Orig Description
Problem F: Ben Toh
As usual, those who called wolves get together on 8 p.m. at the supermarket. The thing they want is only one, a box lunch that is labeled half price. Scrambling for a few discounted box lunch, they fiercely fight every day. And those who are blessed by hunger and appetite the best can acquire the box lunch, while others have to have cup ramen or something with tear in their eyes.
A senior high school student, Sato, is one of wolves. A dormitry he lives doesn't serve a dinner, and his parents don't send so much money. Therefore he absolutely acquire the half-priced box lunch and save his money. Otherwise he have to give up comic books and video games, or begin part-time job.
Since Sato is an excellent wolf, he can acquire the discounted box lunch in 100% probability on the first day. But on the next day, many other wolves cooperate to block him and the probability to get a box lunch will be 50%. Even though he can get, the probability to get will be 25% on the next day of the day. Likewise, if he gets a box lunch on a certain day, the probability to get on the next day will be half. Once he failed to get a box lunch, probability to get would be back to 100%.
He continue to go to supermaket and try to get the discounted box lunch for n days. Please write a program to computes the expected value of the number of the discounted box lunches he can acquire.
Input
Input consists of several datasets.
Input for a single dataset is given as a single integer n.
Input terminates with a dataset where n = 0.
Output
For each dataset, write a line that contains an expected value. You may print any number of digits after the decimal point. Answers that have an error less than 1.0e-2 will be accepted.
Constraints
1 ≤ n ≤ 100,000
Sample Input
1
2
3
0
Output for the Sample Input
1.00000000
1.50000000
2.12500000
Extracted Specification
An integer \( n \) (1 ≤ \( n \) ≤ 100,000). The input terminates with a dataset where \( n = 0 \).
### Example Input:
```
1
2
3
0
```
### Function Signature:
Write a function `f(inputs)` that takes in the input.
def f(inputs: List[int]):
'''
inputs: a list of integers
'''
Test Case Generator
To generate test cases for Problem F, we need to create random datasets adhering to the constraints specified in the problem statement. Here is a test case generator function for the problem:
```python
import random
def tcgen():
# Generate a random number of datasets
num_datasets = random.randint(1, 100) # Let's decide to generate between 1 and 100 datasets
datasets = []
for _ in range(num_datasets):
# Generate a single dataset with random n
n = random.randint(1, 100000)
datasets.append(n)
# Append the terminating dataset
datasets.append(0)
return datasets
# Example usage:
if __name__ == "__main__":
test_cases = tcgen()
for case in test_cases:
print(case)
```
### Explanation
1. **Number of Datasets:** We randomly select the number of datasets to generate (between 1 and 100 datasets in this example).
2. **Generating Each Dataset:** For each dataset, we generate a random integer \( n \) within the specified constraint \( 1 \leq n \leq 100,000 \).
3. **Termination:** After generating the datasets, we append a terminating dataset where \( n = 0 \).
4. **Output:** The function returns a list of datasets including the terminating dataset. In the example usage, we print each dataset.
This function ensures that the generated test cases are within the constraints and include the necessary terminating condition.
Extract Arguments
def extract_arguments(fh):
inputs = []
while True:
n = int(fh.readline().strip())
if n == 0:
break
inputs.append((n,))
return inputs