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 T (1 ≤ T ≤ 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 s integers, each integer wi (1 ≤ wi ≤ 1000).
### Example 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
```
### Function Signature:
Write a function f(inputs) that takes in the input.
def f(inputs: List[Tuple[float, int, List[int]]]):
'''
inputs: a list of tuples, each containing a decimal fraction, an integer, and a list of integers
'''
Test Case Generator
Sure, I can help you write a test case generator for the problem "Mobile Computing." Here is a Python script that generates random test cases for this problem:
```python
import random
def generate_test_case():
# Number of datasets (randomly chosen between 1 to 5 for simplicity)
num_datasets = random.randint(1, 5)
test_cases = []
for _ in range(num_datasets):
# Room width (random float between 0 and 10)
r = round(random.uniform(0.00001, 9.99999), 5) # using 5 decimal places for precision
# Number of stones (between 1 and 6)
s = random.randint(1, 6)
# Weights of the stones (between 1 and 1000)
weights = [random.randint(1, 1000) for _ in range(s)]
test_cases.append((r, s, weights))
return num_datasets, test_cases
def format_test_case(num_datasets, test_cases):
result = [str(num_datasets)]
for r, s, weights in test_cases:
result.append(f"{r}")
result.append(f"{s}")
result.extend(map(str, weights))
return "\n".join(result)
def tcgen():
num_datasets, test_cases = generate_test_case()
return format_test_case(num_datasets, test_cases)
# Example of generating a test case
print(tcgen())
```
### Explanation:
1. **generate_test_case Function**:
- Generates the number of datasets (`num_datasets`), which is a random integer between 1 and 5.
- For each dataset:
- Generates a random room width `r` as a float between 0.00001 and 9.99999, rounded to 5 decimal places.
- Generates a random number of stones `s` between 1 and 6.
- Generates a list of stone weights, each a random integer between 1 and 1000.
2. **format_test_case Function**:
- Formats the generated test cases into the required input format for the problem statement.
- Combines all the parts into a single string suitable for competitive programming input.
3. **tcgen Function**:
- Calls the above functions to generate and format the test cases, then simply prints the result.
You can run this script to get a random test case each time. It ensures the test cases conform to the constraints specified in 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
# if __name__ == "__main__":
# input_path = sys.argv[1]
# with open(input_path, 'r') as fh:
# inputs = extract_arguments(fh)
# f(inputs)