span class="w"> </span><span class="nf">build_tree</span><span class="p">(</span><span class="n">preorder</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="n">inorder</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="nb">Option</span><span class="o"><</span><span class="n">Rc</span><span class="o"><</span><span class="n">RefCell</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>>></span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-9-27" name="__codelineno-9-27" href="#__codelineno-9-27"></a><span class="w"> </span><span class="c1">// inorder の要素からインデックスへの対応を格納するハッシュテーブルを初期化する</span>
|
||||
<a id="__codelineno-9-28" name="__codelineno-9-28" href="#__codelineno-9-28"></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">inorder_map</span><span class="p">:</span><span class="w"> </span><span class="nc">HashMap</span><span class="o"><</span><span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="kt">i32</span><span class="o">></span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">HashMap</span><span class="p">::</span><span class="n">new</span><span class="p">();</span>
|
||||
<a id="__codelineno-9-29" name="__codelineno-9-29" href="#__codelineno-9-29"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">inorder</span><span class="p">.</span><span class="n">len</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-9-30" name="__codelineno-9-30" href="#__codelineno-9-30"></a><span class="w"> </span><span class="n">inorder_map</span><span class="p">.</span><span class="n">insert</span><span class="p">(</span><span class="n">inorder</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">i</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-9-31" name="__codelineno-9-31" href="#__codelineno-9-31"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-9-32" name="__codelineno-9-32" href="#__codelineno-9-32"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">inorder_map</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">inorder</span><span class="p">.</span><span class="n">len</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="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
|
||||
<a id="__codelineno-9-33" name="__codelineno-9-33" href="#__codelineno-9-33"></a><span class="w"> </span><span class="n">root</span>
|
||||
<a id="__codelineno-9-34" name="__codelineno-9-34" href="#__codelineno-9-34"></a><span class="p">}</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">build_tree.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">dfs</span><span class="p">}</span>
|
||||
<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a>
|
||||
<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">buildTree</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">build_tree.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* 二分木を構築：分割統治 */</span>
|
||||
<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="nf">dfs</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">r</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w"> </span><span class="c1">// 部分木区間が空なら終了する</span>
|
||||
<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</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="k">return</span><span class="w"> </span><span class="nb">NULL</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">// ルートノードを初期化する</span>
|
||||
<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="n">TreeNode</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="n">root</span><span class="o">-></span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">preorder</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
|
||||
