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第 1 章   アルゴリズムとの出会い
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第 1 章   アルゴリズムとの出会い
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1.1   アルゴリズムはどこにでもある
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1.2   アルゴリズムとは
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1.3   まとめ
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第 2 章   計算量の解析
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第 2 章   計算量の解析
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2.1   アルゴリズムの効率の評価
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2.2   反復と再帰
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2.3   時間計算量
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2.4   空間計算量
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2.5   まとめ
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2.6   練習問題
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第 3 章   データ構造
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第 3 章   データ構造
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3.1   データ構造の分類
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3.2   基本データ型
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3.3   数値の符号化 *
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3.4   文字エンコーディング *
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3.5   まとめ
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3.6   練習問題
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第 4 章   配列と連結リスト
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第 4 章   配列と連結リスト
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4.1   配列
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4.2   連結リスト
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4.3   リスト
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4.4   メモリとキャッシュ *
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4.5   まとめ
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4.6   練習問題
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第 5 章   スタックとキュー
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第 5 章   スタックとキュー
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5.1   スタック
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5.2   キュー
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5.3   両端キュー
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5.4   まとめ
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5.5   練習問題
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第 6 章   ハッシュテーブル
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第 6 章   ハッシュテーブル
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6.1   ハッシュテーブル
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6.2   ハッシュ衝突
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6.3   ハッシュアルゴリズム
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6.4   まとめ
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6.5   練習問題
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第 7 章   木
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第 7 章   木
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7.1   二分木
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7.2   二分木の走査
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7.3   二分木の配列表現
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7.4   二分探索木
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7.5   AVL 木 *
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7.6   まとめ
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7.7   練習問題
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第 8 章   ヒープ
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第 8 章   ヒープ
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8.1   ヒープ
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8.2   ヒープの構築
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8.3   Top-k 問題
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8.4   まとめ
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8.5   練習問題
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第 9 章   グラフ
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第 9 章   グラフ
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9.1   グラフ
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9.2   グラフの基本操作
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9.3   グラフの走査
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9.4   まとめ
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9.5   練習問題
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第 10 章   探索
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第 10 章   探索
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10.1   二分探索
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<a class="md-nav__link" href="../../chapter_searching/binary_search_insertion/">
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10.2   二分探索で挿入位置を探す
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<a class="md-nav__link" href="../../chapter_searching/binary_search_edge/">
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10.3   二分探索で境界を探す
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<a class="md-nav__link" href="../../chapter_searching/replace_linear_by_hashing/">
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10.4   ハッシュを使った最適化
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<a class="md-nav__link" href="../../chapter_searching/searching_algorithm_revisited/">
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10.5   探索アルゴリズムを改めて考える
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<a class="md-nav__link" href="../../chapter_searching/summary/">
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10.6   まとめ
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10.7   練習問題
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第 11 章   ソート
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第 11 章   ソート
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11.1   ソートアルゴリズム
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<a class="md-nav__link" href="../../chapter_sorting/selection_sort/">
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11.2   選択ソート
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<a class="md-nav__link" href="../../chapter_sorting/bubble_sort/">
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11.3   バブルソート
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11.4   挿入ソート
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<a class="md-nav__link" href="../../chapter_sorting/quick_sort/">
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11.5   クイックソート
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<a class="md-nav__link" href="../../chapter_sorting/merge_sort/">
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11.6   マージソート
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<a class="md-nav__link" href="../../chapter_sorting/heap_sort/">
<span class="md-ellipsis">
11.7   ヒープソート
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</li>
<li class="md-nav__item">
<a class="md-nav__link" href="../../chapter_sorting/bucket_sort/">
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11.8   バケットソート
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<a class="md-nav__link" href="../../chapter_sorting/counting_sort/">
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11.9   カウントソート
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<li class="md-nav__item">
<a class="md-nav__link" href="../../chapter_sorting/radix_sort/">
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11.10   基数ソート
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<a class="md-nav__link" href="../../chapter_sorting/summary/">
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11.11   まとめ
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<a class="md-nav__link" href="../../chapter_sorting/exercises/">
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11.12   練習問題
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第 12 章   分割統治
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第 12 章   分割統治
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12.1   分割統治アルゴリズム
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<a class="md-nav__link" href="../../chapter_divide_and_conquer/binary_search_recur/">
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12.2   分割統治による探索戦略
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12.3   二分木の構築問題
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12.4   ハノイの塔の問題
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12.5   まとめ
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12.6   練習問題
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第 13 章   バックトラッキング
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第 13 章   バックトラッキング
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13.1   バックトラッキングアルゴリズム
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13.2   順列列挙問題
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13.3   部分集合和問題
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13.4   n クイーン問題
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13.5   まとめ
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13.6   練習問題
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第 14 章   動的計画法
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第 14 章   動的計画法
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14.1   動的計画法への第一歩
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<a class="md-nav__link" href="../dp_problem_features/">
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14.2   動的計画法の問題の特徴
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<a class="md-nav__link" href="../dp_solution_pipeline/">
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14.3   動的計画法の解き方
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14.4   0-1 ナップサック問題
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14.5   個数制限なしナップサック問題
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14.6   編集距離問題
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14.6   編集距離問題
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1.   動的計画法の考え方
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2.   コードの実装
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3.   空間の最適化
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14.7   まとめ
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14.8   練習問題
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第 15 章   貪欲法
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<svg viewbox="0 0 512 512" xmlns="http://www.w3.org/2000/svg"><!--! Font Awesome Free 7.2.0 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2026 Fonticons, Inc.--><path d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0M88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24z" fill="currentColor"></path></svg>
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<h1 id="146">14.6   編集距離問題<a class="headerlink" href="#146" title="この見出しへのリンク"></a></h1>
<p>編集距離は Levenshtein 距離とも呼ばれ、一方の文字列をもう一方に変換するために必要な最小の変更回数を表します。情報検索や自然言語処理で、二つの列の類似度を測るためによく使われます。</p>
<div class="admonition question">
<p class="admonition-title">問題</p>
<p>二つの文字列 <span class="arithmatex">\(s\)</span> と <span class="arithmatex">\(t\)</span> が与えられます。<span class="arithmatex">\(s\)</span> を <span class="arithmatex">\(t\)</span> に変換するための最小の編集回数を返してください。</p>
<p>文字列には、文字を一つ挿入する、文字を一つ削除する、文字を任意の文字に置き換える、という 3 種類の編集操作を行えます。</p>
</div>
<p>図 14-27 のように、<code>kitten</code> を <code>sitting</code> に変換するには、置換 2 回と挿入 1 回の計 3 回が必要です。<code>hello</code> を <code>algo</code> に変換するには、置換 2 回と削除 1 回の計 3 回が必要です。</p>
<p><ha-svg-figure class="animation-figure" data-book-key="ja/chapter_dynamic_programming/edit_distance_problem.assets/edit_distance_example.png" data-dark-src="/assets/figure-svg/figures/5d65627b8660c02f8bf70275.json" data-src="/assets/figure-svg/figures/8075644b7c12bcc9dbaf785d.json" style=";--figure-ratio:960.0/540.0"><object data="/ja/chapter_dynamic_programming/edit_distance_problem.assets/edit_distance_example.svg" data-theme="light" tabindex="-1" type="image/svg+xml">編集距離のデータ例</object><object data="/ja/chapter_dynamic_programming/edit_distance_problem.assets/edit_distance_example.dark.svg" data-theme="dark" tabindex="-1" type="image/svg+xml">編集距離のデータ例</object></ha-svg-figure></p>
<p align="center"> 図 14-27   編集距離のデータ例 </p>
<p><strong>編集距離問題は、決定木モデルで自然に説明できます</strong>。文字列が木のノードに対応し、1 回の判断(編集操作)が辺に対応します。</p>
<p>図 14-28 のように、操作を制限しなければ各ノードから多くの辺が伸び、各辺が一つの操作に対応します。つまり、<code>hello</code> から <code>algo</code> への変換には、多くの経路が考えられます。</p>
<p>決定木の観点では、この問題の目標はノード <code>hello</code> とノード <code>algo</code> の間の最短経路を求めることです。</p>
<p><ha-svg-figure class="animation-figure" data-book-key="ja/chapter_dynamic_programming/edit_distance_problem.assets/edit_distance_decision_tree.png" data-dark-src="/assets/figure-svg/figures/1618a48e1290f2b862ca5721.json" data-src="/assets/figure-svg/figures/7ffc90c7e34544fda6e7002e.json" style=";--figure-ratio:960.0/540.0"><object data="/ja/chapter_dynamic_programming/edit_distance_problem.assets/edit_distance_decision_tree.svg" data-theme="light" tabindex="-1" type="image/svg+xml">決定木モデルによる編集距離問題の表現</object><object data="/ja/chapter_dynamic_programming/edit_distance_problem.assets/edit_distance_decision_tree.dark.svg" data-theme="dark" tabindex="-1" type="image/svg+xml">決定木モデルによる編集距離問題の表現</object></ha-svg-figure></p>
<p align="center"> 図 14-28   決定木モデルによる編集距離問題の表現 </p>
<h3 id="1">1.   動的計画法の考え方<a class="headerlink" href="#1" title="この見出しへのリンク"></a></h3>
<p><strong>第 1 段階:各回の選択を考えて状態を定義し、<span class="arithmatex">\(dp\)</span> テーブルを作る</strong></p>
<p>各回の選択は、文字列 <span class="arithmatex">\(s\)</span> に編集操作を 1 回行うことです。</p>
<p>部分問題を作るには、編集するたびに問題を小さくしていきたいところです。文字列 <span class="arithmatex">\(s\)</span> と <span class="arithmatex">\(t\)</span> の長さをそれぞれ <span class="arithmatex">\(n\)</span> と <span class="arithmatex">\(m\)</span> とし、まず末尾の文字 <span class="arithmatex">\(s[n-1]\)</span> と <span class="arithmatex">\(t[m-1]\)</span> を考えます。</p>
<ul>
<li><span class="arithmatex">\(s[n-1]\)</span> と <span class="arithmatex">\(t[m-1]\)</span> が同じなら、それらを飛ばして <span class="arithmatex">\(s[n-2]\)</span> と <span class="arithmatex">\(t[m-2]\)</span> を考えられます。</li>
<li><span class="arithmatex">\(s[n-1]\)</span> と <span class="arithmatex">\(t[m-1]\)</span> が異なるなら、<span class="arithmatex">\(s\)</span> に編集(挿入、削除、置換)を 1 回行って末尾の文字を一致させ、それらを飛ばして、より小さな問題を考えます。</li>
</ul>
<p>つまり、文字列 <span class="arithmatex">\(s\)</span> に対する各回の判断(編集操作)によって、<span class="arithmatex">\(s\)</span> と <span class="arithmatex">\(t\)</span> のまだ対応させていない文字が変わります。そこで、現在考えている <span class="arithmatex">\(s\)</span> の <span class="arithmatex">\(i\)</span> 番目と <span class="arithmatex">\(t\)</span> の <span class="arithmatex">\(j\)</span> 番目の文字を状態とし、<span class="arithmatex">\([i, j]\)</span> と表します。</p>
<p>状態 <span class="arithmatex">\([i, j]\)</span> の部分問題は、<strong><span class="arithmatex">\(s\)</span> の先頭 <span class="arithmatex">\(i\)</span> 文字を <span class="arithmatex">\(t\)</span> の先頭 <span class="arithmatex">\(j\)</span> 文字に変換するための最小編集回数</strong>です。</p>
<p>これで、<span class="arithmatex">\((n+1) \times (m+1)\)</span> の二次元の <span class="arithmatex">\(dp\)</span> テーブルが得られます。</p>
<p><strong>第 2 段階:最適部分構造を見つけ、状態遷移式を導く</strong></p>
<p>部分問題 <span class="arithmatex">\(dp[i, j]\)</span> に対応する二つの文字列の末尾は、<span class="arithmatex">\(s[i-1]\)</span> と <span class="arithmatex">\(t[j-1]\)</span> です。編集操作によって、図 14-29 の 3 通りに分けられます。</p>
<ol>
<li><span class="arithmatex">\(s[i-1]\)</span> の後ろに <span class="arithmatex">\(t[j-1]\)</span> を挿入すると、残る部分問題は <span class="arithmatex">\(dp[i, j-1]\)</span> です。</li>
<li><span class="arithmatex">\(s[i-1]\)</span> を削除すると、残る部分問題は <span class="arithmatex">\(dp[i-1, j]\)</span> です。</li>
<li><span class="arithmatex">\(s[i-1]\)</span> を <span class="arithmatex">\(t[j-1]\)</span> に置換すると、残る部分問題は <span class="arithmatex">\(dp[i-1, j-1]\)</span> です。</li>
</ol>
<p><ha-svg-figure class="animation-figure" data-book-key="ja/chapter_dynamic_programming/edit_distance_problem.assets/edit_distance_state_transfer.png" data-dark-src="/assets/figure-svg/figures/7851e2118859329e623ba197.json" data-src="/assets/figure-svg/figures/4643e7d8cf072aa294ed99c8.json" style=";--figure-ratio:960.0/540.0"><object data="/ja/chapter_dynamic_programming/edit_distance_problem.assets/edit_distance_state_transfer.svg" data-theme="light" tabindex="-1" type="image/svg+xml">編集距離の状態遷移</object><object data="/ja/chapter_dynamic_programming/edit_distance_problem.assets/edit_distance_state_transfer.dark.svg" data-theme="dark" tabindex="-1" type="image/svg+xml">編集距離の状態遷移</object></ha-svg-figure></p>
<p align="center"> 図 14-29   編集距離の状態遷移 </p>
<p>ここから最適部分構造が得られます。<span class="arithmatex">\(dp[i, j]\)</span> の最小編集回数は、<span class="arithmatex">\(dp[i, j-1]\)</span>、<span class="arithmatex">\(dp[i-1, j]\)</span>、<span class="arithmatex">\(dp[i-1, j-1]\)</span> の三つの最小編集回数のうち、最も小さいものに、今回の編集 <span class="arithmatex">\(1\)</span> 回を加えた値です。状態遷移式は次のようになります。</p>
<div class="arithmatex">\[
dp[i, j] = \min(dp[i, j-1], dp[i-1, j], dp[i-1, j-1]) + 1
\]</div>
<p><strong><span class="arithmatex">\(s[i-1]\)</span> と <span class="arithmatex">\(t[j-1]\)</span> が同じなら、その文字を編集する必要はありません</strong>。この場合の状態遷移式は次のとおりです。</p>
<div class="arithmatex">\[
dp[i, j] = dp[i-1, j-1]
\]</div>
<p><strong>第 3 段階:境界条件と状態遷移の順序を決める</strong></p>
<p>両方の文字列が空なら編集回数は <span class="arithmatex">\(0\)</span>、すなわち <span class="arithmatex">\(dp[0, 0] = 0\)</span> です。<span class="arithmatex">\(s\)</span> が空で <span class="arithmatex">\(t\)</span> が空でないなら、最小編集回数は <span class="arithmatex">\(t\)</span> の長さなので、先頭行は <span class="arithmatex">\(dp[0, j] = j\)</span> です。<span class="arithmatex">\(s\)</span> が空でなく <span class="arithmatex">\(t\)</span> が空なら、最小編集回数は <span class="arithmatex">\(s\)</span> の長さなので、先頭列は <span class="arithmatex">\(dp[i, 0] = i\)</span> です。</p>
<p>状態遷移式から、解 <span class="arithmatex">\(dp[i, j]\)</span> は左、上、左上の解に依存します。したがって、二重ループで <span class="arithmatex">\(dp\)</span> テーブル全体を順方向に走査すれば十分です。</p>
<h3 id="2">2.   コードの実装<a class="headerlink" href="#2" title="この見出しへのリンク"></a></h3>
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<div class="highlight"><span class="filename">edit_distance.py</span><pre><span></span><code><a href="#__codelineno-0-1" id="__codelineno-0-1" name="__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">edit_distance_dp</span><span class="p">(</span><span class="n">s</span><span class="p">:</span> <span class="nb">str</span><span class="p">,</span> <span class="n">t</span><span class="p">:</span> <span class="nb">str</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
<a href="#__codelineno-0-2" id="__codelineno-0-2" name="__codelineno-0-2"></a><span class="w"> </span><span class="sd">"""編集距離:動的計画法"""</span>
<a href="#__codelineno-0-3" id="__codelineno-0-3" name="__codelineno-0-3"></a> <span class="n">n</span><span class="p">,</span> <span class="n">m</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">s</span><span class="p">),</span> <span class="nb">len</span><span class="p">(</span><span class="n">t</span><span class="p">)</span>
<a href="#__codelineno-0-4" id="__codelineno-0-4" name="__codelineno-0-4"></a> <span class="n">dp</span> <span class="o">=</span> <span class="p">[[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</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="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)]</span>
<a href="#__codelineno-0-5" id="__codelineno-0-5" name="__codelineno-0-5"></a> <span class="c1"># 状態遷移:先頭行と先頭列</span>
<a href="#__codelineno-0-6" id="__codelineno-0-6" name="__codelineno-0-6"></a> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
<a href="#__codelineno-0-7" id="__codelineno-0-7" name="__codelineno-0-7"></a> <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">i</span>
<a href="#__codelineno-0-8" id="__codelineno-0-8" name="__codelineno-0-8"></a> <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">m</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
<a href="#__codelineno-0-9" id="__codelineno-0-9" name="__codelineno-0-9"></a> <span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">j</span>
<a href="#__codelineno-0-10" id="__codelineno-0-10" name="__codelineno-0-10"></a> <span class="c1"># 状態遷移:残りの行と列</span>
<a href="#__codelineno-0-11" id="__codelineno-0-11" name="__codelineno-0-11"></a> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
<a href="#__codelineno-0-12" id="__codelineno-0-12" name="__codelineno-0-12"></a> <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">m</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
<a href="#__codelineno-0-13" id="__codelineno-0-13" name="__codelineno-0-13"></a> <span class="k">if</span> <span class="n">s</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="o">==</span> <span class="n">t</span><span class="p">[</span><span class="n">j</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]:</span>
<a href="#__codelineno-0-14" id="__codelineno-0-14" name="__codelineno-0-14"></a> <span class="c1"># 2 つの文字が等しい場合、その 2 文字をスキップする</span>
<a href="#__codelineno-0-15" id="__codelineno-0-15" name="__codelineno-0-15"></a> <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">dp</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">j</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span>
<a href="#__codelineno-0-16" id="__codelineno-0-16" name="__codelineno-0-16"></a> <span class="k">else</span><span class="p">:</span>
<a href="#__codelineno-0-17" id="__codelineno-0-17" name="__codelineno-0-17"></a> <span class="c1"># 最小編集回数 = 挿入、削除、置換の 3 操作での最小編集回数 + 1</span>
<a href="#__codelineno-0-18" id="__codelineno-0-18" name="__codelineno-0-18"></a> <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span> <span class="o">-</span> <span class="mi">1</span><span class="p">],</span> <span class="n">dp</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">j</span><span class="p">],</span> <span class="n">dp</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">j</span> <span class="o">-</span> <span class="mi">1</span><span class="p">])</span> <span class="o">+</span> <span class="mi">1</span>
<a href="#__codelineno-0-19" id="__codelineno-0-19" name="__codelineno-0-19"></a> <span class="k">return</span> <span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="n">m</span><span class="p">]</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">edit_distance.cpp</span><pre><span></span><code><a href="#__codelineno-1-1" id="__codelineno-1-1" name="__codelineno-1-1"></a><span class="cm">/* 編集距離:動的計画法 */</span>
<a href="#__codelineno-1-2" id="__codelineno-1-2" name="__codelineno-1-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">editDistanceDP</span><span class="p">(</span><span class="n">string</span><span class="w"> </span><span class="n">s</span><span class="p">,</span><span class="w"> </span><span class="n">string</span><span class="w"> </span><span class="n">t</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-1-3" id="__codelineno-1-3" name="__codelineno-1-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">s</span><span class="p">.</span><span class="n">length</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="n">t</span><span class="p">.</span><span class="n">length</span><span class="p">();</span>
<a href="#__codelineno-1-4" id="__codelineno-1-4" name="__codelineno-1-4"></a><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">dp</span><span class="p">(</span><span class="n">n</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">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="p">(</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="mi">0</span><span class="p">));</span>
