|
| 1 | +{ |
| 2 | + "cells": [ |
| 3 | + { |
| 4 | + "cell_type": "markdown", |
| 5 | + "id": "0c8d5e7b", |
| 6 | + "metadata": {}, |
| 7 | + "source": [ |
| 8 | + "## 1. 問題の分析\n", |
| 9 | + "\n", |
| 10 | + "### 競技プログラミング視点\n", |
| 11 | + "- `Array.filter` の内部実装を手動で再現する問題\n", |
| 12 | + "- 単純な線形走査で O(n) が最適解\n", |
| 13 | + "- 余分なメモリを最小化するため、結果配列への直接 push が最適\n", |
| 14 | + "\n", |
| 15 | + "### 業務開発視点\n", |
| 16 | + "- コールバック関数の型安全性確保(`Fn` 型)\n", |
| 17 | + "- `fn` の戻り値は `any` → 明示的に `Boolean()` で truthiness を評価\n", |
| 18 | + "- 入力配列は破壊しない(Pure function)\n", |
| 19 | + "\n", |
| 20 | + "### TypeScript 特有の考慮点\n", |
| 21 | + "- `Fn` 型で引数 `(n, i)` の型が保証されており、コンパイル時安全\n", |
| 22 | + "- `readonly` 修飾子でイミュータブル性を担保可能\n", |
| 23 | + "\n", |
| 24 | + "---\n", |
| 25 | + "\n", |
| 26 | + "## 2. アルゴリズムアプローチ比較\n", |
| 27 | + "\n", |
| 28 | + "| アプローチ | 時間計算量 | 空間計算量 | TS実装コスト | 型安全性 | 可読性 | 備考 |\n", |
| 29 | + "|---|---|---|---|---|---|---|\n", |
| 30 | + "| **for ループ + push** | O(n) | O(k) | 低 | 高 | 高 | ✅ 最適解 |\n", |
| 31 | + "| for...of + entries() | O(n) | O(k) | 低 | 高 | 中 | index 取得にオーバーヘッド |\n", |
| 32 | + "| reduce | O(n) | O(k) | 中 | 高 | 中 | 関数型スタイルだが若干遅い |\n", |
| 33 | + "\n", |
| 34 | + "> k = フィルタ後の要素数\n", |
| 35 | + "\n", |
| 36 | + "---\n", |
| 37 | + "\n", |
| 38 | + "## 3. 選択したアルゴリズムと理由\n", |
| 39 | + "\n", |
| 40 | + "- **選択**: `for` ループ + 条件付き `push`\n", |
| 41 | + "- **理由**:\n", |
| 42 | + " - インデックス `i` が直接利用可能で `Fn(n, i)` の呼び出しが最も自然\n", |
| 43 | + " - V8エンジンでの JIT 最適化が最も効きやすいシンプルな構造\n", |
| 44 | + " - `Boolean()` による明示的な truthiness 評価で型安全性確保\n", |
| 45 | + " - 制約 `arr.length <= 1000` の範囲では計算量差は無視できるが、最もシンプルで保守性が高い\n", |
| 46 | + "\n", |
| 47 | + "---\n", |
| 48 | + "\n", |
| 49 | + "## 4. 実装コード\n", |
| 50 | + "\n", |
| 51 | + "```typescript\n", |
| 52 | + "// Analyze Complexity\n", |
| 53 | + "// Runtime 42 ms\n", |
| 54 | + "// Beats 69.47%\n", |
| 55 | + "// Memory 55.88 MB\n", |
| 56 | + "// Beats 17.95%\n", |
| 57 | + "type Fn = (n: number, i: number) => any;\n", |
| 58 | + "\n", |
| 59 | + "/**\n", |
| 60 | + " * 配列をコールバック関数でフィルタリングする(Array.filter の手動実装)\n", |
| 61 | + " * @param arr - フィルタ対象の数値配列\n", |
| 62 | + " * @param fn - フィルタ条件コールバック (要素値, インデックス) => truthy/falsy\n", |
| 63 | + " * @returns fn が truthy を返した要素のみを含む新しい配列\n", |
| 64 | + " * @complexity Time: O(n), Space: O(k) ※ k = フィルタ後の要素数\n", |
| 65 | + " */\n", |
| 66 | + "function filter(arr: number[], fn: Fn): number[] {\n", |
| 67 | + " const result: number[] = [];\n", |
| 68 | + "\n", |
| 69 | + " for (let i = 0; i < arr.length; i++) {\n", |
