Problem p00840 - Generation 1

Orig Description

Problem E: Mobile Computing
There is a mysterious planet called Yaen, whose space is 2-dimensional. There are many beautiful
stones on the planet, and the Yaen people love to collect them. They bring the stones back home
and make nice mobile arts of them to decorate their 2-dimensional living rooms.
In their 2-dimensional world, a mobile is defined recursively as follows:
  a stone hung by a string, or
 a rod of length 1 with two sub-mobiles at both ends; the rod
  is hung by a string at the center of gravity of sub-mobiles.
  When the weights of the sub-mobiles are n and m, and their
  distances from the center of gravity are a and b respectively,
  the equation n × a = m × b holds.
For example, if you got three stones with weights 1, 1, and 2, here are some possible mobiles
and their widths:
Given the weights of stones and the width of the room, your task is to design the widest possible
mobile satisfying both of the following conditions.
 It uses all the stones.
 Its width is less than the width of the room.
You should ignore the widths of stones.
In some cases two sub-mobiles hung from both ends of a rod might
overlap (see the figure on the below). Such mobiles are acceptable.
The width of the example is (1/3) + 1 + (1/4).
Input
The first line of the input gives the number of datasets. Then the specified number of datasets
follow. A dataset has the following format.
      r
      s
      w1
       .
       .
       .
      ws
r is a decimal fraction representing the width of the room, which satisfies 0 < r < 10. s is the
number of the stones. You may assume 1 ≤ s ≤ 6. wi is the weight of the i-th stone, which is
an integer. You may assume 1 ≤ wi ≤ 1000.
You can assume that no mobiles whose widths are between r - 0.00001 and r + 0.00001 can be made of given stones.
Output
For each dataset in the input, one line containing a decimal fraction should be output. The
decimal fraction should give the width of the widest possible mobile as defined above. An
output line should not contain extra characters such as spaces.
In case there is no mobile which satisfies the requirement, answer -1 instead.
The answer should not have an error greater than 0.00000001. You may output any number of
digits after the decimal point, provided that the above accuracy condition is satisfied.
Sample Input
5
1.3
3
1
2
1
1.4
3
1
2
1
2.0
3
1
2
1
1.59
4
2
1
1
3
1.7143
4
1
2
3
5
Output for the Sample Input
-1
1.3333333333333335
1.6666666666666667
1.5833333333333335
1.7142857142857142

Extracted Specification

An integer D (1 ≤ D ≤ 100), representing the number of datasets.
For each dataset:
- A decimal fraction r (0 < r < 10).
- An integer s (1 ≤ s ≤ 6).
- A list of integers w of size s, where each integer is between 1 and 1000.

### Example Input:

```
2
1.3
3
1
2
1
1.4
3
1
2
1
```

### Function Signature:
Write a function f(inputs) that takes in the input.
```python
def f(inputs: List[Tuple[float, int, List[int]]]):
    '''
    inputs: a list of tuples, where each tuple contains:
        - a float (the decimal fraction)
        - an integer (the number of elements in the list)
        - a list of integers
    '''
```

Test Case Generator

Sure! Here is a Python test case generator for the given problem statement "Mobile Computing":

```python
import random

def tcgen():
    # Generate a random number of datasets (1 ≤ D ≤ 100)
    D = random.randint(1, 100)
    
    datasets = []
    
    for _ in range(D):
        # Generate a random width of the room, r (0 < r < 10)
        r = round(random.uniform(0.00001, 9.99999), 8)
        
        # Generate a random number of stones, s (1 ≤ s ≤ 6)
        s = random.randint(1, 6)
        
        # Generate random weights for the stones, 1 ≤ wi ≤ 1000
        weights = [random.randint(1, 1000) for _ in range(s)]
        
        datasets.append((r, s, weights))
    
    return D, datasets

# Example usage
if __name__ == "__main__":
    D, datasets = tcgen()
    print(D)
    for r, s, weights in datasets:
        print(r)
        print(s)
        for weight in weights:
            print(weight)
```

Explanation:
1. **Number of Datasets**: We generate a random integer \(D\) between 1 and 100, inclusive, representing the number of datasets.
2. **Width of the Room \(r\)**: For each dataset, we generate a random decimal number \(r\) (0 < \(r\) < 10) with up to 8 decimal places.
3. **Number of Stones \(s\)**: For each dataset, a random integer \(s\) between 1 and 6, inclusive, representing the number of stones.
4. **Weights of Stones**: For the given number of stones \(s\), we generate a list of \(s\) random integers between 1 and 1000, inclusive, representing the weights of the stones.

The `tcgen` function returns the number of datasets and a list of datasets, where each dataset is a tuple containing the width of the room, the number of stones, and the list of weights for the stones.

The example usage at the bottom prints the generated test cases in the format specified by the problem statement.

Extract Arguments

def extract_arguments(fh):
    num_datasets = int(fh.readline().strip())
    datasets = []
    for _ in range(num_datasets):
        r = float(fh.readline().strip())
        s = int(fh.readline().strip())
        weights = [int(fh.readline().strip()) for _ in range(s)]
        datasets.append((r, s, weights))
    return datasets