<a href="#__codelineno-1-5" id="__codelineno-1-5" name="__codelineno-1-5"></a><span class="w"> </span><span class="c1">// 状態遷移:先頭行と先頭列</span>
<a href="#__codelineno-1-6" id="__codelineno-1-6" name="__codelineno-1-6"></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">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</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 href="#__codelineno-1-7" id="__codelineno-1-7" name="__codelineno-1-7"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">0</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 href="#__codelineno-1-8" id="__codelineno-1-8" name="__codelineno-1-8"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-1-9" id="__codelineno-1-9" name="__codelineno-1-9"></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">j</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">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-1-10" id="__codelineno-1-10" name="__codelineno-1-10"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">j</span><span class="p">;</span>
<a href="#__codelineno-1-11" id="__codelineno-1-11" name="__codelineno-1-11"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-1-12" id="__codelineno-1-12" name="__codelineno-1-12"></a><span class="w"> </span><span class="c1">// 状態遷移:残りの行と列</span>
<a href="#__codelineno-1-13" id="__codelineno-1-13" name="__codelineno-1-13"></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">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</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 href="#__codelineno-1-14" id="__codelineno-1-14" name="__codelineno-1-14"></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">j</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">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-1-15" id="__codelineno-1-15" name="__codelineno-1-15"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">s</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">t</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-1-16" id="__codelineno-1-16" name="__codelineno-1-16"></a><span class="w"> </span><span class="c1">// 2 つの文字が等しい場合、その 2 文字をスキップする</span>
<a href="#__codelineno-1-17" id="__codelineno-1-17" name="__codelineno-1-17"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
<a href="#__codelineno-1-18" id="__codelineno-1-18" name="__codelineno-1-18"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-1-19" id="__codelineno-1-19" name="__codelineno-1-19"></a><span class="w"> </span><span class="c1">// 最小編集回数 = 挿入、削除、置換の 3 操作での最小編集回数 + 1</span>
<a href="#__codelineno-1-20" id="__codelineno-1-20" name="__codelineno-1-20"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">min</span><span class="p">(</span><span class="n">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">j</span><span class="p">]),</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">j</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="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
<a href="#__codelineno-1-21" id="__codelineno-1-21" name="__codelineno-1-21"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-1-22" id="__codelineno-1-22" name="__codelineno-1-22"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-1-23" id="__codelineno-1-23" name="__codelineno-1-23"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-1-24" id="__codelineno-1-24" name="__codelineno-1-24"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="n">m</span><span class="p">];</span>
<a href="#__codelineno-1-25" id="__codelineno-1-25" name="__codelineno-1-25"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">edit_distance.java</span><pre><span></span><code><a href="#__codelineno-2-1" id="__codelineno-2-1" name="__codelineno-2-1"></a><span class="cm">/* 編集距離:動的計画法 */</span>
<a href="#__codelineno-2-2" id="__codelineno-2-2" name="__codelineno-2-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">editDistanceDP</span><span class="p">(</span><span class="n">String</span><span class="w"> </span><span class="n">s</span><span class="p">,</span><span class="w"> </span><span class="n">String</span><span class="w"> </span><span class="n">t</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-2-3" id="__codelineno-2-3" name="__codelineno-2-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">s</span><span class="p">.</span><span class="na">length</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="n">t</span><span class="p">.</span><span class="na">length</span><span class="p">();</span>
<a href="#__codelineno-2-4" id="__codelineno-2-4" name="__codelineno-2-4"></a><span class="w"> </span><span class="kt">int</span><span class="o">[][]</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">][</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="o">]</span><span class="p">;</span>
<a href="#__codelineno-2-5" id="__codelineno-2-5" name="__codelineno-2-5"></a><span class="w"> </span><span class="c1">// 状態遷移:先頭行と先頭列</span>
<a href="#__codelineno-2-6" id="__codelineno-2-6" name="__codelineno-2-6"></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">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</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 href="#__codelineno-2-7" id="__codelineno-2-7" name="__codelineno-2-7"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
<a href="#__codelineno-2-8" id="__codelineno-2-8" name="__codelineno-2-8"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-2-9" id="__codelineno-2-9" name="__codelineno-2-9"></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">j</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">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-2-10" id="__codelineno-2-10" name="__codelineno-2-10"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="mi">0</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">j</span><span class="p">;</span>
<a href="#__codelineno-2-11" id="__codelineno-2-11" name="__codelineno-2-11"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-2-12" id="__codelineno-2-12" name="__codelineno-2-12"></a><span class="w"> </span><span class="c1">// 状態遷移:残りの行と列</span>
<a href="#__codelineno-2-13" id="__codelineno-2-13" name="__codelineno-2-13"></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">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</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 href="#__codelineno-2-14" id="__codelineno-2-14" name="__codelineno-2-14"></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">j</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">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-2-15" id="__codelineno-2-15" name="__codelineno-2-15"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">s</span><span class="p">.</span><span class="na">charAt</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">t</span><span class="p">.</span><span class="na">charAt</span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-2-16" id="__codelineno-2-16" name="__codelineno-2-16"></a><span class="w"> </span><span class="c1">// 2 つの文字が等しい場合、その 2 文字をスキップする</span>
<a href="#__codelineno-2-17" id="__codelineno-2-17" name="__codelineno-2-17"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</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="o">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">;</span>
<a href="#__codelineno-2-18" id="__codelineno-2-18" name="__codelineno-2-18"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-2-19" id="__codelineno-2-19" name="__codelineno-2-19"></a><span class="w"> </span><span class="c1">// 最小編集回数 = 挿入、削除、置換の 3 操作での最小編集回数 + 1</span>
<a href="#__codelineno-2-20" id="__codelineno-2-20" name="__codelineno-2-20"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="na">min</span><span class="p">(</span><span class="n">Math</span><span class="p">.</span><span class="na">min</span><span class="p">(</span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</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="o">][</span><span class="n">j</span><span class="o">]</span><span class="p">),</span><span class="w"> </span><span class="n">dp</span><span class="o">[</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="o">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
<a href="#__codelineno-2-21" id="__codelineno-2-21" name="__codelineno-2-21"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-2-22" id="__codelineno-2-22" name="__codelineno-2-22"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-2-23" id="__codelineno-2-23" name="__codelineno-2-23"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-2-24" id="__codelineno-2-24" name="__codelineno-2-24"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">n</span><span class="o">][</span><span class="n">m</span><span class="o">]</span><span class="p">;</span>
<a href="#__codelineno-2-25" id="__codelineno-2-25" name="__codelineno-2-25"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">edit_distance.cs</span><pre><span></span><code><a href="#__codelineno-3-1" id="__codelineno-3-1" name="__codelineno-3-1"></a><span class="cm">/* 編集距離:動的計画法 */</span>
<a href="#__codelineno-3-2" id="__codelineno-3-2" name="__codelineno-3-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">EditDistanceDP</span><span class="p">(</span><span class="kt">string</span><span class="w"> </span><span class="n">s</span><span class="p">,</span><span class="w"> </span><span class="kt">string</span><span class="w"> </span><span class="n">t</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-3-3" id="__codelineno-3-3" name="__codelineno-3-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">s</span><span class="p">.</span><span class="n">Length</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="n">t</span><span class="p">.</span><span class="n">Length</span><span class="p">;</span>
<a href="#__codelineno-3-4" id="__codelineno-3-4" name="__codelineno-3-4"></a><span class="w"> </span><span class="kt">int</span><span class="p">[,]</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">n</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">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
<a href="#__codelineno-3-5" id="__codelineno-3-5" name="__codelineno-3-5"></a><span class="w"> </span><span class="c1">// 状態遷移:先頭行と先頭列</span>
<a href="#__codelineno-3-6" id="__codelineno-3-6" name="__codelineno-3-6"></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">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</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 href="#__codelineno-3-7" id="__codelineno-3-7" name="__codelineno-3-7"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="mi">0</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 href="#__codelineno-3-8" id="__codelineno-3-8" name="__codelineno-3-8"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-3-9" id="__codelineno-3-9" name="__codelineno-3-9"></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">j</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">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-3-10" id="__codelineno-3-10" name="__codelineno-3-10"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">j</span><span class="p">;</span>
<a href="#__codelineno-3-11" id="__codelineno-3-11" name="__codelineno-3-11"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-3-12" id="__codelineno-3-12" name="__codelineno-3-12"></a><span class="w"> </span><span class="c1">// 状態遷移:残りの行と列</span>
<a href="#__codelineno-3-13" id="__codelineno-3-13" name="__codelineno-3-13"></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">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</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 href="#__codelineno-3-14" id="__codelineno-3-14" name="__codelineno-3-14"></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">j</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">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-3-15" id="__codelineno-3-15" name="__codelineno-3-15"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">s</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">t</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-3-16" id="__codelineno-3-16" name="__codelineno-3-16"></a><span class="w"> </span><span class="c1">// 2 つの文字が等しい場合、その 2 文字をスキップする</span>
<a href="#__codelineno-3-17" id="__codelineno-3-17" name="__codelineno-3-17"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
<a href="#__codelineno-3-18" id="__codelineno-3-18" name="__codelineno-3-18"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-3-19" id="__codelineno-3-19" name="__codelineno-3-19"></a><span class="w"> </span><span class="c1">// 最小編集回数 = 挿入、削除、置換の 3 操作での最小編集回数 + 1</span>
<a href="#__codelineno-3-20" id="__codelineno-3-20" name="__codelineno-3-20"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="n">Min</span><span class="p">(</span><span class="n">Math</span><span class="p">.</span><span class="n">Min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">]),</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">j</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="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
<a href="#__codelineno-3-21" id="__codelineno-3-21" name="__codelineno-3-21"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-3-22" id="__codelineno-3-22" name="__codelineno-3-22"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-3-23" id="__codelineno-3-23" name="__codelineno-3-23"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-3-24" id="__codelineno-3-24" name="__codelineno-3-24"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="p">];</span>
<a href="#__codelineno-3-25" id="__codelineno-3-25" name="__codelineno-3-25"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">edit_distance.go</span><pre><span></span><code><a href="#__codelineno-4-1" id="__codelineno-4-1" name="__codelineno-4-1"></a><span class="cm">/* 編集距離:動的計画法 */</span>
<a href="#__codelineno-4-2" id="__codelineno-4-2" name="__codelineno-4-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">editDistanceDP</span><span class="p">(</span><span class="nx">s</span><span class="w"> </span><span class="kt">string</span><span class="p">,</span><span class="w"> </span><span class="nx">t</span><span class="w"> </span><span class="kt">string</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-4-3" id="__codelineno-4-3" name="__codelineno-4-3"></a><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">s</span><span class="p">)</span>
<a href="#__codelineno-4-4" id="__codelineno-4-4" name="__codelineno-4-4"></a><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">t</span><span class="p">)</span>
<a href="#__codelineno-4-5" id="__codelineno-4-5" name="__codelineno-4-5"></a><span class="w"> </span><span class="nx">dp</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([][]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
<a href="#__codelineno-4-6" id="__codelineno-4-6" name="__codelineno-4-6"></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="o">&lt;=</span><span class="w"> </span><span class="nx">n</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 href="#__codelineno-4-7" id="__codelineno-4-7" name="__codelineno-4-7"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</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 href="#__codelineno-4-8" id="__codelineno-4-8" name="__codelineno-4-8"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-4-9" id="__codelineno-4-9" name="__codelineno-4-9"></a><span class="w"> </span><span class="c1">// 状態遷移:先頭行と先頭列</span>
<a href="#__codelineno-4-10" id="__codelineno-4-10" name="__codelineno-4-10"></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">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</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 href="#__codelineno-4-11" id="__codelineno-4-11" name="__codelineno-4-11"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">i</span>
<a href="#__codelineno-4-12" id="__codelineno-4-12" name="__codelineno-4-12"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-4-13" id="__codelineno-4-13" name="__codelineno-4-13"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">m</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-4-14" id="__codelineno-4-14" name="__codelineno-4-14"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">j</span>
<a href="#__codelineno-4-15" id="__codelineno-4-15" name="__codelineno-4-15"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-4-16" id="__codelineno-4-16" name="__codelineno-4-16"></a><span class="w"> </span><span class="c1">// 状態遷移:残りの行と列</span>
<a href="#__codelineno-4-17" id="__codelineno-4-17" name="__codelineno-4-17"></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">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</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 href="#__codelineno-4-18" id="__codelineno-4-18" name="__codelineno-4-18"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">m</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-4-19" id="__codelineno-4-19" name="__codelineno-4-19"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">s</span><span class="p">[</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="o">==</span><span class="w"> </span><span class="nx">t</span><span class="p">[</span><span class="nx">j</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-4-20" id="__codelineno-4-20" name="__codelineno-4-20"></a><span class="w"> </span><span class="c1">// 2 つの文字が等しい場合、その 2 文字をスキップする</span>
<a href="#__codelineno-4-21" id="__codelineno-4-21" name="__codelineno-4-21"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">][</span><span class="nx">j</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
<a href="#__codelineno-4-22" id="__codelineno-4-22" name="__codelineno-4-22"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-4-23" id="__codelineno-4-23" name="__codelineno-4-23"></a><span class="w"> </span><span class="c1">// 最小編集回数 = 挿入、削除、置換の 3 操作での最小編集回数 + 1</span>
<a href="#__codelineno-4-24" id="__codelineno-4-24" name="__codelineno-4-24"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">MinInt</span><span class="p">(</span><span class="nx">MinInt</span><span class="p">(</span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">][</span><span class="nx">j</span><span class="p">]),</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="o">-</span><span class="mi">1</span><span class="p">][</span><span class="nx">j</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
<a href="#__codelineno-4-25" id="__codelineno-4-25" name="__codelineno-4-25"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-4-26" id="__codelineno-4-26" name="__codelineno-4-26"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-4-27" id="__codelineno-4-27" name="__codelineno-4-27"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-4-28" id="__codelineno-4-28" name="__codelineno-4-28"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">n</span><span class="p">][</span><span class="nx">m</span><span class="p">]</span>
<a href="#__codelineno-4-29" id="__codelineno-4-29" name="__codelineno-4-29"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">edit_distance.swift</span><pre><span></span><code><a href="#__codelineno-5-1" id="__codelineno-5-1" name="__codelineno-5-1"></a><span class="cm">/* 編集距離:動的計画法 */</span>
<a href="#__codelineno-5-2" id="__codelineno-5-2" name="__codelineno-5-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">editDistanceDP</span><span class="p">(</span><span class="n">s</span><span class="p">:</span><span class="w"> </span><span class="nb">String</span><span class="p">,</span><span class="w"> </span><span class="n">t</span><span class="p">:</span><span class="w"> </span><span class="nb">String</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-5-3" id="__codelineno-5-3" name="__codelineno-5-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nv">n</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">s</span><span class="p">.</span><span class="n">utf8CString</span><span class="p">.</span><span class="bp">count</span>
<a href="#__codelineno-5-4" id="__codelineno-5-4" name="__codelineno-5-4"></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">t</span><span class="p">.</span><span class="n">utf8CString</span><span class="p">.</span><span class="bp">count</span>
<a href="#__codelineno-5-5" id="__codelineno-5-5" name="__codelineno-5-5"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">dp</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="bp">count</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="bp">count</span><span class="p">:</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
<a href="#__codelineno-5-6" id="__codelineno-5-6" name="__codelineno-5-6"></a><span class="w"> </span><span class="c1">// 状態遷移:先頭行と先頭列</span>
<a href="#__codelineno-5-7" id="__codelineno-5-7" name="__codelineno-5-7"></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">1</span><span class="w"> </span><span class="p">...</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-5-8" id="__codelineno-5-8" name="__codelineno-5-8"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">i</span>
<a href="#__codelineno-5-9" id="__codelineno-5-9" name="__codelineno-5-9"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-5-10" id="__codelineno-5-10" name="__codelineno-5-10"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">...</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-5-11" id="__codelineno-5-11" name="__codelineno-5-11"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">j</span>
<a href="#__codelineno-5-12" id="__codelineno-5-12" name="__codelineno-5-12"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-5-13" id="__codelineno-5-13" name="__codelineno-5-13"></a><span class="w"> </span><span class="c1">// 状態遷移:残りの行と列</span>
<a href="#__codelineno-5-14" id="__codelineno-5-14" name="__codelineno-5-14"></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">1</span><span class="w"> </span><span class="p">...</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-5-15" id="__codelineno-5-15" name="__codelineno-5-15"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">...</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-5-16" id="__codelineno-5-16" name="__codelineno-5-16"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">s</span><span class="p">.</span><span class="n">utf8CString</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="n">t</span><span class="p">.</span><span class="n">utf8CString</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-5-17" id="__codelineno-5-17" name="__codelineno-5-17"></a><span class="w"> </span><span class="c1">// 2 つの文字が等しい場合、その 2 文字をスキップする</span>
<a href="#__codelineno-5-18" id="__codelineno-5-18" name="__codelineno-5-18"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span>
<a href="#__codelineno-5-19" id="__codelineno-5-19" name="__codelineno-5-19"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-5-20" id="__codelineno-5-20" name="__codelineno-5-20"></a><span class="w"> </span><span class="c1">// 最小編集回数 = 挿入、削除、置換の 3 操作での最小編集回数 + 1</span>
