Mathematics: Fundamentals Sherlock and Moving Tiles#227
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✏️ Tip: You can customize this high-level summary in your review settings. 概要新しいJupyterノートブックが「Sherlock_and_Moving_Tiles」問題の数学的解法を追加し、入力検証と最適化を備えた2つのPython実装を提供します。同時に、インタラクティブなHTML可視化ファイルが問題の幾何学的理解を支援する図解とスライダーを含みます。 変更内容
コード レビュー労力の見積もり🎯 2 (Simple) | ⏱️ ~12 分 詩
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Actionable comments posted: 6
Fix all issues with AI Agents 🤖
In
@Mathematics/Fundamentals/HackerRank/Claude/Easy/moving-tiles-visualization.html:
- Around line 111-177: The SVG visualization lacks accessibility metadata and
readable labels; add a descriptive <title> and optional <desc> inside the <svg>
element (e.g., referencing the existing svg element rendering grid and
rectangles), add aria-label and role="img" attributes to the <svg>, and ensure
each meaningful graphic element (the two squares rendered by the rects using
offset1/offset2 and the overlap rect conditioned on overlap) has accessible text
either by linking to <title>/<desc> IDs via aria-labelledby or by adding hidden,
screen-reader-only <text> or <desc> content that mentions which square
corresponds to s1 and s2 and describes the overlap region; also ensure the
legend text elements are semantically discoverable (use <title>/<desc> fragments
or aria-hidden on purely visual elements) so screen readers can convey the
visualization to users.
- Around line 531-557: The function movingTiles lacks input validation for query
values; add checks at the start of movingTiles to ensure every q in queries is
non-negative and q <= l*l (and raise/return an appropriate error or sentinel for
invalid inputs), use the existing variables l and queries to validate, and keep
the early-return for v_diff == 0; ensure behavior is documented and tests
updated to cover negative q and q > l*l cases.
- Around line 9-16: Replace development React/CDN scripts with their production
minified equivalents and add Subresource Integrity (SRI) + crossorigin
attributes for every external script tag: update the React srcs from
react.development.js and react-dom.development.js to
react.production.min.js/react-dom.production.min.js, and add integrity="<!-- SRI
hash here -->" crossorigin="anonymous" to the Tailwind, React, ReactDOM and
Babel standalone <script> tags (or remove Babel standalone for a production
bundle). Ensure each <script> uses the correct production CDN URL and includes a
real SRI hash string in the integrity attribute.
- Around line 40-51: The calculations recompute Math.sqrt(2) multiple times and
don't guard against negative timeSlider; precompute a constant (e.g., const
invSqrt2 = 1/Math.sqrt(2) or const SQRT2 = Math.sqrt(2)) and reuse it in
offset1, offset2, and overlap, and ensure t is non-negative before use (e.g.,
set const t = Math.max(0, timeSlider) or validate timeSlider and
clamp/early-return) so that l, s1, s2, t, offset1, offset2, overlap, and
overlapArea produce correct results even for negative inputs.
In
@Mathematics/Fundamentals/HackerRank/Claude/Easy/Sherlock_and_Moving_Tiles.ipynb:
- Around line 156-167: The loop over queries currently special-cases q ==
max_area and q == 0 but the formula t = (l - sqrt(q)) * factor already yields
correct values for those cases; remove the explicit branches and always compute
time = (l - sqrt(q)) * factor inside the for q in queries loop, then append that
time to results (referencing results, queries, max_area, l, factor to locate the
code).
- Around line 172-185: The function movingTiles_competitive currently divides by
v_diff and will ZeroDivisionError when s1 == s2; add an early guard in
movingTiles_competitive that checks v_diff = abs(s1 - s2) and if v_diff == 0
either raise a clear ValueError (e.g., "s1 and s2 must differ") or handle the
degenerate case per spec, otherwise compute factor = math.sqrt(2) / v_diff and
proceed to return the list comprehension; ensure the guard happens before
computing factor to avoid division by zero.
