菜单
Automated Big-O complexity analysis of code and algorithms. Performs static analysis of loop structures, recursive call trees, space complexity estimation, and amortized analysis with detailed derivation documents.
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Reference for querying the Atlas knowledge graph through its MCP tools — the SECONDARY enrichment/comparison layer that adds best-practice context to systems you have ALREADY scanned from your real sources (`az`, repos, dirs). Use when you need to look up nodes, edges, kinds, clusters, stats, or wiki pages in Atlas to compare against your real inventory. (atlas graph, query atlas, atlas mcp, search the graph, graph neighbors, atlas record, atlas kinds, enrichment layer)
Atlas turns your STATED NEED into a real systems atlas by SCANNING your actual sources (Azure via `az`, git repos, local dirs) and process/data mining them, THEN enriching against the Atlas knowledge graph. Use this skill when asked to inventory/map your real systems, scan your cloud + repos + directories, mine the real processes or data they contain, or collect their real constraints/gotchas. (atlas, scan my systems, inventory our azure account, map my repos, real systems atlas, process mining, data mining, collect nuances, system discovery)
This skill should be used when the user asks to "find skills in the wild", "assimilate popular workflows", "discover SKILL.md files in repos", "research external skills", "find workflow patterns", "survey the skill landscape", "what skills exist out there", or wants to investigate public repositories for extractable processes, babysitter plugins, and reusable procedural insights. Searches GitHub for SKILL.md files, classifies repos by archetype, and maintains structured research under docs/reference-repos/.
基于 SOC 职业分类
| name | complexity-analyzer |
| description | Automated Big-O complexity analysis of code and algorithms. Performs static analysis of loop structures, recursive call trees, space complexity estimation, and amortized analysis with detailed derivation documents. |
| allowed-tools | Bash, Read, Write, Grep, Glob |
| metadata | {"author":"babysitter-sdk","version":"1.0","category":"algorithms-optimization","skill-id":"SK-ALGO-006","priority":"high"} |
| graph | {"domains":["domain:computer-science"],"specializations":["specialization:algorithms-optimization"],"skillAreas":["skill-area:dynamic-programming","skill-area:graph-algorithms","skill-area:mathematical-reasoning"],"roles":["role:backend-engineer","role:computational-scientist"]} |
A specialized skill for automated analysis of algorithm time and space complexity, providing Big-O notation analysis, detailed derivations, and optimization recommendations.
Analyze code and algorithms to determine:
Static Analysis
Complexity Types
Output Formats
AST MCP Server - Advanced code structure analysis:
# Provides AST parsing and complexity analysis
npm install -g @angrysky56/ast-mcp-server
Code Analysis MCP - Natural language code exploration:
# Deep code understanding with data flow analysis
npm install -g code-analysis-mcp
# Analyze a Python function
complexity-analyzer analyze --file solution.py --function two_sum
# Analyze C++ code with detailed derivation
complexity-analyzer analyze --file solution.cpp --verbose
# Compare multiple implementations
complexity-analyzer compare --files impl1.py impl2.py impl3.py
Input Code:
def find_pairs(arr, target):
n = len(arr)
result = []
for i in range(n): # O(n)
for j in range(i+1, n): # O(n-i) iterations
if arr[i] + arr[j] == target:
result.append((i, j))
return result
Analysis Output:
Time Complexity: O(n^2)
- Outer loop: n iterations
- Inner loop: (n-1) + (n-2) + ... + 1 = n(n-1)/2 iterations
- Total: O(n^2)
Space Complexity: O(k) where k = number of pairs found
- result array grows with matches
- Worst case: O(n^2) if all pairs match
Optimization Suggestion:
- Use hash table for O(n) time complexity
- Trade space for time: O(n) space
{
"analysis": {
"function": "string",
"language": "string",
"timeComplexity": {
"notation": "O(n^2)",
"bestCase": "O(1)",
"averageCase": "O(n^2)",
"worstCase": "O(n^2)",
"derivation": [
"Step 1: Outer loop runs n times",
"Step 2: Inner loop runs (n-1), (n-2), ..., 1 times",
"Step 3: Total = sum from 1 to n-1 = n(n-1)/2",
"Step 4: Simplify to O(n^2)"
]
},
"spaceComplexity": {
"notation": "O(n)",
"auxiliary": "O(n)",
"total": "O(n)",
"breakdown": {
"input": "O(n) - input array",
"result": "O(k) - output pairs",
"variables": "O(1) - loop counters"
}
},
"recommendations": [
{
"type": "optimization",
"description": "Use hash table approach",
"newComplexity": "O(n) time, O(n) space",
"tradeoff": "Space for time"
}
]
},
"metadata": {
"analyzedAt": "ISO8601 timestamp",
"confidence": "high|medium|low"
}
}
| Pattern | Complexity | Example |
|---|---|---|
| Single loop | O(n) | for i in range(n) |
| Nested independent | O(n*m) | for i in n: for j in m |
| Nested dependent | O(n^2) | for i in n: for j in range(i) |
| Logarithmic | O(log n) | while n > 0: n //= 2 |
| Nested log | O(n log n) | for i in n: j=1; while j<n: j*=2 |
| Pattern | Recurrence | Complexity |
|---|---|---|
| Linear | T(n) = T(n-1) + O(1) | O(n) |
| Binary | T(n) = T(n/2) + O(1) | O(log n) |
| Divide & Conquer | T(n) = 2T(n/2) + O(n) | O(n log n) |
| Exponential | T(n) = 2T(n-1) + O(1) | O(2^n) |
For recurrence T(n) = aT(n/b) + f(n):
| Case | Condition | Complexity |
|---|---|---|
| 1 | f(n) = O(n^c) where c < log_b(a) | O(n^(log_b(a))) |
| 2 | f(n) = O(n^c) where c = log_b(a) | O(n^c log n) |
| 3 | f(n) = O(n^c) where c > log_b(a) | O(f(n)) |
This skill enhances:
complexity-optimization - Identify and fix complexity bottlenecksleetcode-problem-solving - Verify solution complexityalgorithm-implementation - Validate implementation efficiencycode-review - Complexity-focused code review| Complexity | Name | Example |
|---|---|---|
| O(1) | Constant | Array access, hash lookup |
| O(log n) | Logarithmic | Binary search |
| O(n) | Linear | Array traversal |
| O(n log n) | Linearithmic | Merge sort, heap sort |
| O(n^2) | Quadratic | Nested loops, bubble sort |
| O(n^3) | Cubic | Matrix multiplication (naive) |
| O(2^n) | Exponential | Subsets, recursive fibonacci |
| O(n!) | Factorial | Permutations |
| Error | Cause | Resolution |
|---|---|---|
PARSE_ERROR | Invalid syntax | Check code syntax |
UNSUPPORTED_CONSTRUCT | Complex control flow | Simplify or annotate |
RECURSIVE_DEPTH | Deep recursion | Provide base case hints |
AMBIGUOUS_BOUNDS | Dynamic loop bounds | Annotate with constraints |