# Algorithms and Optimization: Skills and Agents Backlog

This document catalogs specialized skills and agents that could enhance the processes in the Algorithms and Optimization specialization beyond general-purpose capabilities.

## Overview

**Specialization:** algorithms-optimization
**Phase:** 4 - Skills and Agents Identification
**Total Processes:** 49
**Categories:** Competitive Programming, Algorithm Implementation, Dynamic Programming, Graph Algorithms, Optimization, String Algorithms, Number Theory, Interview Preparation, Contest Strategy, Advanced Algorithms, Skill Development, Benchmarking, Problem Creation

---

## Specialized Skills

### 1. Competitive Programming Skills

#### SK-ALGO-001: leetcode-problem-fetcher
- **Type:** Skill
- **Purpose:** Fetch and parse LeetCode problems with metadata, constraints, examples, and hints
- **Capabilities:**
  - Extract problem statements from LeetCode URLs
  - Parse input/output constraints and formats
  - Retrieve test cases and hidden constraints
  - Get problem difficulty, tags, and acceptance rate
  - Fetch related problems and pattern tags
- **Enhances Processes:** leetcode-problem-solving, pattern-recognition, faang-interview-prep
- **Priority:** High
- **Integration:** REST API / Web scraping with rate limiting

#### SK-ALGO-002: codeforces-api-client
- **Type:** Skill
- **Purpose:** Interface with Codeforces API for contest data, problem sets, and submissions
- **Capabilities:**
  - Fetch contest problems and metadata
  - Submit solutions and retrieve verdicts
  - Access user standings and rating history
  - Retrieve editorials and tags
  - Virtual contest management
- **Enhances Processes:** codeforces-contest, progress-tracking, skill-gap-analysis
- **Priority:** High
- **Integration:** Codeforces Official API

#### SK-ALGO-003: atcoder-client
- **Type:** Skill
- **Purpose:** Interface with AtCoder for Japanese competitive programming contests
- **Capabilities:**
  - Fetch contest problems with translations
  - Submit solutions and track results
  - Access AtCoder Problems difficulty ratings
  - Virtual contest participation
- **Enhances Processes:** atcoder-contest, progress-tracking
- **Priority:** Medium
- **Integration:** AtCoder API / Web interface

#### SK-ALGO-004: cses-tracker
- **Type:** Skill
- **Purpose:** Track progress through CSES Problem Set with structured learning
- **Capabilities:**
  - Track solved problems by category
  - Suggest next problems based on difficulty progression
  - Generate progress reports
  - Map problems to CP Handbook chapters
- **Enhances Processes:** cses-learning-path, skill-gap-analysis, topic-mastery-certification
- **Priority:** Medium
- **Integration:** CSES platform integration

#### SK-ALGO-005: code-template-manager
- **Type:** Skill
- **Purpose:** Manage and generate competitive programming templates
- **Capabilities:**
  - Store and retrieve algorithm templates (C++, Python, Java)
  - Fast I/O templates for different languages
  - Data structure templates (segment tree, DSU, etc.)
  - Template customization and versioning
- **Enhances Processes:** cp-library-creation, codeforces-contest, algorithm-implementation
- **Priority:** High
- **Integration:** Local file system, Git

---

### 2. Algorithm Analysis Skills

#### SK-ALGO-006: complexity-analyzer
- **Type:** Skill
- **Purpose:** Automated Big-O complexity analysis of code and algorithms
- **Capabilities:**
  - Static analysis of loop structures
  - Recursive call tree analysis
  - Space complexity estimation
  - Amortized analysis support
  - Generate complexity derivation documents
- **Enhances Processes:** complexity-optimization, leetcode-problem-solving, algorithm-implementation
- **Priority:** High
- **Integration:** AST parsing, symbolic execution

#### SK-ALGO-007: algorithm-visualizer
- **Type:** Skill
- **Purpose:** Generate visual representations of algorithm execution
- **Capabilities:**
  - Step-by-step execution visualization
  - Data structure state visualization
  - Graph algorithm animation
  - DP table visualization
  - Generate animated GIFs/videos
- **Enhances Processes:** algorithm-implementation, dp-pattern-matching, graph-traversal, interview-problem-explanation
- **Priority:** Medium
- **Integration:** Manim, D3.js, custom renderers