<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="w"> </span><span class="n">root</span><span class="o">-></span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">NULL</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="n">root</span><span class="o">-></span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">;</span>
|
||||
<a id="__codelineno-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a><span class="w"> </span><span class="c1">// m を求めて左右部分木を分割する</span>
|
||||
<a id="__codelineno-10-12" name="__codelineno-10-12" href="#__codelineno-10-12"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">[</span><span class="n">preorder</span><span class="p">[</span><span class="n">i</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">// 部分問題：左部分木を構築する</span>
|
||||
<a id="__codelineno-10-14" name="__codelineno-10-14" href="#__codelineno-10-14"></a><span class="w"> </span><span class="n">root</span><span class="o">-></span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">size</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="c1">// 部分問題：右部分木を構築する</span>
|
||||
<a id="__codelineno-10-16" name="__codelineno-10-16" href="#__codelineno-10-16"></a><span class="w"> </span><span class="n">root</span><span class="o">-></span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">r</span><span class="p">,</span><span class="w"> </span><span class="n">size</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="c1">// 根ノードを返す</span>
|
||||
<a id="__codelineno-10-18" name="__codelineno-10-18" href="#__codelineno-10-18"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
|
||||
<a id="__codelineno-10-19" name="__codelineno-10-19" href="#__codelineno-10-19"></a><span class="p">}</span>
|
||||
<a id="__codelineno-10-20" name="__codelineno-10-20" href="#__codelineno-10-20"></a>
|
||||
<a id="__codelineno-10-21" name="__codelineno-10-21" href="#__codelineno-10-21"></a><span class="cm">/* 二分木を構築 */</span>
|
||||
<a id="__codelineno-10-22" name="__codelineno-10-22" href="#__codelineno-10-22"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="nf">buildTree</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">preorderSize</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">inorder</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">inorderSize</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-10-23" name="__codelineno-10-23" href="#__codelineno-10-23"></a><span class="w"> </span><span class="c1">// inorder の要素からインデックスへの対応を格納するハッシュテーブルを初期化する</span>
|
||||
<a id="__codelineno-10-24" name="__codelineno-10-24" href="#__codelineno-10-24"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">inorderMap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">MAX_SIZE</span><span class="p">);</span>
|
||||
<a id="__codelineno-10-25" name="__codelineno-10-25" href="#__codelineno-10-25"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">inorderSize</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-10-26" name="__codelineno-10-26" href="#__codelineno-10-26"></a><span class="w"> </span><span class="n">inorderMap</span><span class="p">[</span><span class="n">inorder</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">i</span><span class="p">;</span>
|
||||
<a id="__codelineno-10-27" name="__codelineno-10-27" href="#__codelineno-10-27"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-10-28" name="__codelineno-10-28" href="#__codelineno-10-28"></a><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">inorderSize</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">inorderSize</span><span class="p">);</span>
|
||||
