Getting it into your agent
One page per mod, every tool's command on it. A separate URL per tool would split the same page into five that compete with each other.
npx skills add Arcadi4/nerdy --skill shortest-pathsgit clone --depth 1 https://github.com/Arcadi4/nerdyWrote this? Show the measurements
A badge with what this costs and how it scanned, read live from this page, so it follows the numbers instead of freezing them. Markdown for a README, HTML for a documentation site or a project page.
[](https://agentmods.dev/skills/arcadi4/nerdy/shortest-paths)<a href="https://agentmods.dev/skills/arcadi4/nerdy/shortest-paths"><img src="https://agentmods.dev/badge/skills/arcadi4/nerdy/shortest-paths/github.svg" alt="Measured on agentmods" height="20"></a>Or the 80×15 button, for a site that already has a row of RSS and ATOM ones. Only the verdict fits; the numbers stay here.
<a href="https://agentmods.dev/skills/arcadi4/nerdy/shortest-paths"><img src="https://agentmods.dev/badge/skills/arcadi4/nerdy/shortest-paths.svg" alt="Reviewed on agentmods" width="80" height="20"></a>What it costs to keep this loaded
Counted locally with the o200k_base tokenizer, which is exact for GPT models; Claude uses its own tokenizer and its counts differ. Treat this as one consistent yardstick across the catalogue rather than a bill. Prices are per million input tokens.
| Model | Per session | Once invoked |
|---|---|---|
| Fable 5.1 | $0.00070 | $0.05691 |
| Opus 5.5 | $0.00028 | $0.02276 |
| Sonnet 5.5 | $0.00014 | $0.01138 |
| Haiku 4.5 | $0.00007 | $0.00569 |
Grade A, and why
shortest-paths scanned grade A with 0 findings against 26 rules in 11 categories — prompt injection, anti-refusal, data exfiltration, privilege escalation, supply chain, agent snooping, system-prompt leakage, SSRF and excessive agency — measured 1mo ago.
A static scan of the body, not an audit. Every finding is printed with the line that produced it so you can judge whether it matters here. A mod is markdown that instructs an agent; that is exactly why what it instructs is worth reading.
Nothing flagged
None of the 26 patterns this scan looks for appear in this file: no shell pipes, no recursive deletes, no credential paths, no hidden text, no instruction-override or anti-refusal phrasing, no agent-config snooping. That is not a guarantee, it is the absence of the things that are checkable.
How it starts
The opening of the file, as written. The whole thing — 516 lines — stays where its author put it; the contents beside it link to each section on GitHub.
Shortest Paths
Overview
Shortest-path answers are decision problems before they are algorithm names. First identify the path model, weight assumptions, graph representation, negative-cycle semantics, and whether the caller needs distances, predecessor trees, actual paths, or cycle witnesses.
Core principle: choose the algorithm whose preconditions match the weights and graph shape, prove correctness with relaxation, dynamic-programming decomposition, or reweighting, then state the production contract for representation, sentinels, overflow, and reconstruction.
Shared CLRS Conventions
- Follow the parent
clrsskill for mathematical formatting: every expression, inequality, recurrence, path weight, and asymptotic bound goes in a display LaTeX block, never in prose, headings, tables, or inline code spans. - Use
elementary-graph-algorithmsfor graph representation basics, breadth-first search on unweighted graphs, depth-first search, topological sorting, and transitive-reachability prerequisites. - State whether the graph is directed or undirected before choosing a shortest-path algorithm. A negative undirected edge creates an immediate negative cycle under the directed-edge model unless the problem defines a different semantics.
- State the representation before giving a running time. Adjacency lists fit single-source and Johnson-style sparse algorithms; adjacency matrices fit dense all-pairs dynamic programs.
- Do not announce that you are reading this skill or applying a checklist. Deliver the polished answer directly.
When to Use
Use this skill for:
- Weighted single-source shortest paths, single-destination reductions, single-pair questions, and all-pairs shortest paths.
- Choosing among breadth-first search, DAG shortest paths, Bellman-Ford, Dijkstra, Floyd-Warshall, Johnson, repeated single-source runs, or min-plus matrix products.
- Negative-edge and negative-cycle questions, including which vertices have finite distance, infinite distance, or unbounded-below distance.
- Relaxation invariants, predecessor subgraphs, shortest-path trees, path reconstruction, and output verification.
- Difference constraints, arbitrage detection, reliability paths, critical paths in acyclic project networks, bitonic-path exercises, and other graph-path reductions.
- Production reviews where the textbook algorithm must be translated into an API contract, library choice, graph representation, memory budget, or cycle-reporting behavior.
What this file has done since we first saw it
Hashed on every crawl. A supply-chain change to an agent config is a question of when, not whether, so the history is kept rather than the latest state alone.
- 1mo ago First seen · 516 lines · 70 tokens per session scan A a2dc98435e19
shortest-paths is a skill published in the GitHub repository Arcadi4/nerdy (6 stars, last pushed 6mo ago), licensed MIT. It adds 70 tokens to every session and 5,691 once invoked, about $0.0003 per session on Opus 5.5. A static security scan graded it A with 0 findings. No closer match exists in the catalogue, so it is treated as the original; first seen 2026-08-31.
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