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Mathematics/Fundamentals/HackerRank/Claude/Easy/Sherlock_and_Moving_Tiles.ipynbMathematics/Fundamentals/HackerRank/Claude/Easy/moving-tiles-visualization.html
🔇 Additional comments (8)
Mathematics/Fundamentals/HackerRank/Claude/Easy/Sherlock_and_Moving_Tiles.ipynb (4)
189-213: LGTM!HackerRankの入出力形式に適切に対応しており、環境変数
OUTPUT_PATHのフォールバック処理も実装されています。本番向け実装を使用する選択は、型安全性と入力検証の観点から適切です。
533-571: LGTM! 優れた実装この実装は、第1セルのproduction版と比較して以下の点で優れています：
- 不要な明示的エッジケース処理（
q == max_area、q == 0）を排除Final型ヒントで定数の不変性を明示- リスト内包表記で簡潔な実装
v_diff == 0のエッジケースを適切に処理数学的に正確で、コードもクリーンです。
89-89: パフォーマンス主張の検証が推奨されます「
sqrt = math.sqrtで 10-15% 高速化」という主張は有益ですが、実際のベンチマーク結果で検証することを推奨します。このマイクロ最適化の効果は、Python のバージョン、入力サイズ、実行環境によって異なる可能性があります。検証用のベンチマークスクリプトを生成しますか？
Also applies to: 623-625
1-790: ノートブック全体の評価このJupyterノートブックは、以下の点で高品質です：
- 数学的厳密性: 幾何学的導出と代数的逆算が正確
- 包括的なドキュメント: 問題の本質、数式の導出、複雑度解析、エッジケース、FAQが充実
- 複数の実装: 本番環境向けと競技プログラミング向けの2つの実装を提供
- 視覚化: ASCII図とMermaidダイアグラムで理解を促進
ただし、
movingTiles_competitive関数のゼロ除算リスク（既にコメント済み）は修正が必要です。Mathematics/Fundamentals/HackerRank/Claude/Easy/moving-tiles-visualization.html (4)
193-214: 計算過程の表示が明確で教育的ですステップバイステップの計算表示と逆算の例は、ユーザーが数学的概念を理解するのに非常に役立ちます。
229-383: 幾何学的導出が体系的で分かりやすい4つのステップ（座標変換、相対的ずれ、重なり部分、面積）による導出プロセスは論理的で、SVG図解により視覚的な理解を促進します。
386-454: 公式の導出と計算量分析が正確です代数的な導出プロセスが明確で、具体的な計算例により理解を深めます。O(q)の時間計算量とO(1)の空間計算量の分析も正確です。
562-590: コードと数式の対応表が理解を促進します実装と数学的表記の明確な対応関係を示すことで、読者がコードの意図を理解しやすくなります。教育的な価値が高いです。
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| <script src="https://cdn.tailwindcss.com"></script> | ||
|
|
||
| <!-- React & ReactDOM CDN --> | ||
| <script crossorigin src="https://unpkg.com/react@18/umd/react.development.js"></script> | ||
| <script crossorigin src="https://unpkg.com/react-dom@18/umd/react-dom.development.js"></script> | ||
|
|
||
| <!-- Babel Standalone (JSXをブラウザで変換) --> | ||
| <script src="https://unpkg.com/@babel/standalone/babel.min.js"></script> |
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CDNリソースのセキュリティとパフォーマンスを改善してください
以下の問題があります:
- セキュリティ: すべてのCDNリソースにSubresource Integrity (SRI)ハッシュが欠けています。これによりサプライチェーン攻撃に対して脆弱になります。
- パフォーマンス: React の開発ビルド（
react.development.js）を使用しています。本番環境ではreact.production.min.jsを使用すべきです。
🔎 推奨される修正
- <script src="https://cdn.tailwindcss.com"></script>
+ <script src="https://cdn.tailwindcss.com" integrity="sha384-..." crossorigin="anonymous"></script>
- <script crossorigin src="https://unpkg.com/react@18/umd/react.development.js"></script>
- <script crossorigin src="https://unpkg.com/react-dom@18/umd/react-dom.development.js"></script>
+ <script crossorigin src="https://unpkg.com/react@18/umd/react.production.min.js" integrity="sha384-..." crossorigin="anonymous"></script>
+ <script crossorigin src="https://unpkg.com/react-dom@18/umd/react-dom.production.min.js" integrity="sha384-..." crossorigin="anonymous"></script>
- <script src="https://unpkg.com/@babel/standalone/babel.min.js"></script>
+ <script src="https://unpkg.com/@babel/standalone/babel.min.js" integrity="sha384-..." crossorigin="anonymous"></script>注: 実際のSRIハッシュは各ライブラリの公式ドキュメントから取得してください。
Committable suggestion skipped: line range outside the PR's diff.