<a id="__codelineno-10-29" name="__codelineno-10-29" href="#__codelineno-10-29"></a><span class="w"> </span><span class="n">free</span><span class="p">(</span><span class="n">inorderMap</span><span class="p">);</span>
|
||||
<a id="__codelineno-10-30" name="__codelineno-10-30" href="#__codelineno-10-30"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
|
||||
<a id="__codelineno-10-31" name="__codelineno-10-31" href="#__codelineno-10-31"></a><span class="p">}</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">build_tree.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">dfs</span><span class="p">}</span>
|
||||
<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a>
|
||||
<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">buildTree</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">build_tree.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* 二分木を構築：分割統治 */</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">dfs</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="n">preorder</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span>
|
||||
<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="w"> </span><span class="n">inorderMap</span><span class="p">:</span><span class="w"> </span><span class="n">Map</span><span class="o"><</span><span class="kt">Int?</span><span class="p">,</span><span class="w"> </span><span class="kt">Int?</span><span class="o">></span><span class="p">,</span>
|
||||
<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="w"> </span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">,</span>
|
||||
<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="w"> </span><span class="n">l</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">,</span>
|
||||
<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="w"> </span><span class="n">r</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span>
|
||||
<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="p">):</span><span class="w"> </span><span class="n">TreeNode? </span><span class="p">{</span>
|
||||
<a id="__codelineno-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></a><span class="w"> </span><span class="c1">// 部分木区間が空なら終了する</span>
|
||||
<a id="__codelineno-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</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="k">return</span><span class="w"> </span><span class="kc">null</span>
|
||||
<a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a><span class="w"> </span><span class="c1">// ルートノードを初期化する</span>
|
||||
<a id="__codelineno-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></a><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="n">preorder</span><span class="o">[</span><span class="n">i</span><span class="o">]</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">// m を求めて左右部分木を分割する</span>
|
||||
<a id="__codelineno-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></a><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">inorderMap</span><span class="o">[</span><span class="n">preorder</span><span class="o">[</span><span class="n">i</span><span class="o">]]!!</span>
|
||||
<a id="__codelineno-11-15" name="__codelineno-11-15" href="#__codelineno-11-15"></a><span class="w"> </span><span class="c1">// 部分問題：左部分木を構築する</span>
|
||||
<a id="__codelineno-11-16" name="__codelineno-11-16" href="#__codelineno-11-16"></a><span class="w"> </span><span class="n">root</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">m</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-11-17" name="__codelineno-11-17" href="#__codelineno-11-17"></a><span class="w"> </span><span class="c1">// 部分問題：右部分木を構築する</span>
|
||||