| 70 | + " if (Boolean(fn(arr[i], i))) {\n", |
| 71 | + " result.push(arr[i]);\n", |
| 72 | + " }\n", |
| 73 | + " }\n", |
| 74 | + "\n", |
| 75 | + " return result;\n", |
| 76 | + "}\n", |
| 77 | + "```\n", |
| 78 | + "\n", |
| 79 | + "---\n", |
| 80 | + "\n", |
| 81 | + "## ポイント解説\n", |
| 82 | + "\n", |
| 83 | + "```\n", |
| 84 | + "arr = [-2, -1, 0, 1, 2], fn = (n) => n + 1\n", |
| 85 | + "\n", |
| 86 | + "i=0: fn(-2) = -1 → Boolean(-1) = true ✅ → result: [-2]\n", |
| 87 | + "i=1: fn(-1) = 0 → Boolean(0) = false ❌\n", |
| 88 | + "i=2: fn( 0) = 1 → Boolean(1) = true ✅ → result: [-2, 0]\n", |
| 89 | + "i=3: fn( 1) = 2 → Boolean(2) = true ✅ → result: [-2, 0, 1]\n", |
| 90 | + "i=4: fn( 2) = 3 → Boolean(3) = true ✅ → result: [-2, 0, 1, 2]\n", |
| 91 | + "```\n", |
| 92 | + "\n", |
| 93 | + "### TypeScript 特有の最適化ポイント\n", |
| 94 | + "\n", |
| 95 | + "| 観点 | 本実装での対応 |\n", |
| 96 | + "|---|---|\n", |
| 97 | + "| **型安全性** | `Fn` 型でコールバックの引数型を保証 |\n", |
| 98 | + "| **Truthiness** | `Boolean(fn(...))` で `any` 型の戻り値を安全に評価 |\n", |
| 99 | + "| **イミュータブル性** | 元の `arr` を破壊せず、新しい `result[]` を返却 |\n", |
| 100 | + "| **Null安全** | `arr.length` ガードにより空配列は自然に空を返す |\n", |
| 101 | + "\n", |
| 102 | + "## ボトルネック分析\n", |
| 103 | + "\n", |
| 104 | + "### Memory 問題: `push` による動的リサイズ\n", |
| 105 | + "\n", |
| 106 | + "```\n", |
| 107 | + "push の内部動作(V8エンジン):\n", |
| 108 | + "[初期] capacity: 4 → [_, _, _, _]\n", |
| 109 | + "push×4 → capacity: 4 ✅ 問題なし\n", |
| 110 | + "push×5 → capacity: 8 ⚠️ 再アロケーション(×2拡張)\n", |
| 111 | + "push×9 → capacity: 16 ⚠️ 再アロケーション\n", |
| 112 | + "...\n", |
| 113 | + "最悪 log₂(n) 回のコピーが発生 → メモリ断片化\n", |
| 114 | + "```\n", |
| 115 | + "\n", |
| 116 | + "### Runtime 問題: `Boolean()` のラッパーコスト\n", |
| 117 | + "\n", |
| 118 | + "```typescript\n", |
| 119 | + "Boolean(fn(arr[i], i)) // ← 関数呼び出しオーバーヘッド\n", |
| 120 | + "```\n", |
| 121 | + "\n", |
| 122 | + "---\n", |
| 123 | + "\n", |
| 124 | + "## 最適化戦略\n", |
| 125 | + "\n", |
| 126 | + "```\n", |
| 127 | + "【Before】動的 push 【After】事前確保 + 書き込みポインタ\n", |
| 128 | + "result = [] result = new Array(arr.length)\n", |
| 129 | + "push → push → push result[count++] = value\n", |
| 130 | + "(内部で何度もリサイズ) (固定メモリ、リサイズなし)\n", |
| 131 | + "最終: result 最終: result.slice(0, count)\n", |
| 132 | + "```\n", |
| 133 | + "\n", |
| 134 | + "---\n", |
| 135 | + "\n", |
| 136 | + "## 最適化実装\n", |
| 137 | + "\n", |
| 138 | + "```typescript\n", |
| 139 | + "// Analyze Complexity\n", |
| 140 | + "// Runtime 38 ms\n", |
| 141 | + "// Beats 87.22%\n", |
| 142 | + "// Memory 55.64 MB\n", |
| 143 | + "// Beats 32.35%\n", |