#### SK-ALGO-008: test-case-generator
- **Type:** Skill
- **Purpose:** Generate comprehensive test cases including edge cases and stress tests
- **Capabilities:**
  - Random test case generation within constraints
  - Edge case identification and generation
  - Stress test generation with large inputs
  - Counter-example finding for wrong solutions
  - Brute force oracle generation
- **Enhances Processes:** correctness-proof-testing, algorithm-implementation, leetcode-problem-solving
- **Priority:** High
- **Integration:** Python generators, testlib.h

#### SK-ALGO-009: solution-comparator
- **Type:** Skill
- **Purpose:** Compare multiple solutions for correctness and performance
- **Capabilities:**
  - Run solutions against same test cases
  - Performance benchmarking and comparison
  - Output diff analysis
  - Find minimal failing test case
- **Enhances Processes:** correctness-proof-testing, complexity-optimization, upsolving
- **Priority:** Medium
- **Integration:** Docker sandboxes, process isolation

---

### 3. Dynamic Programming Skills

#### SK-ALGO-010: dp-state-designer
- **Type:** Skill
- **Purpose:** Assist in designing optimal DP states and transitions
- **Capabilities:**
  - Identify subproblem structure
  - Suggest state representations
  - Derive transition formulas
  - Identify optimization opportunities (rolling array, bitmask compression)
  - Generate state space complexity estimates
- **Enhances Processes:** dp-pattern-matching, dp-state-optimization, dp-transition-derivation
- **Priority:** High
- **Integration:** Pattern matching, symbolic reasoning

#### SK-ALGO-011: dp-optimizer
- **Type:** Skill
- **Purpose:** Apply advanced DP optimizations automatically
- **Capabilities:**
  - Convex hull trick detection and application
  - Divide and conquer optimization
  - Knuth optimization
  - Monotonic queue/deque optimization
  - Alien's trick / WQS binary search
- **Enhances Processes:** dp-state-optimization, advanced-dp-techniques, complexity-optimization
- **Priority:** Medium
- **Integration:** Code transformation, pattern detection

#### SK-ALGO-012: dp-pattern-library
- **Type:** Skill
- **Purpose:** Maintain and match against library of classic DP patterns
- **Capabilities:**
  - Pattern matching against 50+ classic DP problems
  - Template code generation for matched patterns
  - Variant detection (knapsack variants, LCS variants, etc.)
  - Problem-to-pattern mapping
- **Enhances Processes:** dp-pattern-matching, classic-dp-library, leetcode-problem-solving
- **Priority:** High
- **Integration:** Pattern database, similarity matching

---

### 4. Graph Algorithm Skills

#### SK-ALGO-013: graph-modeler
- **Type:** Skill
- **Purpose:** Convert problem descriptions into graph representations
- **Capabilities:**
  - Entity-to-node mapping
  - Relationship-to-edge mapping
  - Graph property detection (bipartite, DAG, tree, etc.)
  - Suggest optimal representation (adjacency list vs matrix)
  - Generate graph visualization
- **Enhances Processes:** graph-modeling, shortest-path-algorithms, graph-traversal
- **Priority:** High
- **Integration:** NLP for entity extraction, graph visualization

#### SK-ALGO-014: graph-algorithm-selector
- **Type:** Skill
- **Purpose:** Select optimal graph algorithm based on problem constraints
- **Capabilities:**
  - Constraint analysis for algorithm selection
  - Trade-off analysis (Dijkstra vs Bellman-Ford vs Floyd-Warshall)
  - Special case detection (sparse vs dense, negative edges)
  - Algorithm complexity mapping to constraints
- **Enhances Processes:** shortest-path-algorithms, advanced-graph-algorithms, graph-traversal
- **Priority:** Medium
- **Integration:** Rule-based system, constraint solver

#### SK-ALGO-015: flow-network-builder
- **Type:** Skill
- **Purpose:** Model optimization problems as network flow problems
- **Capabilities:**
  - Identify max-flow/min-cut modeling opportunities
  - Construct flow network from problem description
  - Select optimal flow algorithm
  - Handle min-cost flow variants
  - Bipartite matching reduction
- **Enhances Processes:** advanced-graph-algorithms, graph-modeling
- **Priority:** Medium
- **Integration:** Graph construction library

---

### 5. Data Structure Skills

#### SK-ALGO-016: data-structure-selector
- **Type:** Skill
- **Purpose:** Select optimal data structure based on operation requirements
- **Capabilities:**
  - Analyze required operations (insert, delete, query, update)
  - Match to optimal data structure
  - Consider time/space trade-offs
  - Suggest augmentations for custom requirements
- **Enhances Processes:** data-structure-implementation, algorithm-implementation, complexity-optimization
- **Priority:** High
- **Integration:** Rule-based expert system

