Problem p02400 - Generation 1

Orig Description

Circle
Write a program which calculates the area and circumference of a circle for given radius r.
Input
A real number r is given.
Output
Print the area and circumference of the circle in a line. Put a single space between them. The output should not contain an absolute error greater than 10-5.
Constraints
 0 < r < 10000
Sample Input 1
2
Sample Output 1
12.566371 12.566371
Sample Input 2
3
Sample Output 2
28.274334 18.849556

Extracted Specification

Canonicalized Input Description: 

A real number r (0 < r < 10000).

### Example Input:

```
2
```

### Function Signature:
Write a function f(r) that takes in the input. 
def f(r: float): 
    ''' 
    r: a real number
    '''

Test Case Generator

Sure! Here is a test case generator for the given problem statement that calculates the area and circumference of a circle for a given radius \( r \).

```python
import random
import math

def tcgen():
    # Generate a random real number r in the range (0, 10000)
    r = random.uniform(1e-5, 9999.99999)
    
    # Calculate the area and circumference
    area = math.pi * r * r
    circumference = 2 * math.pi * r
    
    # Return the generated test case and the expected output
    return r, f"{area:.6f} {circumference:.6f}"

# Example of generating a test case
r, output = tcgen()
print(f"Generated Test Case: r = {r}")
print(f"Expected Output: {output}")
```

### Explanation:

1. **Generating \( r \)**: 
    - We use `random.uniform(1e-5, 9999.99999)` to generate a random floating-point number \( r \) in the range (0, 10000). This ensures that \( r \) is always greater than 0 and less than 10000.
    - The lower bound `1e-5` is used to avoid generating an \( r \) that is too close to 0, which might make the area and circumference calculations trivial.

2. **Calculating the Area and Circumference**:
    - The area of the circle is calculated using the formula \( \text{area} = \pi r^2 \).
    - The circumference of the circle is calculated using the formula \( \text{circumference} = 2 \pi r \).

3. **Formatting the Output**:
    - We format the area and circumference to six decimal places using the format string `"{:.6f}"`, ensuring the output meets the precision requirement.

4. **Returning the Test Case and Expected Output**:
    - The function returns the generated radius \( r \) and the formatted expected output as a string.

5. **Example Usage**:
    - The example usage shows how to generate a test case and print the generated radius and expected output.

You can use this function to generate multiple test cases for your problem.

Extract Arguments

def extract_arguments(fh):
    r = float(fh.readline().strip())
    return r