Problem p01468 - Generation 3

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

An integer N (2 ≤ N ≤ 10^5), representing some quantity or size.
A list of N tuples, where each tuple contains four integers: (x1, y1, x2, y2). Each integer is between 0 and 100. For every tuple, (x1, y1) is not equal to (x2, y2).

### 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, where each tuple contains four integers
    '''
```

Test Case Generator

Sure! Below is a test case generator for the given problem statement:

```python
import random

def generate_line_segment():
    while True:
        x1 = random.randint(0, 100)
        y1 = random.randint(0, 100)
        x2 = random.randint(0, 100)
        y2 = random.randint(0, 100)
        if (x1, y1) != (x2, y2):
            return x1, y1, x2, y2

def tcgen():
    N = random.randint(2, 10**5)
    segments = [generate_line_segment() for _ in range(N)]
    
    return N, segments

# Example usage:
N, segments = tcgen()
print(N)
for seg in segments:
    print(*seg)
```

### Explanation:

1. **Function `generate_line_segment()`**:
    - This function generates a valid line segment by ensuring that the two endpoints are not the same. It keeps generating random coordinates for the endpoints until they are different.
   
2. **Function `tcgen()`**:
    - This function generates a random value for \( N \) within the given constraints (2 ≤ \( N \) ≤ 10^5).
    - It then generates \( N \) line segments using the `generate_line_segment()` function.
    - Finally, it returns \( N \) and the list of segments.

### Example Usage:
When you run the `tcgen()` function, it will output a random test case in the format specified by the problem statement. Here is an example of how it might look:

```plaintext
4
67 2 45 14
32 81 99 0
12 34 56 78
10 20 30 40
```

This output corresponds to \( N = 4 \) and the four generated line segments. You can use this function to generate multiple test cases for testing your solution to the problem.

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