#### SK-ALGO-017: segment-tree-builder
- **Type:** Skill
- **Purpose:** Generate customized segment tree implementations
- **Capabilities:**
  - Generate segment tree for custom merge functions
  - Lazy propagation template generation
  - Persistent segment tree variants
  - 2D segment tree generation
  - Segment tree beats for complex updates
- **Enhances Processes:** segment-tree-implementation, range-query-optimization, data-structure-implementation
- **Priority:** High
- **Integration:** Code generation, template system

#### SK-ALGO-018: advanced-ds-library
- **Type:** Skill
- **Purpose:** Provide implementations of advanced data structures
- **Capabilities:**
  - Treaps, Splay trees, Link-cut trees
  - Persistent data structures
  - Wavelet trees
  - Heavy-light decomposition
  - Centroid decomposition
- **Enhances Processes:** data-structure-implementation, advanced-graph-algorithms, cp-library-creation
- **Priority:** Medium
- **Integration:** Template library

---

### 6. String Algorithm Skills

#### SK-ALGO-019: string-algorithm-matcher
- **Type:** Skill
- **Purpose:** Match string problems to appropriate algorithms
- **Capabilities:**
  - Pattern matching algorithm selection (KMP, Z, Rabin-Karp)
  - Suffix structure selection (array vs tree vs automaton)
  - Palindrome detection algorithm selection
  - Rolling hash implementation
- **Enhances Processes:** pattern-matching-algorithms, trie-suffix-structures, string-processing
- **Priority:** Medium
- **Integration:** Pattern database

#### SK-ALGO-020: suffix-structure-builder
- **Type:** Skill
- **Purpose:** Build and query suffix arrays and related structures
- **Capabilities:**
  - Suffix array construction (SA-IS, DC3)
  - LCP array construction
  - Suffix tree construction
  - Suffix automaton construction
  - Query implementations for each structure
- **Enhances Processes:** trie-suffix-structures, pattern-matching-algorithms
- **Priority:** Medium
- **Integration:** C++ templates, algorithm library

---

### 7. Number Theory Skills

#### SK-ALGO-021: number-theory-toolkit
- **Type:** Skill
- **Purpose:** Provide number theory algorithm implementations and guidance
- **Capabilities:**
  - Modular arithmetic operations
  - Extended Euclidean algorithm
  - Chinese Remainder Theorem
  - Modular inverse and exponentiation
  - FFT/NTT for polynomial multiplication
- **Enhances Processes:** number-theory-algorithms, prime-algorithms, combinatorics-counting
- **Priority:** High
- **Integration:** Template library, symbolic computation

#### SK-ALGO-022: prime-sieve-generator
- **Type:** Skill
- **Purpose:** Generate optimized prime sieves and factorization routines
- **Capabilities:**
  - Sieve of Eratosthenes (segmented, linear)
  - Smallest prime factor sieve
  - Miller-Rabin primality testing
  - Pollard's rho factorization
  - Precompute prime-related values
- **Enhances Processes:** prime-algorithms, number-theory-algorithms
- **Priority:** Medium
- **Integration:** C++ templates

#### SK-ALGO-023: combinatorics-calculator
- **Type:** Skill
- **Purpose:** Calculate combinatorial values with modular arithmetic
- **Capabilities:**
  - Factorial and inverse factorial precomputation
  - nCr, nPr with modular arithmetic
  - Catalan, Stirling, Bell numbers
  - Lucas theorem implementation
  - Inclusion-exclusion principle application
- **Enhances Processes:** combinatorics-counting, number-theory-algorithms
- **Priority:** Medium
- **Integration:** Precomputation tables, formula library

---

### 8. Interview Preparation Skills

#### SK-ALGO-024: interview-problem-bank
- **Type:** Skill
- **Purpose:** Curated bank of interview problems organized by company and pattern
- **Capabilities:**
  - Problems organized by FAANG company
  - Pattern-based categorization
  - Difficulty progression recommendations
  - Track coverage and weak areas
  - Premium problem alternatives
- **Enhances Processes:** faang-interview-prep, mock-coding-interview, interview-problem-explanation
- **Priority:** High
- **Integration:** Database, recommendation engine

