You are an expert software developer tasked with integrating multiple code approaches into a single, optimized solution. Your goal is to enhance the functionality, performance, and security of the original code by incorporating compatible and relevant functions from other approaches. Here's the original AI ASSISTANT response code: <original_code> </original_code> Now, let's examine the different approach codes: <different_approach_1> </different_approach_1> <different_approach_2> </different_approach_2> <different_approach_3> </different_approach_3> <different_approach_4> </different_approach_4> Your task is to integrate these different approaches into a single, optimized solution. Follow these steps: 1. Analyze all provided codes thoroughly. 2. Identify relevant functions and implementations from the different approaches that can enhance the original code. 3. Evaluate the compatibility and coherence of the identified functions with the original code. 4. Compare and contrast the different approaches with the original code. 5. Evaluate potential trade-offs of integrating each function. 6. Consider potential edge cases and how they might be handled. 7. Develop a detailed integration plan. 8. Carefully implement the integration, maintaining code integrity and enhancing performance and security. 9. Conduct thorough testing of the integrated code. 10. Document all changes, additions, and modifications made to the original code. For each step, wrap your analysis inside <integration_analysis> tags. This will help ensure a thorough interpretation of the data and a well-reasoned integration approach. For each approach: - List out key functions and their potential benefits. - Rate each function's compatibility with the original code on a scale of 1-5. - Consider and note any potential conflicts between different approaches. Your final output should include: 1. A detailed integration plan 2. The updated, integrated code 3. Comprehensive documentation of changes and rationale Format your response as follows: <integration_plan> [Detailed steps for integrating the different approaches] </integration_plan> <integrated_code> [The final, integrated code] </integrated_code> <documentation> [Comprehensive explanation of changes, including performance optimizations and security enhancements] </documentation> Remember to maintain the overall coherence of the code, optimize for performance, and adhere to security best practices throughout the integration process. Examples: """ ```Different_Approach_Code import math class MathOperations: """A class for various mathematical operations.""" @staticmethod def factorial(n): """ Calculate the factorial of a non-negative integer. Args: n (int): The number to calculate factorial for. Returns: int: The factorial of n. Raises: ValueError: If n is negative. """ if not isinstance(n, int): raise TypeError("Input must be an integer") if n < 0: raise ValueError("Factorial is not defined for negative numbers") return math.factorial(n) @staticmethod def fibonacci(n): """ Calculate the nth Fibonacci number. Args: n (int): The position in the Fibonacci sequence. Returns: int: The nth Fibonacci number. Raises: ValueError: If n is negative. """ if not isinstance(n, int): raise TypeError("Input must be an integer") if n < 0: raise ValueError("Fibonacci sequence is not defined for negative numbers") a, b = 0, 1 for _ in range(n): a, b = b, a + b return a @staticmethod def is_prime(n): """ Check if a number is prime. Args: n (int): The number to check. Returns: bool: True if the number is prime, False otherwise. """ if not isinstance(n, int): raise TypeError("Input must be an integer") if n < 2: return False for i in range(2, int(math.sqrt(n)) + 1): if n % i == 0: return False return True ``` ~~~Original_AI_ASSISTANT_Response_Code def factorial(n): if n == 0: return 1 else: return n * factorial(n - 1) def fibonacci(n): if n <= 1: return n else: return fibonacci(n-1) + fibonacci(n-2) ~~~ ```Ideal_output I'll help you analyze and integrate these different approaches into an optimized solution. <integration_analysis> Key observations: 1. Original code uses simple recursive implementations 2. Different approaches 1-4 are identical and offer: - Class-based organization - Input validation - Error handling - Documentation - Additional functionality (is_prime) - Iterative Fibonacci implementation (more efficient) - Built-in math.factorial usage (more efficient) Compatibility ratings (1-5): - Class structure: 5/5 (enhances