# Cs Algorithms

> Design and analyse algorithms — correctness proof, complexity analysis (time and space), and stability — with explicit proof of invariants and termination.

- Skill: `quantumquirkxyz/cs-algorithms` (Agent Skill)
- Install (CLI): `npx skillmds@latest add quantumquirkxyz/cs-algorithms`
- Raw SKILL.md: https://api.skillmd.com/api/skills/quantumquirkxyz/cs-algorithms/raw
- Safety review: pending
- Works with: Claude Code, Claude.ai, OpenAI Codex
- Category: Coding & Dev Tools
- Author: quantumquirkxyz (https://skillmd.com/u/quantumquirkxyz)
- Updated: 2026-09-17
- Page: https://skillmd.com/skills/quantumquirkxyz/cs-algorithms

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## Contract

- **Input:** problem description and inputs defined by the skill body.
- **Output:** Markdown artifact with completed process steps.
- **Side effects:** none.
- **Dependencies:** none.
- **Stop condition:** all process steps executed; artifact saved with required sections.
- **Risk:** low.
- **Boundary:** produces reasoning artifact only; no system changes.


# CS Algorithms

Design, analyse, and verify an **algorithm** — its correctness, complexity, stability, and invariants — with an explicit proof structure.

## When to use

- The user needs an algorithm designed or analysed.
- A data structure choice needs justification.
- Performance or correctness requires proof.

## Process

1. Problem statement — input, output, pre/post conditions.
2. Algorithm design — strategy (divide and conquer, greedy, dynamic programming, backtracking, etc.); justify why it fits.
3. Pseudocode / code — clean, with clear variable names.
4. Correctness proof — loop invariant; termination; initialisation, maintenance, termination. Or proof by contradiction / induction for non-loop structures.
5. Complexity analysis — time (best/average/worst), space; use Big-O with justification (count operations, recursion depth).
6. Stability — if numerical, numerical stability; if combinatorial, output stability.
7. Deliver — artifact: problem, design, code/pseudocode, correctness proof, complexity, stability note.