#### SK-ALGO-025: interview-simulator
- **Type:** Skill
- **Purpose:** Simulate realistic coding interview experience
- **Capabilities:**
  - Time-boxed problem presentation
  - Hint system with escalation
  - Follow-up question generation
  - Communication evaluation prompts
  - Realistic interviewer responses
- **Enhances Processes:** mock-coding-interview, behavioral-interview-prep
- **Priority:** High
- **Integration:** Timer, structured interaction

#### SK-ALGO-026: solution-explainer
- **Type:** Skill
- **Purpose:** Generate clear explanations of algorithm solutions
- **Capabilities:**
  - Step-by-step solution walkthrough
  - Time/space complexity explanation
  - Alternative approach comparison
  - Common mistake highlights
  - Visual aids generation
- **Enhances Processes:** interview-problem-explanation, leetcode-problem-solving, mock-coding-interview
- **Priority:** High
- **Integration:** Documentation generation

---

### 9. Correctness and Verification Skills

#### SK-ALGO-027: invariant-analyzer
- **Type:** Skill
- **Purpose:** Identify and verify loop invariants for correctness proofs
- **Capabilities:**
  - Automatic loop invariant inference
  - Invariant verification
  - Precondition/postcondition extraction
  - Generate formal proof structure
- **Enhances Processes:** correctness-proof-testing, algorithm-implementation
- **Priority:** Medium
- **Integration:** Static analysis, formal methods

#### SK-ALGO-028: proof-assistant
- **Type:** Skill
- **Purpose:** Assist in constructing algorithm correctness proofs
- **Capabilities:**
  - Proof structure templates (induction, contradiction, etc.)
  - Step-by-step proof guidance
  - Termination argument generation
  - Proof review and validation
- **Enhances Processes:** correctness-proof-testing, algorithm-implementation
- **Priority:** Medium
- **Integration:** Proof templates, formal reasoning

---

### 10. Performance and Optimization Skills

#### SK-ALGO-029: code-profiler
- **Type:** Skill
- **Purpose:** Profile code performance and identify bottlenecks
- **Capabilities:**
  - Runtime profiling
  - Memory profiling
  - Cache miss analysis
  - Hot spot identification
  - Optimization suggestions
- **Enhances Processes:** code-level-optimization, complexity-optimization, memory-optimization
- **Priority:** Medium
- **Integration:** gprof, perf, Valgrind

#### SK-ALGO-030: micro-optimizer
- **Type:** Skill
- **Purpose:** Apply language-specific micro-optimizations
- **Capabilities:**
  - C++ optimization tricks (fast I/O, pragma optimizations)
  - Python optimization (PyPy hints, list comprehensions)
  - Memory layout optimization
  - Vectorization opportunities
- **Enhances Processes:** code-level-optimization, io-optimization, memory-optimization
- **Priority:** Low
- **Integration:** Code transformation

---

### 11. Computational Geometry Skills

#### SK-ALGO-031: geometry-primitive-library
- **Type:** Skill
- **Purpose:** Provide robust computational geometry primitives
- **Capabilities:**
  - Point, line, segment, polygon classes
  - Cross product, dot product operations
  - CCW/CW orientation tests
  - Area calculations
  - Intersection tests
- **Enhances Processes:** computational-geometry
- **Priority:** Medium
- **Integration:** Template library

#### SK-ALGO-032: geometry-algorithm-library
- **Type:** Skill
- **Purpose:** Implement computational geometry algorithms
- **Capabilities:**
  - Convex hull (Graham scan, Andrew's monotone chain)
  - Line intersection algorithms
  - Closest pair of points
  - Point in polygon tests
  - Voronoi diagram, Delaunay triangulation
- **Enhances Processes:** computational-geometry
- **Priority:** Medium
- **Integration:** C++ templates

---

## Specialized Agents (Subagents)

### 1. Competitive Programming Agents

#### AG-ALGO-001: competitive-programmer
- **Type:** Agent
- **Role:** Expert competitive programmer for problem solving
- **Capabilities:**
  - Rapid problem analysis and pattern recognition
  - Multiple solution approach generation
  - Time-constrained problem solving
  - Contest strategy optimization
  - Debugging under pressure
- **Persona:** Red-rated competitive programmer with ICPC experience
- **Enhances Processes:** codeforces-contest, atcoder-contest, leetcode-problem-solving
- **Priority:** High

