Problem p01562 - Generation 3

Orig Description

Area Folding
 You are given one polygonal line, which is a collection of line segments.
Your task is to calculate the sum of areas  enclosed by the polygonal line.
A point is defined to be "enclosed" if and only if the point is unreachable without crossing at least one line segment from the point at infinity.
Input
The first line contains one integers N (2 ≤ N ≤ 100). 
N is the number of segments.
 Each of the following N lines consists of two integers Xi and Yi (-105 ≤ Xi, Yi ≤ 105, 1 ≤ i ≤ N) which represents a vertex.
A polygonal line is the segments  which connect (Xj, Yj) and (Xj+1, Yj+1) ((Xj, Yj) ≠ (Xj+1, Yj+1), 1 ≤ j ≤ N-1).
The distance between a segment Sj and all  vertices except the end points on segment Sj is guaranteed to be greater than 0.01.
Output
Output the answer in a line.
The answer may be printed with an arbitrary number of decimal digits, but may not contain an absolute or relative error greater than or equal to 10-6.
Sample Input 1
5
0 0
1 1
1 0
0 1
0 0
Output for the Sample Input 1
0.5
Sample Input 2
5
0 0
1 1
1 0
0 1
1 0
Output for the Sample Input 2
0.25
Sample Input 3
21
1 1
-1 1
-1 2
-2 2
-2 1
-1 1
-1 -1
-2 -1
-2 -2
-1 -2
-1 -1
1 -1
1 -2
2 -2
2 -1
1 -1
1 1
2 1
2 2
1 2
1 1
Output for the Sample Input 3
8
Sample Input 4
16
0 0
1 0
1 1
0 1
0 2
0 3
1 3
1 2
2 2
2 3
3 3
3 2
3 1
2 1
2 0
3 0
Output for the Sample Input 4
0
Sample Input 5
7
26 52
33 12
-51 68
16 61
43 -26
87 24
12 10
Output for the Sample Input 5
2714.840579710

Extracted Specification

An integer N (2 ≤ N ≤ 100), representing some quantity or size.
A list of tuples of size N, where each tuple consists of two integers (X, Y) with -105 ≤ X, Y ≤ 105.

### Example Input:

```
5
0 0
1 1
1 0
0 1
0 0
```

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

Test Case Generator

Sure, I can write a test case generator for the "Area Folding" problem. Given the constraints and requirements, the generator will create valid input polygons with random vertices. Here's the code for the test case generator:

```python
import random

def generate_random_points(n):
    points = []
    for _ in range(n):
        x = random.randint(-105, 105)
        y = random.randint(-105, 105)
        points.append((x, y))
    return points

def tcgen():
    # Number of segments (vertices)
    N = random.randint(2, 100)
    
    # Generate N random points ensuring no two consecutive points are the same
    while True:
        points = generate_random_points(N)
        valid = True
        for i in range(1, N):
            if points[i] == points[i - 1]:
                valid = False
                break
        if valid:
            break
    
    # Convert points to the required format
    result = f"{N}\n"
    for x, y in points:
        result += f"{x} {y}\n"
    
    return result.strip()

# Example of generating a test case
print(tcgen())
```

This generator ensures that:

1. The number of vertices \( N \) is within the specified range \([2, 100]\).
2. Each point \((X_i, Y_i)\) is within the range \([-105, 105]\).
3. No two consecutive points are the same.

The generator outputs the test case in the format required by the problem statement. You can run this function multiple times to generate different test cases for your problem.

Extract Arguments

def extract_arguments(fh):
    N = int(fh.readline().strip())
    vertices = []
    for _ in range(N):
        x, y = map(int, fh.readline().strip().split())
        vertices.append((x, y))
    return N, vertices

# if __name__ == "__main__":
#     input_path = sys.argv[1]
#     with open(input_path, 'r') as fh: 
#     N, vertices = extract_arguments(fh)
#     f(N, vertices)