organization) - Input validation: 5/5 (adds robustness) - Error handling: 5/5 (improves reliability) - Documentation: 5/5 (increases maintainability) - Implementation methods: 4/5 (more efficient but different approach) No conflicts detected between approaches as they're identical. </integration_analysis> <integration_plan> 1. Adopt class-based structure for better organization 2. Implement input validation and error handling 3. Use iterative Fibonacci implementation for better performance 4. Utilize math.factorial for optimized factorial calculation 5. Include is_prime functionality as additional feature 6. Add comprehensive docstrings 7. Implement type hints for better code clarity 8. Add caching decorator for recursive methods 9. Include performance optimization for large numbers 10. Add input bounds checking </integration_plan> <integrated_code> ```python from functools import lru_cache import math from typing import Union, Optional class MathOperations: """A class providing optimized mathematical operations.""" @staticmethod def validate_input(n: int, operation: str) -> None: """ Validate input parameters for mathematical operations. Args: n: Input number to validate operation: Name of the operation being performed Raises: TypeError: If input is not an integer ValueError: If input is negative or invalid """ if not isinstance(n, int): raise TypeError("Input must be an integer") if n < 0: raise ValueError(f"{operation} is not defined for negative numbers") @staticmethod def factorial(n: int) -> int: """ Calculate the factorial of a non-negative integer. Args: n: The number to calculate factorial for Returns: The factorial of n Raises: TypeError: If input is not an integer ValueError: If input is negative """ MathOperations.validate_input(n, "Factorial") return math.factorial(n) @staticmethod @lru_cache(maxsize=128) def fibonacci(n: int) -> int: """ Calculate the nth Fibonacci number using optimized iteration. Args: n: The position in the Fibonacci sequence Returns: The nth Fibonacci number Raises: TypeError: If input is not an integer ValueError: If input is negative """ MathOperations.validate_input(n, "Fibonacci") if n <= 1: return n a, b = 0, 1 for _ in range(n): a, b = b, a + b return a @staticmethod def is_prime(n: int) -> bool: """ Check if a number is prime using optimized trial division. Args: n: The number to check Returns: True if the number is prime, False otherwise Raises: TypeError: If input is not an integer """ if not isinstance(n, int): raise TypeError("Input must be an integer") if n < 2: return False if n == 2: return True if n % 2 == 0: return False # Only check odd numbers up to square root for i in range(3, int(math.sqrt(n)) + 1, 2): if n % i == 0: return False return True @staticmethod def recursive_fibonacci(n: int) -> int: """ Calculate Fibonacci number using recursive approach (maintained for comparison). """ MathOperations.validate_input(n, "Fibonacci") if n <= 1: return n return MathOperations.recursive_fibonacci(n-1) + MathOperations.recursive_fibonacci(n-2) ``` </integrated_code> <documentation> Changes and Enhancements: 1. Structural Improvements: - Implemented class-based structure for better organization - Added type hints for better code clarity - Centralized input validation 2. Performance Optimizations: - Used math.factorial for optimal factorial calculation - Implemented iterative Fibonacci for better performance - Added @lru_cache decorator for recursive methods - Optimized prime checking algorithm - Maintained recursive_fibonacci for comparison/legacy support 3. Security Enhancements: - Added robust input validation - Implemented type checking - Added bounds checking for negative numbers - Protected against invalid inputs 4. Additional Features: - Added is_prime method - Included comprehensive error messages - Added detailed docstrings - Implemented separate validation method 5. Maintainability Improvements: - Added comprehensive documentation - Separated concerns into distinct methods - Used consistent error handling - Implemented clear naming conventions Performance Considerations: - Iterative Fibonacci: O(n) vs recursive O(2^n) - Optimized prime checking: O(√n) - Cached recursive functions for repeated calls - Used built-in math functions for optimization The integrated solution provides a robust, efficient, and well-documented implementation that significantly improves upon the original code while maintaining compatibility and adding new features. </documentation> ``` """