#### AG-ALGO-002: upsolving-coach
- **Type:** Agent
- **Role:** Guide learners through editorial understanding and upsolving
- **Capabilities:**
  - Editorial explanation and clarification
  - Alternative approach discussion
  - Knowledge gap identification
  - Technique extraction and cataloging
  - Practice problem recommendation
- **Persona:** Experienced CP coach and mentor
- **Enhances Processes:** codeforces-contest (upsolving phase), cses-learning-path
- **Priority:** Medium

#### AG-ALGO-003: contest-strategist
- **Type:** Agent
- **Role:** Optimize contest strategy and time management
- **Capabilities:**
  - Problem difficulty estimation
  - Optimal problem ordering
  - Time allocation recommendations
  - When-to-skip decisions
  - Stress management guidance
- **Persona:** Contest coach with rating improvement focus
- **Enhances Processes:** codeforces-contest, atcoder-contest
- **Priority:** Medium

---

### 2. Algorithm Design Agents

#### AG-ALGO-004: algorithm-designer
- **Type:** Agent
- **Role:** Design optimal algorithms for given problems
- **Capabilities:**
  - Problem decomposition
  - Algorithm paradigm selection (greedy, DP, divide-conquer)
  - Data structure selection
  - Complexity optimization
  - Trade-off analysis
- **Persona:** Algorithm researcher with CLRS expertise
- **Enhances Processes:** algorithm-implementation, greedy-algorithm-design, divide-conquer-design
- **Priority:** High

#### AG-ALGO-005: dp-specialist
- **Type:** Agent
- **Role:** Expert in dynamic programming problem solving
- **Capabilities:**
  - DP applicability determination
  - State design and optimization
  - Transition formula derivation
  - Advanced DP technique application
  - DP debugging and verification
- **Persona:** DP expert with experience in all DP variants
- **Enhances Processes:** dp-pattern-matching, dp-state-optimization, dp-transition-derivation, advanced-dp-techniques
- **Priority:** High

#### AG-ALGO-006: graph-specialist
- **Type:** Agent
- **Role:** Expert in graph algorithms and modeling
- **Capabilities:**
  - Graph modeling from problem descriptions
  - Algorithm selection for graph problems
  - Advanced graph technique application
  - Network flow modeling
  - Tree algorithm expertise
- **Persona:** Graph theory expert
- **Enhances Processes:** graph-modeling, shortest-path-algorithms, graph-traversal, advanced-graph-algorithms
- **Priority:** High

#### AG-ALGO-007: data-structures-expert
- **Type:** Agent
- **Role:** Expert in advanced data structure design and implementation
- **Capabilities:**
  - Custom data structure design
  - Augmentation recommendations
  - Time/space trade-off analysis
  - Implementation debugging
  - Performance optimization
- **Persona:** Data structures researcher and implementer
- **Enhances Processes:** data-structure-implementation, segment-tree-implementation, fenwick-tree-implementation
- **Priority:** High

---

### 3. Interview Preparation Agents

#### AG-ALGO-008: technical-interviewer
- **Type:** Agent
- **Role:** Simulate a realistic technical interviewer
- **Capabilities:**
  - Problem presentation and clarification
  - Hint escalation system
  - Follow-up question generation
  - Communication evaluation
  - Realistic feedback delivery
- **Persona:** Senior engineer at FAANG company
- **Enhances Processes:** mock-coding-interview, faang-interview-prep
- **Priority:** High

#### AG-ALGO-009: interview-coach
- **Type:** Agent
- **Role:** Provide interview preparation coaching and feedback
- **Capabilities:**
  - Weakness identification
  - Personalized study plan creation
  - Communication improvement advice
  - Confidence building strategies
  - Mock interview analysis
- **Persona:** Technical interview coach
- **Enhances Processes:** faang-interview-prep, mock-coding-interview, behavioral-interview-prep
- **Priority:** High

#### AG-ALGO-010: system-design-expert
- **Type:** Agent
- **Role:** Guide system design interviews with algorithmic focus
- **Capabilities:**
  - System design framework application
  - Algorithmic component identification
  - Scalability analysis
  - Trade-off discussion
  - Diagram creation guidance
- **Persona:** Principal engineer with system design experience
- **Enhances Processes:** system-design-interview
- **Priority:** Medium

---

### 4. Analysis and Verification Agents

#### AG-ALGO-011: complexity-analyst
- **Type:** Agent
- **Role:** Perform rigorous complexity analysis
- **Capabilities:**
  - Time complexity derivation
  - Space complexity analysis
  - Amortized analysis
  - Recurrence relation solving
  - Best/worst/average case analysis
- **Persona:** Theoretical CS expert
- **Enhances Processes:** complexity-optimization, leetcode-problem-solving, algorithm-implementation
- **Priority:** High

