Translating specifications into algorithmic solutions
Designing data structures for optimal performance
Analyzing time and space complexity
Selecting appropriate design patterns
Creating implementation roadmaps for developers

Prerequisites

Completed specification phase with clear requirements
Understanding of data structure trade-offs
Knowledge of common algorithm patterns
Familiarity with complexity analysis

Core Concepts

SPARC Pseudocode Phase

The Pseudocode phase bridges specifications and implementation:

Design algorithmic solutions - Language-agnostic logic
Select optimal data structures - Based on access patterns
Analyze complexity - Time and space requirements
Identify design patterns - Reusable solutions
Create implementation roadmap - Guide for developers

Complexity Classes

Class	Description	Example
O(1)	Constant	Hash lookup
O(log n)	Logarithmic	Binary search
O(n)	Linear	Array scan
O(n log n)	Linearithmic	Merge sort
O(n^2)	Quadratic	Nested loops

Implementation Pattern

Algorithm Structure

ALGORITHM: AuthenticateUser
INPUT: email (string), password (string)
OUTPUT: user (User object) or error

BEGIN
    // Validate inputs
    IF email is empty OR password is empty THEN
        RETURN error("Invalid credentials")
    END IF

    // Retrieve user from database
    user <- Database.findUserByEmail(email)

    IF user is null THEN
        RETURN error("User not found")
    END IF

    // Verify password
    isValid <- PasswordHasher.verify(password, user.passwordHash)

    IF NOT isValid THEN
        // Log failed attempt
        SecurityLog.logFailedLogin(email)
        RETURN error("Invalid credentials")
    END IF

    // Create session
    session <- CreateUserSession(user)

    RETURN {user: user, session: session}
END

Data Structure Selection

DATA STRUCTURES:

UserCache:
    Type: LRU Cache with TTL
    Size: 10,000 entries
    TTL: 5 minutes
    Purpose: Reduce database queries for active users

    Operations:
        - get(userId): O(1)
        - set(userId, userData): O(1)
        - evict(): O(1)

PermissionTree:
    Type: Trie (Prefix Tree)
    Purpose: Efficient permission checking

    Structure:
        root
        +-- users
        |   +-- read
        |   +-- write
        |   +-- delete
        +-- admin
            +-- system
            +-- users

    Operations:
        - hasPermission(path): O(m) where m = path length
        - addPermission(path): O(m)
        - removePermission(path): O(m)

Algorithm Patterns

PATTERN: Rate Limiting (Token Bucket)

ALGORITHM: CheckRateLimit
INPUT: userId (string), action (string)
OUTPUT: allowed (boolean)

CONSTANTS:
    BUCKET_SIZE = 100
    REFILL_RATE = 10 per second

BEGIN
    bucket <- RateLimitBuckets.get(userId + action)

    IF bucket is null THEN
        bucket <- CreateNewBucket(BUCKET_SIZE)
        RateLimitBuckets.set(userId + action, bucket)
    END IF

    // Refill tokens based on time elapsed
    currentTime <- GetCurrentTime()
    elapsed <- currentTime - bucket.lastRefill
    tokensToAdd <- elapsed * REFILL_RATE

    bucket.tokens <- MIN(bucket.tokens + tokensToAdd, BUCKET_SIZE)
    bucket.lastRefill <- currentTime

    // Check if request allowed
    IF bucket.tokens >= 1 THEN
        bucket.tokens <- bucket.tokens - 1
        RETURN true
    ELSE
        RETURN false
    END IF
END

Configuration

# sparc-pseudocode-config.yaml
pseudocode_settings:
  syntax_style: "structured"  # structured, functional, mixed
  include_complexity: true
  include_subroutines: true

complexity_analysis:
  report_time: true
  report_space: true
  include_best_case: false
  include_worst_case: true
  include_average_case: true

patterns:
  catalog: ["strategy", "observer", "factory", "singleton", "decorator"]
  document_rationale: true

Usage Examples

Example 1: Search Algorithm

ALGORITHM: OptimizedSearch
INPUT: query (string), filters (object), limit (integer)
OUTPUT: results (array of items)

SUBROUTINES:
    BuildSearchIndex()
    ScoreResult(item, query)
    ApplyFilters(items, filters)

BEGIN
    // Phase 1: Query preprocessing
    normalizedQuery <- NormalizeText(query)
    queryTokens <- Tokenize(normalizedQuery)

    // Phase 2: Index lookup
    candidates <- SET()
    FOR EACH token IN queryTokens DO
        matches <- SearchIndex.get(token)
        candidates <- candidates UNION matches
    END FOR

    // Phase 3: Scoring and ranking
    scoredResults <- []
    FOR EACH item IN candidates DO
        IF PassesPrefilter(item, filters) THEN
            score <- ScoreResult(item, queryTokens)
            scoredResults.append({item: item, score: score})
        END IF
    END FOR

    // Phase 4: Sort and filter
    scoredResults.sortByDescending(score)
    finalResults <- ApplyFilters(scoredResults, filters)

