Skill

role-algorithms:algorithm-design

Designs algorithms with formal analysis — Big-O/Theta/Omega, amortized analysis, recurrence relations (Master theorem), correctness proofs (loop invariants, induction, reduction), and paradigm selection (greedy, divide-and-conquer, dynamic programming, backtracking). Use when analyzing efficiency, proving correctness, comparing approaches, or selecting optimal algorithms for given constraints.

Install

npx claudepluginhub rnavarych/alpha-engineer --plugin role-algorithms

Tool Access

This skill is limited to using the following tools:

ReadGrepGlobBash

Preview

- Analyzing algorithm efficiency and comparing time/space bounds

Supporting Assets

references/asymptotic-analysis.mdreferences/correctness-and-tradeoffs.mdreferences/design-paradigms.md

SKILL.md

Similar Skills

skill-lookup

Searches, retrieves, and installs Agent Skills from prompts.chat registry using MCP tools like search_skills and get_skill. Activates for finding skills, browsing catalogs, or extending Claude.

prompts.chat

157.6k

prompt-lookup

Searches prompts.chat for AI prompt templates by keyword or category, retrieves by ID with variable handling, and improves prompts via AI. Use for discovering or enhancing prompts.

prompts.chat

157.6k

Agent Development

6 files

Guides agent creation for Claude Code plugins with file templates, frontmatter specs (name, description, model), triggering examples, system prompts, and best practices.

plugin-dev

83.2k

Stats

Parent Repo Stars9

Parent Repo Forks0

Last CommitMar 3, 2026

Actions

View Source View Plugin View on GitHub View README

role-algorithms:algorithm-design

When to use

Analyzing algorithm efficiency and comparing time/space bounds

Selecting the right paradigm: greedy, divide-and-conquer, DP, or backtracking

Proving algorithm correctness with loop invariants or induction

Solving recurrence relations and applying the Master theorem

Evaluating space-time trade-offs under memory or latency constraints

Explaining why a greedy choice is (or is not) valid

Core principles

Prove before you code — choose a paradigm and establish correctness argument before implementation

Tight bounds over loose bounds — Big-Theta tells the truth; Big-O alone can mislead

Constants matter at small n — O(n log n) with large constants can lose to O(n²) for n < 10,000

Amortized cost is not average cost — a single expensive operation does not break O(1) amortized

Greedy requires proof — exchange argument or cut property; intuition is not a proof

Reference Files

references/asymptotic-analysis.md — notation (O/Ω/Θ/o), practical interpretation, amortized methods (aggregate, accounting, potential), recurrence relations and Master theorem

references/design-paradigms.md — greedy (exchange argument, classic examples), divide-and-conquer (split/merge decisions), dynamic programming (when DP beats greedy), backtracking (pruning strategies)

references/correctness-and-tradeoffs.md — loop invariants, structural induction, reduction proofs, space-time trade-off decision matrix

Algorithm Design

When to use

Analyzing algorithm efficiency and comparing time/space bounds
Selecting the right paradigm: greedy, divide-and-conquer, DP, or backtracking
Proving algorithm correctness with loop invariants or induction
Solving recurrence relations and applying the Master theorem
Evaluating space-time trade-offs under memory or latency constraints
Explaining why a greedy choice is (or is not) valid

Core principles

Prove before you code — choose a paradigm and establish correctness argument before implementation
Tight bounds over loose bounds — Big-Theta tells the truth; Big-O alone can mislead
Constants matter at small n — O(n log n) with large constants can lose to O(n²) for n < 10,000
Amortized cost is not average cost — a single expensive operation does not break O(1) amortized
Greedy requires proof — exchange argument or cut property; intuition is not a proof

Reference Files

references/asymptotic-analysis.md — notation (O/Ω/Θ/o), practical interpretation, amortized methods (aggregate, accounting, potential), recurrence relations and Master theorem
references/design-paradigms.md — greedy (exchange argument, classic examples), divide-and-conquer (split/merge decisions), dynamic programming (when DP beats greedy), backtracking (pruning strategies)
references/correctness-and-tradeoffs.md — loop invariants, structural induction, reduction proofs, space-time trade-off decision matrix