Problem p01468 - Generation 1

Orig Description

Problem Statement
You are given $N$ line segments $s_1, s_2, ..., s_N$. Find the minimum value of dist$(s_i, s_j)$, for $1 \leq i,j \leq N, i \ne j$.
Here, dist$(s_i, s_j)$ is defined as
$\sqrt{(x_i-x_j)^2 + (y_i-y_j)^2}$, where $(x_i,y_i)$ is a point on $s_i$ and $(x_j,y_j)$ is a point on $s_j$
Below is an illustration of the Sample Input dataset.
Input
The input is in the following format. All given numbers are integers.
N
x_{1,1} y_{1,1} x_{1,2} y_{1,2}
x_{2,1} y_{2,1} x_{2,2} y_{2,2}
...
x_{N,1} y_{N,1} x_{N,2} y_{N,2}
Each $s_i$ is a line segment with endpoints $(x_{i,1}, y_{i,1})$ and $(x_{i,2}, y_{i,2})$.
Constraints
$2 \leq N \leq 10^5$
$0 \leq x_{i,j}, y_{i,j} \leq 100$
$(x_{i,1}, y_{i,1}) \neq (x_{i,2}, y_{i,2})$
Output
Print the minimum value in one line. The output value must not contain an error greater than $10^{-5}$.
Sample Input 1
4
2 0 2 25
0 30 15 20
16 20 5 15
23 0 23 30
Output for the Sample Input 1
0.41380294
Sample Input 2
6
0 0 0 5
1 3 3 5
6 0 6 10
7 4 10 4
11 1 11 3
7 0 10 0
Output for the Sample Input 2
1.00000000
Sample Input 3
6
5 5 5 45
7 45 19 45
7 30 19 30
21 34 21 44
26 45 36 28
45 45 26 5
Output for the Sample Input 3
0.83553169
Sample Input 4
11
10 10 10 90
10 90 35 90
10 60 35 60
35 60 35 90
40 10 40 90
37 45 60 45
60 10 60 45
65 10 65 90
65 90 90 90
65 60 90 65
90 60 90 90
Output for the Sample Input 4
0.00000000

Extracted Specification

Canonicalized Input Description:

An integer N (2 ≤ N ≤ 10^5), representing some quantity or size.
N tuples of integers (a, b, c, d) where 0 ≤ a, b, c, d ≤ 100 and (a, b) ≠ (c, d).

### Example Input:

```
4
2 0 2 25
0 30 15 20
16 20 5 15
23 0 23 30
```

### Function Signature:
Write a function f(N, segments) that takes in the input. 
```python
def f(N: int, segments: List[Tuple[int, int, int, int]]):
    '''
    N: an integer
    segments: a list of tuples, each containing four integers
    '''
```

Test Case Generator

Sure, I can help you create a test case generator for the given problem. Below is a Python function that generates random test cases according to the problem constraints:

```python
import random

def generate_random_point():
    """Generate a random point within the given constraints."""
    return (random.randint(0, 100), random.randint(0, 100))

def generate_random_line_segment():
    """Generate a random line segment ensuring the endpoints are distinct."""
    while True:
        p1 = generate_random_point()
        p2 = generate_random_point()
        if p1 != p2:
            return p1, p2

def tcgen():
    """Generate a test case for the line segment distance problem."""
    N = random.randint(2, 10**5)  # Number of line segments

    segments = []
    for _ in range(N):
        (x1, y1), (x2, y2) = generate_random_line_segment()
        segments.append((x1, y1, x2, y2))

    return N, segments

def format_test_case(N, segments):
    """Format the test case in the required input format."""
    result = [str(N)]
    for (x1, y1, x2, y2) in segments:
        result.append(f"{x1} {y1} {x2} {y2}")
    return "\n".join(result)

# Example usage
N, segments = tcgen()
formatted_test_case = format_test_case(N, segments)
print(formatted_test_case)
```

### Explanation:

1. **generate_random_point**: Generates a random point \((x, y)\) within the range [0, 100].
2. **generate_random_line_segment**: Generates a random line segment with two distinct endpoints.
3. **tcgen**: Generates a random test case with \(N\) line segments.
4. **format_test_case**: Formats the generated test case into the required input format.

### Example Output:
Running this code will produce output similar to this (the actual values will be random):

```
4
2 0 2 25
0 30 15 20
16 20 5 15
23 0 23 30
```

This approach ensures that all generated test cases comply with the given constraints and are formatted correctly for use in competitive programming challenges.

Extract Arguments

def extract_arguments(fh):
    N = int(fh.readline().strip())
    segments = []
    for _ in range(N):
        x1, y1, x2, y2 = map(int, fh.readline().strip().split())
        segments.append(((x1, y1), (x2, y2)))
    return N, segments