<a id="__codelineno-11-18" name="__codelineno-11-18" href="#__codelineno-11-18"></a><span class="w"> </span><span class="n">root</span><span class="p">.</span><span class="na">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">r</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="c1">// 根ノードを返す</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">root</span>
|
||||
<a id="__codelineno-11-21" name="__codelineno-11-21" href="#__codelineno-11-21"></a><span class="p">}</span>
|
||||
<a id="__codelineno-11-22" name="__codelineno-11-22" href="#__codelineno-11-22"></a>
|
||||
<a id="__codelineno-11-23" name="__codelineno-11-23" href="#__codelineno-11-23"></a><span class="cm">/* 二分木を構築 */</span>
|
||||
<a id="__codelineno-11-24" name="__codelineno-11-24" href="#__codelineno-11-24"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">buildTree</span><span class="p">(</span><span class="n">preorder</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span><span class="w"> </span><span class="n">inorder</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">):</span><span class="w"> </span><span class="n">TreeNode? </span><span class="p">{</span>
|
||||
<a id="__codelineno-11-25" name="__codelineno-11-25" href="#__codelineno-11-25"></a><span class="w"> </span><span class="c1">// inorder の要素からインデックスへの対応を格納するハッシュテーブルを初期化する</span>
|
||||
<a id="__codelineno-11-26" name="__codelineno-11-26" href="#__codelineno-11-26"></a><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">inorderMap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">HashMap</span><span class="o"><</span><span class="kt">Int?</span><span class="p">,</span><span class="w"> </span><span class="kt">Int?</span><span class="o">></span><span class="p">()</span>
|
||||
<a id="__codelineno-11-27" name="__codelineno-11-27" href="#__codelineno-11-27"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">inorder</span><span class="p">.</span><span class="na">indices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-11-28" name="__codelineno-11-28" href="#__codelineno-11-28"></a><span class="w"> </span><span class="n">inorderMap</span><span class="o">[</span><span class="n">inorder</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">i</span>
|
||||
<a id="__codelineno-11-29" name="__codelineno-11-29" href="#__codelineno-11-29"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-11-30" name="__codelineno-11-30" href="#__codelineno-11-30"></a><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="n">inorder</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><span class="p">)</span>
|
||||
<a id="__codelineno-11-31" name="__codelineno-11-31" href="#__codelineno-11-31"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">root</span>
|
||||
<a id="__codelineno-11-32" name="__codelineno-11-32" href="#__codelineno-11-32"></a><span class="p">}</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">build_tree.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">dfs</span><span class="p">}</span>
|
||||
<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a>
|
||||
<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">build_tree</span><span class="p">}</span>
|
||||
<div class="highlight"><span class="filename">build_tree.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### 二分木を構築：分割統治 ###</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">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorder_map</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">r</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"># 部分木区間が空なら終了する</span>
|
||||
<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="mi">0</span>
|
||||
<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a>