🤖 Prompt for AI Agents
In
@Mathematics/Fundamentals/HackerRank/Claude/Easy/moving-tiles-visualization.html
around lines 9-16, Replace development React/CDN scripts with their production
minified equivalents and add Subresource Integrity (SRI) + crossorigin
attributes for every external script tag: update the React srcs from
react.development.js and react-dom.development.js to
react.production.min.js/react-dom.production.min.js, and add integrity="<!-- SRI
hash here -->" crossorigin="anonymous" to the Tailwind, React, ReactDOM and
Babel standalone <script> tags (or remove Babel standalone for a production
bundle). Ensure each <script> uses the correct production CDN URL and includes a
real SRI hash string in the integrity attribute.
Comment on lines
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| const l = 100; // 正方形の一辺（ピクセル） | ||
| const s1 = 3; | ||
| const s2 = 1; | ||
| const t = timeSlider; | ||
|
|
||
| // 時刻tでの各正方形の位置 | ||
| const offset1 = (s1 * t) / Math.sqrt(2); | ||
| const offset2 = (s2 * t) / Math.sqrt(2); | ||
|
|
||
| // 重なり部分の一辺 | ||
| const overlap = Math.max(0, l - (Math.abs(s1 - s2) * t) / Math.sqrt(2)); | ||
| const overlapArea = overlap * overlap; |
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🧹 Nitpick | 🔵 Trivial
定数の事前計算とエッジケースの考慮
現在の実装は正しいですが、以下の改善が可能です:
Math.sqrt(2)が複数回計算されています（lines 46, 47, 50）timeSliderが負の値になる可能性のチェックがありません
🔎 推奨される改善
+ const SQRT2 = Math.sqrt(2);
+
// 可視化用のパラメータ
const l = 100; // 正方形の一辺（ピクセル）
const s1 = 3;
const s2 = 1;
- const t = timeSlider;
+ const t = Math.max(0, timeSlider);
// 時刻tでの各正方形の位置
- const offset1 = (s1 * t) / Math.sqrt(2);
- const offset2 = (s2 * t) / Math.sqrt(2);
+ const offset1 = (s1 * t) / SQRT2;
+ const offset2 = (s2 * t) / SQRT2;
// 重なり部分の一辺
- const overlap = Math.max(0, l - (Math.abs(s1 - s2) * t) / Math.sqrt(2));
+ const overlap = Math.max(0, l - (Math.abs(s1 - s2) * t) / SQRT2);
const overlapArea = overlap * overlap;Committable suggestion skipped: line range outside the PR's diff.
🤖 Prompt for AI Agents
In
@Mathematics/Fundamentals/HackerRank/Claude/Easy/moving-tiles-visualization.html
around lines 40-51, The calculations recompute Math.sqrt(2) multiple times and
don't guard against negative timeSlider; precompute a constant (e.g., const
invSqrt2 = 1/Math.sqrt(2) or const SQRT2 = Math.sqrt(2)) and reuse it in
offset1, offset2, and overlap, and ensure t is non-negative before use (e.g.,
set const t = Math.max(0, timeSlider) or validate timeSlider and
clamp/early-return) so that l, s1, s2, t, offset1, offset2, overlap, and
overlapArea produce correct results even for negative inputs.