    // Phase 5: Pagination
    RETURN finalResults.slice(0, limit)
END

SUBROUTINE: ScoreResult
INPUT: item, queryTokens
OUTPUT: score (float)

BEGIN
    score <- 0

    // Title match (highest weight)
    titleMatches <- CountTokenMatches(item.title, queryTokens)
    score <- score + (titleMatches * 10)

    // Description match (medium weight)
    descMatches <- CountTokenMatches(item.description, queryTokens)
    score <- score + (descMatches * 5)

    // Tag match (lower weight)
    tagMatches <- CountTokenMatches(item.tags, queryTokens)
    score <- score + (tagMatches * 2)

    // Boost by recency
    daysSinceUpdate <- (CurrentDate - item.updatedAt).days
    recencyBoost <- 1 / (1 + daysSinceUpdate * 0.1)
    score <- score * recencyBoost

    RETURN score
END

Example 2: Design Patterns

PATTERN: Strategy Pattern

INTERFACE: AuthenticationStrategy
    authenticate(credentials): User or Error

CLASS: EmailPasswordStrategy IMPLEMENTS AuthenticationStrategy
    authenticate(credentials):
        // Email/password logic

CLASS: OAuthStrategy IMPLEMENTS AuthenticationStrategy
    authenticate(credentials):
        // OAuth logic

CLASS: AuthenticationContext
    strategy: AuthenticationStrategy

    executeAuthentication(credentials):
        RETURN strategy.authenticate(credentials)

---

PATTERN: Observer Pattern

CLASS: EventEmitter
    listeners: Map<eventName, List<callback>>

    on(eventName, callback):
        IF NOT listeners.has(eventName) THEN
            listeners.set(eventName, [])
        END IF
        listeners.get(eventName).append(callback)

    emit(eventName, data):
        IF listeners.has(eventName) THEN
            FOR EACH callback IN listeners.get(eventName) DO
                callback(data)
            END FOR
        END IF

Example 3: Complexity Analysis

ANALYSIS: User Authentication Flow

Time Complexity:
    - Email validation: O(1)
    - Database lookup: O(log n) with index
    - Password verification: O(1) - fixed bcrypt rounds
    - Session creation: O(1)
    - Total: O(log n)

Space Complexity:
    - Input storage: O(1)
    - User object: O(1)
    - Session data: O(1)
    - Total: O(1)

ANALYSIS: Search Algorithm

Time Complexity:
    - Query preprocessing: O(m) where m = query length
    - Index lookup: O(k * log n) where k = token count
    - Scoring: O(p) where p = candidate count
    - Sorting: O(p log p)
    - Filtering: O(p)
    - Total: O(p log p) dominated by sorting

Space Complexity:
    - Token storage: O(k)
    - Candidate set: O(p)
    - Scored results: O(p)
    - Total: O(p)

Optimization Notes:
    - Use inverted index for O(1) token lookup
    - Implement early termination for large result sets
    - Consider approximate algorithms for >10k results

Execution Checklist

Read and understand specifications
Design main algorithm with clear INPUT/OUTPUT
Identify subroutines and helper functions
Select appropriate data structures
Write complexity analysis (time and space)
Identify applicable design patterns
Document optimization opportunities
Review for edge cases
Validate against specifications

Best Practices

Language Agnostic: Don't use language-specific syntax
Clear Logic: Focus on algorithm flow, not implementation details
Handle Edge Cases: Include error handling in pseudocode
Document Complexity: Always analyze time/space complexity
Use Meaningful Names: Variable names should explain purpose
Modular Design: Break complex algorithms into subroutines

Error Handling

Issue	Resolution
Unclear complexity	Break down into primitive operations
Missing edge cases	Review input validation and error paths
Overly complex	Decompose into smaller subroutines
No data structure justification	Document access patterns and requirements

Metrics & Success Criteria

All algorithms have documented complexity
Subroutines are clearly defined
Data structures are justified with operations
Design patterns are identified where applicable
Pseudocode is language-agnostic

Integration Points

MCP Tools

// Store pseudocode phase completion
  action: "store",
  key: "sparc/pseudocode/algorithms",
  namespace: "coordination",
  value: JSON.stringify({
    algorithms: ["AuthenticateUser", "CheckRateLimit"],
    patterns: ["strategy", "observer"],
    complexity: "O(log n)",
    timestamp: Date.now()
  })
}

Hooks

# Pre-pseudocode hook

# Post-pseudocode hook

Prerequisites

Core Concepts

SPARC Pseudocode Phase

Complexity Classes

Implementation Pattern

Algorithm Structure

Data Structure Selection

Algorithm Patterns

Configuration

Usage Examples

Example 1: Search Algorithm

Example 2: Design Patterns

Example 3: Complexity Analysis

Execution Checklist

Best Practices

Error Handling

Metrics & Success Criteria

Integration Points

MCP Tools

Hooks

Related Skills

References

Version History

sparc-pseudocode

SPARC Pseudocode Agent

Quick Start

When to Use

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