Large Language Models excel at code generation, yet competitive programming exposes a persistent failure mode: existing multi-agent pipelines distribute work over generic planner, coder, and debugger roles and delegate the choice of algorithmic technique to the backbone alone. We present MARS (Multi-Agent Relay of Specialized LLMs), a prompt-only framework in which each agent is a topic specialist—dynamic programming, graphs, strings, geometry, and so on—grounded by retrieval-augmented generation over an algorithm-theory corpus. Given a problem, retrieval selects a small team of relevant specialists; a starter writes an initial C++17 solution, and each subsequent turn runs the candidate against public examples in a sandbox, lets the active specialist keep, repair, or hand off the draft, and forwards a structured packet to the next specialist. A single infrastructure-fixer pass normalizes boilerplate at the end. On the CodeContests test split with Gemma 4, MARS reaches 0.624 ± 0.006 pass rate at 2.3 relay steps per task, +13.9pp over direct prompting, closing most of the gap to CodeSIM at 0.731 with 3.3× lower wall-clock cost and substantially smaller variance in per-task token spend.