np-completeness

np-completeness is a skill for Claude Code, Codex from Arcadi4/nerdy. It costs 73 tokens per session (3,679 once invoked), scanned A, original, MIT.

A guide to classifying decision problems by whether proposed answers can be checked efficiently and whether problems can be converted into one another efficiently. NP-complete problems are among the hardest problems whose answers can be checked efficiently.

In plain words
What is it for?
Use it for P, NP, NP-hard, and NP-complete classifications, polynomial-time reductions, SAT, CLIQUE, vertex cover, Hamiltonian cycle, TSP, and subset sum.
Why use it?
It helps produce complete hardness proofs instead of relying on an incorrect reduction direction or ignoring how inputs are encoded.

Skill for Claude CodeCodex

Install

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.

agentmods
npx agentmods add skills/arcadi4/nerdy/np-completeness
Any agent
npx skills add Arcadi4/nerdy --skill np-completeness
Clone the repo
git clone --depth 1 https://github.com/Arcadi4/nerdy

Made for: Claude Code, Codex.

Wrote 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.

agentmods badge for np-completeness

README.md
[![agentmods](https://agentmods.dev/badge/skills/arcadi4/nerdy/np-completeness.svg)](https://agentmods.dev/skills/arcadi4/nerdy/np-completeness)
Your own site
<a href="https://agentmods.dev/skills/arcadi4/nerdy/np-completeness"><img src="https://agentmods.dev/badge/skills/arcadi4/nerdy/np-completeness.svg" alt="Measured on agentmods" height="20"></a>
Per session 73 Skills are progressive disclosure: only the name and description are preloaded; the body loads when the skill is used.
When invoked 3,679 The whole file, excluding the scripts and references it only reads on demand.
Security scan A 0 findings. Scan, not verified.
Origin original No closer match found in the catalogue.
Token cost

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.

ModelPer sessionOnce invoked
Fable 5 $0.00073 $0.03679
Opus 5 $0.00036 $0.01840
Sonnet 5 $0.00015 $0.00736
Haiku 4.5 $0.00007 $0.00368

Measured 4d ago against content hash 797fd5160f8f, method: parsed. Prices are Anthropic first-party input rates as of 2026-08-30, from the pricing page.

Security

Grade A, and why

np-completeness 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 4d 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.

clrs/np-completeness/SKILL.md · 312 lines

How it starts

The opening of the file, as written. The whole thing — 312 lines — stays where its author put it; the contents beside it link to each section on GitHub.

NP-Completeness

Overview

NP-completeness answers whether an exact polynomial-time algorithm is plausible under the chapter model. Treat every proof as a certificate-and-reduction audit: define the decision language, prove verifiability, reduce from a known hard source in the correct direction, and prove both answer preservation and polynomial construction size.

Core principle: an NP-completeness proof is incomplete unless it separately proves membership in NP, maps arbitrary source instances to target instances without solving them, proves both directions of equivalence, and accounts for encoding length.

Shared CLRS Conventions

  • Follow the parent clrs skill for mathematical formatting: every language definition, reduction relation, asymptotic bound, threshold, and symbolic assignment belongs in display LaTeX blocks.
  • Keep tables verbal. Put reduction relations, targets, and construction formulas in display blocks near the table instead of inside table cells.
  • Use elementary-graph-algorithms for ordinary graph traversal, shortest-paths for shortest-path algorithms, linear-programming for LP modeling, and this skill when the task asks for NP membership, NP-hardness, reductions, encoding, or exact hardness evidence.
  • Do not announce that you are using this skill. Deliver the polished classification, reduction, or review directly.

When to Use

Use this skill when a task involves:

  • proving a decision problem is in P, in NP, NP-hard, NP-complete, or related to co-NP;
  • converting optimization hardness into a bound decision version;
  • building or reviewing a polynomial-time reduction;
  • choosing among CIRCUIT-SAT, SAT, 3-CNF-SAT, CLIQUE, VERTEX-COVER, HAM-CYCLE, TSP, or SUBSET-SUM as a source problem;
  • checking whether a numeric algorithm is pseudo-polynomial rather than polynomial in the input length;
  • explaining why an exact polynomial algorithm for one NP-complete problem would imply the standard collapse.

Do not use this skill merely because an algorithm is slow. Use it when the answer must reason about formal decision languages, certificates, reductions, or encoding-sensitive polynomial time.

Read the full file on GitHub · 312 lines

Changes

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.

  1. 4d ago First seen · 312 lines · 73 tokens per session scan A 797fd5160f8f

Subscribe to this mod's changes

np-completeness is a skill published in the GitHub repository Arcadi4/nerdy (7 stars, last pushed 4mo ago), licensed MIT. It adds 73 tokens to every session and 3,679 once invoked, about $0.0004 per session on Opus 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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