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, y) representing coordinates, and each integer is between -10^4 and 10^4.
A string L, representing a line equation in the format "ax + by + c = 0", where a, b, and c are integers (-10^4 ≤ a, b, c ≤ 10^4).
### Example Input:
```
3
1 2
-3 4
5 -6
3x + 4y + 2 = 0
```
### Function Signature:
Write a function f(N, P, L) that takes in the input.
def f(N: int, P: List[Tuple[int, int]], L: str):
'''
N: an integer
P: a list of tuples, each containing two integers
L: a string representing a line equation
'''
Test Case Generator
Sure, I can help you generate a test case for the problem statement "Mirror Labyrinth." Since the problem statement is incomplete, I'll make some assumptions to complete it and generate a test case generator accordingly.
### Assumptions to Complete the Problem Statement:
- The map is a 2D plane split by a straight vertical line at \( x = M \).
- Each building is represented as a polygon defined by a list of vertices (points in 2D).
- The points of the polygon are given in a specific order (clockwise or counterclockwise).
- The input will consist of:
1. An integer \( M \) representing the x-coordinate of the vertical dividing line.
2. An integer \( B \) representing the number of buildings in one area.
3. For each building, an integer \( V \) representing the number of vertices of the polygon, followed by the list of \( V \) points in the form \( (x, y) \).
**Input**
1. An integer \( M \) (the x-coordinate of the vertical dividing line).
2. An integer \( B \) representing the number of buildings.
3. For each building:
- An integer \( V \) (the number of vertices of the polygon).
- A sequence of \( V \) pairs of integers \( (x, y) \) representing the vertices of the polygon.
**Output**
For each building, the mirrored polygon's vertices.
### Example
#### Input
```
2
2
4
1 1
3 1
3 3
1 3
3
2 2
4 2
4 4
2 4
```
#### Output
```
-1 1
1 1
1 3
-1 3
0 2
-2 2
-2 4
0 4
```
### Test Case Generator
```python
import random
def generate_point():
return (random.randint(-10**3, 10**3), random.randint(-10**3, 10**3))
def generate_polygon(num_vertices):
return [generate_point() for _ in range(num_vertices)]
def tcgen():
M = random.randint(-10**3, 10**3)
B = random.randint(1, 10)
buildings = []
for _ in range(B):
V = random.randint(3, 10) # Polygons have at least 3 vertices
vertices = generate_polygon(V)
buildings.append((V, vertices))
return M, B, buildings
def format_input(M, B, buildings):
input_str = f"{M}\n{B}\n"
for V, vertices in buildings:
input_str += f"{V}\n"
for x, y in vertices:
input_str += f"{x} {y}\n"
return input_str.strip()
# Example Usage:
M, B, buildings = tcgen()
print(format_input(M, B, buildings))
```
### Explanation:
- The `tcgen` function generates a random test case.
- `generate_point` creates a random point within the range \([-10^3, 10^3]\).
- `generate_polygon` creates a polygon with a specified number of vertices.
- The `format_input` function formats the generated test case into the required input format for the problem.
Feel free to modify the ranges or constraints to better fit the actual problem statement if my assumptions were incorrect.
Extract Arguments
def extract_arguments(fh):
# Read the number of buildings
M = int(fh.readline().strip())
buildings = []
for _ in range(M):
# Read the number of points in the polygon
P = int(fh.readline().strip())
# Read the points
points = []
for _ in range(P):
x, y = map(int, fh.readline().strip().split())
points.append((x, y))
buildings.append(points)
# Read the coefficients of the line equation
a, b, c = map(int, fh.readline().strip().split())
return M, buildings, (a, b, c)