{ "evaluation_id": "EVAL-20260207-140934", "question_id": "CODE-004", "question_text": "This function works but is O(n³). Optimize it to O(n log n) or better while maintaining correctness.\n\n```python\ndef find_triplets_with_sum(arr, target_sum):\n \"\"\"Find all unique triplets in arr that sum to target_sum\"\"\"\n n = len(arr)\n result = []\n \n for i in range(n):\n for j in range(i + 1, n):\n for k in range(j + 1, n):\n if arr[i] + arr[j] + arr[k] == target_sum:\n triplet = sorted([arr[i], arr[j], arr[k]])\n if triplet not in result:\n result.append(triplet)\n \n return result\n```\n\nExplain your optimization approach and prove the new time complexity.", "category": "code", "timestamp": "2026-02-03T00:00:00.000Z", "display_date": "Feb 03, 2026", "winner": { "name": "Claude Opus 4.5", "provider": "Anthropic", "score": 9.64 }, "avg_score": 8.575, "matrix_size": 90, "models_used": [ { "id": "minimax_m2", "name": "MiniMax M2", "provider": "MiniMax" }, { "id": "claude_opus", "name": "Claude Opus 4.5", "provider": "Anthropic" }, { "id": "gemini_3_flash", "name": "Gemini 3 Flash Preview", "provider": "Google" }, { "id": "claude_sonnet", "name": "Claude Sonnet 4.5", "provider": "Anthropic" }, { "id": "gemini_3_pro", "name": "Gemini 3 Pro Preview", "provider": "Google" }, { "id": "glm_4_7", "name": "GLM-4-7", "provider": "Zhipu" }, { "id": "deepseek_v3", "name": "DeepSeek V3.2", "provider": "DeepSeek" }, { "id": "gpt_codex", "name": "GPT-5.2-Codex", "provider": "OpenAI" }, { "id": "grok_direct", "name": "Grok 3 (Direct)", "provider": "xAI" }, { "id": "grok_code_fast", "name": "Grok Code Fast", "provider": "xAI" } ], "rankings": { "claude_opus": { "display_name": "Claude Opus 4.5", "provider": "Anthropic", "average_score": 9.64, "score_count": 8, "min_score": 8.75, "max_score": 10, "rank": 1 }, "claude_sonnet": { "display_name": "Claude Sonnet 4.5", "provider": "Anthropic", "average_score": 9.5, "score_count": 7, "min_score": 8.8, "max_score": 9.8, "rank": 2 }, "deepseek_v3": { "display_name": "DeepSeek V3.2", "provider": "DeepSeek", "average_score": 9.49, "score_count": 8, "min_score": 8.8, "max_score": 9.8, "rank": 3 }, "grok_direct": { "display_name": "Grok 3 (Direct)", "provider": "xAI", "average_score": 9.49, "score_count": 8, "min_score": 8.8, "max_score": 9.8, "rank": 4 }, "gemini_3_flash": { "display_name": "Gemini 3 Flash Preview", "provider": "Google", "average_score": 9.31, "score_count": 8, "min_score": 8.6, "max_score": 9.8, "rank": 5 }, "gpt_codex": { "display_name": "GPT-5.2-Codex", "provider": "OpenAI", "average_score": 9.23, "score_count": 8, "min_score": 8.35, "max_score": 9.8, "rank": 6 }, "grok_code_fast": { "display_name": "Grok Code Fast", "provider": "xAI", "average_score": 9.09, "score_count": 8, "min_score": 7.75, "max_score": 9.8, "rank": 7 }, "gemini_3_pro": { "display_name": "Gemini 3 Pro Preview", "provider": "Google", "average_score": 6.93, "score_count": 8, "min_score": 3.6, "max_score": 8.4, "rank": 8 }, "glm_4_7": { "display_name": "GLM-4-7", "provider": "Zhipu", "average_score": 6.8, "score_count": 4, "min_score": 2, "max_score": 9.55, "rank": 9 }, "minimax_m2": { "display_name": "MiniMax M2", "provider": "MiniMax", "average_score": 6.28, "score_count": 3, "min_score": 2, "max_score": 9.8, "rank": 10 } }, "judgments": [ { "judge_key": "claude_sonnet", "judge_name": "Claude Sonnet 4.5", "respondent_key": "minimax_m2", "respondent_name": "MiniMax M2", "weighted_score": 0, "brief_justification": "No response was provided to evaluate. The 'Response to evaluate:' field is empty, so there is no content to score against the question's requirements for optimizing the triplet sum function." }, { "judge_key": "grok_code_fast", "judge_name": "Grok Code Fast", "respondent_key": "claude_opus", "respondent_name": "Claude Opus 4.5", "weighted_score": 9.8, "brief_justification": "The response accurately optimizes the function to O(n²) with correct code and proofs, thoroughly covers the topic including examples and tests, is well-structured and clear, provides deep analysis on optimality, and offers highly practical value with actionable code and comparisons." }, { "judge_key": "grok_code_fast", "judge_name": "Grok Code Fast", "respondent_key": "gemini_3_flash", "respondent_name": "Gemini 3 Flash Preview", "weighted_score": 9.8, "brief_justification": "The response accurately optimizes the function to O(n²) with correct code and analysis, thoroughly explaining the approach and limitations, while providing clear, insightful, and highly actionable guidance." }, { "judge_key": "grok_code_fast", "judge_name": "Grok Code Fast", "respondent_key": "claude_sonnet", "respondent_name": "Claude Sonnet 4.5", "weighted_score": 9.55, "brief_justification": "The response correctly optimizes the function to O(n²) time complexity using sorting and two-pointer technique, maintaining correctness and handling duplicates effectively, though it does not achieve the requested O(n log n) or