ALGOGEN: Tool-Generated Verifiable Traces for Reliable Algorithm Visualization

Contemporary LLM-based coding agents produce code as black-box outputs: the rationale behind each line is hidden, the evolution of the code through benchmark-driven repair is ephemeral, and post-hoc auditing is impossible. We present a code generation concept that addresses these shortcomings through three complementary mechanisms: (i) a relational snippet-history schema that records, per repair event, the benchmark reference, round number, failure text, and LLM explanation, enabling full provenance queries; (ii) a browser-based visualisation tool that renders this history as heat-mapped, hover-annotated source code; and (iii) a competitive fractional position-key indexing scheme with tree-node delimiters that assigns stable, lexicographically-ordered identifiers to each code snippet, enabling fine-grained tracking without disrupting surrounding lines. We evaluate TraceCoder on 30 algorithmic programming tasks spanning string processing, mathematical computation, and data-structure manipulation, across two provider configurations. Of these, 10 exhaust the 6-iteration budget on tasks with subtle edge-case behaviour. Mean Chg% reaches 30%, three in ten code snippets carry a traceable repair-event row, compared to 21% when using Gemini 2.0 Flash as sole provider on a 20-task subset. Three detailed case studies demonstrate how the system explains which specific benchmark failures shaped each line of the final program. The proposed mechanism makes the internal "narrative" of automated code generation auditable and replayable, a property essential for trust and accountability in production deployments.

High pass rates on established programming benchmarks such as HumanEval and LiveCodeBench do not always show whether a model can reason about algorithms. Many fixed benchmarks eventually become part of the public training ecosystem through released problem statements, editorials, and generated solutions, allowing later models to improve partly by exposure rather than by stronger algorithmic ability. We introduce ALGOBENCH, a framework that automatically builds novel algorithmic problems from known competitive-programming problems through structured constraint-shifting transformations. Each accepted ALGOBENCH variant is traceable to a source problem, but must make the original reference algorithm fail. Beyond pass@$k$, we introduce complexity-aware metrics -- including OPTT, OPTS, TRAPRATE, GAPT, and CONSENS -- to test whether a solution is not only functionally correct but also asymptotically suitable for the generated problem. Experiments across multiple LLMs and prompting strategies show that performance drops sharply on ALGOBENCH variants, retrieval can increase reuse of the old algorithm, and many correct-looking solutions fail to meet the required complexity. Error analysis shows that failures are mainly algorithmic rather than implementation-level, suggesting that ALGOBENCH evaluates adaptation beyond functional correctness.

Large language models can generate executable code for educational animations, but the resulting renders often exhibit visual defects, including element overlap, misalignment, and broken animation continuity. These defects cannot be reliably detected from the code alone and become apparent only after execution. We formalize this problem as render-feedback-aware constrained code generation: given a natural language specification, the model must generate executable code whose rendered output satisfies structured quality criteria that can be evaluated only after rendering. To address this problem, we introduce OmniManim, a render-feedback-aware educational animation generation framework built around a shared scene state, explicit visual planning, structured post-render diagnostics, and localized repair. Within OmniManim, the Vision Agent is a task-specific visual planning module: it predicts sparse keyframe layouts with coarse-to-fine bounding-box denoising and optimizes an interpolation-aware objective to reduce intermediate-frame failures induced by downstream animation interpolation. We further construct two datasets, ManimLayout-1K and EduRequire-500, and provide a reproducible evaluation protocol covering executability, instructional quality, visual quality, and efficiency. On EduRequire-500, OmniManim improves measured render quality over both single-model baselines and existing multi-agent frameworks. Systematic ablation studies further verify that explicit visual planning, especially its coarse spatial prior, bounding-box refinement, and interpolation-aware optimization, is central to these gains.