Comment on lines
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| <svg width="400" height="400" className="border bg-gray-50"> | ||
| {/* グリッド */} | ||
| <line x1="0" y1="200" x2="400" y2="200" stroke="#ddd" /> | ||
| <line x1="200" y1="0" x2="200" y2="400" stroke="#ddd" /> | ||
| <line | ||
| x1="0" | ||
| y1="0" | ||
| x2="400" | ||
| y2="400" | ||
| stroke="#ddd" | ||
| strokeDasharray="5,5" | ||
| /> | ||
|
|
||
| {/* 正方形2（青） */} | ||
| <rect | ||
| x={200 - l / 2 + offset2} | ||
| y={200 - l / 2 + offset2} | ||
| width={l} | ||
| height={l} | ||
| fill="rgba(59, 130, 246, 0.3)" | ||
| stroke="blue" | ||
| strokeWidth="2" | ||
| /> | ||
|
|
||
| {/* 正方形1（赤） */} | ||
| <rect | ||
| x={200 - l / 2 + offset1} | ||
| y={200 - l / 2 + offset1} | ||
| width={l} | ||
| height={l} | ||
| fill="rgba(239, 68, 68, 0.3)" | ||
| stroke="red" | ||
| strokeWidth="2" | ||
| /> | ||
|
|
||
| {/* 重なり領域の強調 */} | ||
| {overlap > 0 && ( | ||
| <rect | ||
| x={200 - l / 2 + Math.max(offset1, offset2)} | ||
| y={200 - l / 2 + Math.max(offset1, offset2)} | ||
| width={overlap} | ||
| height={overlap} | ||
| fill="rgba(34, 197, 94, 0.5)" | ||
| stroke="green" | ||
| strokeWidth="2" | ||
| /> | ||
| )} | ||
|
|
||
| {/* 凡例 */} | ||
| <rect x="10" y="10" width="15" height="15" fill="rgba(239, 68, 68, 0.3)" stroke="red" strokeWidth="1" /> | ||
| <text x="30" y="22" className="text-xs" fill="#333"> | ||
| 正方形1 (速度: {s1}) | ||
| </text> | ||
| <rect x="10" y="30" width="15" height="15" fill="rgba(59, 130, 246, 0.3)" stroke="blue" strokeWidth="1" /> | ||
| <text x="30" y="42" className="text-xs" fill="#333"> | ||
| 正方形2 (速度: {s2}) | ||
| </text> | ||
| <rect x="10" y="50" width="15" height="15" fill="rgba(34, 197, 94, 0.5)" stroke="green" strokeWidth="1" /> | ||
| <text x="30" y="62" className="text-xs" fill="#333"> | ||
| 重なり領域 | ||
| </text> | ||
|
|
||
| {/* y=x 方向のラベル */} | ||
| <text x="350" y="390" className="text-xs" fill="#999"> | ||
| y = x 方向 | ||
| </text> | ||
| </svg> |
Contributor
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SVG可視化のアクセシビリティを改善してください
SVGに以下のアクセシビリティ機能が欠けています:
aria-labelまたは<title>要素による説明- スクリーンリーダー用の代替テキスト
- SVG内のテキスト要素のアクセシビリティ
これにより、視覚障害のあるユーザーが可視化の内容を理解できません。
🔎 推奨される修正
- <svg width="400" height="400" className="border bg-gray-50">
+ <svg
+ width="400"
+ height="400"
+ className="border bg-gray-50"
+ role="img"
+ aria-label="2つの正方形の移動と重なりを示す動的シミュレーション図"
+ >
+ <title>Moving Tiles シミュレーション</title>
+ <desc>
+ 時刻 {t.toFixed(1)} 秒における2つの正方形の位置。
+ 赤い正方形（速度{s1}）と青い正方形（速度{s2}）が
+ y=x方向に移動し、緑色の領域が重なり部分を示します。
+ </desc>
{/* グリッド */}🤖 Prompt for AI Agents
In
@Mathematics/Fundamentals/HackerRank/Claude/Easy/moving-tiles-visualization.html
around lines 111-177, The SVG visualization lacks accessibility metadata and
readable labels; add a descriptive <title> and optional <desc> inside the <svg>
element (e.g., referencing the existing svg element rendering grid and
rectangles), add aria-label and role="img" attributes to the <svg>, and ensure
each meaningful graphic element (the two squares rendered by the rects using
offset1/offset2 and the overlap rect conditioned on overlap) has accessible text
either by linking to <title>/<desc> IDs via aria-labelledby or by adding hidden,
screen-reader-only <text> or <desc> content that mentions which square
corresponds to s1 and s2 and describes the overlap region; also ensure the
legend text elements are semantically discoverable (use <title>/<desc> fragments
or aria-hidden on purely visual elements) so screen readers can convey the
visualization to users.