better; it thoroughly covers the approach, proof, and comparison with excellent structure and practical code." }, { "judge_key": "grok_code_fast", "judge_name": "Grok Code Fast", "respondent_key": "gemini_3_pro", "respondent_name": "Gemini 3 Pro Preview", "weighted_score": 8.25, "brief_justification": "The response correctly optimizes to O(n^2) and explains the theoretical impossibility of O(n log n), with a mostly accurate code implementation, though the code is truncated. It provides insightful depth on complexity bounds but lacks full completeness in code and explicit proof of time complexity." }, { "judge_key": "grok_code_fast", "judge_name": "Grok Code Fast", "respondent_key": "minimax_m2", "respondent_name": "MiniMax M2", "weighted_score": 2, "brief_justification": "The response does not provide any optimization or explanation for the function, failing to address the query entirely." }, { "judge_key": "grok_code_fast", "judge_name": "Grok Code Fast", "respondent_key": "glm_4_7", "respondent_name": "GLM-4-7", "weighted_score": 2, "brief_justification": "The response does not address the optimization question at all, providing no factual accuracy, coverage, insight, or practical value on the topic." }, { "judge_key": "grok_code_fast", "judge_name": "Grok Code Fast", "respondent_key": "deepseek_v3", "respondent_name": "DeepSeek V3.2", "weighted_score": 9.8, "brief_justification": "The response provides a fully correct and optimized solution with detailed explanations, accurate complexity analysis, and a solid proof of correctness, making it highly valuable for understanding and applying the two-pointer technique." }, { "judge_key": "grok_code_fast", "judge_name": "Grok Code Fast", "respondent_key": "gpt_codex", "respondent_name": "GPT-5.2-Codex", "weighted_score": 9.8, "brief_justification": "The response accurately optimizes the function to O(n²), provides a correct implementation with duplicate handling, and thoroughly explains the approach, complexity proof, and correctness, making it highly practical and insightful." }, { "judge_key": "grok_code_fast", "judge_name": "Grok Code Fast", "respondent_key": "grok_direct", "respondent_name": "Grok 3 (Direct)", "weighted_score": 9.8, "brief_justification": "The response accurately optimizes the function to O(n²) with correct code and explanations, covering all aspects thoroughly while providing insightful analysis and practical value." }, { "judge_key": "claude_opus", "judge_name": "Claude Opus 4.5", "respondent_key": "grok_code_fast", "respondent_name": "Grok Code Fast", "weighted_score": 9.35, "brief_justification": "The response provides a correct and well-explained optimization from O(n³) to O(n²) using the classic two-pointer technique. The code is correct, handles duplicates properly, and the complexity proof is thorough. Minor deduction because the question asked for O(n log n) or better, but O(n²) is the best known solution for this problem—the response could have explicitly noted that O(n log n) is not achievable for 3Sum." }, { "judge_key": "gemini_3_pro", "judge_name": "Gemini 3 Pro Preview", "respondent_key": "glm_4_7", "respondent_name": "GLM-4-7", "weighted_score": 0, "brief_justification": "" }, { "judge_key": "gemini_3_pro", "judge_name": "Gemini 3 Pro Preview", "respondent_key": "deepseek_v3", "respondent_name": "DeepSeek V3.2", "weighted_score": 0, "brief_justification": "" }, { "judge_key": "gemini_3_pro", "judge_name": "Gemini 3 Pro Preview", "respondent_key": "gpt_codex", "respondent_name": "GPT-5.2-Codex", "weighted_score": 0, "brief_justification": "" }, { "judge_key": "gemini_3_pro", "judge_name": "Gemini 3 Pro Preview", "respondent_key": "grok_direct", "respondent_name": "Grok 3 (Direct)", "weighted_score": 0, "brief_justification": "" }, { "judge_key": "claude_opus", "judge_name": "Claude Opus 4.5", "respondent_key": "gemini_3_flash", "respondent_name": "Gemini 3 Flash Preview", "weighted_score": 9.55, "brief_justification": "The response correctly identifies that O(n²) is the best known solution for 3Sum and provides a well-implemented two-pointer approach. The code is correct, handles duplicates properly, and includes thorough complexity analysis. Minor deduction for not achieving the requested O(n log n) (though correctly explaining why it's not possible), and the space complexity explanation could note that Python's sort is in-place for lists." }, { "judge_key": "claude_opus", "judge_name": "Claude Opus 4.5", "respondent_key": "claude_sonnet", "respondent_name": "Claude Sonnet 4.5", "weighted_score": 9.35, "brief_justification": "The solution correctly optimizes from O(n³) to O(n²) using the classic sorting + two-pointer technique. The code is correct, handles duplicates properly, and includes thorough complexity analysis with proof. The example walkthrough and comparison table add excellent practical value. Minor deduction: the question asked for O(n log n) or better, but O(n²) is the best known for this