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 ≤ 1000), representing some quantity or size.
A list of tuples P of size N, where each tuple contains two integers (x, y) representing coordinates, and both x and y are between -10^6 and 10^6.
A string S with a length between 1 and 1000, containing only characters from the set {'L', 'R', 'U', 'D'}.
### Example Input:
```
4
1 2
3 4
-1 -2
-3 -4
LRUD
```
### Function Signature:
Write a function f(N, P, S) that takes in the input.
```python
def f(N: int, P: List[Tuple[int, int]], S: str):
'''
N: an integer
P: a list of tuples with integer coordinates
S: a string
'''
```
Test Case Generator
Sure! Let's create a test case generator for the given problem statement "Mirror Labyrinth". To ensure we have a complete problem statement and to generate accurate test cases, I'll make some assumptions. If there are additional details or specific requirements, please let me know.
### 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 the polygon are considered as part of the building.
**Input**
1. An integer \(N\) (1 ≤ \(N\) ≤ 100), representing the number of buildings.
2. For each building:
- An integer \(M\) (3 ≤ \(M\) ≤ 100), representing the number of vertices in the polygon.
- A list of \(M\) pairs of integers \((x, y)\), representing the coordinates of the vertices.
3. A line represented by the equation \(Ax + By + C = 0\), where \(A\), \(B\), and \(C\) are integers.
**Output**
Print the coordinates of the mirrored image of each building.
**Examples**
_Input_
```
2
4
1 1
5 1
5 5
1 5
3
-1 -1
-3 -1
-2 -4
1 -1 0
```
_Output_
```
4
-1 -1
-5 -1
-5 -5
-1 -5
3
1 -1
3 -1
2 -4
```
### Test Case Generator
Here is a Python test case generator for the "Mirror Labyrinth" problem:
```python
import random
def tcgen():
N = random.randint(1, 100)
buildings = []
for _ in range(N):
M = random.randint(3, 100)
vertices = []
for _ in range(M):
x = random.randint(-1000, 1000)
y = random.randint(-1000, 1000)
vertices.append((x, y))
buildings.append(vertices)
A = random.randint(-100, 100)
B = random.randint(-100, 100)
C = random.randint(-1000, 1000)
if A == 0 and B == 0:
A = 1 # Ensuring the line equation is valid
return N, buildings, (A, B, C)
# Example usage
N, buildings, line = tcgen()
print(N)
for building in buildings:
print(len(building))
for vertex in building:
print(vertex[0], vertex[1])
print(line[0], line[1], line[2])
```
### Explanation
1. **Number of Buildings (N)**: Randomly generates an integer between 1 and 100.
2. **Buildings**: For each building:
- **Number of Vertices (M)**: Randomly generates an integer between 3 and 100.
- **Vertices**: For each vertex, generate random coordinates \(x\) and \(y\) between -1000 and 1000.
3. **Line Equation (A, B, C)**: Randomly generates integers for \(A\), \(B\), and \(C\) with constraints to ensure the line equation is valid.
This generator will produce a variety of test cases with different configurations of buildings and lines, which should be useful for robustly testing your solution to the "Mirror Labyrinth" problem.
Extract Arguments
def extract_arguments(fh):
L = list(map(float, fh.readline().strip().split()))
M = int(fh.readline().strip())
def read_polygon(num_points):
polygon = []
for _ in range(num_points):
x, y = map(float, fh.readline().strip().split())
polygon.append((x, y))
return polygon
polygons_A = []
for _ in range(M):
num_points = int(fh.readline().strip())
polygons_A.append(read_polygon(num_points))
N = int(fh.readline().strip())
polygons_B = []
for _ in range(N):
num_points = int(fh.readline().strip())
polygons_B.append(read_polygon(num_points))
return L, polygons_A, polygons_B