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| def movingTiles(l: int, s1: int, s2: int, queries: List[int]) -> List[float]: | ||
| """ | ||
| 2つの正方形の重なり面積から時刻を計算 | ||
|
|
||
| 数学的根拠: | ||
| - 重なり面積: A(t) = [l - |s1-s2|*t/√2]² | ||
| - 逆算: t = (l - √q) * √2 / |s1-s2| | ||
|
|
||
| Time Complexity: O(q) where q = len(queries) | ||
| Space Complexity: O(1) (excluding output) | ||
| """ | ||
| # 関数呼び出しオーバーヘッド削減 | ||
| sqrt = math.sqrt | ||
|
|
||
| # 速度差の絶対値 | ||
| v_diff = abs(s1 - s2) | ||
|
|
||
| # エッジケース: 速度が同じ場合 | ||
| if v_diff == 0: | ||
| return [0.0] * len(queries) | ||
|
|
||
| # 定数の事前計算: √2 / |s1 - s2| | ||
| factor = 1.4142135623730951 / v_diff | ||
|
|
||
| # 各クエリに対して時刻を計算 | ||
| # t = (l - √q) * factor | ||
| return [(l - sqrt(q)) * factor for q in queries]`} |
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🧹 Nitpick | 🔵 Trivial
入力検証の追加を検討してください
実装は数学的に正確ですが、以下の入力検証が欠けています:
queriesの値が負でないことの確認queriesの値がl²を超えないことの確認（物理的に不可能）
これらのケースは仕様によっては発生しない可能性がありますが、防御的プログラミングの観点から検証を追加することをお勧めします。
🔎 推奨される改善
def movingTiles(l: int, s1: int, s2: int, queries: List[int]) -> List[float]:
"""
2つの正方形の重なり面積から時刻を計算
数学的根拠:
- 重なり面積: A(t) = [l - |s1-s2|*t/√2]²
- 逆算: t = (l - √q) * √2 / |s1-s2|
Time Complexity: O(q) where q = len(queries)
Space Complexity: O(1) (excluding output)
+
+ Args:
+ l: 正方形の一辺の長さ (> 0)
+ s1: 正方形1の速度 (>= 0)
+ s2: 正方形2の速度 (>= 0)
+ queries: 重なり面積のリスト (0 <= q <= l²)
+
+ Returns:
+ 各クエリに対応する時刻のリスト
"""
# 関数呼び出しオーバーヘッド削減
sqrt = math.sqrt
# 速度差の絶対値
v_diff = abs(s1 - s2)
# エッジケース: 速度が同じ場合
if v_diff == 0:
return [0.0] * len(queries)
# 定数の事前計算: √2 / |s1 - s2|
factor = 1.4142135623730951 / v_diff
+
+ # 境界値
+ max_area = l * l
# 各クエリに対して時刻を計算
# t = (l - √q) * factor
- return [(l - sqrt(q)) * factor for q in queries]
+ return [
+ (l - sqrt(min(max(0, q), max_area))) * factor
+ for q in queries
+ ]🤖 Prompt for AI Agents
In
@Mathematics/Fundamentals/HackerRank/Claude/Easy/moving-tiles-visualization.html
around lines 531-557, The function movingTiles lacks input validation for query
values; add checks at the start of movingTiles to ensure every q in queries is
non-negative and q <= l*l (and raise/return an appropriate error or sentinel for
invalid inputs), use the existing variables l and queries to validate, and keep
the early-return for v_diff == 0; ensure behavior is documented and tests
updated to cover negative q and q > l*l cases.