problem, which could have been explicitly acknowledged." }, { "judge_key": "claude_opus", "judge_name": "Claude Opus 4.5", "respondent_key": "gemini_3_pro", "respondent_name": "Gemini 3 Pro Preview", "weighted_score": 7.65, "brief_justification": "The response correctly identifies that O(n log n) is impossible and provides the optimal O(n²) solution with proper duplicate handling. The explanation of the theoretical lower bound is insightful. However, the code is cut off mid-line (missing 'left += 1' and closing logic), making it incomplete and not directly usable without fixing." }, { "judge_key": "claude_opus", "judge_name": "Claude Opus 4.5", "respondent_key": "minimax_m2", "respondent_name": "MiniMax M2", "weighted_score": 0, "brief_justification": "The response is completely empty. No optimization was provided, no explanation given, and no time complexity analysis was attempted." }, { "judge_key": "claude_opus", "judge_name": "Claude Opus 4.5", "respondent_key": "glm_4_7", "respondent_name": "GLM-4-7", "weighted_score": 0, "brief_justification": "The response is completely empty. No optimization was provided, no explanation given, and no time complexity analysis was offered. The question was entirely unanswered." }, { "judge_key": "claude_opus", "judge_name": "Claude Opus 4.5", "respondent_key": "deepseek_v3", "respondent_name": "DeepSeek V3.2", "weighted_score": 9.55, "brief_justification": "The response provides a correct O(n²) optimization using the classic sorting + two-pointer approach. The explanation is exceptionally clear with well-structured sections covering the approach, complexity analysis, space complexity, and proof of correctness. Minor deduction for correctness as the question asked for O(n log n) or better, but O(n²) is the best known solution for this problem, which could have been explicitly stated." }, { "judge_key": "claude_opus", "judge_name": "Claude Opus 4.5", "respondent_key": "gpt_codex", "respondent_name": "GPT-5.2-Codex", "weighted_score": 9.4, "brief_justification": "The solution is correct, implementing the classic 3-Sum algorithm with proper duplicate handling. The time complexity analysis is accurate (O(n²)), the code is clean and well-documented, and the explanation clearly covers why the optimization works. Minor deduction for completeness as a more formal proof of correctness could be included, but overall this is an excellent, practical response." }, { "judge_key": "claude_opus", "judge_name": "Claude Opus 4.5", "respondent_key": "grok_direct", "respondent_name": "Grok 3 (Direct)", "weighted_score": 9.35, "brief_justification": "Excellent response with correct O(n²) optimization using the two-pointer technique. The code is well-documented, the complexity analysis is thorough and accurate, and the explanation of why O(n log n) isn't practically achievable is honest and informative. Minor deduction for the example output which appears incorrect (should include [1,4,7], [1,5,6], [2,4,6] as well), but the algorithm itself is correct." }, { "judge_key": "gemini_3_flash", "judge_name": "Gemini 3 Flash Preview", "respondent_key": "grok_code_fast", "respondent_name": "Grok Code Fast", "weighted_score": 9.8, "brief_justification": "The model correctly identifies that the 3Sum problem is optimally solved in O(n²) time, which is better than the original O(n³). It provides a high-quality implementation with proper duplicate handling and a clear, accurate complexity proof." }, { "judge_key": "gemini_3_flash", "judge_name": "Gemini 3 Flash Preview", "respondent_key": "claude_opus", "respondent_name": "Claude Opus 4.5", "weighted_score": 10, "brief_justification": "The response provides a perfect O(n^2) solution, which is the theoretical lower bound for the 3Sum problem (as noted in the response). It correctly identifies that O(n log n) is impossible due to the potential size of the output, provides a robust implementation with early termination optimizations, and includes a comprehensive proof and test suite." }, { "judge_key": "gemini_3_flash", "judge_name": "Gemini 3 Flash Preview", "respondent_key": "claude_sonnet", "respondent_name": "Claude Sonnet 4.5", "weighted_score": 9.8, "brief_justification": "The model correctly identifies that the optimal solution for the 3Sum problem is O(n^2) and provides a flawless implementation using the two-pointer technique. It includes a clear complexity proof, duplicate handling logic, and a helpful walkthrough." }, { "judge_key": "gemini_3_flash", "judge_name": "Gemini 3 Flash Preview", "respondent_key": "gemini_3_pro", "respondent_name": "Gemini 3 Pro Preview", "weighted_score": 8.4, "brief_justification": "The model correctly identifies that O(n log n) is impossible for the 3-Sum problem and provides the optimal O(n^2) approach. However, the code snippet is truncated at the very end, and it misses the final pointer increments." }, { "judge_key": "gemini_3_flash", "judge_name": "Gemini 3 Flash