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 N tuples, each containing two integers (Xi, Yi) where -105 ≤ Xi, Yi ≤ 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
Certainly! Here is a test case generator for the given "Area Folding" problem statement:
```python
import random
def generate_polygonal_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():
N = random.randint(2, 100)
points = generate_polygonal_points(N)
# Ensure that all points are unique by converting to a set and back to a list
while len(set(points)) < N:
points = generate_polygonal_points(N)
return N, points
def format_test_case(N, points):
test_case = f"{N}\n"
for point in points:
test_case += f"{point[0]} {point[1]}\n"
return test_case
# Generate a test case
N, points = tcgen()
formatted_test_case = format_test_case(N, points)
print(formatted_test_case)
```
### Explanation:
1. **generate_polygonal_points(N)**: This function generates `N` points with random `X` and `Y` coordinates within the specified range (-105 to 105).
2. **tcgen()**: This function generates the complete test case. First, it generates a random integer `N` between 2 and 100 (inclusive). It then generates `N` unique points using the `generate_polygonal_points` function.
3. **format_test_case(N, points)**: This function converts the generated test case into the required format. It combines `N` and the points into a single formatted string.
4. The **while loop** inside `tcgen()** ensures that all the generated points are unique by converting the list of points into a set and back to a list. If duplicates are found (i.e., the length of the set is less than `N`), it regenerates the points.
5. The script finally generates a test case and prints it in the required format.
You can run the above script to generate test cases for the "Area Folding" problem. Each run will produce a different test case within the given constraints.
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)