The rapid advancement of large language models (LLMs) has opened new avenues for automating complex problem-solving tasks such as algorithmic coding and competitive programming. This paper introduces a novel evaluation technique, LLM-ProS, to assess the performance of state-of-the-art LLMs on International Collegiate Programming Contest (ICPC) -style problems. Using a curated dataset of 83 World Finals problems from 2011 to 2016 and 2024, we benchmark the models’ reasoning, accuracy, and efficiency. We evaluate four models—GPT-4o, Mistral Large, Llama-3.1-405B, and the o1 family (o1-mini and o1-preview)—across critical metrics like correctness, resource utilization, and response calibration. Our results reveal significant differences in the models’ abilities to generalize, adapt, and solve novel problems. Additionally, we investigate the impact of training methodologies, dataset contamination, and chain-of-thought reasoning on model performance. The findings provide new insights into optimizing LLMs for algorithmic tasks, highlighting both the strengths and limitations of current models.