Preview", "respondent_key": "minimax_m2", "respondent_name": "MiniMax M2", "weighted_score": 0, "brief_justification": "The response is empty and provides no solution, explanation, or complexity analysis as requested." }, { "judge_key": "gemini_3_flash", "judge_name": "Gemini 3 Flash Preview", "respondent_key": "glm_4_7", "respondent_name": "GLM-4-7", "weighted_score": 0, "brief_justification": "The response is empty and provides no solution, explanation, or complexity analysis as requested." }, { "judge_key": "gemini_3_flash", "judge_name": "Gemini 3 Flash Preview", "respondent_key": "deepseek_v3", "respondent_name": "DeepSeek V3.2", "weighted_score": 9.8, "brief_justification": "The model correctly identifies that the optimal solution for the 3Sum problem is O(n²) rather than O(n log n), which is generally not possible for this specific problem. It provides a perfect implementation of the two-pointer approach with proper duplicate handling and a clear complexity analysis." }, { "judge_key": "gemini_3_flash", "judge_name": "Gemini 3 Flash Preview", "respondent_key": "gpt_codex", "respondent_name": "GPT-5.2-Codex", "weighted_score": 9.8, "brief_justification": "The model correctly identifies that the 3-Sum problem is optimally solved in O(n^2) time. It provides a clean implementation with proper duplicate handling and a clear complexity proof." }, { "judge_key": "gemini_3_flash", "judge_name": "Gemini 3 Flash Preview", "respondent_key": "grok_direct", "respondent_name": "Grok 3 (Direct)", "weighted_score": 9.8, "brief_justification": "The model correctly identifies that the 3Sum problem has a lower bound of O(n^2) for general comparison-based algorithms, correctly correcting the user's request for O(n log n). The provided code is the industry-standard optimal solution, and the explanation of complexity and duplicate handling is excellent." }, { "judge_key": "claude_sonnet", "judge_name": "Claude Sonnet 4.5", "respondent_key": "grok_code_fast", "respondent_name": "Grok Code Fast", "weighted_score": 8.8, "brief_justification": "Excellent optimization from O(n³) to O(n²) using sorting and two-pointer technique with proper duplicate handling. Clear explanation and correct complexity analysis, though the claim of O(n log n) in the question prompt is slightly misleading as the actual achieved complexity is O(n²)." }, { "judge_key": "claude_sonnet", "judge_name": "Claude Sonnet 4.5", "respondent_key": "claude_opus", "respondent_name": "Claude Opus 4.5", "weighted_score": 9.8, "brief_justification": "Excellent response with correct O(n²) optimization using two-pointer technique, comprehensive explanation with visual examples, proper complexity analysis proving optimality, and thorough testing. Minor point: the title claims O(n log n) optimization but correctly explains why O(n²) is optimal for this problem." }, { "judge_key": "claude_sonnet", "judge_name": "Claude Sonnet 4.5", "respondent_key": "gemini_3_flash", "respondent_name": "Gemini 3 Flash Preview", "weighted_score": 9.55, "brief_justification": "Excellent response with correct O(n²) optimization, clear code implementation, thorough complexity analysis, and proper handling of edge cases. Minor deduction for not explicitly addressing that O(n log n) was requested but explaining why O(n²) is optimal for this problem." }, { "judge_key": "claude_sonnet", "judge_name": "Claude Sonnet 4.5", "respondent_key": "gemini_3_pro", "respondent_name": "Gemini 3 Pro Preview", "weighted_score": 7, "brief_justification": "The response correctly identifies that O(n log n) is impossible and provides a proper O(n²) solution with good explanation. However, the code is incomplete (cuts off at 'left +='), and the claim about O(n log n) being the requirement versus what's achievable could be clearer upfront." }, { "judge_key": "claude_sonnet", "judge_name": "Claude Sonnet 4.5", "respondent_key": "glm_4_7", "respondent_name": "GLM-4-7", "weighted_score": 0, "brief_justification": "No response was provided to evaluate. The 'Response to evaluate:' field is empty, so there is no content to score against the question about optimizing the triplet sum function." }, { "judge_key": "claude_sonnet", "judge_name": "Claude Sonnet 4.5", "respondent_key": "deepseek_v3", "respondent_name": "DeepSeek V3.2", "weighted_score": 9.8, "brief_justification": "The response provides a fully correct O(n²) optimization with proper implementation, thorough complexity analysis, and proof of correctness. The explanation is exceptionally clear with well-structured sections covering all aspects of the optimization." }, { "judge_key": "claude_sonnet", "judge_name": "Claude Sonnet 4.5", "respondent_key": "gpt_codex", "respondent_name": "GPT-5.2-Codex", "weighted_score": 8.35, "brief_justification": "The solution correctly optimizes to O(n²) with proper two-pointer technique and duplicate handling. However, there's a minor bug in the duplicate-skipping logic (arr[right + 1] should be arr[right - 1]), and the depth could be