Orig Description
Score: 300 points
Problem Statement
Consider an analog clock whose hour and minute hands are A and B centimeters long, respectively.
An endpoint of the hour hand and an endpoint of the minute hand are fixed at the same point, around which each hand rotates clockwise at constant angular velocity. It takes the hour and minute hands 12 hours and 1 hour to make one full rotation, respectively.
At 0 o'clock, the two hands overlap each other. H hours and M minutes later, what is the distance in centimeters between the unfixed endpoints of the hands?
Constraints
All values in input are integers.
1 \leq A, B \leq 1000
0 \leq H \leq 11
0 \leq M \leq 59
Input
Input is given from Standard Input in the following format:
A B H M
Output
Print the answer without units. Your output will be accepted when its absolute or relative error from the correct value is at most 10^{-9}.
Sample Input 13 4 9 0
Sample Output 15.00000000000000000000
The two hands will be in the positions shown in the figure below, so the answer is 5 centimeters.
Sample Input 23 4 10 40
Sample Output 24.56425719433005567605
The two hands will be in the positions shown in the figure below. Note that each hand always rotates at constant angular velocity.
Extracted Specification
An integer A (1 ≤ A ≤ 1000).
An integer B (1 ≤ B ≤ 1000).
An integer H (0 ≤ H ≤ 11).
An integer M (0 ≤ M ≤ 59).
### Example Input:
```
13 4 9 0
```
### Function Signature:
Write a function f(A, B, H, M) that takes in the input.
def f(A: int, B: int, H: int, M: int):
'''
A: an integer
B: an integer
H: an integer
M: an integer
'''
Test Case Generator
Certainly! Below is a test case generator for the given problem statement. This generator will create random values for \(A\), \(B\), \(H\), and \(M\) according to the constraints specified.
```python
import random
def tcgen():
A = random.randint(1, 1000)
B = random.randint(1, 1000)
H = random.randint(0, 11)
M = random.randint(0, 59)
return A, B, H, M
# Example of generating a test case
if __name__ == "__main__":
A, B, H, M = tcgen()
print(f"{A} {B} {H} {M}")
```
### Explanation:
- `A` and `B` are generated randomly between 1 and 1000 inclusive, representing the lengths of the hour and minute hands, respectively.
- `H` is generated randomly between 0 and 11 inclusive, representing the hour on the clock.
- `M` is generated randomly between 0 and 59 inclusive, representing the minutes on the clock.
### Example Output:
Running the generator might give you output like:
```
715 932 4 37
```
You can use this output as an input for your program to test its correctness. Each time you run the generator, it will produce different values, giving you a wide variety of test cases.
Extract Arguments
def extract_arguments(fh):
A, B, H, M = map(int, fh.readline().strip().split())
return A, B, H, M