<a href="#__codelineno-5-21" id="__codelineno-5-21" name="__codelineno-5-21"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="bp">min</span><span class="p">(</span><span class="bp">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">j</span><span class="p">]),</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">j</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="o">+</span><span class="w"> </span><span class="mi">1</span>
<a href="#__codelineno-5-22" id="__codelineno-5-22" name="__codelineno-5-22"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-5-23" id="__codelineno-5-23" name="__codelineno-5-23"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-5-24" id="__codelineno-5-24" name="__codelineno-5-24"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-5-25" id="__codelineno-5-25" name="__codelineno-5-25"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="n">m</span><span class="p">]</span>
<a href="#__codelineno-5-26" id="__codelineno-5-26" name="__codelineno-5-26"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">edit_distance.js</span><pre><span></span><code><a href="#__codelineno-6-1" id="__codelineno-6-1" name="__codelineno-6-1"></a><span class="cm">/* 編集距離:動的計画法 */</span>
<a href="#__codelineno-6-2" id="__codelineno-6-2" name="__codelineno-6-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">editDistanceDP</span><span class="p">(</span><span class="nx">s</span><span class="p">,</span><span class="w"> </span><span class="nx">t</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-6-3" id="__codelineno-6-3" name="__codelineno-6-3"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">s</span><span class="p">.</span><span class="nx">length</span><span class="p">,</span>
<a href="#__codelineno-6-4" id="__codelineno-6-4" name="__codelineno-6-4"></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">t</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
<a href="#__codelineno-6-5" id="__codelineno-6-5" name="__codelineno-6-5"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">.</span><span class="kr">from</span><span class="p">({</span><span class="w"> </span><span class="nx">length</span><span class="o">:</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="w"> </span><span class="p">},</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</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="nx">fill</span><span class="p">(</span><span class="mf">0</span><span class="p">));</span>
<a href="#__codelineno-6-6" id="__codelineno-6-6" name="__codelineno-6-6"></a><span class="w"> </span><span class="c1">// 状態遷移:先頭行と先頭列</span>
<a href="#__codelineno-6-7" id="__codelineno-6-7" name="__codelineno-6-7"></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">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</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 href="#__codelineno-6-8" id="__codelineno-6-8" name="__codelineno-6-8"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="mf">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">i</span><span class="p">;</span>
<a href="#__codelineno-6-9" id="__codelineno-6-9" name="__codelineno-6-9"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-6-10" id="__codelineno-6-10" name="__codelineno-6-10"></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">j</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">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">m</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-6-11" id="__codelineno-6-11" name="__codelineno-6-11"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="mf">0</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">j</span><span class="p">;</span>
<a href="#__codelineno-6-12" id="__codelineno-6-12" name="__codelineno-6-12"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-6-13" id="__codelineno-6-13" name="__codelineno-6-13"></a><span class="w"> </span><span class="c1">// 状態遷移:残りの行と列</span>
<a href="#__codelineno-6-14" id="__codelineno-6-14" name="__codelineno-6-14"></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">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</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 href="#__codelineno-6-15" id="__codelineno-6-15" name="__codelineno-6-15"></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">j</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">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">m</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-6-16" id="__codelineno-6-16" name="__codelineno-6-16"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">s</span><span class="p">.</span><span class="nx">charAt</span><span class="p">(</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="o">===</span><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">charAt</span><span class="p">(</span><span class="nx">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-6-17" id="__codelineno-6-17" name="__codelineno-6-17"></a><span class="w"> </span><span class="c1">// 2 つの文字が等しい場合、その 2 文字をスキップする</span>
<a href="#__codelineno-6-18" id="__codelineno-6-18" name="__codelineno-6-18"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</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="nx">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">];</span>
<a href="#__codelineno-6-19" id="__codelineno-6-19" name="__codelineno-6-19"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-6-20" id="__codelineno-6-20" name="__codelineno-6-20"></a><span class="w"> </span><span class="c1">// 最小編集回数 = 挿入、削除、置換の 3 操作での最小編集回数 + 1</span>
<a href="#__codelineno-6-21" id="__codelineno-6-21" name="__codelineno-6-21"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span>
<a href="#__codelineno-6-22" id="__codelineno-6-22" name="__codelineno-6-22"></a><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">min</span><span class="p">(</span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">],</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</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="nx">j</span><span class="p">],</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</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="nx">j</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="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
<a href="#__codelineno-6-23" id="__codelineno-6-23" name="__codelineno-6-23"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-6-24" id="__codelineno-6-24" name="__codelineno-6-24"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-6-25" id="__codelineno-6-25" name="__codelineno-6-25"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-6-26" id="__codelineno-6-26" name="__codelineno-6-26"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">n</span><span class="p">][</span><span class="nx">m</span><span class="p">];</span>
<a href="#__codelineno-6-27" id="__codelineno-6-27" name="__codelineno-6-27"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">edit_distance.ts</span><pre><span></span><code><a href="#__codelineno-7-1" id="__codelineno-7-1" name="__codelineno-7-1"></a><span class="cm">/* 編集距離:動的計画法 */</span>
<a href="#__codelineno-7-2" id="__codelineno-7-2" name="__codelineno-7-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">editDistanceDP</span><span class="p">(</span><span class="nx">s</span><span class="o">:</span><span class="w"> </span><span class="kt">string</span><span class="p">,</span><span class="w"> </span><span class="nx">t</span><span class="o">:</span><span class="w"> </span><span class="kt">string</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-7-3" id="__codelineno-7-3" name="__codelineno-7-3"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">s</span><span class="p">.</span><span class="nx">length</span><span class="p">,</span>
<a href="#__codelineno-7-4" id="__codelineno-7-4" name="__codelineno-7-4"></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">t</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
<a href="#__codelineno-7-5" id="__codelineno-7-5" name="__codelineno-7-5"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">.</span><span class="kr">from</span><span class="p">({</span><span class="w"> </span><span class="nx">length</span><span class="o">:</span><span class="w"> </span><span class="kt">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="w"> </span><span class="p">},</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=&gt;</span>
<a href="#__codelineno-7-6" id="__codelineno-7-6" name="__codelineno-7-6"></a><span class="w"> </span><span class="nb">Array</span><span class="p">.</span><span class="kr">from</span><span class="p">({</span><span class="w"> </span><span class="nx">length</span><span class="o">:</span><span class="w"> </span><span class="kt">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="w"> </span><span class="p">},</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span>
<a href="#__codelineno-7-7" id="__codelineno-7-7" name="__codelineno-7-7"></a><span class="w"> </span><span class="p">);</span>
<a href="#__codelineno-7-8" id="__codelineno-7-8" name="__codelineno-7-8"></a><span class="w"> </span><span class="c1">// 状態遷移:先頭行と先頭列</span>
<a href="#__codelineno-7-9" id="__codelineno-7-9" name="__codelineno-7-9"></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">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</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 href="#__codelineno-7-10" id="__codelineno-7-10" name="__codelineno-7-10"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="mf">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">i</span><span class="p">;</span>
<a href="#__codelineno-7-11" id="__codelineno-7-11" name="__codelineno-7-11"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-7-12" id="__codelineno-7-12" name="__codelineno-7-12"></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">j</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">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">m</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-7-13" id="__codelineno-7-13" name="__codelineno-7-13"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="mf">0</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">j</span><span class="p">;</span>
<a href="#__codelineno-7-14" id="__codelineno-7-14" name="__codelineno-7-14"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-7-15" id="__codelineno-7-15" name="__codelineno-7-15"></a><span class="w"> </span><span class="c1">// 状態遷移:残りの行と列</span>
<a href="#__codelineno-7-16" id="__codelineno-7-16" name="__codelineno-7-16"></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">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</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 href="#__codelineno-7-17" id="__codelineno-7-17" name="__codelineno-7-17"></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">j</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">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">m</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-7-18" id="__codelineno-7-18" name="__codelineno-7-18"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">s</span><span class="p">.</span><span class="nx">charAt</span><span class="p">(</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="o">===</span><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">charAt</span><span class="p">(</span><span class="nx">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-7-19" id="__codelineno-7-19" name="__codelineno-7-19"></a><span class="w"> </span><span class="c1">// 2 つの文字が等しい場合、その 2 文字をスキップする</span>
<a href="#__codelineno-7-20" id="__codelineno-7-20" name="__codelineno-7-20"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</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="nx">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">];</span>
<a href="#__codelineno-7-21" id="__codelineno-7-21" name="__codelineno-7-21"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-7-22" id="__codelineno-7-22" name="__codelineno-7-22"></a><span class="w"> </span><span class="c1">// 最小編集回数 = 挿入、削除、置換の 3 操作での最小編集回数 + 1</span>
<a href="#__codelineno-7-23" id="__codelineno-7-23" name="__codelineno-7-23"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span>
<a href="#__codelineno-7-24" id="__codelineno-7-24" name="__codelineno-7-24"></a><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">min</span><span class="p">(</span><span class="nx">dp</span><span class="p">[</span><span class="nx">i</span><span class="p">][</span><span class="nx">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">],</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</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="nx">j</span><span class="p">],</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</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="nx">j</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="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
<a href="#__codelineno-7-25" id="__codelineno-7-25" name="__codelineno-7-25"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-7-26" id="__codelineno-7-26" name="__codelineno-7-26"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-7-27" id="__codelineno-7-27" name="__codelineno-7-27"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-7-28" id="__codelineno-7-28" name="__codelineno-7-28"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">n</span><span class="p">][</span><span class="nx">m</span><span class="p">];</span>
<a href="#__codelineno-7-29" id="__codelineno-7-29" name="__codelineno-7-29"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">edit_distance.dart</span><pre><span></span><code><a href="#__codelineno-8-1" id="__codelineno-8-1" name="__codelineno-8-1"></a><span class="cm">/* 編集距離:動的計画法 */</span>
<a href="#__codelineno-8-2" id="__codelineno-8-2" name="__codelineno-8-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">editDistanceDP</span><span class="p">(</span><span class="kt">String</span><span class="w"> </span><span class="n">s</span><span class="p">,</span><span class="w"> </span><span class="kt">String</span><span class="w"> </span><span class="n">t</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-8-3" id="__codelineno-8-3" name="__codelineno-8-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">s</span><span class="p">.</span><span class="n">length</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="n">t</span><span class="p">.</span><span class="n">length</span><span class="p">;</span>
<a href="#__codelineno-8-4" id="__codelineno-8-4" name="__codelineno-8-4"></a><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">generate</span><span class="p">(</span><span class="n">n</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="p">(</span><span class="n">_</span><span class="p">)</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</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="m">0</span><span class="p">));</span>
<a href="#__codelineno-8-5" id="__codelineno-8-5" name="__codelineno-8-5"></a><span class="w"> </span><span class="c1">// 状態遷移:先頭行と先頭列</span>
<a href="#__codelineno-8-6" id="__codelineno-8-6" name="__codelineno-8-6"></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">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</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 href="#__codelineno-8-7" id="__codelineno-8-7" name="__codelineno-8-7"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="m">0</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 href="#__codelineno-8-8" id="__codelineno-8-8" name="__codelineno-8-8"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-8-9" id="__codelineno-8-9" name="__codelineno-8-9"></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">j</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">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-8-10" id="__codelineno-8-10" name="__codelineno-8-10"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="m">0</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">j</span><span class="p">;</span>
<a href="#__codelineno-8-11" id="__codelineno-8-11" name="__codelineno-8-11"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-8-12" id="__codelineno-8-12" name="__codelineno-8-12"></a><span class="w"> </span><span class="c1">// 状態遷移:残りの行と列</span>
<a href="#__codelineno-8-13" id="__codelineno-8-13" name="__codelineno-8-13"></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">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</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 href="#__codelineno-8-14" id="__codelineno-8-14" name="__codelineno-8-14"></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">j</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">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-8-15" id="__codelineno-8-15" name="__codelineno-8-15"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">s</span><span class="p">[</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="o">==</span><span class="w"> </span><span class="n">t</span><span class="p">[</span><span class="n">j</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="p">{</span>
<a href="#__codelineno-8-16" id="__codelineno-8-16" name="__codelineno-8-16"></a><span class="w"> </span><span class="c1">// 2 つの文字が等しい場合、その 2 文字をスキップする</span>
<a href="#__codelineno-8-17" id="__codelineno-8-17" name="__codelineno-8-17"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</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="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">];</span>
<a href="#__codelineno-8-18" id="__codelineno-8-18" name="__codelineno-8-18"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-8-19" id="__codelineno-8-19" name="__codelineno-8-19"></a><span class="w"> </span><span class="c1">// 最小編集回数 = 挿入、削除、置換の 3 操作での最小編集回数 + 1</span>
<a href="#__codelineno-8-20" id="__codelineno-8-20" name="__codelineno-8-20"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">min</span><span class="p">(</span><span class="n">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</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">dp</span><span class="p">[</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="n">j</span><span class="p">]),</span><span class="w"> </span><span class="n">dp</span><span class="p">[</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="n">j</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="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
<a href="#__codelineno-8-21" id="__codelineno-8-21" name="__codelineno-8-21"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-8-22" id="__codelineno-8-22" name="__codelineno-8-22"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-8-23" id="__codelineno-8-23" name="__codelineno-8-23"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-8-24" id="__codelineno-8-24" name="__codelineno-8-24"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="n">m</span><span class="p">];</span>
<a href="#__codelineno-8-25" id="__codelineno-8-25" name="__codelineno-8-25"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">edit_distance.rs</span><pre><span></span><code><a href="#__codelineno-9-1" id="__codelineno-9-1" name="__codelineno-9-1"></a><span class="cm">/* 編集距離:動的計画法 */</span>
<a href="#__codelineno-9-2" id="__codelineno-9-2" name="__codelineno-9-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">edit_distance_dp</span><span class="p">(</span><span class="n">s</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="kt">str</span><span class="p">,</span><span class="w"> </span><span class="n">t</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="kt">str</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-9-3" id="__codelineno-9-3" name="__codelineno-9-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">s</span><span class="p">.</span><span class="n">len</span><span class="p">(),</span><span class="w"> </span><span class="n">t</span><span class="p">.</span><span class="n">len</span><span class="p">());</span>
<a href="#__codelineno-9-4" id="__codelineno-9-4" name="__codelineno-9-4"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="fm">vec!</span><span class="p">[</span><span class="mi">0</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">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
<a href="#__codelineno-9-5" id="__codelineno-9-5" name="__codelineno-9-5"></a><span class="w"> </span><span class="c1">// 状態遷移:先頭行と先頭列</span>
<a href="#__codelineno-9-6" id="__codelineno-9-6" name="__codelineno-9-6"></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">1</span><span class="o">..=</span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-9-7" id="__codelineno-9-7" name="__codelineno-9-7"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</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 href="#__codelineno-9-8" id="__codelineno-9-8" name="__codelineno-9-8"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-9-9" id="__codelineno-9-9" name="__codelineno-9-9"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">..</span><span class="n">m</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-9-10" id="__codelineno-9-10" name="__codelineno-9-10"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span><span class="p">;</span>
<a href="#__codelineno-9-11" id="__codelineno-9-11" name="__codelineno-9-11"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-9-12" id="__codelineno-9-12" name="__codelineno-9-12"></a><span class="w"> </span><span class="c1">// 状態遷移:残りの行と列</span>
<a href="#__codelineno-9-13" id="__codelineno-9-13" name="__codelineno-9-13"></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">1</span><span class="o">..=</span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-9-14" id="__codelineno-9-14" name="__codelineno-9-14"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">..=</span><span class="n">m</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-9-15" id="__codelineno-9-15" name="__codelineno-9-15"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">s</span><span class="p">.</span><span class="n">chars</span><span class="p">().</span><span class="n">nth</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">t</span><span class="p">.</span><span class="n">chars</span><span class="p">().</span><span class="n">nth</span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-9-16" id="__codelineno-9-16" name="__codelineno-9-16"></a><span class="w"> </span><span class="c1">// 2 つの文字が等しい場合、その 2 文字をスキップする</span>
<a href="#__codelineno-9-17" id="__codelineno-9-17" name="__codelineno-9-17"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
<a href="#__codelineno-9-18" id="__codelineno-9-18" name="__codelineno-9-18"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-9-19" id="__codelineno-9-19" name="__codelineno-9-19"></a><span class="w"> </span><span class="c1">// 最小編集回数 = 挿入、削除、置換の 3 操作での最小編集回数 + 1</span>
<a href="#__codelineno-9-20" id="__codelineno-9-20" name="__codelineno-9-20"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span>