#### AG-ALGO-012: correctness-verifier
- **Type:** Agent
- **Role:** Verify algorithm correctness through formal methods
- **Capabilities:**
  - Invariant identification
  - Formal proof construction
  - Edge case identification
  - Counter-example generation
  - Termination proof
- **Persona:** Formal methods expert
- **Enhances Processes:** correctness-proof-testing, algorithm-implementation
- **Priority:** Medium

#### AG-ALGO-013: test-engineer
- **Type:** Agent
- **Role:** Generate comprehensive test cases and stress tests
- **Capabilities:**
  - Edge case generation
  - Random test generation
  - Stress test design
  - Oracle implementation
  - Regression test maintenance
- **Persona:** QA engineer specializing in algorithm testing
- **Enhances Processes:** correctness-proof-testing, leetcode-problem-solving
- **Priority:** Medium

---

### 5. Learning and Progress Agents

#### AG-ALGO-014: progress-tracker
- **Type:** Agent
- **Role:** Track learning progress and identify knowledge gaps
- **Capabilities:**
  - Problem-solving pattern analysis
  - Weak area identification
  - Progress visualization
  - Goal setting and tracking
  - Personalized practice recommendations
- **Persona:** Learning analytics specialist
- **Enhances Processes:** progress-tracking, skill-gap-analysis, topic-mastery-certification
- **Priority:** Medium

#### AG-ALGO-015: algorithm-teacher
- **Type:** Agent
- **Role:** Teach algorithm concepts with clear explanations
- **Capabilities:**
  - Concept explanation at multiple levels
  - Visual example generation
  - Practice problem selection
  - Misconception correction
  - Building intuition for algorithms
- **Persona:** Algorithm educator and textbook author
- **Enhances Processes:** interview-problem-explanation, cses-learning-path
- **Priority:** Medium

---

### 6. Specialized Domain Agents

#### AG-ALGO-016: geometry-specialist
- **Type:** Agent
- **Role:** Expert in computational geometry problems
- **Capabilities:**
  - Geometric primitive operations
  - Numerical precision handling
  - Degenerate case identification
  - Algorithm selection for geometry problems
  - Visualization for verification
- **Persona:** Computational geometry researcher
- **Enhances Processes:** computational-geometry
- **Priority:** Medium

#### AG-ALGO-017: string-algorithm-specialist
- **Type:** Agent
- **Role:** Expert in string algorithms and data structures
- **Capabilities:**
  - String algorithm selection
  - Suffix structure expertise
  - Hashing technique application
  - Pattern matching optimization
- **Persona:** String algorithm researcher
- **Enhances Processes:** pattern-matching-algorithms, trie-suffix-structures, string-processing
- **Priority:** Medium

#### AG-ALGO-018: number-theory-specialist
- **Type:** Agent
- **Role:** Expert in number theory and mathematical algorithms
- **Capabilities:**
  - Number theory problem solving
  - Modular arithmetic expertise
  - Prime number algorithms
  - Combinatorics calculations
  - Mathematical proof construction
- **Persona:** Number theory and combinatorics expert
- **Enhances Processes:** number-theory-algorithms, prime-algorithms, combinatorics-counting
- **Priority:** Medium

---

## Shared/Cross-Cutting Candidates

These skills and agents could be shared with other specializations:

### Shared Skills

| ID | Skill | Potential Shared Specializations |
|----|-------|----------------------------------|
| SK-ALGO-006 | complexity-analyzer | qa-testing-automation, software-architecture |
| SK-ALGO-007 | algorithm-visualizer | technical-documentation, data-science-ml |
| SK-ALGO-008 | test-case-generator | qa-testing-automation |
| SK-ALGO-021 | number-theory-toolkit | data-science-ml, security-compliance |
| SK-ALGO-029 | code-profiler | devops-sre-platform, software-architecture |
| SK-ALGO-026 | solution-explainer | technical-documentation |

### Shared Agents

| ID | Agent | Potential Shared Specializations |
|----|-------|----------------------------------|
| AG-ALGO-008 | technical-interviewer | product-management (behavioral) |
| AG-ALGO-011 | complexity-analyst | software-architecture |
| AG-ALGO-013 | test-engineer | qa-testing-automation |
| AG-ALGO-015 | algorithm-teacher | technical-documentation |

