Orig Description
Mirror Labyrinth
You are a proud and brave hero, and you have finally reached the lair of the Demon King. However, to reach the Demon King's throne room, you must first clear the final map he has prepared.
In this map, everything is transformed into a two-dimensional plane view seen from above. Humans are transformed into mere points on this map. The map is divided into two areas by a straight line. When a person is in one of the areas, their mirror image is projected onto the other area in a position that is symmetric to the line.
There are multiple buildings in each area. These buildings are made up of polygons that are formed by connecting multiple points. The area inside the polygon and the area on
Extracted Specification
### Canonicalized Input Description:
An integer N (1 ≤ N ≤ 10^3), representing some quantity or size.
A list of tuples P of size N, where each tuple consists of two integers x and y (−10^4 ≤ x, y ≤ 10^4), representing some coordinates or points.
A list of M tuples B, each of size K, where each tuple consists of K pairs of integers (x, y) (−10^4 ≤ x, y ≤ 10^4), representing some polygons.
### Example Input:
```
3
2 3
-1 4
5 6
2
4
1 2
2 3
3 4
4 5
3
0 0
-1 -1
-2 -2
```
### Function Signature:
Write a function f(N, P, B) that takes in the input.
```python
def f(N: int, P: List[Tuple[int, int]], B: List[List[Tuple[int, int]]]):
'''
N: an integer
P: a list of tuples, each containing two integers
B: a list of lists, each containing tuples of two integers
'''
```
Test Case Generator
Sure, I can help you with that! To generate a test case for the "Mirror Labyrinth" problem, we need to consider various elements such as the map dimensions, the straight line dividing the areas, and the buildings represented by polygons.
Here's a detailed test case generator for the "Mirror Labyrinth" problem:
### Problem Statement: Mirror Labyrinth
**Description**
You are a proud and brave hero, and you have finally reached the lair of the Demon King. However, to reach the Demon King's throne room, you must first clear the final map he has prepared.
In this map, everything is transformed into a two-dimensional plane view seen from above. Humans are transformed into mere points on this map. The map is divided into two areas by a straight line. When a person is in one of the areas, their mirror image is projected onto the other area in a position that is symmetric to the line.
There are multiple buildings in each area. These buildings are made up of polygons that are formed by connecting multiple points. The area inside the polygon and the area on the boundary of it are considered occupied by the building.
**Input**
1. An integer \(N\) (1 ≤ \(N\) ≤ 10^3), representing the number of polygons (buildings) in the map.
2. For each polygon:
- An integer \(M\) (3 ≤ \(M\) ≤ 100), representing the number of vertices in the polygon.
- \(M\) pairs of integers \( (x_i, y_i) \) where \((-10^9 ≤ x_i, y_i ≤ 10^9)\) are the coordinates of the vertices of the polygon.
3. A description of the straight line that divides the map into two areas. The line can be described by:
- Two points \( (x1, y1) \) and \( (x2, y2) \) through which the line passes.
**Output**
Print the transformed map with the mirror images of the buildings in the appropriate areas.
**Examples**
_Input_
```
2
4
1 1
3 1
3 3
1 3
3
2 2
4 2
3 4
0 0 1 0
```
_Output_
```
Transformed map with mirror images
```
### Test Case Generator
Below is the Python code to generate a test case for the "Mirror Labyrinth" problem:
```python
import random
def generate_polygon():
M = random.randint(3, 100)
vertices = []
for _ in range(M):
x = random.randint(-10**9, 10**9)
y = random.randint(-10**9, 10**9)
vertices.append((x, y))
return M, vertices
def generate_straight_line():
x1 = random.randint(-10**9, 10**9)
y1 = random.randint(-10**9, 10**9)
x2 = random.randint(-10**9, 10**9)
y2 = random.randint(-10**9, 10**9)
return (x1, y1, x2, y2)
def tcgen():
N = random.randint(1, 1000)
polygons = []
for _ in range(N):
M, vertices = generate_polygon()
polygons.append((M, vertices))
line = generate_straight_line()
return N, polygons, line
def format_test_case(N, polygons, line):
test_case = []
test_case.append(str(N))
for M, vertices in polygons:
test_case.append(str(M))
for x, y in vertices:
test_case.append(f"{x} {y}")
test_case.append(f"{line[0]} {line[1]} {line[2]} {line[3]}")
return "\n".join(test_case)
# Generate and format a test case
N, polygons, line = tcgen()
test_case = format_test_case(N, polygons, line)
print(test_case)
```
### Explanation
1. **generate_polygon()**: Generates a random polygon with vertices within the coordinate range \([-10^9, 10^9]\).
2. **generate_straight_line()**: Generates coordinates for two points that define the straight line.
3. **tcgen()**: Generates the entire test case including the number of polygons, their vertices, and the straight line.
4. **format_test_case()**: Formats the generated data into the required input format for the problem.
This code will create a test case for the "Mirror Labyrinth" problem, ensuring that it meets the specified constraints.
Extract Arguments
def extract_arguments(fh):
N = int(fh.readline().strip())
areas = []
for _ in range(N):
points = int(fh.readline().strip())
polygon = [tuple(map(int, fh.readline().strip().split())) for _ in range(points)]
areas.append(polygon)
return N, areas
# if __name__ == "__main__":
# input_path = sys.argv[1]
# with open(input_path, 'r') as fh:
# N, areas = extract_arguments(fh)
# f(N, areas)