Large Language Models (LLMs) are rapidly entering software engineering education. As students turn to them for Data Structures and Algorithms (DSA) tutoring, a critical question emerges: do they foster genuine problem-solving skills or merely supply polished answers? Moreover, their competence in DSA remains underexplored beyond benchmarks likely contaminated with training data. We evaluate four LLMs—GPT-4o, Claude 3.7 Sonnet, Llama 3.2, and DeepSeek R1—on 80 LeetCode Top Interview 150 problems and 100 recent Weekly Contest problems, assessing code correctness, maintainability, and explanatory reasoning. Results show that while Claude and DeepSeek perform best on harder problems, all models’ average success rates drop by 49% on novel problems, revealing a critical gap in translating theoretical insights into effective implementations. On the novel problems, DeepSeek attained the highest success rate (70%) with fewer prompt turns but produced the least maintainable code, whereas Claude solved fewer (50%) yet generated the most maintainable solutions, highlighting a trade-off between correctness and pedagogical value. These findings suggest that LLMs are capable reasoning partners yet insufficient for autonomous problem-solving. Thus, educators must carefully integrate these tools into curricula, emphasizing students’ critical reasoning and debugging skills, and develop assessments that either leverage or withstand LLM assistance. Our work contributes a rigorous, multidimensional evaluation framework and practical recommendations for AI-assisted learning in software engineering (SE) and computer science (CS) education, underscoring critical evaluation over reliance on automated solutions.