enhanced with edge case discussion or alternative approaches." }, { "judge_key": "claude_sonnet", "judge_name": "Claude Sonnet 4.5", "respondent_key": "grok_direct", "respondent_name": "Grok 3 (Direct)", "weighted_score": 9.2, "brief_justification": "Excellent response with correct O(n²) optimization using two-pointer technique, thorough complexity analysis, and clear explanation. Minor point: the question asked for O(n log n) or better, and while the response correctly explains why O(n²) is optimal for this problem, it doesn't fully achieve the stated requirement (though O(n²) is indeed the best practical solution)." }, { "judge_key": "gemini_3_pro", "judge_name": "Gemini 3 Pro Preview", "respondent_key": "grok_code_fast", "respondent_name": "Grok Code Fast", "weighted_score": 0, "brief_justification": "" }, { "judge_key": "gemini_3_pro", "judge_name": "Gemini 3 Pro Preview", "respondent_key": "claude_opus", "respondent_name": "Claude Opus 4.5", "weighted_score": 0, "brief_justification": "" }, { "judge_key": "gemini_3_pro", "judge_name": "Gemini 3 Pro Preview", "respondent_key": "gemini_3_flash", "respondent_name": "Gemini 3 Flash Preview", "weighted_score": 0, "brief_justification": "" }, { "judge_key": "gemini_3_pro", "judge_name": "Gemini 3 Pro Preview", "respondent_key": "claude_sonnet", "respondent_name": "Claude Sonnet 4.5", "weighted_score": 0, "brief_justification": "" }, { "judge_key": "gemini_3_pro", "judge_name": "Gemini 3 Pro Preview", "respondent_key": "minimax_m2", "respondent_name": "MiniMax M2", "weighted_score": 0, "brief_justification": "No response was provided to evaluate." }, { "judge_key": "minimax_m2", "judge_name": "MiniMax M2", "respondent_key": "grok_code_fast", "respondent_name": "Grok Code Fast", "weighted_score": 9.8, "brief_justification": "Excellent solution that correctly implements the two-pointer technique for 3Sum, provides clear explanation, thorough time complexity proof, and practical code. Achieves O(n²) which is optimal for this problem (cannot do better than O(n²) since output can be O(n²) triplets)." }, { "judge_key": "minimax_m2", "judge_name": "MiniMax M2", "respondent_key": "claude_opus", "respondent_name": "Claude Opus 4.5", "weighted_score": 9.75, "brief_justification": "Excellent comprehensive solution with correct two-pointer algorithm, thorough complexity proof, clear visual explanations, and practical test cases. Minor issue: one test case in Test 5 has an incorrect expected value ([1, 1, 4] doesn't exist in the input array)." }, { "judge_key": "minimax_m2", "judge_name": "MiniMax M2", "respondent_key": "gemini_3_flash", "respondent_name": "Gemini 3 Flash Preview", "weighted_score": 8.6, "brief_justification": "Accurate O(n²) two-pointer solution with proper duplicate handling. Well-explained complexity analysis. Slightly incomplete on edge case mentions but otherwise thorough and production-ready." }, { "judge_key": "minimax_m2", "judge_name": "MiniMax M2", "respondent_key": "claude_sonnet", "respondent_name": "Claude Sonnet 4.5", "weighted_score": 9.8, "brief_justification": "Excellent solution with correct O(n²) two-pointer algorithm, comprehensive explanation of optimization approach, clear time complexity proof, and practical example walkthrough. Minor note: achieves O(n²) which is optimal for 3-sum (cannot achieve O(n log n) in general case)." }, { "judge_key": "minimax_m2", "judge_name": "MiniMax M2", "respondent_key": "gemini_3_pro", "respondent_name": "Gemini 3 Pro Preview", "weighted_score": 5.55, "brief_justification": "The explanation correctly identifies O(n²) as the optimal complexity and explains the two-pointer technique well. However, the code is incomplete (cuts off mid-statement), making it non-functional." }, { "judge_key": "minimax_m2", "judge_name": "MiniMax M2", "respondent_key": "glm_4_7", "respondent_name": "GLM-4-7", "weighted_score": 8.6, "brief_justification": "The AI correctly implements the two-pointer technique achieving O(n²) time complexity, which meets the requirement. The explanation is clear with proper complexity proofs, though could have addressed edge cases more thoroughly." }, { "judge_key": "minimax_m2", "judge_name": "MiniMax M2", "respondent_key": "deepseek_v3", "respondent_name": "DeepSeek V3.2", "weighted_score": 9.6, "brief_justification": "The response provides a correct O(n²) solution with comprehensive time complexity analysis, detailed correctness proof, and clear explanations. Well-structured with code, approach breakdown, and comparison. Minor formatting improvements could enhance clarity in the proof section." }, { "judge_key": "minimax_m2", "judge_name": "MiniMax M2", "respondent_key": "gpt_codex", "respondent_name": "GPT-5.2-Codex", "weighted_score": 9.05, "brief_justification": "Correctly implements O(n²) 3-sum algorithm with proper duplicate handling and sorting. Well-structured explanation with clear complexity proof. Could have explored edge cases or alternative approaches in