Fibonacci Calculator

Problem Overview

The issue involves a coding problem or complex technical task described as "31". This may reference a specific function, algorithm, or logic that needs to be developed or debugged. However, further detail is required to provide a tailored solution.

Analysis

1. Code Examination:

   • As the specific code or problem statement is not provided in your request, the first step would typically involve a close examination of the existing code base to identify logical flaws, inefficiencies, or bugs.

2. Previous Attempts Review:

   • Gathering information on any previously attempted solutions or strategies could help pinpoint what approaches succeeded or failed, influencing the design of a new solution.

Proposed Solution Approach

Since the specific nature of the problem is not identified, I will outline a generic approach to a common coding issue—finding the 31st Fibonacci number. This is a fundamental problem in algorithm development that addresses both recursion and iteration for performance considerations.

Steps to Develop the Solution

1. Method Selection: Use an iterative approach for efficiency and simplicity over a recursive solution, which can lead to performance bottlenecks due to excessive calls.

2. Implementation: The following Python code snippet illustrates how to compute the 31st Fibonacci number.

Code Development

def fibonacci(n):
    """
    Computes the n-th Fibonacci number iteratively.

    Parameters:
    n (int): The index of the Fibonacci sequence.

    Returns:
    int: The n-th Fibonacci number.
    """
    if n < 0:
        raise ValueError("Input cannot be negative.")
    elif n == 0:
        return 0
    elif n == 1:
        return 1

    a, b = 0, 1  # Starting values for Fibonacci sequence
    for _ in range(2, n + 1):
        a, b = b, a + b  # Update the last two Fibonacci numbers

    return b  # b is now the n-th Fibonacci number

Code Explanation

• The function fibonacci(n) takes an integer n as input.
• It checks for valid input, ensuring n is non-negative.
• Iteratively computes the Fibonacci numbers up to the nth position using a for loop.
• Returns the value at the nth position which corresponds to the Fibonacci number.

Code Usage Example

To obtain the 31st Fibonacci number using the above function, you can execute the following code snippet:

if __name__ == "__main__":
    try:
        index = 31
        result = fibonacci(index)
        print(f"The 31st Fibonacci number is: {result}")
    except ValueError as e:
        print(e)

Execution Result

When this code is executed, the expected output will be:

The 31st Fibonacci number is: 1346269

Conclusion

This structured approach ensures efficiency in calculating Fibonacci numbers, particularly for larger indices without excessive computational resources. If the problem "31" refers to a different context, please provide additional details to refine the solution accordingly.

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