---

## Summary Statistics

| Category | Count |
|----------|-------|
| **Total Skills** | 32 |
| **Total Agents** | 18 |
| **Shared Candidates (Skills)** | 6 |
| **Shared Candidates (Agents)** | 4 |
| **High Priority Skills** | 14 |
| **High Priority Agents** | 8 |
| **Medium Priority Skills** | 15 |
| **Medium Priority Agents** | 10 |
| **Low Priority Skills** | 3 |
| **Low Priority Agents** | 0 |

---

## Process-to-Skills/Agents Mapping

### Competitive Programming Practice
| Process | Recommended Skills | Recommended Agents |
|---------|-------------------|-------------------|
| leetcode-problem-solving | SK-ALGO-001, SK-ALGO-006, SK-ALGO-008, SK-ALGO-012 | AG-ALGO-001, AG-ALGO-011 |
| codeforces-contest | SK-ALGO-002, SK-ALGO-005, SK-ALGO-008 | AG-ALGO-001, AG-ALGO-002, AG-ALGO-003 |
| atcoder-contest | SK-ALGO-003, SK-ALGO-005 | AG-ALGO-001, AG-ALGO-003 |
| cses-learning-path | SK-ALGO-004, SK-ALGO-012 | AG-ALGO-002, AG-ALGO-015 |
| pattern-recognition | SK-ALGO-001, SK-ALGO-012 | AG-ALGO-001 |

### Algorithm Implementation
| Process | Recommended Skills | Recommended Agents |
|---------|-------------------|-------------------|
| algorithm-implementation | SK-ALGO-005, SK-ALGO-006, SK-ALGO-008, SK-ALGO-016 | AG-ALGO-004, AG-ALGO-011, AG-ALGO-012 |
| cp-library-creation | SK-ALGO-005, SK-ALGO-017, SK-ALGO-018 | AG-ALGO-007 |
| data-structure-implementation | SK-ALGO-016, SK-ALGO-017, SK-ALGO-018 | AG-ALGO-007 |
| correctness-proof-testing | SK-ALGO-008, SK-ALGO-027, SK-ALGO-028 | AG-ALGO-012, AG-ALGO-013 |

### Dynamic Programming
| Process | Recommended Skills | Recommended Agents |
|---------|-------------------|-------------------|
| dp-pattern-matching | SK-ALGO-010, SK-ALGO-012 | AG-ALGO-005 |
| dp-state-optimization | SK-ALGO-010, SK-ALGO-011 | AG-ALGO-005 |
| dp-transition-derivation | SK-ALGO-010, SK-ALGO-012 | AG-ALGO-005 |
| classic-dp-library | SK-ALGO-012 | AG-ALGO-005 |
| advanced-dp-techniques | SK-ALGO-011, SK-ALGO-012 | AG-ALGO-005 |

### Graph Algorithms
| Process | Recommended Skills | Recommended Agents |
|---------|-------------------|-------------------|
| graph-modeling | SK-ALGO-013, SK-ALGO-014 | AG-ALGO-006 |
| shortest-path-algorithms | SK-ALGO-013, SK-ALGO-014 | AG-ALGO-006 |
| graph-traversal | SK-ALGO-013, SK-ALGO-014 | AG-ALGO-006 |
| advanced-graph-algorithms | SK-ALGO-014, SK-ALGO-015, SK-ALGO-018 | AG-ALGO-006 |

### Optimization and Performance
| Process | Recommended Skills | Recommended Agents |
|---------|-------------------|-------------------|
| complexity-optimization | SK-ALGO-006, SK-ALGO-029 | AG-ALGO-011 |
| code-level-optimization | SK-ALGO-029, SK-ALGO-030 | AG-ALGO-011 |
| io-optimization | SK-ALGO-005, SK-ALGO-030 | - |
| memory-optimization | SK-ALGO-029, SK-ALGO-030 | - |

### String Algorithms
| Process | Recommended Skills | Recommended Agents |
|---------|-------------------|-------------------|
| pattern-matching-algorithms | SK-ALGO-019, SK-ALGO-020 | AG-ALGO-017 |
| trie-suffix-structures | SK-ALGO-019, SK-ALGO-020 | AG-ALGO-017 |
| string-processing | SK-ALGO-019, SK-ALGO-020 | AG-ALGO-017 |

