Algorithm Design

Algorithm Design

Formalize methods into algorithm pseudocode and system architecture diagrams.

Input

• $0 — Method description or implementation to formalize

References

• Algorithm and diagram templates: ~/.claude/skills/algorithm-design/references/algorithm-templates.md

Workflow

Step 1: Formalize the Algorithm

• Define clear inputs and outputs
• Identify the main loop / recursive structure
• Specify all parameters and their types
• Write step-by-step pseudocode

Step 2: Generate LaTeX Pseudocode

Use algorithm + algpseudocode environments:

\begin{algorithm}[t]
\caption{Method Name}
\label{alg:method}
\begin{algorithmic}[1]
\Require Input $x$, parameters $\theta$
\Ensure Output $y$
\State Initialize ...
\For{$t = 1$ to $T$}
    \State $z_t \gets f(x_t; \theta)$
    \If{convergence criterion met}
        \State \textbf{break}
    \EndIf
\EndFor
\State \Return $y$
\end{algorithmic}
\end{algorithm}

Step 3: Generate UML Diagrams (Mermaid)

Class Diagram

classDiagram
    class Model {
        +forward(x: Tensor) Tensor
        +train_step(batch) float
    }

Sequence Diagram

sequenceDiagram
    participant M as Main
    participant D as DataLoader
    M->>D: load_data()
    D-->>M: batches

Step 4: Verify Consistency

• Every pseudocode step must map to a code module
• Every class in the UML must exist in the implementation
• Parameter names must match between pseudocode and code

Rules

• Use standard algorithmic notation (not code syntax)
• Number lines for easy reference
• Include complexity analysis as a comment or proposition
• Use \Require / \Ensure for inputs/outputs
• Keep pseudocode at the right abstraction level — not too detailed, not too vague

Related Skills

• Upstream: atomic-decomposition, math-reasoning
• Downstream: experiment-code, paper-writing-section
• See also: symbolic-equation