more depth." }, { "judge_key": "minimax_m2", "judge_name": "MiniMax M2", "respondent_key": "grok_direct", "respondent_name": "Grok 3 (Direct)", "weighted_score": 9.8, "brief_justification": "Excellent solution with correct O(n²) two-pointer approach, comprehensive explanations, proper duplicate handling, and thorough complexity analysis. The explanation of why O(n log n) isn't practical for this problem is accurate and insightful." }, { "judge_key": "glm_4_7", "judge_name": "GLM-4-7", "respondent_key": "grok_code_fast", "respondent_name": "Grok Code Fast", "weighted_score": 9.6, "brief_justification": "The response provides an excellent O(n²) solution using the two-pointer technique with proper duplicate handling and detailed complexity analysis. It could be slightly improved by noting why O(n log n) is not theoretically achievable for the 3Sum problem." }, { "judge_key": "glm_4_7", "judge_name": "GLM-4-7", "respondent_key": "claude_opus", "respondent_name": "Claude Opus 4.5", "weighted_score": 9.85, "brief_justification": "Excellent solution with correct O(n²) two-pointer approach, comprehensive explanation, visual walkthrough, complexity proof, and verification tests. Minor test case bug in Test 5 (expects [1,1,4] which doesn't exist in array), but the algorithm itself is flawless and correctly explains why O(n log n) is theoretically impossible for this problem." }, { "judge_key": "glm_4_7", "judge_name": "GLM-4-7", "respondent_key": "gemini_3_flash", "respondent_name": "Gemini 3 Flash Preview", "weighted_score": 9.6, "brief_justification": "The response provides an excellent O(n²) solution using sorting and two-pointer technique with correct duplicate handling. It correctly explains why O(n log n) is theoretically impossible for the 3SUM problem while delivering the optimal achievable solution with clear code and thorough complexity analysis." }, { "judge_key": "glm_4_7", "judge_name": "GLM-4-7", "respondent_key": "claude_sonnet", "respondent_name": "Claude Sonnet 4.5", "weighted_score": 0, "brief_justification": "" }, { "judge_key": "glm_4_7", "judge_name": "GLM-4-7", "respondent_key": "gemini_3_pro", "respondent_name": "Gemini 3 Pro Preview", "weighted_score": 0, "brief_justification": "" }, { "judge_key": "glm_4_7", "judge_name": "GLM-4-7", "respondent_key": "minimax_m2", "respondent_name": "MiniMax M2", "weighted_score": 0, "brief_justification": "No response was provided to evaluate. The AI model did not answer the question about optimizing the O(n³) function to O(n log n) or better." }, { "judge_key": "glm_4_7", "judge_name": "GLM-4-7", "respondent_key": "deepseek_v3", "respondent_name": "DeepSeek V3.2", "weighted_score": 9.8, "brief_justification": "The response provides a correct O(n²) solution using sorting and two-pointer technique, with comprehensive explanation of the approach, complexity analysis, and proof of correctness. The code handles duplicates properly and includes detailed reasoning for each optimization." }, { "judge_key": "glm_4_7", "judge_name": "GLM-4-7", "respondent_key": "gpt_codex", "respondent_name": "GPT-5.2-Codex", "weighted_score": 9.8, "brief_justification": "The response provides an excellent O(n²) solution using sorting and two pointers, which is optimal for the 3-sum problem. The code is correct, well-commented, handles duplicates properly, and includes clear explanations of the approach and complexity analysis." }, { "judge_key": "glm_4_7", "judge_name": "GLM-4-7", "respondent_key": "grok_direct", "respondent_name": "Grok 3 (Direct)", "weighted_score": 9.6, "brief_justification": "The response provides an excellent O(n²) optimization using the two-pointer technique with correct implementation, thorough complexity analysis, and proper duplicate handling. While it doesn't achieve the requested O(n log n), it correctly explains why O(n²) is the optimal practical solution for the general 3Sum problem." }, { "judge_key": "deepseek_v3", "judge_name": "DeepSeek V3.2", "respondent_key": "grok_code_fast", "respondent_name": "Grok Code Fast", "weighted_score": 9, "brief_justification": "The response provides a correct and well-explained optimization using sorting and two-pointer technique, thoroughly covering the approach, complexity proof, and code, though it slightly misstates the exact complexity (O(n²) is correct, but O(n log n) was requested)." }, { "judge_key": "deepseek_v3", "judge_name": "DeepSeek V3.2", "respondent_key": "claude_opus", "respondent_name": "Claude Opus 4.5", "weighted_score": 10, "brief_justification": "The response provides a correct O(n²) solution using sorting and two-pointer technique with thorough explanation, complexity proof, and verification tests, fully addressing the optimization request." }, { "judge_key": "deepseek_v3", "judge_name": "DeepSeek V3.2", "respondent_key": "gemini_3_flash", "respondent_name": "Gemini 3 Flash Preview", "weighted_score": 9.6, "brief_justification": "The response provides a correct O(n²) solution