<a href="#__codelineno-9-21" id="__codelineno-9-21" name="__codelineno-9-21"></a><span class="w"> </span><span class="n">std</span><span class="p">::</span><span class="n">cmp</span><span class="p">::</span><span class="n">min</span><span class="p">(</span><span class="n">std</span><span class="p">::</span><span class="n">cmp</span><span class="p">::</span><span class="n">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">j</span><span class="p">]),</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">j</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="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
<a href="#__codelineno-9-22" id="__codelineno-9-22" name="__codelineno-9-22"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-9-23" id="__codelineno-9-23" name="__codelineno-9-23"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-9-24" id="__codelineno-9-24" name="__codelineno-9-24"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-9-25" id="__codelineno-9-25" name="__codelineno-9-25"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="n">m</span><span class="p">]</span>
<a href="#__codelineno-9-26" id="__codelineno-9-26" name="__codelineno-9-26"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">edit_distance.c</span><pre><span></span><code><a href="#__codelineno-10-1" id="__codelineno-10-1" name="__codelineno-10-1"></a><span class="cm">/* 編集距離:動的計画法 */</span>
<a href="#__codelineno-10-2" id="__codelineno-10-2" name="__codelineno-10-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">editDistanceDP</span><span class="p">(</span><span class="kt">char</span><span class="w"> </span><span class="o">*</span><span class="n">s</span><span class="p">,</span><span class="w"> </span><span class="kt">char</span><span class="w"> </span><span class="o">*</span><span class="n">t</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-10-3" id="__codelineno-10-3" name="__codelineno-10-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">**</span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">malloc</span><span class="p">((</span><span class="n">n</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="o">*</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="p">));</span>
<a href="#__codelineno-10-4" id="__codelineno-10-4" name="__codelineno-10-4"></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">&lt;=</span><span class="w"> </span><span class="n">n</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 href="#__codelineno-10-5" id="__codelineno-10-5" name="__codelineno-10-5"></a><span class="w"> </span><span class="n">dp</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">calloc</span><span class="p">(</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="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">));</span>
<a href="#__codelineno-10-6" id="__codelineno-10-6" name="__codelineno-10-6"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-10-7" id="__codelineno-10-7" name="__codelineno-10-7"></a><span class="w"> </span><span class="c1">// 状態遷移:先頭行と先頭列</span>
<a href="#__codelineno-10-8" id="__codelineno-10-8" name="__codelineno-10-8"></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">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</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 href="#__codelineno-10-9" id="__codelineno-10-9" name="__codelineno-10-9"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">0</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 href="#__codelineno-10-10" id="__codelineno-10-10" name="__codelineno-10-10"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-10-11" id="__codelineno-10-11" name="__codelineno-10-11"></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">j</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">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-10-12" id="__codelineno-10-12" name="__codelineno-10-12"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">j</span><span class="p">;</span>
<a href="#__codelineno-10-13" id="__codelineno-10-13" name="__codelineno-10-13"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-10-14" id="__codelineno-10-14" name="__codelineno-10-14"></a><span class="w"> </span><span class="c1">// 状態遷移:残りの行と列</span>
<a href="#__codelineno-10-15" id="__codelineno-10-15" name="__codelineno-10-15"></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">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</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 href="#__codelineno-10-16" id="__codelineno-10-16" name="__codelineno-10-16"></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">j</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">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-10-17" id="__codelineno-10-17" name="__codelineno-10-17"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">s</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">t</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-10-18" id="__codelineno-10-18" name="__codelineno-10-18"></a><span class="w"> </span><span class="c1">// 2 つの文字が等しい場合、その 2 文字をスキップする</span>
<a href="#__codelineno-10-19" id="__codelineno-10-19" name="__codelineno-10-19"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
<a href="#__codelineno-10-20" id="__codelineno-10-20" name="__codelineno-10-20"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-10-21" id="__codelineno-10-21" name="__codelineno-10-21"></a><span class="w"> </span><span class="c1">// 最小編集回数 = 挿入、削除、置換の 3 操作での最小編集回数 + 1</span>
<a href="#__codelineno-10-22" id="__codelineno-10-22" name="__codelineno-10-22"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">myMin</span><span class="p">(</span><span class="n">myMin</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">j</span><span class="p">]),</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">j</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="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
<a href="#__codelineno-10-23" id="__codelineno-10-23" name="__codelineno-10-23"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-10-24" id="__codelineno-10-24" name="__codelineno-10-24"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-10-25" id="__codelineno-10-25" name="__codelineno-10-25"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-10-26" id="__codelineno-10-26" name="__codelineno-10-26"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="n">m</span><span class="p">];</span>
<a href="#__codelineno-10-27" id="__codelineno-10-27" name="__codelineno-10-27"></a><span class="w"> </span><span class="c1">// メモリを解放する</span>
<a href="#__codelineno-10-28" id="__codelineno-10-28" name="__codelineno-10-28"></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">&lt;=</span><span class="w"> </span><span class="n">n</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 href="#__codelineno-10-29" id="__codelineno-10-29" name="__codelineno-10-29"></a><span class="w"> </span><span class="n">free</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
<a href="#__codelineno-10-30" id="__codelineno-10-30" name="__codelineno-10-30"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-10-31" id="__codelineno-10-31" name="__codelineno-10-31"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
<a href="#__codelineno-10-32" id="__codelineno-10-32" name="__codelineno-10-32"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">edit_distance.kt</span><pre><span></span><code><a href="#__codelineno-11-1" id="__codelineno-11-1" name="__codelineno-11-1"></a><span class="cm">/* 編集距離:動的計画法 */</span>
<a href="#__codelineno-11-2" id="__codelineno-11-2" name="__codelineno-11-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">editDistanceDP</span><span class="p">(</span><span class="n">s</span><span class="p">:</span><span class="w"> </span><span class="kt">String</span><span class="p">,</span><span class="w"> </span><span class="n">t</span><span class="p">:</span><span class="w"> </span><span class="kt">String</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-11-3" id="__codelineno-11-3" name="__codelineno-11-3"></a><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">s</span><span class="p">.</span><span class="na">length</span>
<a href="#__codelineno-11-4" id="__codelineno-11-4" name="__codelineno-11-4"></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">t</span><span class="p">.</span><span class="na">length</span>
<a href="#__codelineno-11-5" id="__codelineno-11-5" name="__codelineno-11-5"></a><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Array</span><span class="p">(</span><span class="n">n</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="p">{</span><span class="w"> </span><span class="n">IntArray</span><span class="p">(</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="p">}</span>
<a href="#__codelineno-11-6" id="__codelineno-11-6" name="__codelineno-11-6"></a><span class="w"> </span><span class="c1">// 状態遷移:先頭行と先頭列</span>
<a href="#__codelineno-11-7" id="__codelineno-11-7" name="__codelineno-11-7"></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="m">1.</span><span class="p">.</span><span class="na">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-11-8" id="__codelineno-11-8" name="__codelineno-11-8"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="m">0</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span>
<a href="#__codelineno-11-9" id="__codelineno-11-9" name="__codelineno-11-9"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-11-10" id="__codelineno-11-10" name="__codelineno-11-10"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">1.</span><span class="p">.</span><span class="na">m</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-11-11" id="__codelineno-11-11" name="__codelineno-11-11"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="m">0</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">j</span>
<a href="#__codelineno-11-12" id="__codelineno-11-12" name="__codelineno-11-12"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-11-13" id="__codelineno-11-13" name="__codelineno-11-13"></a><span class="w"> </span><span class="c1">// 状態遷移:残りの行と列</span>
<a href="#__codelineno-11-14" id="__codelineno-11-14" name="__codelineno-11-14"></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="m">1.</span><span class="p">.</span><span class="na">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-11-15" id="__codelineno-11-15" name="__codelineno-11-15"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">1.</span><span class="p">.</span><span class="na">m</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-11-16" id="__codelineno-11-16" name="__codelineno-11-16"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">s</span><span class="o">[</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="o">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">t</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-11-17" id="__codelineno-11-17" name="__codelineno-11-17"></a><span class="w"> </span><span class="c1">// 2 つの文字が等しい場合、その 2 文字をスキップする</span>
<a href="#__codelineno-11-18" id="__codelineno-11-18" name="__codelineno-11-18"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</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="o">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]</span>
<a href="#__codelineno-11-19" id="__codelineno-11-19" name="__codelineno-11-19"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-11-20" id="__codelineno-11-20" name="__codelineno-11-20"></a><span class="w"> </span><span class="c1">// 最小編集回数 = 挿入、削除、置換の 3 操作での最小編集回数 + 1</span>
<a href="#__codelineno-11-21" id="__codelineno-11-21" name="__codelineno-11-21"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">min</span><span class="p">(</span><span class="n">min</span><span class="p">(</span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</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="o">][</span><span class="n">j</span><span class="o">]</span><span class="p">),</span><span class="w"> </span><span class="n">dp</span><span class="o">[</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="o">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span>
<a href="#__codelineno-11-22" id="__codelineno-11-22" name="__codelineno-11-22"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-11-23" id="__codelineno-11-23" name="__codelineno-11-23"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-11-24" id="__codelineno-11-24" name="__codelineno-11-24"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-11-25" id="__codelineno-11-25" name="__codelineno-11-25"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">n</span><span class="o">][</span><span class="n">m</span><span class="o">]</span>
<a href="#__codelineno-11-26" id="__codelineno-11-26" name="__codelineno-11-26"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">edit_distance.rb</span><pre><span></span><code><a href="#__codelineno-12-1" id="__codelineno-12-1" name="__codelineno-12-1"></a><span class="c1">### 編集距離:動的計画法 ###</span>
<a href="#__codelineno-12-2" id="__codelineno-12-2" name="__codelineno-12-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">edit_distance_dp</span><span class="p">(</span><span class="n">s</span><span class="p">,</span><span class="w"> </span><span class="n">t</span><span class="p">)</span>
<a href="#__codelineno-12-3" id="__codelineno-12-3" name="__codelineno-12-3"></a><span class="w"> </span><span class="n">n</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="n">s</span><span class="o">.</span><span class="n">length</span><span class="p">,</span><span class="w"> </span><span class="n">t</span><span class="o">.</span><span class="n">length</span>
<a href="#__codelineno-12-4" id="__codelineno-12-4" name="__codelineno-12-4"></a><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</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="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-12-5" id="__codelineno-12-5" name="__codelineno-12-5"></a><span class="w"> </span><span class="c1"># 状態遷移:先頭行と先頭列</span>
<a href="#__codelineno-12-6" id="__codelineno-12-6" name="__codelineno-12-6"></a><span class="w"> </span><span class="p">(</span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">))</span><span class="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">i</span><span class="o">|</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="mi">0</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 href="#__codelineno-12-7" id="__codelineno-12-7" name="__codelineno-12-7"></a><span class="w"> </span><span class="p">(</span><span class="mi">1</span><span class="o">...</span><span class="p">(</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="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">j</span><span class="o">|</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="mi">0</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-12-8" id="__codelineno-12-8" name="__codelineno-12-8"></a><span class="w"> </span><span class="c1"># 状態遷移:残りの行と列</span>
<a href="#__codelineno-12-9" id="__codelineno-12-9" name="__codelineno-12-9"></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">1</span><span class="o">...</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
<a href="#__codelineno-12-10" id="__codelineno-12-10" name="__codelineno-12-10"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="p">(</span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
<a href="#__codelineno-12-11" id="__codelineno-12-11" name="__codelineno-12-11"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">s</span><span class="o">[</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="o">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">t</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span>
<a href="#__codelineno-12-12" id="__codelineno-12-12" name="__codelineno-12-12"></a><span class="w"> </span><span class="c1"># 2 つの文字が等しい場合、その 2 文字をスキップする</span>
<a href="#__codelineno-12-13" id="__codelineno-12-13" name="__codelineno-12-13"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</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="o">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span>
<a href="#__codelineno-12-14" id="__codelineno-12-14" name="__codelineno-12-14"></a><span class="w"> </span><span class="k">else</span>
<a href="#__codelineno-12-15" id="__codelineno-12-15" name="__codelineno-12-15"></a><span class="w"> </span><span class="c1"># 最小編集回数 = 挿入、削除、置換の 3 操作での最小編集回数 + 1</span>
<a href="#__codelineno-12-16" id="__codelineno-12-16" name="__codelineno-12-16"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</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="o">][</span><span class="n">j</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</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="o">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]].</span><span class="n">min</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
<a href="#__codelineno-12-17" id="__codelineno-12-17" name="__codelineno-12-17"></a><span class="w"> </span><span class="k">end</span>
<a href="#__codelineno-12-18" id="__codelineno-12-18" name="__codelineno-12-18"></a><span class="w"> </span><span class="k">end</span>
<a href="#__codelineno-12-19" id="__codelineno-12-19" name="__codelineno-12-19"></a><span class="w"> </span><span class="k">end</span>
<a href="#__codelineno-12-20" id="__codelineno-12-20" name="__codelineno-12-20"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">n</span><span class="o">][</span><span class="n">m</span><span class="o">]</span>
<a href="#__codelineno-12-21" id="__codelineno-12-21" name="__codelineno-12-21"></a><span class="k">end</span>
</code></pre></div>
</div>
</div>
</div>
<details class="pythontutor">
<summary>実行の可視化</summary>
<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20edit_distance_dp%28s%3A%20str,%20t%3A%20str%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E7%B7%A8%E9%9B%86%E8%B7%9D%E9%9B%A2%EF%BC%9A%E5%8B%95%E7%9A%84%E8%A8%88%E7%94%BB%E6%B3%95%22%22%22%0A%20%20%20%20n,%20m%20%3D%20len%28s%29,%20len%28t%29%0A%20%20%20%20dp%20%3D%20%5B%5B0%5D%20%2A%20%28m%20%2B%201%29%20for%20_%20in%20range%28n%20%2B%201%29%5D%0A%20%20%20%20%23%20%E7%8A%B6%E6%85%8B%E9%81%B7%E7%A7%BB%EF%BC%9A%E5%85%88%E9%A0%AD%E8%A1%8C%E3%81%A8%E5%85%88%E9%A0%AD%E5%88%97%0A%20%20%20%20for%20i%20in%20range%281,%20n%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20dp%5Bi%5D%5B0%5D%20%3D%20i%0A%20%20%20%20for%20j%20in%20range%281,%20m%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20dp%5B0%5D%5Bj%5D%20%3D%20j%0A%20%20%20%20%23%20%E7%8A%B6%E6%85%8B%E9%81%B7%E7%A7%BB%EF%BC%9A%E6%AE%8B%E3%82%8A%E3%81%AE%E8%A1%8C%E3%81%A8%E5%88%97%0A%20%20%20%20for%20i%20in%20range%281,%20n%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20for%20j%20in%20range%281,%20m%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20s%5Bi%20-%201%5D%20%3D%3D%20t%5Bj%20-%201%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%23%202%20%E3%81%A4%E3%81%AE%E6%96%87%E5%AD%97%E3%81%8C%E7%AD%89%E3%81%97%E3%81%84%E5%A0%B4%E5%90%88%E3%80%81%E3%81%9D%E3%81%AE%202%20%E6%96%87%E5%AD%97%E3%82%92%E3%82%B9%E3%82%AD%E3%83%83%E3%83%97%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20dp%5Bi%5D%5Bj%5D%20%3D%20dp%5Bi%20-%201%5D%5Bj%20-%201%5D%0A%20%20%20%20%20%20%20%20%20%20%20%20else%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E6%9C%80%E5%B0%8F%E7%B7%A8%E9%9B%86%E5%9B%9E%E6%95%B0%20%3D%20%E6%8C%BF%E5%85%A5%E3%80%81%E5%89%8A%E9%99%A4%E3%80%81%E7%BD%AE%E6%8F%9B%E3%81%AE%203%20%E6%93%8D%E4%BD%9C%E3%81%A7%E3%81%AE%E6%9C%80%E5%B0%8F%E7%B7%A8%E9%9B%86%E5%9B%9E%E6%95%B0%20%2B%201%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20dp%5Bi%5D%5Bj%5D%20%3D%20min%28dp%5Bi%5D%5Bj%20-%201%5D,%20dp%5Bi%20-%201%5D%5Bj%5D,%20dp%5Bi%20-%201%5D%5Bj%20-%201%5D%29%20%2B%201%0A%20%20%20%20return%20dp%5Bn%5D%5Bm%5D%0A%0A%0A%22%22%22%E5%AE%9F%E8%A1%8C%E7%94%A8%E3%82%B3%E3%83%BC%E3%83%89%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20s%20%3D%20%22bag%22%0A%20%20%20%20t%20%3D%20%22pack%22%0A%20%20%20%20n,%20m%20%3D%20len%28s%29,%20len%28t%29%0A%0A%20%20%20%20%23%20%E5%8B%95%E7%9A%84%E8%A8%88%E7%94%BB%E6%B3%95%0A%20%20%20%20res%20%3D%20edit_distance_dp%28s,%20t%29%0A%20%20%20%20print%28f%22%7Bs%7D%20%E3%82%92%20%7Bt%7D%20%E3%81%AB%E5%A4%89%E6%9B%B4%E3%81%99%E3%82%8B%E3%81%AB%E3%81%AF%E6%9C%80%E4%BD%8E%20%7Bres%7D%20%E5%9B%9E%E3%81%AE%E7%B7%A8%E9%9B%86%E3%81%8C%E5%BF%85%E8%A6%81%22%29&amp;codeDivHeight=472&amp;codeDivWidth=350&amp;cumulative=false&amp;curInstr=6&amp;heapPrimitives=nevernest&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false" title="実行の可視化"> </iframe></div>
<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20edit_distance_dp%28s%3A%20str,%20t%3A%20str%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E7%B7%A8%E9%9B%86%E8%B7%9D%E9%9B%A2%EF%BC%9A%E5%8B%95%E7%9A%84%E8%A8%88%E7%94%BB%E6%B3%95%22%22%22%0A%20%20%20%20n,%20m%20%3D%20len%28s%29,%20len%28t%29%0A%20%20%20%20dp%20%3D%20%5B%5B0%5D%20%2A%20%28m%20%2B%201%29%20for%20_%20in%20range%28n%20%2B%201%29%5D%0A%20%20%20%20%23%20%E7%8A%B6%E6%85%8B%E9%81%B7%E7%A7%BB%EF%BC%9A%E5%85%88%E9%A0%AD%E8%A1%8C%E3%81%A8%E5%85%88%E9%A0%AD%E5%88%97%0A%20%20%20%20for%20i%20in%20range%281,%20n%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20dp%5Bi%5D%5B0%5D%20%3D%20i%0A%20%20%20%20for%20j%20in%20range%281,%20m%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20dp%5B0%5D%5Bj%5D%20%3D%20j%0A%20%20%20%20%23%20%E7%8A%B6%E6%85%8B%E9%81%B7%E7%A7%BB%EF%BC%9A%E6%AE%8B%E3%82%8A%E3%81%AE%E8%A1%8C%E3%81%A8%E5%88%97%0A%20%20%20%20for%20i%20in%20range%281,%20n%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20for%20j%20in%20range%281,%20m%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20s%5Bi%20-%201%5D%20%3D%3D%20t%5Bj%20-%201%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%23%202%20%E3%81%A4%E3%81%AE%E6%96%87%E5%AD%97%E3%81%8C%E7%AD%89%E3%81%97%E3%81%84%E5%A0%B4%E5%90%88%E3%80%81%E3%81%9D%E3%81%AE%202%20%E6%96%87%E5%AD%97%E3%82%92%E3%82%B9%E3%82%AD%E3%83%83%E3%83%97%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20dp%5Bi%5D%5Bj%5D%20%3D%20dp%5Bi%20-%201%5D%5Bj%20-%201%5D%0A%20%20%20%20%20%20%20%20%20%20%20%20else%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E6%9C%80%E5%B0%8F%E7%B7%A8%E9%9B%86%E5%9B%9E%E6%95%B0%20%3D%20%E6%8C%BF%E5%85%A5%E3%80%81%E5%89%8A%E9%99%A4%E3%80%81%E7%BD%AE%E6%8F%9B%E3%81%AE%203%20%E6%93%8D%E4%BD%9C%E3%81%A7%E3%81%AE%E6%9C%80%E5%B0%8F%E7%B7%A8%E9%9B%86%E5%9B%9E%E6%95%B0%20%2B%201%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20dp%5Bi%5D%5Bj%5D%20%3D%20min%28dp%5Bi%5D%5Bj%20-%201%5D,%20dp%5Bi%20-%201%5D%5Bj%5D,%20dp%5Bi%20-%201%5D%5Bj%20-%201%5D%29%20%2B%201%0A%20%20%20%20return%20dp%5Bn%5D%5Bm%5D%0A%0A%0A%22%22%22%E5%AE%9F%E8%A1%8C%E7%94%A8%E3%82%B3%E3%83%BC%E3%83%89%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20s%20%3D%20%22bag%22%0A%20%20%20%20t%20%3D%20%22pack%22%0A%20%20%20%20n,%20m%20%3D%20len%28s%29,%20len%28t%29%0A%0A%20%20%20%20%23%20%E5%8B%95%E7%9A%84%E8%A8%88%E7%94%BB%E6%B3%95%0A%20%20%20%20res%20%3D%20edit_distance_dp%28s,%20t%29%0A%20%20%20%20print%28f%22%7Bs%7D%20%E3%82%92%20%7Bt%7D%20%E3%81%AB%E5%A4%89%E6%9B%B4%E3%81%99%E3%82%8B%E3%81%AB%E3%81%AF%E6%9C%80%E4%BD%8E%20%7Bres%7D%20%E5%9B%9E%E3%81%AE%E7%B7%A8%E9%9B%86%E3%81%8C%E5%BF%85%E8%A6%81%22%29&amp;codeDivHeight=800&amp;codeDivWidth=600&amp;cumulative=false&amp;curInstr=6&amp;heapPrimitives=nevernest&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false" rel="noopener noreferrer" target="_blank">全画面で表示 &gt;</a></div></p>
