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 minimun-spanning-treesgit 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/minimun-spanning-trees)<a href="https://agentmods.dev/skills/arcadi4/nerdy/minimun-spanning-trees"><img src="https://agentmods.dev/badge/skills/arcadi4/nerdy/minimun-spanning-trees/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/minimun-spanning-trees"><img src="https://agentmods.dev/badge/skills/arcadi4/nerdy/minimun-spanning-trees.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 | $0.00057 | $0.04313 |
| Opus 5.5 | $0.00023 | $0.01725 |
| Sonnet 5.5 | $0.00011 | $0.00863 |
| Haiku 4.5 | $0.00006 | $0.00431 |
Grade A, and why
minimun-spanning-trees 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 — 406 lines — stays where its author put it; the contents beside it link to each section on GitHub.
Minimum Spanning Trees
Overview
Minimum-spanning-tree answers should not justify greedy choices by weight intuition alone. They must identify the maintained forest, the cut or cycle that certifies the next edge, and the data-structure contract that makes the stated bound real.
Core principle: prove an edge is safe by a cut-and-paste exchange, then implement the greedy rule with the representation that actually exposes the needed light edge.
Shared Formatting Conventions
- Follow the parent
clrsskill for mathematical formatting: every expression, inequality, objective, or asymptotic bound goes in a display LaTeX block, never in prose, tables, headings, or inline code spans. - This rule applies to production comparison tables too: table cells may say "same comparison bound," "near-linear disjoint-set term," or "the textbook Fibonacci-heap bound," but the actual symbolic bounds must appear in display blocks outside the table.
- Use
greedy-algorithmsfor the general exchange-proof discipline,elementary-graph-algorithmsfor graph representation contracts, anddata-structures-for-disjoint-setsfor union-find details. - State that the graph is connected and undirected before using minimum-spanning-tree theorems. If it is disconnected, switch to a minimum spanning forest.
- State the graph representation before giving a running time.
- Preserve tie behavior: equal-weight light edges can yield different minimum spanning trees with the same total weight.
When to Use
Use this skill for:
- Minimum spanning trees, minimum spanning forests, network-design trees, and wiring-style connection problems.
- Safe-edge, cut, light-edge, cycle, bottleneck, and exchange arguments.
- Kruskal's algorithm, Prim's algorithm, Boruvka-style contraction, or MST preprocessing.
- Updating an existing minimum spanning tree after one edge weight changes or one vertex is added.
- Comparing union-find, binary-heap priority queues, Fibonacci heaps, adjacency lists, and adjacency matrices for MST implementations.
- Second-best minimum spanning tree questions and max-edge-on-tree-path reasoning.
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 · 406 lines · 57 tokens per session scan A 99b9ca228fcd
minimun-spanning-trees is a skill published in the GitHub repository Arcadi4/nerdy (6 stars, last pushed 6mo ago), licensed MIT. It adds 57 tokens to every session and 4,313 once invoked, about $0.0002 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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