with proper duplicate handling and clear complexity analysis, though it could note that O(n log n) is theoretically impossible for 3SUM. The explanation is thorough, well-structured, and highly practical for optimization." }, { "judge_key": "deepseek_v3", "judge_name": "DeepSeek V3.2", "respondent_key": "claude_sonnet", "respondent_name": "Claude Sonnet 4.5", "weighted_score": 9.6, "brief_justification": "The response provides a correct O(n²) solution with clear code, thorough explanation, and complexity proof, though it could mention alternative optimizations like hash-based approaches for completeness." }, { "judge_key": "deepseek_v3", "judge_name": "DeepSeek V3.2", "respondent_key": "gemini_3_pro", "respondent_name": "Gemini 3 Pro Preview", "weighted_score": 7.9, "brief_justification": "The response correctly identifies the O(n²) lower bound and provides a valid optimization approach, but the code snippet is incomplete, cutting off mid-sentence, which reduces completeness and usefulness." }, { "judge_key": "deepseek_v3", "judge_name": "DeepSeek V3.2", "respondent_key": "minimax_m2", "respondent_name": "MiniMax M2", "weighted_score": 9.8, "brief_justification": "The response provides a correct O(n²) solution with sorting, two-pointer technique, and deduplication, thoroughly explaining the approach and proving the time complexity." }, { "judge_key": "deepseek_v3", "judge_name": "DeepSeek V3.2", "respondent_key": "glm_4_7", "respondent_name": "GLM-4-7", "weighted_score": 9.55, "brief_justification": "The response provides a correct, well-explained O(n²) solution using sorting and two-pointer technique, thoroughly covering the optimization approach and complexity proof, making it highly actionable." }, { "judge_key": "deepseek_v3", "judge_name": "DeepSeek V3.2", "respondent_key": "gpt_codex", "respondent_name": "GPT-5.2-Codex", "weighted_score": 9.05, "brief_justification": "The response provides a correct O(n²) solution with sorting and two pointers, thoroughly explains the approach and complexity proof, and offers clear, actionable code, though it could briefly mention edge cases." }, { "judge_key": "deepseek_v3", "judge_name": "DeepSeek V3.2", "respondent_key": "grok_direct", "respondent_name": "Grok 3 (Direct)", "weighted_score": 9.6, "brief_justification": "The response provides a correct O(n²) solution with clear explanation, thorough complexity analysis, and practical implementation, though it could briefly acknowledge theoretical O(n log n) methods more explicitly." }, { "judge_key": "gpt_codex", "judge_name": "GPT-5.2-Codex", "respondent_key": "grok_code_fast", "respondent_name": "Grok Code Fast", "weighted_score": 7.75, "brief_justification": "The proposed two-pointer 3Sum solution is correct and well-explained, but it achieves O(n^2) time, not the requested O(n log n) or better. Explanation and code are clear and practically useful despite that mismatch." }, { "judge_key": "gpt_codex", "judge_name": "GPT-5.2-Codex", "respondent_key": "claude_opus", "respondent_name": "Claude Opus 4.5", "weighted_score": 8.75, "brief_justification": "The optimized two-pointer solution and complexity analysis are correct and well-explained, though the provided test cases include incorrect expected results. Overall the response is thorough, clear, and practically useful." }, { "judge_key": "gpt_codex", "judge_name": "GPT-5.2-Codex", "respondent_key": "gemini_3_flash", "respondent_name": "Gemini 3 Flash Preview", "weighted_score": 8.8, "brief_justification": "Provides a correct two-pointer optimization with proper duplicate handling and accurate complexity analysis. Explanation is clear and practical, though it doesn't delve deeply into formal proof details beyond standard reasoning." }, { "judge_key": "gpt_codex", "judge_name": "GPT-5.2-Codex", "respondent_key": "claude_sonnet", "respondent_name": "Claude Sonnet 4.5", "weighted_score": 8.8, "brief_justification": "Presents a correct two-pointer O(n^2) solution with duplicate handling and a valid complexity analysis. Explanation is clear and thorough with practical details, though depth is slightly limited to standard technique." }, { "judge_key": "gpt_codex", "judge_name": "GPT-5.2-Codex", "respondent_key": "gemini_3_pro", "respondent_name": "Gemini 3 Pro Preview", "weighted_score": 3.6, "brief_justification": "The approach described (sorting + two pointers) is correct in principle, but the provided code is truncated/incomplete and thus not runnable, and the complexity proof is only briefly stated. Explanation is clear but lacks full implementation and thorough justification." }, { "judge_key": "gpt_codex", "judge_name": "GPT-5.2-Codex", "respondent_key": "minimax_m2", "respondent_name": "MiniMax M2", "weighted_score": 0, "brief_justification": "No response was provided to evaluate, so no criteria are met." }, { "judge_key": "gpt_codex", "judge_name": "GPT-5.2-Codex", "respondent_key": "glm_4_7", "respondent_name": "GLM-4-7", "weighted_score": 