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| " results = []\n", | ||
| " for q in queries:\n", | ||
| " if q == max_area:\n", | ||
| " # 完全に重なっている状態 (t = 0)\n", | ||
| " results.append(0.0)\n", | ||
| " elif q == 0:\n", | ||
| " # 完全に離れた状態\n", | ||
| " time = l * factor\n", | ||
| " results.append(time)\n", | ||
| " else:\n", | ||
| " time = (l - sqrt(q)) * factor\n", | ||
| " results.append(time)\n", |
Contributor
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🧹 Nitpick | 🔵 Trivial
不要な明示的エッジケース処理
q == max_area および q == 0 の明示的なチェックは不要です。数式 t = (l - sqrt(q)) * factor はこれらのケースを自動的に正しく処理します：
q == max_area(つまりq == l²) の場合:sqrt(l²) = lなのでt = (l - l) * factor = 0q == 0の場合:sqrt(0) = 0なのでt = l * factor
明示的な分岐を削除することで、コードがよりシンプルになり、保守性が向上します。
🔎 提案される簡略化
- # 各クエリに対して時刻を計算
- # t = (l - √q) * √2 / |s1 - s2|
- results = []
- for q in queries:
- if q == max_area:
- # 完全に重なっている状態 (t = 0)
- results.append(0.0)
- elif q == 0:
- # 完全に離れた状態
- time = l * factor
- results.append(time)
- else:
- time = (l - sqrt(q)) * factor
- results.append(time)
-
- return results
+ # 各クエリに対して時刻を計算
+ # t = (l - √q) * √2 / |s1 - s2|
+ return [(l - sqrt(q)) * factor for q in queries]📝 Committable suggestion
‼️ IMPORTANT
Carefully review the code before committing. Ensure that it accurately replaces the highlighted code, contains no missing lines, and has no issues with indentation. Thoroughly test & benchmark the code to ensure it meets the requirements.
Suggested change
| " results = []\n", | |
| " for q in queries:\n", | |
| " if q == max_area:\n", | |
| " # 完全に重なっている状態 (t = 0)\n", | |
| " results.append(0.0)\n", | |
| " elif q == 0:\n", | |
| " # 完全に離れた状態\n", | |
| " time = l * factor\n", | |
| " results.append(time)\n", | |
| " else:\n", | |
| " time = (l - sqrt(q)) * factor\n", | |
| " results.append(time)\n", | |
| # 各クエリに対して時刻を計算 | |
| # t = (l - √q) * √2 / |s1 - s2| | |
| return [(l - sqrt(q)) * factor for q in queries] |
🤖 Prompt for AI Agents
In
@Mathematics/Fundamentals/HackerRank/Claude/Easy/Sherlock_and_Moving_Tiles.ipynb
around lines 156-167, The loop over queries currently special-cases q ==
max_area and q == 0 but the formula t = (l - sqrt(q)) * factor already yields
correct values for those cases; remove the explicit branches and always compute
time = (l - sqrt(q)) * factor inside the for q in queries loop, then append that
time to results (referencing results, queries, max_area, l, factor to locate the
code).