</details>
<p>図 14-30 のように、編集距離問題の状態遷移はナップサック問題によく似ており、どちらも二次元の表を埋める過程と捉えられます。</p>
<div class="tabbed-set tabbed-alternate" data-figure-sequence="" data-tabs="2:15"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio"/><input id="__tabbed_2_2" name="__tabbed_2" type="radio"/><input id="__tabbed_2_3" name="__tabbed_2" type="radio"/><input id="__tabbed_2_4" name="__tabbed_2" type="radio"/><input id="__tabbed_2_5" name="__tabbed_2" type="radio"/><input id="__tabbed_2_6" name="__tabbed_2" type="radio"/><input id="__tabbed_2_7" name="__tabbed_2" type="radio"/><input id="__tabbed_2_8" name="__tabbed_2" type="radio"/><input id="__tabbed_2_9" name="__tabbed_2" type="radio"/><input id="__tabbed_2_10" name="__tabbed_2" type="radio"/><input id="__tabbed_2_11" name="__tabbed_2" type="radio"/><input id="__tabbed_2_12" name="__tabbed_2" type="radio"/><input id="__tabbed_2_13" name="__tabbed_2" type="radio"/><input id="__tabbed_2_14" name="__tabbed_2" type="radio"/><input id="__tabbed_2_15" name="__tabbed_2" type="radio"/><div class="tabbed-labels"><label for="__tabbed_2_1">&lt;1&gt;</label><label for="__tabbed_2_2">&lt;2&gt;</label><label for="__tabbed_2_3">&lt;3&gt;</label><label for="__tabbed_2_4">&lt;4&gt;</label><label for="__tabbed_2_5">&lt;5&gt;</label><label for="__tabbed_2_6">&lt;6&gt;</label><label for="__tabbed_2_7">&lt;7&gt;</label><label for="__tabbed_2_8">&lt;8&gt;</label><label for="__tabbed_2_9">&lt;9&gt;</label><label for="__tabbed_2_10">&lt;10&gt;</label><label for="__tabbed_2_11">&lt;11&gt;</label><label for="__tabbed_2_12">&lt;12&gt;</label><label for="__tabbed_2_13">&lt;13&gt;</label><label for="__tabbed_2_14">&lt;14&gt;</label><label for="__tabbed_2_15">&lt;15&gt;</label></div>
<div class="tabbed-content">
<div class="tabbed-block">
<p><ha-svg-figure class="animation-figure" data-book-key="ja/chapter_dynamic_programming/edit_distance_problem.assets/edit_distance_dp_step1.png" data-dark-src="/assets/figure-svg/figures/1bd4d0989f71a4f320c15cdc.json" data-src="/assets/figure-svg/figures/26c3e7efaac605fb7520a42e.json" style=";--figure-ratio:960.0/540.0"><object data="/ja/chapter_dynamic_programming/edit_distance_problem.assets/edit_distance_dp_step1.svg" data-theme="light" tabindex="-1" type="image/svg+xml">編集距離を動的計画法で求める流れ</object><object data="/ja/chapter_dynamic_programming/edit_distance_problem.assets/edit_distance_dp_step1.dark.svg" data-theme="dark" tabindex="-1" type="image/svg+xml">編集距離を動的計画法で求める流れ</object></ha-svg-figure></p>
</div>
<div class="tabbed-block">
<p><ha-svg-figure class="animation-figure" data-book-key="ja/chapter_dynamic_programming/edit_distance_problem.assets/edit_distance_dp_step2.png" data-dark-src="/assets/figure-svg/figures/c82ee45c4e803c7071ac0546.json" data-src="/assets/figure-svg/figures/5861ec184f7c9d058a18a81c.json" style=";--figure-ratio:960.0/540.0"><object data="/ja/chapter_dynamic_programming/edit_distance_problem.assets/edit_distance_dp_step2.svg" data-theme="light" tabindex="-1" type="image/svg+xml">編集距離を動的計画法で求める流れ:手順 2</object><object data="/ja/chapter_dynamic_programming/edit_distance_problem.assets/edit_distance_dp_step2.dark.svg" data-theme="dark" tabindex="-1" type="image/svg+xml">編集距離を動的計画法で求める流れ:手順 2</object></ha-svg-figure></p>
</div>
<div class="tabbed-block">
<p><ha-svg-figure class="animation-figure" data-book-key="ja/chapter_dynamic_programming/edit_distance_problem.assets/edit_distance_dp_step3.png" data-dark-src="/assets/figure-svg/figures/595e5bd2b09e33cbe38c7e1b.json" data-src="/assets/figure-svg/figures/c920277b30044fb3dfdc855f.json" style=";--figure-ratio:960.0/540.0"><object data="/ja/chapter_dynamic_programming/edit_distance_problem.assets/edit_distance_dp_step3.svg" data-theme="light" tabindex="-1" type="image/svg+xml">編集距離を動的計画法で求める流れ:手順 3</object><object data="/ja/chapter_dynamic_programming/edit_distance_problem.assets/edit_distance_dp_step3.dark.svg" data-theme="dark" tabindex="-1" type="image/svg+xml">編集距離を動的計画法で求める流れ:手順 3</object></ha-svg-figure></p>
</div>
<div class="tabbed-block">
<p><ha-svg-figure class="animation-figure" data-book-key="ja/chapter_dynamic_programming/edit_distance_problem.assets/edit_distance_dp_step4.png" data-dark-src="/assets/figure-svg/figures/b1d224b166bc3cd67f6f40e8.json" data-src="/assets/figure-svg/figures/d49a503a27cd353911b4bae3.json" style=";--figure-ratio:960.0/540.0"><object data="/ja/chapter_dynamic_programming/edit_distance_problem.assets/edit_distance_dp_step4.svg" data-theme="light" tabindex="-1" type="image/svg+xml">編集距離を動的計画法で求める流れ:手順 4</object><object data="/ja/chapter_dynamic_programming/edit_distance_problem.assets/edit_distance_dp_step4.dark.svg" data-theme="dark" tabindex="-1" type="image/svg+xml">編集距離を動的計画法で求める流れ:手順 4</object></ha-svg-figure></p>
</div>
<div class="tabbed-block">
<p><ha-svg-figure class="animation-figure" data-book-key="ja/chapter_dynamic_programming/edit_distance_problem.assets/edit_distance_dp_step5.png" data-dark-src="/assets/figure-svg/figures/c5c6764b976938d2d951dc73.json" data-src="/assets/figure-svg/figures/8f57406860258f787c4935e4.json" style=";--figure-ratio:960.0/540.0"><object data="/ja/chapter_dynamic_programming/edit_distance_problem.assets/edit_distance_dp_step5.svg" data-theme="light" tabindex="-1" type="image/svg+xml">編集距離を動的計画法で求める流れ:手順 5</object><object data="/ja/chapter_dynamic_programming/edit_distance_problem.assets/edit_distance_dp_step5.dark.svg" data-theme="dark" tabindex="-1" type="image/svg+xml">編集距離を動的計画法で求める流れ:手順 5</object></ha-svg-figure></p>
</div>
<div class="tabbed-block">
<p><ha-svg-figure class="animation-figure" data-book-key="ja/chapter_dynamic_programming/edit_distance_problem.assets/edit_distance_dp_step6.png" data-dark-src="/assets/figure-svg/figures/58caac5c2ebfff8dd7716c73.json" data-src="/assets/figure-svg/figures/fedfd0988d9485ec23f81494.json" style=";--figure-ratio:960.0/540.0"><object data="/ja/chapter_dynamic_programming/edit_distance_problem.assets/edit_distance_dp_step6.svg" data-theme="light" tabindex="-1" type="image/svg+xml">編集距離を動的計画法で求める流れ:手順 6</object><object data="/ja/chapter_dynamic_programming/edit_distance_problem.assets/edit_distance_dp_step6.dark.svg" data-theme="dark" tabindex="-1" type="image/svg+xml">編集距離を動的計画法で求める流れ:手順 6</object></ha-svg-figure></p>
</div>
<div class="tabbed-block">
<p><ha-svg-figure class="animation-figure" data-book-key="ja/chapter_dynamic_programming/edit_distance_problem.assets/edit_distance_dp_step7.png" data-dark-src="/assets/figure-svg/figures/821f9daff80e19e91f0429d4.json" data-src="/assets/figure-svg/figures/1016afa7bce60afbaa7ca0c7.json" style=";--figure-ratio:960.0/540.0"><object data="/ja/chapter_dynamic_programming/edit_distance_problem.assets/edit_distance_dp_step7.svg" data-theme="light" tabindex="-1" type="image/svg+xml">編集距離を動的計画法で求める流れ:手順 7</object><object data="/ja/chapter_dynamic_programming/edit_distance_problem.assets/edit_distance_dp_step7.dark.svg" data-theme="dark" tabindex="-1" type="image/svg+xml">編集距離を動的計画法で求める流れ:手順 7</object></ha-svg-figure></p>
</div>
<div class="tabbed-block">
<p><ha-svg-figure class="animation-figure" data-book-key="ja/chapter_dynamic_programming/edit_distance_problem.assets/edit_distance_dp_step8.png" data-dark-src="/assets/figure-svg/figures/c51d602b2677fde600437046.json" data-src="/assets/figure-svg/figures/4b6d18c84f5677a258ec1814.json" style=";--figure-ratio:960.0/540.0"><object data="/ja/chapter_dynamic_programming/edit_distance_problem.assets/edit_distance_dp_step8.svg" data-theme="light" tabindex="-1" type="image/svg+xml">編集距離を動的計画法で求める流れ:手順 8</object><object data="/ja/chapter_dynamic_programming/edit_distance_problem.assets/edit_distance_dp_step8.dark.svg" data-theme="dark" tabindex="-1" type="image/svg+xml">編集距離を動的計画法で求める流れ:手順 8</object></ha-svg-figure></p>
</div>
<div class="tabbed-block">
<p><ha-svg-figure class="animation-figure" data-book-key="ja/chapter_dynamic_programming/edit_distance_problem.assets/edit_distance_dp_step9.png" data-dark-src="/assets/figure-svg/figures/03f1ceb272c0780e92e233e4.json" data-src="/assets/figure-svg/figures/4aa4aad2dfecb9103f41ccab.json" style=";--figure-ratio:960.0/540.0"><object data="/ja/chapter_dynamic_programming/edit_distance_problem.assets/edit_distance_dp_step9.svg" data-theme="light" tabindex="-1" type="image/svg+xml">編集距離を動的計画法で求める流れ:手順 9</object><object data="/ja/chapter_dynamic_programming/edit_distance_problem.assets/edit_distance_dp_step9.dark.svg" data-theme="dark" tabindex="-1" type="image/svg+xml">編集距離を動的計画法で求める流れ:手順 9</object></ha-svg-figure></p>
</div>
<div class="tabbed-block">
<p><ha-svg-figure class="animation-figure" data-book-key="ja/chapter_dynamic_programming/edit_distance_problem.assets/edit_distance_dp_step10.png" data-dark-src="/assets/figure-svg/figures/cbc186934dc9952dfe4d8a3d.json" data-src="/assets/figure-svg/figures/012212cf3827b54c8be57c78.json" style=";--figure-ratio:960.0/540.0"><object data="/ja/chapter_dynamic_programming/edit_distance_problem.assets/edit_distance_dp_step10.svg" data-theme="light" tabindex="-1" type="image/svg+xml">編集距離を動的計画法で求める流れ:手順 10</object><object data="/ja/chapter_dynamic_programming/edit_distance_problem.assets/edit_distance_dp_step10.dark.svg" data-theme="dark" tabindex="-1" type="image/svg+xml">編集距離を動的計画法で求める流れ:手順 10</object></ha-svg-figure></p>
</div>
<div class="tabbed-block">
<p><ha-svg-figure class="animation-figure" data-book-key="ja/chapter_dynamic_programming/edit_distance_problem.assets/edit_distance_dp_step11.png" data-dark-src="/assets/figure-svg/figures/96b9c455d8c2043f6652ab41.json" data-src="/assets/figure-svg/figures/7351077952cc449ab6a25ec6.json" style=";--figure-ratio:960.0/540.0"><object data="/ja/chapter_dynamic_programming/edit_distance_problem.assets/edit_distance_dp_step11.svg" data-theme="light" tabindex="-1" type="image/svg+xml">編集距離を動的計画法で求める流れ:手順 11</object><object data="/ja/chapter_dynamic_programming/edit_distance_problem.assets/edit_distance_dp_step11.dark.svg" data-theme="dark" tabindex="-1" type="image/svg+xml">編集距離を動的計画法で求める流れ:手順 11</object></ha-svg-figure></p>
</div>
<div class="tabbed-block">
<p><ha-svg-figure class="animation-figure" data-book-key="ja/chapter_dynamic_programming/edit_distance_problem.assets/edit_distance_dp_step12.png" data-dark-src="/assets/figure-svg/figures/8b36c5f09f44d5a3bc80ce6f.json" data-src="/assets/figure-svg/figures/21ee852d5daa00b4b9f839da.json" style=";--figure-ratio:960.0/540.0"><object data="/ja/chapter_dynamic_programming/edit_distance_problem.assets/edit_distance_dp_step12.svg" data-theme="light" tabindex="-1" type="image/svg+xml">編集距離を動的計画法で求める流れ:手順 12</object><object data="/ja/chapter_dynamic_programming/edit_distance_problem.assets/edit_distance_dp_step12.dark.svg" data-theme="dark" tabindex="-1" type="image/svg+xml">編集距離を動的計画法で求める流れ:手順 12</object></ha-svg-figure></p>
</div>
<div class="tabbed-block">
<p><ha-svg-figure class="animation-figure" data-book-key="ja/chapter_dynamic_programming/edit_distance_problem.assets/edit_distance_dp_step13.png" data-dark-src="/assets/figure-svg/figures/68d98e9807fa9f11707bfec4.json" data-src="/assets/figure-svg/figures/2175f6cf67f6d19aac5dbc35.json" style=";--figure-ratio:960.0/540.0"><object data="/ja/chapter_dynamic_programming/edit_distance_problem.assets/edit_distance_dp_step13.svg" data-theme="light" tabindex="-1" type="image/svg+xml">編集距離を動的計画法で求める流れ:手順 13</object><object data="/ja/chapter_dynamic_programming/edit_distance_problem.assets/edit_distance_dp_step13.dark.svg" data-theme="dark" tabindex="-1" type="image/svg+xml">編集距離を動的計画法で求める流れ:手順 13</object></ha-svg-figure></p>
</div>
<div class="tabbed-block">
<p><ha-svg-figure class="animation-figure" data-book-key="ja/chapter_dynamic_programming/edit_distance_problem.assets/edit_distance_dp_step14.png" data-dark-src="/assets/figure-svg/figures/eb30a76e671f9dbc00f1638a.json" data-src="/assets/figure-svg/figures/b4107ca24cfd73de5ebf0f7a.json" style=";--figure-ratio:960.0/540.0"><object data="/ja/chapter_dynamic_programming/edit_distance_problem.assets/edit_distance_dp_step14.svg" data-theme="light" tabindex="-1" type="image/svg+xml">編集距離を動的計画法で求める流れ:手順 14</object><object data="/ja/chapter_dynamic_programming/edit_distance_problem.assets/edit_distance_dp_step14.dark.svg" data-theme="dark" tabindex="-1" type="image/svg+xml">編集距離を動的計画法で求める流れ:手順 14</object></ha-svg-figure></p>
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<div class="tabbed-block">
<p><ha-svg-figure class="animation-figure" data-book-key="ja/chapter_dynamic_programming/edit_distance_problem.assets/edit_distance_dp_step15.png" data-dark-src="/assets/figure-svg/figures/36dd97c0d49385ac36fb77ef.json" data-src="/assets/figure-svg/figures/9792a40fc228c5116c68b48a.json" style=";--figure-ratio:960.0/540.0"><object data="/ja/chapter_dynamic_programming/edit_distance_problem.assets/edit_distance_dp_step15.svg" data-theme="light" tabindex="-1" type="image/svg+xml">編集距離を動的計画法で求める流れ:手順 15</object><object data="/ja/chapter_dynamic_programming/edit_distance_problem.assets/edit_distance_dp_step15.dark.svg" data-theme="dark" tabindex="-1" type="image/svg+xml">編集距離を動的計画法で求める流れ:手順 15</object></ha-svg-figure></p>
</div>
</div>
</div>
<p align="center"> 図 14-30   編集距離を動的計画法で求める流れ </p>
<h3 id="3">3.   空間の最適化<a class="headerlink" href="#3" title="この見出しへのリンク"></a></h3>
<p><span class="arithmatex">\(dp[i,j]\)</span> は、上の <span class="arithmatex">\(dp[i-1, j]\)</span>、左の <span class="arithmatex">\(dp[i, j-1]\)</span>、左上の <span class="arithmatex">\(dp[i-1, j-1]\)</span> から遷移します。順方向に走査すると左上の <span class="arithmatex">\(dp[i-1, j-1]\)</span> が失われ、逆方向では <span class="arithmatex">\(dp[i, j-1]\)</span> を先に計算できません。そのため、どちらの順序もそのままでは使えません。</p>
<p>そこで、変数 <code>leftup</code> に左上の解 <span class="arithmatex">\(dp[i-1, j-1]\)</span> を一時保存すれば、左と上の解だけを考えればよくなります。これは個数制限なしナップサック問題と同じ状況なので、順方向に走査できます。コードを次に示します。</p>
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<div class="highlight"><span class="filename">edit_distance.py</span><pre><span></span><code><a href="#__codelineno-13-1" id="__codelineno-13-1" name="__codelineno-13-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">edit_distance_dp_comp</span><span class="p">(</span><span class="n">s</span><span class="p">:</span> <span class="nb">str</span><span class="p">,</span> <span class="n">t</span><span class="p">:</span> <span class="nb">str</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
<a href="#__codelineno-13-2" id="__codelineno-13-2" name="__codelineno-13-2"></a><span class="w"> </span><span class="sd">"""編集距離:空間を最適化した動的計画法"""</span>
<a href="#__codelineno-13-3" id="__codelineno-13-3" name="__codelineno-13-3"></a> <span class="n">n</span><span class="p">,</span> <span class="n">m</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">s</span><span class="p">),</span> <span class="nb">len</span><span class="p">(</span><span class="n">t</span><span class="p">)</span>
<a href="#__codelineno-13-4" id="__codelineno-13-4" name="__codelineno-13-4"></a> <span class="n">dp</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="p">(</span><span class="n">m</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
<a href="#__codelineno-13-5" id="__codelineno-13-5" name="__codelineno-13-5"></a> <span class="c1"># 状態遷移:先頭行</span>
<a href="#__codelineno-13-6" id="__codelineno-13-6" name="__codelineno-13-6"></a> <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">m</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
<a href="#__codelineno-13-7" id="__codelineno-13-7" name="__codelineno-13-7"></a> <span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">j</span>
<a href="#__codelineno-13-8" id="__codelineno-13-8" name="__codelineno-13-8"></a> <span class="c1"># 状態遷移:残りの行</span>
<a href="#__codelineno-13-9" id="__codelineno-13-9" name="__codelineno-13-9"></a> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
<a href="#__codelineno-13-10" id="__codelineno-13-10" name="__codelineno-13-10"></a> <span class="c1"># 状態遷移:先頭列</span>
<a href="#__codelineno-13-11" id="__codelineno-13-11" name="__codelineno-13-11"></a> <span class="n">leftup</span> <span class="o">=</span> <span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="c1"># dp[i-1, j-1] を一時保存する</span>
<a href="#__codelineno-13-12" id="__codelineno-13-12" name="__codelineno-13-12"></a> <span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">+=</span> <span class="mi">1</span>
<a href="#__codelineno-13-13" id="__codelineno-13-13" name="__codelineno-13-13"></a> <span class="c1"># 状態遷移:残りの列</span>
<a href="#__codelineno-13-14" id="__codelineno-13-14" name="__codelineno-13-14"></a> <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">m</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
<a href="#__codelineno-13-15" id="__codelineno-13-15" name="__codelineno-13-15"></a> <span class="n">temp</span> <span class="o">=</span> <span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span>
<a href="#__codelineno-13-16" id="__codelineno-13-16" name="__codelineno-13-16"></a> <span class="k">if</span> <span class="n">s</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="o">==</span> <span class="n">t</span><span class="p">[</span><span class="n">j</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]:</span>
<a href="#__codelineno-13-17" id="__codelineno-13-17" name="__codelineno-13-17"></a> <span class="c1"># 2 つの文字が等しい場合、その 2 文字をスキップする</span>
<a href="#__codelineno-13-18" id="__codelineno-13-18" name="__codelineno-13-18"></a> <span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">leftup</span>
<a href="#__codelineno-13-19" id="__codelineno-13-19" name="__codelineno-13-19"></a> <span class="k">else</span><span class="p">:</span>
<a href="#__codelineno-13-20" id="__codelineno-13-20" name="__codelineno-13-20"></a> <span class="c1"># 最小編集回数 = 挿入、削除、置換の 3 操作での最小編集回数 + 1</span>
<a href="#__codelineno-13-21" id="__codelineno-13-21" name="__codelineno-13-21"></a> <span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">j</span> <span class="o">-</span> <span class="mi">1</span><span class="p">],</span> <span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">],</span> <span class="n">leftup</span><span class="p">)</span> <span class="o">+</span> <span class="mi">1</span>
<a href="#__codelineno-13-22" id="__codelineno-13-22" name="__codelineno-13-22"></a> <span class="n">leftup</span> <span class="o">=</span> <span class="n">temp</span> <span class="c1"># 次の反復の dp[i-1, j-1] に更新する</span>
<a href="#__codelineno-13-23" id="__codelineno-13-23" name="__codelineno-13-23"></a> <span class="k">return</span> <span class="n">dp</span><span class="p">[</span><span class="n">m</span><span class="p">]</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">edit_distance.cpp</span><pre><span></span><code><a href="#__codelineno-14-1" id="__codelineno-14-1" name="__codelineno-14-1"></a><span class="cm">/* 編集距離:空間を最適化した動的計画法 */</span>
<a href="#__codelineno-14-2" id="__codelineno-14-2" name="__codelineno-14-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">editDistanceDPComp</span><span class="p">(</span><span class="n">string</span><span class="w"> </span><span class="n">s</span><span class="p">,</span><span class="w"> </span><span class="n">string</span><span class="w"> </span><span class="n">t</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-14-3" id="__codelineno-14-3" name="__codelineno-14-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">s</span><span class="p">.</span><span class="n">length</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="n">t</span><span class="p">.</span><span class="n">length</span><span class="p">();</span>
<a href="#__codelineno-14-4" id="__codelineno-14-4" name="__codelineno-14-4"></a><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">dp</span><span class="p">(</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="mi">0</span><span class="p">);</span>
<a href="#__codelineno-14-5" id="__codelineno-14-5" name="__codelineno-14-5"></a><span class="w"> </span><span class="c1">// 状態遷移:先頭行</span>
<a href="#__codelineno-14-6" id="__codelineno-14-6" name="__codelineno-14-6"></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">j</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">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-14-7" id="__codelineno-14-7" name="__codelineno-14-7"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">j</span><span class="p">;</span>
<a href="#__codelineno-14-8" id="__codelineno-14-8" name="__codelineno-14-8"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-14-9" id="__codelineno-14-9" name="__codelineno-14-9"></a><span class="w"> </span><span class="c1">// 状態遷移:残りの行</span>
<a href="#__codelineno-14-10" id="__codelineno-14-10" name="__codelineno-14-10"></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">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</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 href="#__codelineno-14-11" id="__codelineno-14-11" name="__codelineno-14-11"></a><span class="w"> </span><span class="c1">// 状態遷移:先頭列</span>
<a href="#__codelineno-14-12" id="__codelineno-14-12" name="__codelineno-14-12"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">leftup</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">];</span><span class="w"> </span><span class="c1">// dp[i-1, j-1] を一時保存する</span>
<a href="#__codelineno-14-13" id="__codelineno-14-13" name="__codelineno-14-13"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</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 href="#__codelineno-14-14" id="__codelineno-14-14" name="__codelineno-14-14"></a><span class="w"> </span><span class="c1">// 状態遷移:残りの列</span>
<a href="#__codelineno-14-15" id="__codelineno-14-15" name="__codelineno-14-15"></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">j</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">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-14-16" id="__codelineno-14-16" name="__codelineno-14-16"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">];</span>
<a href="#__codelineno-14-17" id="__codelineno-14-17" name="__codelineno-14-17"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">s</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">t</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-14-18" id="__codelineno-14-18" name="__codelineno-14-18"></a><span class="w"> </span><span class="c1">// 2 つの文字が等しい場合、その 2 文字をスキップする</span>
<a href="#__codelineno-14-19" id="__codelineno-14-19" name="__codelineno-14-19"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">leftup</span><span class="p">;</span>
<a href="#__codelineno-14-20" id="__codelineno-14-20" name="__codelineno-14-20"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-14-21" id="__codelineno-14-21" name="__codelineno-14-21"></a><span class="w"> </span><span class="c1">// 最小編集回数 = 挿入、削除、置換の 3 操作での最小編集回数 + 1</span>
<a href="#__codelineno-14-22" id="__codelineno-14-22" name="__codelineno-14-22"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">min</span><span class="p">(</span><span class="n">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]),</span><span class="w"> </span><span class="n">leftup</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
