Advanced prompting techniques for complex coding tasks

Implement a TypeScript function to find the longest increasing subsequence in an array.

Think through this problem step by step:
1. First, define what we're looking for precisely
2. Consider the naive approach and its limitations
3. Develop a dynamic programming solution
4. Analyze the time and space complexity
5. Implement the optimized solution with appropriate comments

Then write the final solution with full TypeScript typing.

I need to implement a caching layer for our API service that handles user authentication.

Before writing any code, let's step back and consider:
1. What are the key requirements for a caching system in an authentication context?
2. What are the security implications we need to address?
3. What caching strategies would be appropriate for different types of authentication data?
4. How should we handle cache invalidation when credentials change?
5. What are the performance vs. consistency tradeoffs of different approaches?

After analyzing these aspects, recommend an architectural approach and then implement 
a TypeScript class that provides this caching functionality.

Create a Python FastAPI application for a book management system.

The API should conform to this JSON schema for book objects:

{
  "type": "object",
  "properties": {
    "id": {
      "type": "string",
      "format": "uuid",
      "description": "Unique identifier for the book"
    },
    "title": {
      "type": "string",
      "minLength": 1,
      "maxLength": 100
    },
    "author": {
      "type": "object",
      "properties": {
        "name": { "type": "string" },
        "biography": { "type": "string", "nullable": true }
      },
      "required": ["name"]
    },
    "publication_year": {
      "type": "integer",
      "minimum": 1000,
      "maximum": 2100
    },
    "genres": {
      "type": "array",
      "items": { "type": "string" },
      "minItems": 1
    },
    "available_copies": {
      "type": "integer",
      "minimum": 0
    }
  },
  "required": ["title", "author", "publication_year", "genres"]
}

Implement the complete API with endpoints for CRUD operations, proper validation, error handling, and data persistence using SQLAlchemy.

Implement an efficient Python function to detect cycles in a directed graph.

Generate three different approaches to solving this problem:
1. A solution using depth-first search
2. A solution using Tarjan's algorithm
3. A solution using topological sorting

For each approach, explain its:
- Time and space complexity
- Key advantages
- Potential limitations

Then, recommend which approach is best for a graph with approximately 10,000 nodes and 50,000 edges, and implement that solution with full type annotations and documentation.

We need to build a TypeScript library for handling complex form validation with 
nested fields, async validation rules, and dependency tracking between fields.

Let's approach this in stages:

Stage 1: First, design the core interfaces for the validation library without 
implementation. Focus on how developers would use this API and what types they 
would interact with.

[After reviewing the interfaces]

Stage 2: Implement the core validation engine that can process validation rules 
and track field validity state.

[After reviewing the core implementation]

Stage 3: Add support for field dependencies where validating one field requires 
values from other fields.

[After reviewing dependencies implementation]

Stage 4: Implement asynchronous validation support with proper loading states 
and error handling.

Create a Python data pipeline for processing time series sensor data with anomaly detection.

Technical Requirements:
- Input: CSV files with timestamp, sensor_id, and multiple reading columns
- Output: Processed data in Parquet format with anomalies flagged
- Performance: Must process 50GB of data in under 30 minutes on standard hardware
- Deployment: Must work within an Apache Airflow environment

Functional Description:
The system monitors industrial equipment through multiple sensors. Each sensor 
generates readings every 5 seconds. We need to identify anomalies that might indicate equipment failure, specifically looking for:

1. Sudden spikes or drops in readings
2. Gradual drift beyond acceptable thresholds
3. Unusual patterns compared to historical data for similar time periods
4. Correlation anomalies between related sensors

Implementation Guidance:
- Use pandas for initial data loading but switch to Dask for processing at scale
- Implement statistical anomaly detection using robust algorithms suitable for time series
- Include proper logging and error handling
- Design the pipeline to be fault-tolerant and resumable
- Structure the code to make adding new anomaly detection algorithms easy in the future

Start by defining the core data structures and pipeline architecture, then implement the main processing components.

Let's build a TypeScript state management library similar to Redux but with improved TypeScript type safety and less boilerplate.

First iteration: Design the core types and basic store implementation with actions and reducers.

[Review the first output and then continue]

Great, now let's address these issues:
1. The type inference could be improved for action creators
2. We need better handling of async actions
3. Add support for middleware with proper typing

[Review the second iteration and continue]

Now let's enhance it with:
1. Add selector functions with memoization
2. Implement proper devtools integration
3. Create a React hook API for consuming the store

[Final review]

Finally, create a complete example using this library to manage a simple application state,
demonstrating all the features we've implemented.