|
||||
<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w"> </span><span class="c1"># ルートノードを初期化する</span>
|
||||
<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="no">TreeNode</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">preorder</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">)</span>
|
||||
<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w"> </span><span class="c1"># m を求めて左右部分木を分割する</span>
|
||||
<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">inorder_map</span><span class="o">[</span><span class="n">preorder</span><span class="o">[</span><span class="n">i</span><span class="o">]]</span>
|
||||
<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w"> </span><span class="c1"># 部分問題：左部分木を構築する</span>
|
||||
<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="w"> </span><span class="n">root</span><span class="o">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorder_map</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">m</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-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="w"> </span><span class="c1"># 部分問題：右部分木を構築する</span>
|
||||
<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a><span class="w"> </span><span class="n">root</span><span class="o">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorder_map</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">r</span><span class="p">)</span>
|
||||
<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a>
|
||||
<a id="__codelineno-12-15" name="__codelineno-12-15" href="#__codelineno-12-15"></a><span class="w"> </span><span class="c1"># 根ノードを返す</span>
|
||||
<a id="__codelineno-12-16" name="__codelineno-12-16" href="#__codelineno-12-16"></a><span class="w"> </span><span class="n">root</span>
|
||||
<a id="__codelineno-12-17" name="__codelineno-12-17" href="#__codelineno-12-17"></a><span class="k">end</span>
|
||||
<a id="__codelineno-12-18" name="__codelineno-12-18" href="#__codelineno-12-18"></a>
|
||||
<a id="__codelineno-12-19" name="__codelineno-12-19" href="#__codelineno-12-19"></a><span class="c1">### 二分木を構築 ###</span>
|
||||
<a id="__codelineno-12-20" name="__codelineno-12-20" href="#__codelineno-12-20"></a><span class="k">def</span><span class="w"> </span><span class="nf">build_tree</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorder</span><span class="p">)</span>
|
||||
<a id="__codelineno-12-21" name="__codelineno-12-21" href="#__codelineno-12-21"></a><span class="w"> </span><span class="c1"># inorder の要素からインデックスへの対応を格納するハッシュテーブルを初期化する</span>
|
||||
<a id="__codelineno-12-22" name="__codelineno-12-22" href="#__codelineno-12-22"></a><span class="w"> </span><span class="n">inorder_map</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{}</span>
|
||||
<a id="__codelineno-12-23" name="__codelineno-12-23" href="#__codelineno-12-23"></a><span class="w"> </span><span class="n">inorder</span><span class="o">.</span><span class="n">each_with_index</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="o">|</span><span class="w"> </span><span class="n">inorder_map</span><span class="o">[</span><span class="n">val</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-12-24" name="__codelineno-12-24" href="#__codelineno-12-24"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorder_map</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">inorder</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><span class="p">)</span>
|
||||
<a id="__codelineno-12-25" name="__codelineno-12-25" href="#__codelineno-12-25"></a><span class="k">end</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<p>以下の図は、二分木を構築する再帰過程を示しています。各ノードは再帰の「下降」段階で作成され、各エッジ（参照）は「上昇」段階で形成されます。</p>