Comment on lines
+172
to
+185
| "def movingTiles_competitive(l: int, s1: int, s2: int, queries: List[int]) -> List[float]:\n", | ||
| " \"\"\"\n", | ||
| " 競技プログラミング向け実装 (性能最優先)\n", | ||
| " \n", | ||
| " エラーハンドリング省略、最小限のコード\n", | ||
| " \n", | ||
| " Time Complexity: O(q)\n", | ||
| " Space Complexity: O(1) (出力を除く)\n", | ||
| " \"\"\"\n", | ||
| " sqrt = math.sqrt\n", | ||
| " v_diff = abs(s1 - s2)\n", | ||
| " factor = 1.4142135623730951 / v_diff # math.sqrt(2) の定数化\n", | ||
| " \n", | ||
| " return [(l - sqrt(q)) * factor for q in queries]\n", |
Contributor
There was a problem hiding this comment.
ゼロ除算の潜在的リスク
s1 == s2 の場合、v_diff = 0 となり、factor = 1.4142135623730951 / v_diff でゼロ除算エラー（ZeroDivisionError）が発生します。問題の制約で s1 ≠ s2 が保証されていない場合、このケースを処理する必要があります。
🔎 提案される修正
def movingTiles_competitive(l: int, s1: int, s2: int, queries: List[int]) -> List[float]:
"""
競技プログラミング向け実装 (性能最優先)
エラーハンドリング省略、最小限のコード
Time Complexity: O(q)
Space Complexity: O(1) (出力を除く)
"""
sqrt = math.sqrt
v_diff = abs(s1 - s2)
+ if v_diff == 0:
+ return [0.0] * len(queries)
factor = 1.4142135623730951 / v_diff # math.sqrt(2) の定数化
return [(l - sqrt(q)) * factor for q in queries]📝 Committable suggestion
‼️ IMPORTANT
Carefully review the code before committing. Ensure that it accurately replaces the highlighted code, contains no missing lines, and has no issues with indentation. Thoroughly test & benchmark the code to ensure it meets the requirements.
Suggested change
| "def movingTiles_competitive(l: int, s1: int, s2: int, queries: List[int]) -> List[float]:\n", | |
| " \"\"\"\n", | |
| " 競技プログラミング向け実装 (性能最優先)\n", | |
| " \n", | |
| " エラーハンドリング省略、最小限のコード\n", | |
| " \n", | |
| " Time Complexity: O(q)\n", | |
| " Space Complexity: O(1) (出力を除く)\n", | |
| " \"\"\"\n", | |
| " sqrt = math.sqrt\n", | |
| " v_diff = abs(s1 - s2)\n", | |
| " factor = 1.4142135623730951 / v_diff # math.sqrt(2) の定数化\n", | |
| " \n", | |
| " return [(l - sqrt(q)) * factor for q in queries]\n", | |
| def movingTiles_competitive(l: int, s1: int, s2: int, queries: List[int]) -> List[float]: | |
| """ | |
| 競技プログラミング向け実装 (性能最優先) | |
| エラーハンドリング省略、最小限のコード | |
| Time Complexity: O(q) | |
| Space Complexity: O(1) (出力を除く) | |
| """ | |
| sqrt = math.sqrt | |
| v_diff = abs(s1 - s2) | |
| if v_diff == 0: | |
| return [0.0] * len(queries) | |
| factor = 1.4142135623730951 / v_diff # math.sqrt(2) の定数化 | |
| return [(l - sqrt(q)) * factor for q in queries] |
🤖 Prompt for AI Agents
In
@Mathematics/Fundamentals/HackerRank/Claude/Easy/Sherlock_and_Moving_Tiles.ipynb
around lines 172-185, The function movingTiles_competitive currently divides by
v_diff and will ZeroDivisionError when s1 == s2; add an early guard in
movingTiles_competitive that checks v_diff = abs(s1 - s2) and if v_diff == 0
either raise a clear ValueError (e.g., "s1 and s2 must differ") or handle the
degenerate case per spec, otherwise compute factor = math.sqrt(2) / v_diff and
proceed to return the list comprehension; ensure the guard happens before
computing factor to avoid division by zero.
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