<a href="#__codelineno-14-23" id="__codelineno-14-23" name="__codelineno-14-23"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-14-24" id="__codelineno-14-24" name="__codelineno-14-24"></a><span class="w"> </span><span class="n">leftup</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="p">;</span><span class="w"> </span><span class="c1">// 次の反復の dp[i-1, j-1] に更新する</span>
<a href="#__codelineno-14-25" id="__codelineno-14-25" name="__codelineno-14-25"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-14-26" id="__codelineno-14-26" name="__codelineno-14-26"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-14-27" id="__codelineno-14-27" name="__codelineno-14-27"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">m</span><span class="p">];</span>
<a href="#__codelineno-14-28" id="__codelineno-14-28" name="__codelineno-14-28"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">edit_distance.java</span><pre><span></span><code><a href="#__codelineno-15-1" id="__codelineno-15-1" name="__codelineno-15-1"></a><span class="cm">/* 編集距離:空間を最適化した動的計画法 */</span>
<a href="#__codelineno-15-2" id="__codelineno-15-2" name="__codelineno-15-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">editDistanceDPComp</span><span class="p">(</span><span class="n">String</span><span class="w"> </span><span class="n">s</span><span class="p">,</span><span class="w"> </span><span class="n">String</span><span class="w"> </span><span class="n">t</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-15-3" id="__codelineno-15-3" name="__codelineno-15-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">s</span><span class="p">.</span><span class="na">length</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="n">t</span><span class="p">.</span><span class="na">length</span><span class="p">();</span>
<a href="#__codelineno-15-4" id="__codelineno-15-4" name="__codelineno-15-4"></a><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</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="o">]</span><span class="p">;</span>
<a href="#__codelineno-15-5" id="__codelineno-15-5" name="__codelineno-15-5"></a><span class="w"> </span><span class="c1">// 状態遷移:先頭行</span>
<a href="#__codelineno-15-6" id="__codelineno-15-6" name="__codelineno-15-6"></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">j</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">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-15-7" id="__codelineno-15-7" name="__codelineno-15-7"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">j</span><span class="p">;</span>
<a href="#__codelineno-15-8" id="__codelineno-15-8" name="__codelineno-15-8"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-15-9" id="__codelineno-15-9" name="__codelineno-15-9"></a><span class="w"> </span><span class="c1">// 状態遷移:残りの行</span>
<a href="#__codelineno-15-10" id="__codelineno-15-10" name="__codelineno-15-10"></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">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</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 href="#__codelineno-15-11" id="__codelineno-15-11" name="__codelineno-15-11"></a><span class="w"> </span><span class="c1">// 状態遷移:先頭列</span>
<a href="#__codelineno-15-12" id="__codelineno-15-12" name="__codelineno-15-12"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">leftup</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="p">;</span><span class="w"> </span><span class="c1">// dp[i-1, j-1] を一時保存する</span>
<a href="#__codelineno-15-13" id="__codelineno-15-13" name="__codelineno-15-13"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
<a href="#__codelineno-15-14" id="__codelineno-15-14" name="__codelineno-15-14"></a><span class="w"> </span><span class="c1">// 状態遷移:残りの列</span>
<a href="#__codelineno-15-15" id="__codelineno-15-15" name="__codelineno-15-15"></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">j</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">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-15-16" id="__codelineno-15-16" name="__codelineno-15-16"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="p">;</span>
<a href="#__codelineno-15-17" id="__codelineno-15-17" name="__codelineno-15-17"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">s</span><span class="p">.</span><span class="na">charAt</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">t</span><span class="p">.</span><span class="na">charAt</span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-15-18" id="__codelineno-15-18" name="__codelineno-15-18"></a><span class="w"> </span><span class="c1">// 2 つの文字が等しい場合、その 2 文字をスキップする</span>
<a href="#__codelineno-15-19" id="__codelineno-15-19" name="__codelineno-15-19"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">leftup</span><span class="p">;</span>
<a href="#__codelineno-15-20" id="__codelineno-15-20" name="__codelineno-15-20"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-15-21" id="__codelineno-15-21" name="__codelineno-15-21"></a><span class="w"> </span><span class="c1">// 最小編集回数 = 挿入、削除、置換の 3 操作での最小編集回数 + 1</span>
<a href="#__codelineno-15-22" id="__codelineno-15-22" name="__codelineno-15-22"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="na">min</span><span class="p">(</span><span class="n">Math</span><span class="p">.</span><span class="na">min</span><span class="p">(</span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="p">),</span><span class="w"> </span><span class="n">leftup</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
<a href="#__codelineno-15-23" id="__codelineno-15-23" name="__codelineno-15-23"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-15-24" id="__codelineno-15-24" name="__codelineno-15-24"></a><span class="w"> </span><span class="n">leftup</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="p">;</span><span class="w"> </span><span class="c1">// 次の反復の dp[i-1, j-1] に更新する</span>
<a href="#__codelineno-15-25" id="__codelineno-15-25" name="__codelineno-15-25"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-15-26" id="__codelineno-15-26" name="__codelineno-15-26"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-15-27" id="__codelineno-15-27" name="__codelineno-15-27"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">m</span><span class="o">]</span><span class="p">;</span>
<a href="#__codelineno-15-28" id="__codelineno-15-28" name="__codelineno-15-28"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">edit_distance.cs</span><pre><span></span><code><a href="#__codelineno-16-1" id="__codelineno-16-1" name="__codelineno-16-1"></a><span class="cm">/* 編集距離:空間を最適化した動的計画法 */</span>
<a href="#__codelineno-16-2" id="__codelineno-16-2" name="__codelineno-16-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">EditDistanceDPComp</span><span class="p">(</span><span class="kt">string</span><span class="w"> </span><span class="n">s</span><span class="p">,</span><span class="w"> </span><span class="kt">string</span><span class="w"> </span><span class="n">t</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-16-3" id="__codelineno-16-3" name="__codelineno-16-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">s</span><span class="p">.</span><span class="n">Length</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="n">t</span><span class="p">.</span><span class="n">Length</span><span class="p">;</span>
<a href="#__codelineno-16-4" id="__codelineno-16-4" name="__codelineno-16-4"></a><span class="w"> </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</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 href="#__codelineno-16-5" id="__codelineno-16-5" name="__codelineno-16-5"></a><span class="w"> </span><span class="c1">// 状態遷移:先頭行</span>
<a href="#__codelineno-16-6" id="__codelineno-16-6" name="__codelineno-16-6"></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">j</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">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-16-7" id="__codelineno-16-7" name="__codelineno-16-7"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">j</span><span class="p">;</span>
<a href="#__codelineno-16-8" id="__codelineno-16-8" name="__codelineno-16-8"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-16-9" id="__codelineno-16-9" name="__codelineno-16-9"></a><span class="w"> </span><span class="c1">// 状態遷移:残りの行</span>
<a href="#__codelineno-16-10" id="__codelineno-16-10" name="__codelineno-16-10"></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">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</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 href="#__codelineno-16-11" id="__codelineno-16-11" name="__codelineno-16-11"></a><span class="w"> </span><span class="c1">// 状態遷移:先頭列</span>
<a href="#__codelineno-16-12" id="__codelineno-16-12" name="__codelineno-16-12"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">leftup</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">];</span><span class="w"> </span><span class="c1">// dp[i-1, j-1] を一時保存する</span>
<a href="#__codelineno-16-13" id="__codelineno-16-13" name="__codelineno-16-13"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</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 href="#__codelineno-16-14" id="__codelineno-16-14" name="__codelineno-16-14"></a><span class="w"> </span><span class="c1">// 状態遷移:残りの列</span>
<a href="#__codelineno-16-15" id="__codelineno-16-15" name="__codelineno-16-15"></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">j</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">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-16-16" id="__codelineno-16-16" name="__codelineno-16-16"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">];</span>
<a href="#__codelineno-16-17" id="__codelineno-16-17" name="__codelineno-16-17"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">s</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">t</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-16-18" id="__codelineno-16-18" name="__codelineno-16-18"></a><span class="w"> </span><span class="c1">// 2 つの文字が等しい場合、その 2 文字をスキップする</span>
<a href="#__codelineno-16-19" id="__codelineno-16-19" name="__codelineno-16-19"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">leftup</span><span class="p">;</span>
<a href="#__codelineno-16-20" id="__codelineno-16-20" name="__codelineno-16-20"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-16-21" id="__codelineno-16-21" name="__codelineno-16-21"></a><span class="w"> </span><span class="c1">// 最小編集回数 = 挿入、削除、置換の 3 操作での最小編集回数 + 1</span>
<a href="#__codelineno-16-22" id="__codelineno-16-22" name="__codelineno-16-22"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="n">Min</span><span class="p">(</span><span class="n">Math</span><span class="p">.</span><span class="n">Min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]),</span><span class="w"> </span><span class="n">leftup</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
<a href="#__codelineno-16-23" id="__codelineno-16-23" name="__codelineno-16-23"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-16-24" id="__codelineno-16-24" name="__codelineno-16-24"></a><span class="w"> </span><span class="n">leftup</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="p">;</span><span class="w"> </span><span class="c1">// 次の反復の dp[i-1, j-1] に更新する</span>
<a href="#__codelineno-16-25" id="__codelineno-16-25" name="__codelineno-16-25"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-16-26" id="__codelineno-16-26" name="__codelineno-16-26"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-16-27" id="__codelineno-16-27" name="__codelineno-16-27"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">m</span><span class="p">];</span>
<a href="#__codelineno-16-28" id="__codelineno-16-28" name="__codelineno-16-28"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">edit_distance.go</span><pre><span></span><code><a href="#__codelineno-17-1" id="__codelineno-17-1" name="__codelineno-17-1"></a><span class="cm">/* 編集距離:空間を最適化した動的計画法 */</span>
<a href="#__codelineno-17-2" id="__codelineno-17-2" name="__codelineno-17-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">editDistanceDPComp</span><span class="p">(</span><span class="nx">s</span><span class="w"> </span><span class="kt">string</span><span class="p">,</span><span class="w"> </span><span class="nx">t</span><span class="w"> </span><span class="kt">string</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-17-3" id="__codelineno-17-3" name="__codelineno-17-3"></a><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">s</span><span class="p">)</span>
<a href="#__codelineno-17-4" id="__codelineno-17-4" name="__codelineno-17-4"></a><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">t</span><span class="p">)</span>
<a href="#__codelineno-17-5" id="__codelineno-17-5" name="__codelineno-17-5"></a><span class="w"> </span><span class="nx">dp</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</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 href="#__codelineno-17-6" id="__codelineno-17-6" name="__codelineno-17-6"></a><span class="w"> </span><span class="c1">// 状態遷移:先頭行</span>
<a href="#__codelineno-17-7" id="__codelineno-17-7" name="__codelineno-17-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">m</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-17-8" id="__codelineno-17-8" name="__codelineno-17-8"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">j</span>
<a href="#__codelineno-17-9" id="__codelineno-17-9" name="__codelineno-17-9"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-17-10" id="__codelineno-17-10" name="__codelineno-17-10"></a><span class="w"> </span><span class="c1">// 状態遷移:残りの行</span>
<a href="#__codelineno-17-11" id="__codelineno-17-11" name="__codelineno-17-11"></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">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</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 href="#__codelineno-17-12" id="__codelineno-17-12" name="__codelineno-17-12"></a><span class="w"> </span><span class="c1">// 状態遷移:先頭列</span>
<a href="#__codelineno-17-13" id="__codelineno-17-13" name="__codelineno-17-13"></a><span class="w"> </span><span class="nx">leftUp</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="c1">// dp[i-1, j-1] を一時保存する</span>
<a href="#__codelineno-17-14" id="__codelineno-17-14" name="__codelineno-17-14"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">i</span>
<a href="#__codelineno-17-15" id="__codelineno-17-15" name="__codelineno-17-15"></a><span class="w"> </span><span class="c1">// 状態遷移:残りの列</span>
<a href="#__codelineno-17-16" id="__codelineno-17-16" name="__codelineno-17-16"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">m</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-17-17" id="__codelineno-17-17" name="__codelineno-17-17"></a><span class="w"> </span><span class="nx">temp</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span>
<a href="#__codelineno-17-18" id="__codelineno-17-18" name="__codelineno-17-18"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">s</span><span class="p">[</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="o">==</span><span class="w"> </span><span class="nx">t</span><span class="p">[</span><span class="nx">j</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-17-19" id="__codelineno-17-19" name="__codelineno-17-19"></a><span class="w"> </span><span class="c1">// 2 つの文字が等しい場合、その 2 文字をスキップする</span>
<a href="#__codelineno-17-20" id="__codelineno-17-20" name="__codelineno-17-20"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">leftUp</span>
<a href="#__codelineno-17-21" id="__codelineno-17-21" name="__codelineno-17-21"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-17-22" id="__codelineno-17-22" name="__codelineno-17-22"></a><span class="w"> </span><span class="c1">// 最小編集回数 = 挿入、削除、置換の 3 操作での最小編集回数 + 1</span>
<a href="#__codelineno-17-23" id="__codelineno-17-23" name="__codelineno-17-23"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">MinInt</span><span class="p">(</span><span class="nx">MinInt</span><span class="p">(</span><span class="nx">dp</span><span class="p">[</span><span class="nx">j</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">j</span><span class="p">]),</span><span class="w"> </span><span class="nx">leftUp</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
<a href="#__codelineno-17-24" id="__codelineno-17-24" name="__codelineno-17-24"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-17-25" id="__codelineno-17-25" name="__codelineno-17-25"></a><span class="w"> </span><span class="nx">leftUp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">temp</span><span class="w"> </span><span class="c1">// 次の反復の dp[i-1, j-1] に更新する</span>
<a href="#__codelineno-17-26" id="__codelineno-17-26" name="__codelineno-17-26"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-17-27" id="__codelineno-17-27" name="__codelineno-17-27"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-17-28" id="__codelineno-17-28" name="__codelineno-17-28"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">m</span><span class="p">]</span>
<a href="#__codelineno-17-29" id="__codelineno-17-29" name="__codelineno-17-29"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">edit_distance.swift</span><pre><span></span><code><a href="#__codelineno-18-1" id="__codelineno-18-1" name="__codelineno-18-1"></a><span class="cm">/* 編集距離:空間を最適化した動的計画法 */</span>
<a href="#__codelineno-18-2" id="__codelineno-18-2" name="__codelineno-18-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">editDistanceDPComp</span><span class="p">(</span><span class="n">s</span><span class="p">:</span><span class="w"> </span><span class="nb">String</span><span class="p">,</span><span class="w"> </span><span class="n">t</span><span class="p">:</span><span class="w"> </span><span class="nb">String</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-18-3" id="__codelineno-18-3" name="__codelineno-18-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nv">n</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">s</span><span class="p">.</span><span class="n">utf8CString</span><span class="p">.</span><span class="bp">count</span>
<a href="#__codelineno-18-4" id="__codelineno-18-4" name="__codelineno-18-4"></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">t</span><span class="p">.</span><span class="n">utf8CString</span><span class="p">.</span><span class="bp">count</span>
<a href="#__codelineno-18-5" id="__codelineno-18-5" name="__codelineno-18-5"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">dp</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="bp">count</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 href="#__codelineno-18-6" id="__codelineno-18-6" name="__codelineno-18-6"></a><span class="w"> </span><span class="c1">// 状態遷移:先頭行</span>
<a href="#__codelineno-18-7" id="__codelineno-18-7" name="__codelineno-18-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">...</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-18-8" id="__codelineno-18-8" name="__codelineno-18-8"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">j</span>
<a href="#__codelineno-18-9" id="__codelineno-18-9" name="__codelineno-18-9"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-18-10" id="__codelineno-18-10" name="__codelineno-18-10"></a><span class="w"> </span><span class="c1">// 状態遷移:残りの行</span>
<a href="#__codelineno-18-11" id="__codelineno-18-11" name="__codelineno-18-11"></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">1</span><span class="w"> </span><span class="p">...</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-18-12" id="__codelineno-18-12" name="__codelineno-18-12"></a><span class="w"> </span><span class="c1">// 状態遷移:先頭列</span>
<a href="#__codelineno-18-13" id="__codelineno-18-13" name="__codelineno-18-13"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">leftup</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="c1">// dp[i-1, j-1] を一時保存する</span>
<a href="#__codelineno-18-14" id="__codelineno-18-14" name="__codelineno-18-14"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">i</span>
<a href="#__codelineno-18-15" id="__codelineno-18-15" name="__codelineno-18-15"></a><span class="w"> </span><span class="c1">// 状態遷移:残りの列</span>
<a href="#__codelineno-18-16" id="__codelineno-18-16" name="__codelineno-18-16"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">...</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-18-17" id="__codelineno-18-17" name="__codelineno-18-17"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nv">temp</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span>
<a href="#__codelineno-18-18" id="__codelineno-18-18" name="__codelineno-18-18"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">s</span><span class="p">.</span><span class="n">utf8CString</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="n">t</span><span class="p">.</span><span class="n">utf8CString</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-18-19" id="__codelineno-18-19" name="__codelineno-18-19"></a><span class="w"> </span><span class="c1">// 2 つの文字が等しい場合、その 2 文字をスキップする</span>
<a href="#__codelineno-18-20" id="__codelineno-18-20" name="__codelineno-18-20"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">leftup</span>
<a href="#__codelineno-18-21" id="__codelineno-18-21" name="__codelineno-18-21"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-18-22" id="__codelineno-18-22" name="__codelineno-18-22"></a><span class="w"> </span><span class="c1">// 最小編集回数 = 挿入、削除、置換の 3 操作での最小編集回数 + 1</span>
<a href="#__codelineno-18-23" id="__codelineno-18-23" name="__codelineno-18-23"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="bp">min</span><span class="p">(</span><span class="bp">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]),</span><span class="w"> </span><span class="n">leftup</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
<a href="#__codelineno-18-24" id="__codelineno-18-24" name="__codelineno-18-24"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-18-25" id="__codelineno-18-25" name="__codelineno-18-25"></a><span class="w"> </span><span class="n">leftup</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">temp</span><span class="w"> </span><span class="c1">// 次の反復の dp[i-1, j-1] に更新する</span>
<a href="#__codelineno-18-26" id="__codelineno-18-26" name="__codelineno-18-26"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-18-27" id="__codelineno-18-27" name="__codelineno-18-27"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-18-28" id="__codelineno-18-28" name="__codelineno-18-28"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">m</span><span class="p">]</span>
<a href="#__codelineno-18-29" id="__codelineno-18-29" name="__codelineno-18-29"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">edit_distance.js</span><pre><span></span><code><a href="#__codelineno-19-1" id="__codelineno-19-1" name="__codelineno-19-1"></a><span class="cm">/* 編集距離:空間を最適化した動的計画法 */</span>
<a href="#__codelineno-19-2" id="__codelineno-19-2" name="__codelineno-19-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">editDistanceDPComp</span><span class="p">(</span><span class="nx">s</span><span class="p">,</span><span class="w"> </span><span class="nx">t</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-19-3" id="__codelineno-19-3" name="__codelineno-19-3"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">s</span><span class="p">.</span><span class="nx">length</span><span class="p">,</span>