|
||||
<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=class%20TreeNode%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E5%88%86%E6%9C%A8%E3%83%8E%E3%83%BC%E3%83%89%E3%82%AF%E3%83%A9%E3%82%B9%22%22%22%0A%20%20%20%20def%20__init__%28self%2C%20val%3A%20int%20%3D%200%29%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%20%20%23%20%E3%83%8E%E3%83%BC%E3%83%89%E5%80%A4%0A%20%20%20%20%20%20%20%20self.left%3A%20TreeNode%20%7C%20None%20%3D%20None%20%20%23%20%E5%B7%A6%E5%AD%90%E3%83%8E%E3%83%BC%E3%83%89%E3%81%B8%E3%81%AE%E5%8F%82%E7%85%A7%0A%20%20%20%20%20%20%20%20self.right%3A%20TreeNode%20%7C%20None%20%3D%20None%20%20%23%20%E5%8F%B3%E5%AD%90%E3%83%8E%E3%83%BC%E3%83%89%E3%81%B8%E3%81%AE%E5%8F%82%E7%85%A7%0A%0Adef%20dfs%28%0A%20%20%20%20preorder%3A%20list%5Bint%5D%2C%0A%20%20%20%20inorder_map%3A%20dict%5Bint%2C%20int%5D%2C%0A%20%20%20%20i%3A%20int%2C%0A%20%20%20%20l%3A%20int%2C%0A%20%20%20%20r%3A%20int%2C%0A%29%20-%3E%20TreeNode%20%7C%20None%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E5%88%86%E6%9C%A8%E3%82%92%E6%A7%8B%E7%AF%89%EF%BC%9A%E5%88%86%E5%89%B2%E7%B5%B1%E6%B2%BB%22%22%22%0A%20%20%20%20%23%20%E9%83%A8%E5%88%86%E6%9C%A8%E5%8C%BA%E9%96%93%E3%81%8C%E7%A9%BA%E3%81%AA%E3%82%89%E7%B5%82%E4%BA%86%E3%81%99%E3%82%8B%0A%20%20%20%20if%20r%20-%20l%20%3C%200%3A%0A%20%20%20%20%20%20%20%20return%20None%0A%20%20%20%20%23%20%E3%83%AB%E3%83%BC%E3%83%88%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%E3%81%99%E3%82%8B%0A%20%20%20%20root%20%3D%20TreeNode%28preorder%5Bi%5D%29%0A%20%20%20%20%23%20m%20%E3%82%92%E6%B1%82%E3%82%81%E3%81%A6%E5%B7%A6%E5%8F%B3%E9%83%A8%E5%88%86%E6%9C%A8%E3%82%92%E5%88%86%E5%89%B2%E3%81%99%E3%82%8B%0A%20%20%20%20m%20%3D%20inorder_map%5Bpreorder%5Bi%5D%5D%0A%20%20%20%20%23%20%E9%83%A8%E5%88%86%E5%95%8F%E9%A1%8C%EF%BC%9A%E5%B7%A6%E9%83%A8%E5%88%86%E6%9C%A8%E3%82%92%E6%A7%8B%E7%AF%89%E3%81%99%E3%82%8B%0A%20%20%20%20root.left%20%3D%20dfs%28preorder%2C%20inorder_map%2C%20i%20%2B%201%2C%20l%2C%20m%20-%201%29%0A%20%20%20%20%23%20%E9%83%A8%E5%88%86%E5%95%8F%E9%A1%8C%EF%BC%9A%E5%8F%B3%E9%83%A8%E5%88%86%E6%9C%A8%E3%82%92%E6%A7%8B%E7%AF%89%E3%81%99%E3%82%8B%0A%20%20%20%20root.right%20%3D%20dfs%28preorder%2C%20inorder_map%2C%20i%20%2B%201%20%2B%20m%20-%20l%2C%20m%20%2B%201%2C%20r%29%0A%20%20%20%20%23%20%E6%A0%B9%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E8%BF%94%E3%81%99%0A%20%20%20%20return%20root%0A%0A%0Adef%20build_tree%28preorder%3A%20list%5Bint%5D%2C%20inorder%3A%20list%5Bint%5D%29%20-%3E%20TreeNode%20%7C%20None%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E5%88%86%E6%9C%A8%E3%82%92%E6%A7%8B%E7%AF%89%22%22%22%0A%20%20%20%20%23%20inorder%20%E3%81%AE%E8%A6%81%E7%B4%A0%E3%81%8B%E3%82%89%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%81%B8%E3%81%AE%E5%AF%BE%E5%BF%9C%E3%82%92%E6%A0%BC%E7%B4%8D%E3%81%99%E3%82%8B%E3%83%8F%E3%83%83%E3%82%B7%E3%83%A5%E3%83%86%E3%83%BC%E3%83%96%E3%83%AB%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%E3%81%99%E3%82%8B%0A%20%20%20%20inorder_map%20%3D%20%7Bval%3A%20i%20for%20i%2C%20val%20in%20enumerate%28inorder%29%7D%0A%20%20%20%20root%20%3D%20dfs%28preorder%2C%20inorder_map%2C%200%2C%200%2C%20len%28inorder%29%20-%201%29%0A%20%20%20%20return%20root%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20preorder%20%3D%20%5B3%2C%209%2C%202%2C%201%2C%207%5D%0A%20%20%20%20inorder%20%3D%20%5B9%2C%203%2C%201%2C%202%2C%207%5D%0A%20%20%20%20print%28f%22%E5%89%8D%E9%A0%86%E8%B5%B0%E6%9F%BB%20%3D%20%7Bpreorder%7D%22%29%0A%20%20%20%20print%28f%22%E4%B8%AD%E9%A0%86%E8%B5%B0%E6%9F%BB%20%3D%20%7Binorder%7D%22%29%0A%20%20%20%20root%20%3D%20build_tree%28preorder%2C%20inorder%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=21&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=class%20TreeNode%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E5%88%86%E6%9C%A8%E3%83%8E%E3%83%BC%E3%83%89%E3%82%AF%E3%83%A9%E3%82%B9%22%22%22%0A%20%20%20%20def%20__init__%28self%2C%20val%3A%20int%20%3D%200%29%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%20%20%23%20%E3%83%8E%E3%83%BC%E3%83%89%E5%80%A4%0A%20%20%20%20%20%20%20%20self.left%3A%20TreeNode%20%7C%20None%20%3D%20None%20%20%23%20%E5%B7%A6%E5%AD%90%E3%83%8E%E3%83%BC%E3%83%89%E3%81%B8%E3%81%AE%E5%8F%82%E7%85%A7%0A%20%20%20%20%20%20%20%20self.right%3A%20TreeNode%20%7C%20None%20%3D%20None%20%20%23%20%E5%8F%B3%E5%AD%90%E3%83%8E%E3%83%BC%E3%83%89%E3%81%B8%E3%81%AE%E5%8F%82%E7%85%A7%0A%0Adef%20dfs%28%0A%20%20%20%20preorder%3A%20list%5Bint%5D%2C%0A%20%20%20%20inorder_map%3A%20dict%5Bint%2C%20int%5D%2C%0A%20%20%20%20i%3A%20int%2C%0A%20%20%20%20l%3A%20int%2C%0A%20%20%20%20r%3A%20int%2C%0A%29%20-%3E%20TreeNode%20%7C%20None%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E5%88%86%E6%9C%A8%E3%82%92%E6%A7%8B%E7%AF%89%EF%BC%9A%E5%88%86%E5%89%B2%E7%B5%B1%E6%B2%BB%22%22%22%0A%20%20%20%20%23%20%E9%83%A8%E5%88%86%E6%9C%A8%E5%8C%BA%E9%96%93%E3%81%8C%E7%A9%BA%E3%81%AA%E3%82%89%E7%B5%82%E4%BA%86%E3%81%99%E3%82%8B%0A%20%20%20%20if%20r%20-%20l%20%3C%200%3A%0A%20%20%20%20%20%20%20%20return%20None%0A%20%20%20%20%23%20%E3%83%AB%E3%83%BC%E3%83%88%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%E3%81%99%E3%82%8B%0A%20%20%20%20root%20%3D%20TreeNode%28preorder%5Bi%5D%29%0A%20%20%20%20%23%20m%20%E3%82%92%E6%B1%82%E3%82%81%E3%81%A6%E5%B7%A6%E5%8F%B3%E9%83%A8%E5%88%86%E6%9C%A8%E3%82%92%E5%88%86%E5%89%B2%E3%81%99%E3%82%8B%0A%20%20%20%20m%20%3D%20inorder_map%5Bpreorder%5Bi%5D%5D%0A%20%20%20%20%23%20%E9%83%A8%E5%88%86%E5%95%8F%E9%A1%8C%EF%BC%9A%E5%B7%A6%E9%83%A8%E5%88%86%E6%9C%A8%E3%82%92%E6%A7%8B%E7%AF%89%E3%81%99%E3%82%8B%0A%20%20%20%20root.left%20%3D%20dfs%28preorder%2C%20inorder_map%2C%20i%20%2B%201%2C%20l%2C%20m%20-%201%29%0A%20%20%20%20%23%20%E9%83%A8%E5%88%86%E5%95%8F%E9%A1%8C%EF%BC%9A%E5%8F%B3%E9%83%A8%E5%88%86%E6%9C%A8%E3%82%92%E6%A7%8B%E7%AF%89%E3%81%99%E3%82%8B%0A%20%20%20%20root.right%20%3D%20dfs%28preorder%2C%20inorder_map%2C%20i%20%2B%201%20%2B%20m%20-%20l%2C%20m%20%2B%201%2C%20r%29%0A%20%20%20%20%23%20%E6%A0%B9%E3%83%8E%E3%83%BC%E3%83%89%E3%82%92%E8%BF%94%E3%81%99%0A%20%20%20%20return%20root%0A%0A%0Adef%20build_tree%28preorder%3A%20list%5Bint%5D%2C%20inorder%3A%20list%5Bint%5D%29%20-%3E%20TreeNode%20%7C%20None%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E5%88%86%E6%9C%A8%E3%82%92%E6%A7%8B%E7%AF%89%22%22%22%0A%20%20%20%20%23%20inorder%20%E3%81%AE%E8%A6%81%E7%B4%A0%E3%81%8B%E3%82%89%E3%82%A4%E3%83%B3%E3%83%87%E3%83%83%E3%82%AF%E3%82%B9%E3%81%B8%E3%81%AE%E5%AF%BE%E5%BF%9C%E3%82%92%E6%A0%BC%E7%B4%8D%E3%81%99%E3%82%8B%E3%83%8F%E3%83%83%E3%82%B7%E3%83%A5%E3%83%86%E3%83%BC%E3%83%96%E3%83%AB%E3%82%92%E5%88%9D%E6%9C%9F%E5%8C%96%E3%81%99%E3%82%8B%0A%20%20%20%20inorder_map%20%3D%20%7Bval%3A%20i%20for%20i%2C%20val%20in%20enumerate%28inorder%29%7D%0A%20%20%20%20root%20%3D%20dfs%28preorder%2C%20inorder_map%2C%200%2C%200%2C%20len%28inorder%29%20-%201%29%0A%20%20%20%20return%20root%0A%0A%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20preorder%20%3D%20%5B3%2C%209%2C%202%2C%201%2C%207%5D%0A%20%20%20%20inorder%20%3D%20%5B9%2C%203%2C%201%2C%202%2C%207%5D%0A%20%20%20%20print%28f%22%E5%89%8D%E9%A0%86%E8%B5%B0%E6%9F%BB%20%3D%20%7Bpreorder%7D%22%29%0A%20%20%20%20print%28f%22%E4%B8%AD%E9%A0%86%E8%B5%B0%E6%9F%BB%20%3D%20%7Binorder%7D%22%29%0A%20%20%20%20root%20%3D%20build_tree%28preorder%2C%20inorder%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=21&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>