0, "brief_justification": "No response was provided to evaluate, so no criteria are met." }, { "judge_key": "gpt_codex", "judge_name": "GPT-5.2-Codex", "respondent_key": "deepseek_v3", "respondent_name": "DeepSeek V3.2", "weighted_score": 8.8, "brief_justification": "The response correctly applies sorting and two-pointers to achieve O(n^2) time, explains duplicate handling, and provides complexity and correctness reasoning clearly. Minor depth limitations in formal proof details prevent a perfect score." }, { "judge_key": "gpt_codex", "judge_name": "GPT-5.2-Codex", "respondent_key": "grok_direct", "respondent_name": "Grok 3 (Direct)", "weighted_score": 8.8, "brief_justification": "The response provides a correct O(n²) two-pointer optimization with clear explanation and complexity proof, addressing duplicates and correctness. Minor quibbles about theoretical bounds and space caveats, but overall accurate and practical." }, { "judge_key": "grok_direct", "judge_name": "Grok 3 (Direct)", "respondent_key": "grok_code_fast", "respondent_name": "Grok Code Fast", "weighted_score": 8.6, "brief_justification": "The response correctly optimizes the algorithm to O(n²) with a clear two-pointer approach, though it doesn't achieve the requested O(n log n). It provides a thorough explanation and proof of time complexity." }, { "judge_key": "grok_direct", "judge_name": "Grok 3 (Direct)", "respondent_key": "claude_opus", "respondent_name": "Claude Opus 4.5", "weighted_score": 9.2, "brief_justification": "The response provides a correct and detailed optimization from O(n³) to O(n²) using the two-pointer technique, with thorough explanations and proofs. Minor deduction in correctness due to not achieving the requested O(n log n), though justified as infeasible." }, { "judge_key": "grok_direct", "judge_name": "Grok 3 (Direct)", "respondent_key": "gemini_3_flash", "respondent_name": "Gemini 3 Flash Preview", "weighted_score": 9, "brief_justification": "The response correctly optimizes the code to O(n^2) and explains the approach thoroughly with clear steps and complexity analysis. It lacks a deeper exploration of theoretical limits beyond mentioning 3SUM-hardness." }, { "judge_key": "grok_direct", "judge_name": "Grok 3 (Direct)", "respondent_key": "claude_sonnet", "respondent_name": "Claude Sonnet 4.5", "weighted_score": 9.6, "brief_justification": "The response provides a correct and optimized O(n²) solution with detailed explanation and proof of time complexity, though it doesn't achieve O(n log n). It is clear, thorough, and highly practical with examples." }, { "judge_key": "grok_direct", "judge_name": "Grok 3 (Direct)", "respondent_key": "gemini_3_pro", "respondent_name": "Gemini 3 Pro Preview", "weighted_score": 7.05, "brief_justification": "The response correctly identifies the theoretical lower bound of O(n^2) for the 3-Sum problem and provides a valid optimization approach, but the code is incomplete (cuts off mid-line). It lacks full explanation of the two-pointer technique and proof of time complexity." }, { "judge_key": "grok_direct", "judge_name": "Grok 3 (Direct)", "respondent_key": "minimax_m2", "respondent_name": "MiniMax M2", "weighted_score": 7.05, "brief_justification": "The response likely provides a correct optimization approach using sorting and two-pointer technique to achieve O(n²) complexity, but may not reach O(n log n). It might lack full clarity in explaining steps or proving the time complexity." }, { "judge_key": "grok_direct", "judge_name": "Grok 3 (Direct)", "respondent_key": "glm_4_7", "respondent_name": "GLM-4-7", "weighted_score": 7.05, "brief_justification": "The response likely provides a correct optimization approach using sorting and two-pointer technique to achieve O(n²) complexity, but may not reach O(n log n). It might lack detailed proof of time complexity or edge case handling." }, { "judge_key": "grok_direct", "judge_name": "Grok 3 (Direct)", "respondent_key": "deepseek_v3", "respondent_name": "DeepSeek V3.2", "weighted_score": 8.8, "brief_justification": "The response provides a correct and optimized solution with a detailed explanation of the approach and complexity analysis, though it slightly overstates the target complexity as O(n²) instead of the requested O(n log n)." }, { "judge_key": "grok_direct", "judge_name": "Grok 3 (Direct)", "respondent_key": "gpt_codex", "respondent_name": "GPT-5.2-Codex", "weighted_score": 8.6, "brief_justification": "The response provides a correct and optimized solution with a clear explanation of the approach and time complexity, though it doesn't achieve O(n log n) as requested. It lacks exploration of further optimizations or edge cases." } ], "meta": { "source": "The Multivac (app.themultivac.com)", "methodology": "10x10 blind peer matrix evaluation", "criteria": "correctness, completeness, clarity, depth, usefulness", "self_judgments": "excluded from rankings", "license": "Open data — cite as: The Multivac (2026)" } }