<a href="#__codelineno-19-4" id="__codelineno-19-4" name="__codelineno-19-4"></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">t</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
<a href="#__codelineno-19-5" id="__codelineno-19-5" name="__codelineno-19-5"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">dp</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">Array</span><span class="p">(</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="nx">fill</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
<a href="#__codelineno-19-6" id="__codelineno-19-6" name="__codelineno-19-6"></a><span class="w"> </span><span class="c1">// 状態遷移:先頭行</span>
<a href="#__codelineno-19-7" id="__codelineno-19-7" name="__codelineno-19-7"></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">j</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">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">m</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-19-8" id="__codelineno-19-8" name="__codelineno-19-8"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">j</span><span class="p">;</span>
<a href="#__codelineno-19-9" id="__codelineno-19-9" name="__codelineno-19-9"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-19-10" id="__codelineno-19-10" name="__codelineno-19-10"></a><span class="w"> </span><span class="c1">// 状態遷移:残りの行</span>
<a href="#__codelineno-19-11" id="__codelineno-19-11" name="__codelineno-19-11"></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">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</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 href="#__codelineno-19-12" id="__codelineno-19-12" name="__codelineno-19-12"></a><span class="w"> </span><span class="c1">// 状態遷移:先頭列</span>
<a href="#__codelineno-19-13" id="__codelineno-19-13" name="__codelineno-19-13"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">leftup</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="mf">0</span><span class="p">];</span><span class="w"> </span><span class="c1">// dp[i-1, j-1] を一時保存する</span>
<a href="#__codelineno-19-14" id="__codelineno-19-14" name="__codelineno-19-14"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="mf">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">i</span><span class="p">;</span>
<a href="#__codelineno-19-15" id="__codelineno-19-15" name="__codelineno-19-15"></a><span class="w"> </span><span class="c1">// 状態遷移:残りの列</span>
<a href="#__codelineno-19-16" id="__codelineno-19-16" name="__codelineno-19-16"></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">j</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">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">m</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-19-17" id="__codelineno-19-17" name="__codelineno-19-17"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">j</span><span class="p">];</span>
<a href="#__codelineno-19-18" id="__codelineno-19-18" name="__codelineno-19-18"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">s</span><span class="p">.</span><span class="nx">charAt</span><span class="p">(</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="o">===</span><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">charAt</span><span class="p">(</span><span class="nx">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-19-19" id="__codelineno-19-19" name="__codelineno-19-19"></a><span class="w"> </span><span class="c1">// 2 つの文字が等しい場合、その 2 文字をスキップする</span>
<a href="#__codelineno-19-20" id="__codelineno-19-20" name="__codelineno-19-20"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">leftup</span><span class="p">;</span>
<a href="#__codelineno-19-21" id="__codelineno-19-21" name="__codelineno-19-21"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-19-22" id="__codelineno-19-22" name="__codelineno-19-22"></a><span class="w"> </span><span class="c1">// 最小編集回数 = 挿入、削除、置換の 3 操作での最小編集回数 + 1</span>
<a href="#__codelineno-19-23" id="__codelineno-19-23" name="__codelineno-19-23"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">min</span><span class="p">(</span><span class="nx">dp</span><span class="p">[</span><span class="nx">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">],</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">j</span><span class="p">],</span><span class="w"> </span><span class="nx">leftup</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
<a href="#__codelineno-19-24" id="__codelineno-19-24" name="__codelineno-19-24"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-19-25" id="__codelineno-19-25" name="__codelineno-19-25"></a><span class="w"> </span><span class="nx">leftup</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">temp</span><span class="p">;</span><span class="w"> </span><span class="c1">// 次の反復の dp[i-1, j-1] に更新する</span>
<a href="#__codelineno-19-26" id="__codelineno-19-26" name="__codelineno-19-26"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-19-27" id="__codelineno-19-27" name="__codelineno-19-27"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-19-28" id="__codelineno-19-28" name="__codelineno-19-28"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">m</span><span class="p">];</span>
<a href="#__codelineno-19-29" id="__codelineno-19-29" name="__codelineno-19-29"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">edit_distance.ts</span><pre><span></span><code><a href="#__codelineno-20-1" id="__codelineno-20-1" name="__codelineno-20-1"></a><span class="cm">/* 編集距離:空間を最適化した動的計画法 */</span>
<a href="#__codelineno-20-2" id="__codelineno-20-2" name="__codelineno-20-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">editDistanceDPComp</span><span class="p">(</span><span class="nx">s</span><span class="o">:</span><span class="w"> </span><span class="kt">string</span><span class="p">,</span><span class="w"> </span><span class="nx">t</span><span class="o">:</span><span class="w"> </span><span class="kt">string</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-20-3" id="__codelineno-20-3" name="__codelineno-20-3"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">s</span><span class="p">.</span><span class="nx">length</span><span class="p">,</span>
<a href="#__codelineno-20-4" id="__codelineno-20-4" name="__codelineno-20-4"></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">t</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
<a href="#__codelineno-20-5" id="__codelineno-20-5" name="__codelineno-20-5"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">dp</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">Array</span><span class="p">(</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="nx">fill</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
<a href="#__codelineno-20-6" id="__codelineno-20-6" name="__codelineno-20-6"></a><span class="w"> </span><span class="c1">// 状態遷移:先頭行</span>
<a href="#__codelineno-20-7" id="__codelineno-20-7" name="__codelineno-20-7"></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">j</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">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">m</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-20-8" id="__codelineno-20-8" name="__codelineno-20-8"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">j</span><span class="p">;</span>
<a href="#__codelineno-20-9" id="__codelineno-20-9" name="__codelineno-20-9"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-20-10" id="__codelineno-20-10" name="__codelineno-20-10"></a><span class="w"> </span><span class="c1">// 状態遷移:残りの行</span>
<a href="#__codelineno-20-11" id="__codelineno-20-11" name="__codelineno-20-11"></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">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">n</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 href="#__codelineno-20-12" id="__codelineno-20-12" name="__codelineno-20-12"></a><span class="w"> </span><span class="c1">// 状態遷移:先頭列</span>
<a href="#__codelineno-20-13" id="__codelineno-20-13" name="__codelineno-20-13"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">leftup</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="mf">0</span><span class="p">];</span><span class="w"> </span><span class="c1">// dp[i-1, j-1] を一時保存する</span>
<a href="#__codelineno-20-14" id="__codelineno-20-14" name="__codelineno-20-14"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="mf">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">i</span><span class="p">;</span>
<a href="#__codelineno-20-15" id="__codelineno-20-15" name="__codelineno-20-15"></a><span class="w"> </span><span class="c1">// 状態遷移:残りの列</span>
<a href="#__codelineno-20-16" id="__codelineno-20-16" name="__codelineno-20-16"></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">j</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">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="nx">m</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-20-17" id="__codelineno-20-17" name="__codelineno-20-17"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">j</span><span class="p">];</span>
<a href="#__codelineno-20-18" id="__codelineno-20-18" name="__codelineno-20-18"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">s</span><span class="p">.</span><span class="nx">charAt</span><span class="p">(</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="o">===</span><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">charAt</span><span class="p">(</span><span class="nx">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-20-19" id="__codelineno-20-19" name="__codelineno-20-19"></a><span class="w"> </span><span class="c1">// 2 つの文字が等しい場合、その 2 文字をスキップする</span>
<a href="#__codelineno-20-20" id="__codelineno-20-20" name="__codelineno-20-20"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">leftup</span><span class="p">;</span>
<a href="#__codelineno-20-21" id="__codelineno-20-21" name="__codelineno-20-21"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-20-22" id="__codelineno-20-22" name="__codelineno-20-22"></a><span class="w"> </span><span class="c1">// 最小編集回数 = 挿入、削除、置換の 3 操作での最小編集回数 + 1</span>
<a href="#__codelineno-20-23" id="__codelineno-20-23" name="__codelineno-20-23"></a><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">min</span><span class="p">(</span><span class="nx">dp</span><span class="p">[</span><span class="nx">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">],</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">j</span><span class="p">],</span><span class="w"> </span><span class="nx">leftup</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
<a href="#__codelineno-20-24" id="__codelineno-20-24" name="__codelineno-20-24"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-20-25" id="__codelineno-20-25" name="__codelineno-20-25"></a><span class="w"> </span><span class="nx">leftup</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">temp</span><span class="p">;</span><span class="w"> </span><span class="c1">// 次の反復の dp[i-1, j-1] に更新する</span>
<a href="#__codelineno-20-26" id="__codelineno-20-26" name="__codelineno-20-26"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-20-27" id="__codelineno-20-27" name="__codelineno-20-27"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-20-28" id="__codelineno-20-28" name="__codelineno-20-28"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">dp</span><span class="p">[</span><span class="nx">m</span><span class="p">];</span>
<a href="#__codelineno-20-29" id="__codelineno-20-29" name="__codelineno-20-29"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">edit_distance.dart</span><pre><span></span><code><a href="#__codelineno-21-1" id="__codelineno-21-1" name="__codelineno-21-1"></a><span class="cm">/* 編集距離:空間を最適化した動的計画法 */</span>
<a href="#__codelineno-21-2" id="__codelineno-21-2" name="__codelineno-21-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">editDistanceDPComp</span><span class="p">(</span><span class="kt">String</span><span class="w"> </span><span class="n">s</span><span class="p">,</span><span class="w"> </span><span class="kt">String</span><span class="w"> </span><span class="n">t</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-21-3" id="__codelineno-21-3" name="__codelineno-21-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">s</span><span class="p">.</span><span class="n">length</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="n">t</span><span class="p">.</span><span class="n">length</span><span class="p">;</span>
<a href="#__codelineno-21-4" id="__codelineno-21-4" name="__codelineno-21-4"></a><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</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="m">0</span><span class="p">);</span>
<a href="#__codelineno-21-5" id="__codelineno-21-5" name="__codelineno-21-5"></a><span class="w"> </span><span class="c1">// 状態遷移:先頭行</span>
<a href="#__codelineno-21-6" id="__codelineno-21-6" name="__codelineno-21-6"></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">j</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">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-21-7" id="__codelineno-21-7" name="__codelineno-21-7"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">j</span><span class="p">;</span>
<a href="#__codelineno-21-8" id="__codelineno-21-8" name="__codelineno-21-8"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-21-9" id="__codelineno-21-9" name="__codelineno-21-9"></a><span class="w"> </span><span class="c1">// 状態遷移:残りの行</span>
<a href="#__codelineno-21-10" id="__codelineno-21-10" name="__codelineno-21-10"></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">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</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 href="#__codelineno-21-11" id="__codelineno-21-11" name="__codelineno-21-11"></a><span class="w"> </span><span class="c1">// 状態遷移:先頭列</span>
<a href="#__codelineno-21-12" id="__codelineno-21-12" name="__codelineno-21-12"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">leftup</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="m">0</span><span class="p">];</span><span class="w"> </span><span class="c1">// dp[i-1, j-1] を一時保存する</span>
<a href="#__codelineno-21-13" id="__codelineno-21-13" name="__codelineno-21-13"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="m">0</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 href="#__codelineno-21-14" id="__codelineno-21-14" name="__codelineno-21-14"></a><span class="w"> </span><span class="c1">// 状態遷移:残りの列</span>
<a href="#__codelineno-21-15" id="__codelineno-21-15" name="__codelineno-21-15"></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">j</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">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-21-16" id="__codelineno-21-16" name="__codelineno-21-16"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">];</span>
<a href="#__codelineno-21-17" id="__codelineno-21-17" name="__codelineno-21-17"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">s</span><span class="p">[</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="o">==</span><span class="w"> </span><span class="n">t</span><span class="p">[</span><span class="n">j</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="p">{</span>
<a href="#__codelineno-21-18" id="__codelineno-21-18" name="__codelineno-21-18"></a><span class="w"> </span><span class="c1">// 2 つの文字が等しい場合、その 2 文字をスキップする</span>
<a href="#__codelineno-21-19" id="__codelineno-21-19" name="__codelineno-21-19"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">leftup</span><span class="p">;</span>
<a href="#__codelineno-21-20" id="__codelineno-21-20" name="__codelineno-21-20"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-21-21" id="__codelineno-21-21" name="__codelineno-21-21"></a><span class="w"> </span><span class="c1">// 最小編集回数 = 挿入、削除、置換の 3 操作での最小編集回数 + 1</span>
<a href="#__codelineno-21-22" id="__codelineno-21-22" name="__codelineno-21-22"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">min</span><span class="p">(</span><span class="n">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">j</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">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]),</span><span class="w"> </span><span class="n">leftup</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
<a href="#__codelineno-21-23" id="__codelineno-21-23" name="__codelineno-21-23"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-21-24" id="__codelineno-21-24" name="__codelineno-21-24"></a><span class="w"> </span><span class="n">leftup</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="p">;</span><span class="w"> </span><span class="c1">// 次の反復の dp[i-1, j-1] に更新する</span>
<a href="#__codelineno-21-25" id="__codelineno-21-25" name="__codelineno-21-25"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-21-26" id="__codelineno-21-26" name="__codelineno-21-26"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-21-27" id="__codelineno-21-27" name="__codelineno-21-27"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">m</span><span class="p">];</span>
<a href="#__codelineno-21-28" id="__codelineno-21-28" name="__codelineno-21-28"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">edit_distance.rs</span><pre><span></span><code><a href="#__codelineno-22-1" id="__codelineno-22-1" name="__codelineno-22-1"></a><span class="cm">/* 編集距離:空間を最適化した動的計画法 */</span>
<a href="#__codelineno-22-2" id="__codelineno-22-2" name="__codelineno-22-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">edit_distance_dp_comp</span><span class="p">(</span><span class="n">s</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="kt">str</span><span class="p">,</span><span class="w"> </span><span class="n">t</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="kt">str</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-22-3" id="__codelineno-22-3" name="__codelineno-22-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">s</span><span class="p">.</span><span class="n">len</span><span class="p">(),</span><span class="w"> </span><span class="n">t</span><span class="p">.</span><span class="n">len</span><span class="p">());</span>
<a href="#__codelineno-22-4" id="__codelineno-22-4" name="__codelineno-22-4"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="mi">0</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 href="#__codelineno-22-5" id="__codelineno-22-5" name="__codelineno-22-5"></a><span class="w"> </span><span class="c1">// 状態遷移:先頭行</span>
<a href="#__codelineno-22-6" id="__codelineno-22-6" name="__codelineno-22-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">..</span><span class="n">m</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-22-7" id="__codelineno-22-7" name="__codelineno-22-7"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span><span class="p">;</span>
<a href="#__codelineno-22-8" id="__codelineno-22-8" name="__codelineno-22-8"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-22-9" id="__codelineno-22-9" name="__codelineno-22-9"></a><span class="w"> </span><span class="c1">// 状態遷移:残りの行</span>
<a href="#__codelineno-22-10" id="__codelineno-22-10" name="__codelineno-22-10"></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">1</span><span class="o">..=</span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-22-11" id="__codelineno-22-11" name="__codelineno-22-11"></a><span class="w"> </span><span class="c1">// 状態遷移:先頭列</span>
<a href="#__codelineno-22-12" id="__codelineno-22-12" name="__codelineno-22-12"></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">leftup</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">];</span><span class="w"> </span><span class="c1">// dp[i-1, j-1] を一時保存する</span>
<a href="#__codelineno-22-13" id="__codelineno-22-13" name="__codelineno-22-13"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</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 href="#__codelineno-22-14" id="__codelineno-22-14" name="__codelineno-22-14"></a><span class="w"> </span><span class="c1">// 状態遷移:残りの列</span>
<a href="#__codelineno-22-15" id="__codelineno-22-15" name="__codelineno-22-15"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">..=</span><span class="n">m</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-22-16" id="__codelineno-22-16" name="__codelineno-22-16"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">];</span>
<a href="#__codelineno-22-17" id="__codelineno-22-17" name="__codelineno-22-17"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">s</span><span class="p">.</span><span class="n">chars</span><span class="p">().</span><span class="n">nth</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">t</span><span class="p">.</span><span class="n">chars</span><span class="p">().</span><span class="n">nth</span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-22-18" id="__codelineno-22-18" name="__codelineno-22-18"></a><span class="w"> </span><span class="c1">// 2 つの文字が等しい場合、その 2 文字をスキップする</span>
<a href="#__codelineno-22-19" id="__codelineno-22-19" name="__codelineno-22-19"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">leftup</span><span class="p">;</span>
<a href="#__codelineno-22-20" id="__codelineno-22-20" name="__codelineno-22-20"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-22-21" id="__codelineno-22-21" name="__codelineno-22-21"></a><span class="w"> </span><span class="c1">// 最小編集回数 = 挿入、削除、置換の 3 操作での最小編集回数 + 1</span>
<a href="#__codelineno-22-22" id="__codelineno-22-22" name="__codelineno-22-22"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">std</span><span class="p">::</span><span class="n">cmp</span><span class="p">::</span><span class="n">min</span><span class="p">(</span><span class="n">std</span><span class="p">::</span><span class="n">cmp</span><span class="p">::</span><span class="n">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]),</span><span class="w"> </span><span class="n">leftup</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
<a href="#__codelineno-22-23" id="__codelineno-22-23" name="__codelineno-22-23"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-22-24" id="__codelineno-22-24" name="__codelineno-22-24"></a><span class="w"> </span><span class="n">leftup</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="p">;</span><span class="w"> </span><span class="c1">// 次の反復の dp[i-1, j-1] に更新する</span>
<a href="#__codelineno-22-25" id="__codelineno-22-25" name="__codelineno-22-25"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-22-26" id="__codelineno-22-26" name="__codelineno-22-26"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-22-27" id="__codelineno-22-27" name="__codelineno-22-27"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">m</span><span class="p">]</span>
<a href="#__codelineno-22-28" id="__codelineno-22-28" name="__codelineno-22-28"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">edit_distance.c</span><pre><span></span><code><a href="#__codelineno-23-1" id="__codelineno-23-1" name="__codelineno-23-1"></a><span class="cm">/* 編集距離:空間を最適化した動的計画法 */</span>