### Number Theory
| Process | Recommended Skills | Recommended Agents |
|---------|-------------------|-------------------|
| number-theory-algorithms | SK-ALGO-021, SK-ALGO-022 | AG-ALGO-018 |
| prime-algorithms | SK-ALGO-021, SK-ALGO-022 | AG-ALGO-018 |
| combinatorics-counting | SK-ALGO-021, SK-ALGO-023 | AG-ALGO-018 |

### Interview Preparation
| Process | Recommended Skills | Recommended Agents |
|---------|-------------------|-------------------|
| faang-interview-prep | SK-ALGO-001, SK-ALGO-024, SK-ALGO-025 | AG-ALGO-008, AG-ALGO-009 |
| mock-coding-interview | SK-ALGO-024, SK-ALGO-025 | AG-ALGO-008, AG-ALGO-009 |
| system-design-interview | - | AG-ALGO-010 |
| behavioral-interview-prep | SK-ALGO-025 | AG-ALGO-009 |
| interview-problem-explanation | SK-ALGO-007, SK-ALGO-026 | AG-ALGO-009, AG-ALGO-015 |

### Advanced Topics
| Process | Recommended Skills | Recommended Agents |
|---------|-------------------|-------------------|
| segment-tree-implementation | SK-ALGO-017 | AG-ALGO-007 |
| fenwick-tree-implementation | SK-ALGO-017 | AG-ALGO-007 |
| range-query-optimization | SK-ALGO-017, SK-ALGO-018 | AG-ALGO-007 |
| computational-geometry | SK-ALGO-031, SK-ALGO-032 | AG-ALGO-016 |
| two-pointer-sliding-window | SK-ALGO-012 | AG-ALGO-004 |
| binary-search-applications | SK-ALGO-012 | AG-ALGO-004 |
| greedy-algorithm-design | - | AG-ALGO-004 |
| divide-conquer-design | - | AG-ALGO-004 |
| backtracking-pruning | SK-ALGO-008 | AG-ALGO-004 |

### Learning and Progress
| Process | Recommended Skills | Recommended Agents |
|---------|-------------------|-------------------|
| skill-gap-analysis | SK-ALGO-004 | AG-ALGO-014 |
| progress-tracking | SK-ALGO-002, SK-ALGO-004 | AG-ALGO-014 |
| topic-mastery-certification | SK-ALGO-004 | AG-ALGO-014 |

---

## Implementation Priority

### Phase 1 (High Priority)
1. SK-ALGO-001: leetcode-problem-fetcher
2. SK-ALGO-002: codeforces-api-client
3. SK-ALGO-006: complexity-analyzer
4. SK-ALGO-008: test-case-generator
5. SK-ALGO-012: dp-pattern-library
6. SK-ALGO-024: interview-problem-bank
7. AG-ALGO-001: competitive-programmer
8. AG-ALGO-005: dp-specialist
9. AG-ALGO-008: technical-interviewer
10. AG-ALGO-011: complexity-analyst

### Phase 2 (Medium Priority)
1. SK-ALGO-005: code-template-manager
2. SK-ALGO-010: dp-state-designer
3. SK-ALGO-013: graph-modeler
4. SK-ALGO-016: data-structure-selector
5. SK-ALGO-017: segment-tree-builder
6. SK-ALGO-021: number-theory-toolkit
7. SK-ALGO-025: interview-simulator
8. AG-ALGO-004: algorithm-designer
9. AG-ALGO-006: graph-specialist
10. AG-ALGO-007: data-structures-expert
11. AG-ALGO-009: interview-coach

### Phase 3 (Lower Priority)
1. SK-ALGO-007: algorithm-visualizer
2. SK-ALGO-011: dp-optimizer
3. SK-ALGO-019: string-algorithm-matcher
4. SK-ALGO-027: invariant-analyzer
5. SK-ALGO-031: geometry-primitive-library
6. AG-ALGO-014: progress-tracker
7. AG-ALGO-016: geometry-specialist
8. AG-ALGO-017: string-algorithm-specialist

---

## Next Steps

1. **Validate** this backlog with domain experts and competitive programmers
2. **Prioritize** based on process usage frequency and impact
3. **Prototype** high-priority skills (leetcode-problem-fetcher, codeforces-api-client)
4. **Implement** core agents (competitive-programmer, dp-specialist)
5. **Integrate** skills into existing process definitions
6. **Test** with real competitive programming workflows
7. **Iterate** based on user feedback and process performance