| 144 | + "type Fn = (n: number, i: number) => any;\n", |
| 145 | + "\n", |
| 146 | + "/**\n", |
| 147 | + " * 配列をコールバック関数でフィルタリングする(メモリ最適化版)\n", |
| 148 | + " * @param arr - フィルタ対象の数値配列\n", |
| 149 | + " * @param fn - フィルタ条件コールバック (要素値, インデックス) => truthy/falsy\n", |
| 150 | + " * @returns fn が truthy を返した要素のみを含む新しい配列\n", |
| 151 | + " * @complexity Time: O(n), Space: O(n) → 実効 O(k)\n", |
| 152 | + " */\n", |
| 153 | + "function filter(arr: number[], fn: Fn): number[] {\n", |
| 154 | + " // ✅ 最大サイズで事前確保 → push による動的リサイズを排除\n", |
| 155 | + " const result = new Array<number>(arr.length);\n", |
| 156 | + " let count = 0;\n", |
| 157 | + "\n", |
| 158 | + " for (let i = 0; i < arr.length; i++) {\n", |
| 159 | + " // ✅ Boolean() ラッパー除去 → 暗黙の truthy 評価で直接分岐\n", |
| 160 | + " if (fn(arr[i], i)) {\n", |
| 161 | + " result[count++] = arr[i];\n", |
| 162 | + " }\n", |
| 163 | + " }\n", |
| 164 | + "\n", |
| 165 | + " // ✅ 実際に使用した分だけ切り出し\n", |
| 166 | + " return result.slice(0, count);\n", |
| 167 | + "}\n", |
| 168 | + "```\n", |
| 169 | + "\n", |
| 170 | + "---\n", |
| 171 | + "\n", |
| 172 | + "## 最適化ポイント早見表\n", |
| 173 | + "\n", |
| 174 | + "| 項目 | Before | After | 効果 |\n", |
| 175 | + "|---|---|---|---|\n", |
| 176 | + "| **メモリ確保** | `[]` + 動的 push | `new Array(n)` 事前確保 | 再アロケーション排除 |\n", |
| 177 | + "| **Truthiness評価** | `Boolean(fn(...))` | `if (fn(...))` 直接評価 | 関数呼び出しコスト削減 |\n", |
| 178 | + "| **書き込み方式** | `push()` | `result[count++]` 直接代入 | 配列操作オーバーヘッド削減 |\n", |
| 179 | + "| **最終出力** | `result` そのまま | `result.slice(0, count)` | 未使用領域を切り捨て |\n", |
| 180 | + "\n", |
| 181 | + "---\n", |
| 182 | + "\n", |
| 183 | + "## トレードオフ\n", |
| 184 | + "\n", |
| 185 | + "```\n", |
| 186 | + "new Array(n) → slice(0, count) の構造:\n", |
| 187 | + "\n", |
| 188 | + "メリット: V8 が連続メモリ領域を1回確保 → GC 負荷軽減\n", |
| 189 | + "デメリット: slice() で最終的に O(k) のコピーが1回発生\n", |
| 190 | + "\n", |
| 191 | + "→ arr.length <= 1000 の制約下では\n", |
| 192 | + " push の累積コピーコスト >> slice の1回コピーコスト\n", |
| 193 | + " ∴ トータルでメモリ効率・速度ともに優位\n", |
| 194 | + "```" |
| 195 | + ] |
| 196 | + } |
| 197 | + ], |
| 198 | + "metadata": { |
| 199 | + "kernelspec": { |
| 200 | + "display_name": "TypeScript", |
| 201 | + "language": "typescript", |
| 202 | + "name": "typescript" |
| 203 | + }, |
| 204 | + "language_info": { |
| 205 | + "file_extension": ".ts", |
| 206 | + "mimetype": "text/typescript", |
| 207 | + "name": "typescript", |
| 208 | + "version": "5.9.3" |
| 209 | + } |
| 210 | + }, |
| 211 | + "nbformat": 4, |
| 212 | + "nbformat_minor": 5 |
| 213 | +} |
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