<a href="#__codelineno-23-2" id="__codelineno-23-2" name="__codelineno-23-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">editDistanceDPComp</span><span class="p">(</span><span class="kt">char</span><span class="w"> </span><span class="o">*</span><span class="n">s</span><span class="p">,</span><span class="w"> </span><span class="kt">char</span><span class="w"> </span><span class="o">*</span><span class="n">t</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-23-3" id="__codelineno-23-3" name="__codelineno-23-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">calloc</span><span class="p">(</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="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">));</span>
<a href="#__codelineno-23-4" id="__codelineno-23-4" name="__codelineno-23-4"></a><span class="w"> </span><span class="c1">// 状態遷移:先頭行</span>
<a href="#__codelineno-23-5" id="__codelineno-23-5" name="__codelineno-23-5"></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">j</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">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-23-6" id="__codelineno-23-6" name="__codelineno-23-6"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">j</span><span class="p">;</span>
<a href="#__codelineno-23-7" id="__codelineno-23-7" name="__codelineno-23-7"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-23-8" id="__codelineno-23-8" name="__codelineno-23-8"></a><span class="w"> </span><span class="c1">// 状態遷移:残りの行</span>
<a href="#__codelineno-23-9" id="__codelineno-23-9" name="__codelineno-23-9"></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">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</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 href="#__codelineno-23-10" id="__codelineno-23-10" name="__codelineno-23-10"></a><span class="w"> </span><span class="c1">// 状態遷移:先頭列</span>
<a href="#__codelineno-23-11" id="__codelineno-23-11" name="__codelineno-23-11"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">leftup</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">];</span><span class="w"> </span><span class="c1">// dp[i-1, j-1] を一時保存する</span>
<a href="#__codelineno-23-12" id="__codelineno-23-12" name="__codelineno-23-12"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</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 href="#__codelineno-23-13" id="__codelineno-23-13" name="__codelineno-23-13"></a><span class="w"> </span><span class="c1">// 状態遷移:残りの列</span>
<a href="#__codelineno-23-14" id="__codelineno-23-14" name="__codelineno-23-14"></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">j</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">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-23-15" id="__codelineno-23-15" name="__codelineno-23-15"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">];</span>
<a href="#__codelineno-23-16" id="__codelineno-23-16" name="__codelineno-23-16"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">s</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">t</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-23-17" id="__codelineno-23-17" name="__codelineno-23-17"></a><span class="w"> </span><span class="c1">// 2 つの文字が等しい場合、その 2 文字をスキップする</span>
<a href="#__codelineno-23-18" id="__codelineno-23-18" name="__codelineno-23-18"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">leftup</span><span class="p">;</span>
<a href="#__codelineno-23-19" id="__codelineno-23-19" name="__codelineno-23-19"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-23-20" id="__codelineno-23-20" name="__codelineno-23-20"></a><span class="w"> </span><span class="c1">// 最小編集回数 = 挿入、削除、置換の 3 操作での最小編集回数 + 1</span>
<a href="#__codelineno-23-21" id="__codelineno-23-21" name="__codelineno-23-21"></a><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">myMin</span><span class="p">(</span><span class="n">myMin</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]),</span><span class="w"> </span><span class="n">leftup</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
<a href="#__codelineno-23-22" id="__codelineno-23-22" name="__codelineno-23-22"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-23-23" id="__codelineno-23-23" name="__codelineno-23-23"></a><span class="w"> </span><span class="n">leftup</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="p">;</span><span class="w"> </span><span class="c1">// 次の反復の dp[i-1, j-1] に更新する</span>
<a href="#__codelineno-23-24" id="__codelineno-23-24" name="__codelineno-23-24"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-23-25" id="__codelineno-23-25" name="__codelineno-23-25"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-23-26" id="__codelineno-23-26" name="__codelineno-23-26"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">m</span><span class="p">];</span>
<a href="#__codelineno-23-27" id="__codelineno-23-27" name="__codelineno-23-27"></a><span class="w"> </span><span class="c1">// メモリを解放する</span>
<a href="#__codelineno-23-28" id="__codelineno-23-28" name="__codelineno-23-28"></a><span class="w"> </span><span class="n">free</span><span class="p">(</span><span class="n">dp</span><span class="p">);</span>
<a href="#__codelineno-23-29" id="__codelineno-23-29" name="__codelineno-23-29"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
<a href="#__codelineno-23-30" id="__codelineno-23-30" name="__codelineno-23-30"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">edit_distance.kt</span><pre><span></span><code><a href="#__codelineno-24-1" id="__codelineno-24-1" name="__codelineno-24-1"></a><span class="cm">/* 編集距離:空間を最適化した動的計画法 */</span>
<a href="#__codelineno-24-2" id="__codelineno-24-2" name="__codelineno-24-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">editDistanceDPComp</span><span class="p">(</span><span class="n">s</span><span class="p">:</span><span class="w"> </span><span class="kt">String</span><span class="p">,</span><span class="w"> </span><span class="n">t</span><span class="p">:</span><span class="w"> </span><span class="kt">String</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-24-3" id="__codelineno-24-3" name="__codelineno-24-3"></a><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">s</span><span class="p">.</span><span class="na">length</span>
<a href="#__codelineno-24-4" id="__codelineno-24-4" name="__codelineno-24-4"></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">t</span><span class="p">.</span><span class="na">length</span>
<a href="#__codelineno-24-5" id="__codelineno-24-5" name="__codelineno-24-5"></a><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">IntArray</span><span class="p">(</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 href="#__codelineno-24-6" id="__codelineno-24-6" name="__codelineno-24-6"></a><span class="w"> </span><span class="c1">// 状態遷移:先頭行</span>
<a href="#__codelineno-24-7" id="__codelineno-24-7" name="__codelineno-24-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">1.</span><span class="p">.</span><span class="na">m</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-24-8" id="__codelineno-24-8" name="__codelineno-24-8"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">j</span>
<a href="#__codelineno-24-9" id="__codelineno-24-9" name="__codelineno-24-9"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-24-10" id="__codelineno-24-10" name="__codelineno-24-10"></a><span class="w"> </span><span class="c1">// 状態遷移:残りの行</span>
<a href="#__codelineno-24-11" id="__codelineno-24-11" name="__codelineno-24-11"></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="m">1.</span><span class="p">.</span><span class="na">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-24-12" id="__codelineno-24-12" name="__codelineno-24-12"></a><span class="w"> </span><span class="c1">// 状態遷移:先頭列</span>
<a href="#__codelineno-24-13" id="__codelineno-24-13" name="__codelineno-24-13"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">leftup</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="m">0</span><span class="o">]</span><span class="w"> </span><span class="c1">// dp[i-1, j-1] を一時保存する</span>
<a href="#__codelineno-24-14" id="__codelineno-24-14" name="__codelineno-24-14"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="m">0</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span>
<a href="#__codelineno-24-15" id="__codelineno-24-15" name="__codelineno-24-15"></a><span class="w"> </span><span class="c1">// 状態遷移:残りの列</span>
<a href="#__codelineno-24-16" id="__codelineno-24-16" name="__codelineno-24-16"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="m">1.</span><span class="p">.</span><span class="na">m</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-24-17" id="__codelineno-24-17" name="__codelineno-24-17"></a><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="o">]</span>
<a href="#__codelineno-24-18" id="__codelineno-24-18" name="__codelineno-24-18"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">s</span><span class="o">[</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="o">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">t</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-24-19" id="__codelineno-24-19" name="__codelineno-24-19"></a><span class="w"> </span><span class="c1">// 2 つの文字が等しい場合、その 2 文字をスキップする</span>
<a href="#__codelineno-24-20" id="__codelineno-24-20" name="__codelineno-24-20"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">leftup</span>
<a href="#__codelineno-24-21" id="__codelineno-24-21" name="__codelineno-24-21"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a href="#__codelineno-24-22" id="__codelineno-24-22" name="__codelineno-24-22"></a><span class="w"> </span><span class="c1">// 最小編集回数 = 挿入、削除、置換の 3 操作での最小編集回数 + 1</span>
<a href="#__codelineno-24-23" id="__codelineno-24-23" name="__codelineno-24-23"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">min</span><span class="p">(</span><span class="n">min</span><span class="p">(</span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="p">),</span><span class="w"> </span><span class="n">leftup</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span>
<a href="#__codelineno-24-24" id="__codelineno-24-24" name="__codelineno-24-24"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-24-25" id="__codelineno-24-25" name="__codelineno-24-25"></a><span class="w"> </span><span class="n">leftup</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="w"> </span><span class="c1">// 次の反復の dp[i-1, j-1] に更新する</span>
<a href="#__codelineno-24-26" id="__codelineno-24-26" name="__codelineno-24-26"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-24-27" id="__codelineno-24-27" name="__codelineno-24-27"></a><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-24-28" id="__codelineno-24-28" name="__codelineno-24-28"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">m</span><span class="o">]</span>
<a href="#__codelineno-24-29" id="__codelineno-24-29" name="__codelineno-24-29"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">edit_distance.rb</span><pre><span></span><code><a href="#__codelineno-25-1" id="__codelineno-25-1" name="__codelineno-25-1"></a><span class="c1">### 編集距離:空間を最適化した動的計画法 ###</span>
<a href="#__codelineno-25-2" id="__codelineno-25-2" name="__codelineno-25-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">edit_distance_dp_comp</span><span class="p">(</span><span class="n">s</span><span class="p">,</span><span class="w"> </span><span class="n">t</span><span class="p">)</span>
<a href="#__codelineno-25-3" id="__codelineno-25-3" name="__codelineno-25-3"></a><span class="w"> </span><span class="n">n</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="n">s</span><span class="o">.</span><span class="n">length</span><span class="p">,</span><span class="w"> </span><span class="n">t</span><span class="o">.</span><span class="n">length</span>
<a href="#__codelineno-25-4" id="__codelineno-25-4" name="__codelineno-25-4"></a><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="o">.</span><span class="n">new</span><span class="p">(</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="mi">0</span><span class="p">)</span>
<a href="#__codelineno-25-5" id="__codelineno-25-5" name="__codelineno-25-5"></a><span class="w"> </span><span class="c1"># 状態遷移:先頭行</span>
<a href="#__codelineno-25-6" id="__codelineno-25-6" name="__codelineno-25-6"></a><span class="w"> </span><span class="p">(</span><span class="mi">1</span><span class="o">...</span><span class="p">(</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="o">.</span><span class="n">each</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="o">|</span><span class="n">j</span><span class="o">|</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="p">}</span>
<a href="#__codelineno-25-7" id="__codelineno-25-7" name="__codelineno-25-7"></a><span class="w"> </span><span class="c1"># 状態遷移:残りの行</span>
<a href="#__codelineno-25-8" id="__codelineno-25-8" name="__codelineno-25-8"></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">1</span><span class="o">...</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
<a href="#__codelineno-25-9" id="__codelineno-25-9" name="__codelineno-25-9"></a><span class="w"> </span><span class="c1"># 状態遷移:先頭列</span>
<a href="#__codelineno-25-10" id="__codelineno-25-10" name="__codelineno-25-10"></a><span class="w"> </span><span class="n">leftup</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">.</span><span class="n">first</span><span class="w"> </span><span class="c1"># dp[i-1, j-1] を一時保存する</span>
<a href="#__codelineno-25-11" id="__codelineno-25-11" name="__codelineno-25-11"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
<a href="#__codelineno-25-12" id="__codelineno-25-12" name="__codelineno-25-12"></a><span class="w"> </span><span class="c1"># 状態遷移:残りの列</span>
<a href="#__codelineno-25-13" id="__codelineno-25-13" name="__codelineno-25-13"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">...</span><span class="p">(</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 href="#__codelineno-25-14" id="__codelineno-25-14" name="__codelineno-25-14"></a><span class="w"> </span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="o">]</span>
<a href="#__codelineno-25-15" id="__codelineno-25-15" name="__codelineno-25-15"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">s</span><span class="o">[</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="o">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">t</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span>
<a href="#__codelineno-25-16" id="__codelineno-25-16" name="__codelineno-25-16"></a><span class="w"> </span><span class="c1"># 2 つの文字が等しい場合、その 2 文字をスキップする</span>
<a href="#__codelineno-25-17" id="__codelineno-25-17" name="__codelineno-25-17"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">leftup</span>
<a href="#__codelineno-25-18" id="__codelineno-25-18" name="__codelineno-25-18"></a><span class="w"> </span><span class="k">else</span>
<a href="#__codelineno-25-19" id="__codelineno-25-19" name="__codelineno-25-19"></a><span class="w"> </span><span class="c1"># 最小編集回数 = 挿入、削除、置換の 3 操作での最小編集回数 + 1</span>
<a href="#__codelineno-25-20" id="__codelineno-25-20" name="__codelineno-25-20"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">leftup</span><span class="o">].</span><span class="n">min</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
<a href="#__codelineno-25-21" id="__codelineno-25-21" name="__codelineno-25-21"></a><span class="w"> </span><span class="k">end</span>
<a href="#__codelineno-25-22" id="__codelineno-25-22" name="__codelineno-25-22"></a><span class="w"> </span><span class="n">leftup</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="w"> </span><span class="c1"># 次の反復の dp[i-1, j-1] に更新する</span>
<a href="#__codelineno-25-23" id="__codelineno-25-23" name="__codelineno-25-23"></a><span class="w"> </span><span class="k">end</span>
<a href="#__codelineno-25-24" id="__codelineno-25-24" name="__codelineno-25-24"></a><span class="w"> </span><span class="k">end</span>
<a href="#__codelineno-25-25" id="__codelineno-25-25" name="__codelineno-25-25"></a><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">m</span><span class="o">]</span>
<a href="#__codelineno-25-26" id="__codelineno-25-26" name="__codelineno-25-26"></a><span class="k">end</span>
</code></pre></div>
</div>
</div>
</div>
<details class="pythontutor">
<summary>実行の可視化</summary>
<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20edit_distance_dp_comp%28s%3A%20str,%20t%3A%20str%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E7%B7%A8%E9%9B%86%E8%B7%9D%E9%9B%A2%EF%BC%9A%E7%A9%BA%E9%96%93%E3%82%92%E6%9C%80%E9%81%A9%E5%8C%96%E3%81%97%E3%81%9F%E5%8B%95%E7%9A%84%E8%A8%88%E7%94%BB%E6%B3%95%22%22%22%0A%20%20%20%20n,%20m%20%3D%20len%28s%29,%20len%28t%29%0A%20%20%20%20dp%20%3D%20%5B0%5D%20%2A%20%28m%20%2B%201%29%0A%20%20%20%20%23%20%E7%8A%B6%E6%85%8B%E9%81%B7%E7%A7%BB%EF%BC%9A%E5%85%88%E9%A0%AD%E8%A1%8C%0A%20%20%20%20for%20j%20in%20range%281,%20m%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20dp%5Bj%5D%20%3D%20j%0A%20%20%20%20%23%20%E7%8A%B6%E6%85%8B%E9%81%B7%E7%A7%BB%EF%BC%9A%E6%AE%8B%E3%82%8A%E3%81%AE%E8%A1%8C%0A%20%20%20%20for%20i%20in%20range%281,%20n%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20%23%20%E7%8A%B6%E6%85%8B%E9%81%B7%E7%A7%BB%EF%BC%9A%E5%85%88%E9%A0%AD%E5%88%97%0A%20%20%20%20%20%20%20%20leftup%20%3D%20dp%5B0%5D%20%20%23%20dp%5Bi-1,%20j-1%5D%20%E3%82%92%E4%B8%80%E6%99%82%E4%BF%9D%E5%AD%98%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20dp%5B0%5D%20%2B%3D%201%0A%20%20%20%20%20%20%20%20%23%20%E7%8A%B6%E6%85%8B%E9%81%B7%E7%A7%BB%EF%BC%9A%E6%AE%8B%E3%82%8A%E3%81%AE%E5%88%97%0A%20%20%20%20%20%20%20%20for%20j%20in%20range%281,%20m%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20temp%20%3D%20dp%5Bj%5D%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20s%5Bi%20-%201%5D%20%3D%3D%20t%5Bj%20-%201%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%23%202%20%E3%81%A4%E3%81%AE%E6%96%87%E5%AD%97%E3%81%8C%E7%AD%89%E3%81%97%E3%81%84%E5%A0%B4%E5%90%88%E3%80%81%E3%81%9D%E3%81%AE%202%20%E6%96%87%E5%AD%97%E3%82%92%E3%82%B9%E3%82%AD%E3%83%83%E3%83%97%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20dp%5Bj%5D%20%3D%20leftup%0A%20%20%20%20%20%20%20%20%20%20%20%20else%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E6%9C%80%E5%B0%8F%E7%B7%A8%E9%9B%86%E5%9B%9E%E6%95%B0%20%3D%20%E6%8C%BF%E5%85%A5%E3%80%81%E5%89%8A%E9%99%A4%E3%80%81%E7%BD%AE%E6%8F%9B%E3%81%AE%203%20%E6%93%8D%E4%BD%9C%E3%81%A7%E3%81%AE%E6%9C%80%E5%B0%8F%E7%B7%A8%E9%9B%86%E5%9B%9E%E6%95%B0%20%2B%201%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20dp%5Bj%5D%20%3D%20min%28dp%5Bj%20-%201%5D,%20dp%5Bj%5D,%20leftup%29%20%2B%201%0A%20%20%20%20%20%20%20%20%20%20%20%20leftup%20%3D%20temp%20%20%23%20%E6%AC%A1%E3%81%AE%E5%8F%8D%E5%BE%A9%E3%81%AE%20dp%5Bi-1,%20j-1%5D%20%E3%81%AB%E6%9B%B4%E6%96%B0%E3%81%99%E3%82%8B%0A%20%20%20%20return%20dp%5Bm%5D%0A%0A%0A%22%22%22%E5%AE%9F%E8%A1%8C%E7%94%A8%E3%82%B3%E3%83%BC%E3%83%89%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20s%20%3D%20%22bag%22%0A%20%20%20%20t%20%3D%20%22pack%22%0A%20%20%20%20n,%20m%20%3D%20len%28s%29,%20len%28t%29%0A%0A%20%20%20%20%23%20%E7%A9%BA%E9%96%93%E3%82%92%E6%9C%80%E9%81%A9%E5%8C%96%E3%81%97%E3%81%9F%E5%8B%95%E7%9A%84%E8%A8%88%E7%94%BB%E6%B3%95%0A%20%20%20%20res%20%3D%20edit_distance_dp_comp%28s,%20t%29%0A%20%20%20%20print%28f%22%7Bs%7D%20%E3%82%92%20%7Bt%7D%20%E3%81%AB%E5%A4%89%E6%9B%B4%E3%81%99%E3%82%8B%E3%81%AB%E3%81%AF%E6%9C%80%E4%BD%8E%20%7Bres%7D%20%E5%9B%9E%E3%81%AE%E7%B7%A8%E9%9B%86%E3%81%8C%E5%BF%85%E8%A6%81%22%29&amp;codeDivHeight=472&amp;codeDivWidth=350&amp;cumulative=false&amp;curInstr=6&amp;heapPrimitives=nevernest&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false" title="実行の可視化"> </iframe></div>
<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20edit_distance_dp_comp%28s%3A%20str,%20t%3A%20str%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E7%B7%A8%E9%9B%86%E8%B7%9D%E9%9B%A2%EF%BC%9A%E7%A9%BA%E9%96%93%E3%82%92%E6%9C%80%E9%81%A9%E5%8C%96%E3%81%97%E3%81%9F%E5%8B%95%E7%9A%84%E8%A8%88%E7%94%BB%E6%B3%95%22%22%22%0A%20%20%20%20n,%20m%20%3D%20len%28s%29,%20len%28t%29%0A%20%20%20%20dp%20%3D%20%5B0%5D%20%2A%20%28m%20%2B%201%29%0A%20%20%20%20%23%20%E7%8A%B6%E6%85%8B%E9%81%B7%E7%A7%BB%EF%BC%9A%E5%85%88%E9%A0%AD%E8%A1%8C%0A%20%20%20%20for%20j%20in%20range%281,%20m%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20dp%5Bj%5D%20%3D%20j%0A%20%20%20%20%23%20%E7%8A%B6%E6%85%8B%E9%81%B7%E7%A7%BB%EF%BC%9A%E6%AE%8B%E3%82%8A%E3%81%AE%E8%A1%8C%0A%20%20%20%20for%20i%20in%20range%281,%20n%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20%23%20%E7%8A%B6%E6%85%8B%E9%81%B7%E7%A7%BB%EF%BC%9A%E5%85%88%E9%A0%AD%E5%88%97%0A%20%20%20%20%20%20%20%20leftup%20%3D%20dp%5B0%5D%20%20%23%20dp%5Bi-1,%20j-1%5D%20%E3%82%92%E4%B8%80%E6%99%82%E4%BF%9D%E5%AD%98%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20dp%5B0%5D%20%2B%3D%201%0A%20%20%20%20%20%20%20%20%23%20%E7%8A%B6%E6%85%8B%E9%81%B7%E7%A7%BB%EF%BC%9A%E6%AE%8B%E3%82%8A%E3%81%AE%E5%88%97%0A%20%20%20%20%20%20%20%20for%20j%20in%20range%281,%20m%20%2B%201%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20temp%20%3D%20dp%5Bj%5D%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20s%5Bi%20-%201%5D%20%3D%3D%20t%5Bj%20-%201%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%23%202%20%E3%81%A4%E3%81%AE%E6%96%87%E5%AD%97%E3%81%8C%E7%AD%89%E3%81%97%E3%81%84%E5%A0%B4%E5%90%88%E3%80%81%E3%81%9D%E3%81%AE%202%20%E6%96%87%E5%AD%97%E3%82%92%E3%82%B9%E3%82%AD%E3%83%83%E3%83%97%E3%81%99%E3%82%8B%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20dp%5Bj%5D%20%3D%20leftup%0A%20%20%20%20%20%20%20%20%20%20%20%20else%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E6%9C%80%E5%B0%8F%E7%B7%A8%E9%9B%86%E5%9B%9E%E6%95%B0%20%3D%20%E6%8C%BF%E5%85%A5%E3%80%81%E5%89%8A%E9%99%A4%E3%80%81%E7%BD%AE%E6%8F%9B%E3%81%AE%203%20%E6%93%8D%E4%BD%9C%E3%81%A7%E3%81%AE%E6%9C%80%E5%B0%8F%E7%B7%A8%E9%9B%86%E5%9B%9E%E6%95%B0%20%2B%201%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20dp%5Bj%5D%20%3D%20min%28dp%5Bj%20-%201%5D,%20dp%5Bj%5D,%20leftup%29%20%2B%201%0A%20%20%20%20%20%20%20%20%20%20%20%20leftup%20%3D%20temp%20%20%23%20%E6%AC%A1%E3%81%AE%E5%8F%8D%E5%BE%A9%E3%81%AE%20dp%5Bi-1,%20j-1%5D%20%E3%81%AB%E6%9B%B4%E6%96%B0%E3%81%99%E3%82%8B%0A%20%20%20%20return%20dp%5Bm%5D%0A%0A%0A%22%22%22%E5%AE%9F%E8%A1%8C%E7%94%A8%E3%82%B3%E3%83%BC%E3%83%89%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20s%20%3D%20%22bag%22%0A%20%20%20%20t%20%3D%20%22pack%22%0A%20%20%20%20n,%20m%20%3D%20len%28s%29,%20len%28t%29%0A%0A%20%20%20%20%23%20%E7%A9%BA%E9%96%93%E3%82%92%E6%9C%80%E9%81%A9%E5%8C%96%E3%81%97%E3%81%9F%E5%8B%95%E7%9A%84%E8%A8%88%E7%94%BB%E6%B3%95%0A%20%20%20%20res%20%3D%20edit_distance_dp_comp%28s,%20t%29%0A%20%20%20%20print%28f%22%7Bs%7D%20%E3%82%92%20%7Bt%7D%20%E3%81%AB%E5%A4%89%E6%9B%B4%E3%81%99%E3%82%8B%E3%81%AB%E3%81%AF%E6%9C%80%E4%BD%8E%20%7Bres%7D%20%E5%9B%9E%E3%81%AE%E7%B7%A8%E9%9B%86%E3%81%8C%E5%BF%85%E8%A6%81%22%29&amp;codeDivHeight=800&amp;codeDivWidth=600&amp;cumulative=false&amp;curInstr=6&amp;heapPrimitives=nevernest&amp;origin=opt-frontend.js&amp;py=311&amp;rawInputLstJSON=%5B%5D&amp;textReferences=false" rel="noopener noreferrer" target="_blank">全画面で表示 &gt;</a></div></p>
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