|
||||
<p>下図は二分木を構築する再帰過程を示しています。各ノードは下向きに「再帰していく」過程で生成され、各辺（参照）は上向きに「戻る」過程で張られます。</p>
|
||||
<div class="tabbed-set tabbed-alternate" data-tabs="2:9"><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" /><div class="tabbed-labels"><label for="__tabbed_2_1"><1></label><label for="__tabbed_2_2"><2></label><label for="__tabbed_2_3"><3></label><label for="__tabbed_2_4"><4></label><label for="__tabbed_2_5"><5></label><label for="__tabbed_2_6"><6></label><label for="__tabbed_2_7"><7></label><label for="__tabbed_2_8"><8></label><label for="__tabbed_2_9"><9></label></div>
|
||||
<div class="tabbed-content">
|
||||
<div class="tabbed-block">
|
||||
<p><img alt="二分木構築の再帰過程" class="animation-figure" src="../build_binary_tree_problem.assets/built_tree_step1.png" /></p>
|
||||
<p><img alt="二分木を構築する再帰過程" class="animation-figure" src="../build_binary_tree_problem.assets/built_tree_step1.png" /></p>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<p><img alt="built_tree_step2" class="animation-figure" src="../build_binary_tree_problem.assets/built_tree_step2.png" /></p>
|
||||
@@ -4660,14 +4929,14 @@
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<p align="center"> 図 12-8 二分木構築の再帰過程 </p>
|
||||
<p align="center"> 図 12-8 二分木を構築する再帰過程 </p>
|
||||
|
||||
<p>各再帰関数の <code>preorder</code> と <code>inorder</code> シーケンスの分割は以下の図に示されています。</p>
|
||||
<p><img alt="各再帰関数での分割" class="animation-figure" src="../build_binary_tree_problem.assets/built_tree_overall.png" /></p>
|
||||
<p align="center"> 図 12-9 各再帰関数での分割 </p>
|
||||
<p>各再帰関数における前順走査 <code>preorder</code> と中順走査 <code>inorder</code> の分割結果を下図に示します。</p>
|
||||
<p><img alt="各再帰関数での分割結果" class="animation-figure" src="../build_binary_tree_problem.assets/built_tree_overall.png" /></p>
|
||||
<p align="center"> 図 12-9 各再帰関数での分割結果 </p>
|
||||
|
||||
<p>二分木が <span class="arithmatex">\(n\)</span> 個のノードを持つと仮定すると、各ノードの初期化（再帰関数 <code>dfs()</code> の呼び出し）には <span class="arithmatex">\(O(1)\)</span> 時間がかかります。<strong>したがって、全体の時間計算量は <span class="arithmatex">\(O(n)\)</span> です</strong>。</p>
|
||||
<p>ハッシュテーブルは <code>inorder</code> 要素からそのインデックスへのマッピングを格納するため、<span class="arithmatex">\(O(n)\)</span> スペースが必要です。最悪の場合、二分木が連結リストに退化すると、再帰の深さは <span class="arithmatex">\(n\)</span> に達し、<span class="arithmatex">\(O(n)\)</span> のスタックスペースを消費する可能性があります。<strong>したがって、全体の空間計算量は <span class="arithmatex">\(O(n)\)</span> です</strong>。</p>
|
||||
<p>木のノード数を <span class="arithmatex">\(n\)</span> とすると、各ノードの初期化（再帰関数 <code>dfs()</code> の 1 回の実行）には <span class="arithmatex">\(O(1)\)</span> 時間かかります。<strong>したがって、全体の時間計算量は <span class="arithmatex">\(O(n)\)</span></strong> です。</p>
|
||||
<p>ハッシュテーブルには <code>inorder</code> の要素からインデックスへの対応を保存するため、空間計算量は <span class="arithmatex">\(O(n)\)</span> です。最悪の場合、すなわち二分木が連結リストに退化すると、再帰の深さは <span class="arithmatex">\(n\)</span> に達し、<span class="arithmatex">\(O(n)\)</span> のスタックフレーム空間を使用します。<strong>したがって、全体の空間計算量は <span class="arithmatex">\(O(n)\)</span></strong> です。</p>
|
||||
|
||||
<!-- Source file information -->
|
||||
|
||||
@@ -4714,7 +4983,7 @@ aria-label="フッター"
|
||||
<a
|
||||
href="../hanota_problem/"
|
||||
class="md-footer__link md-footer__link--next"
|
||||
aria-label="次: 12.4 &nbsp; ハノイの塔問題"
|
||||
aria-label="次: 12.4 &nbsp; ハノイの塔の問題"
|
||||
rel="next"
|
||||
>
|
||||
<div class="md-footer__title">
|
||||
@@ -4722,7 +4991,7 @@ aria-label="フッター"
|
||||
次
|
||||
</span>
|
||||
<div class="md-ellipsis">
|
||||
12.4 ハノイの塔問題
|
||||
12.4 ハノイの塔の問題
|
||||
</div>
|
||||
</div>
|
||||
<div class="md-footer__button md-icon">
|
||||
|
||||
Reference in New Issue
Block a user