Problem p01547 - Generation 1

Orig Description

The Last Line of Defense
In a certain country that was frequently invaded by unidentified creatures, it was decided to protect important facilities with a new defense weapon.
This weapon can damage unidentified creatures by filling a polygonal area with a special gas. If the concentration of the gas changes during the invasion of the unidentified creature, it will cause damage equal to the absolute value of the concentration difference. No damage is caused when the gas concentration is moving in the same area. 
With current technology, the concentration of gas can only be constant, so the country decided to deploy multiple new defense weapons. The gas concentration is the same for all weapons, and the parts included in the areas of multiple weapons have their concentrations added together.
Based on the location where the unidentified creature appears and the location of the important facility, please find the minimum damage that the unidentified creature will receive when invading the important facility. 
However, it is assumed that the intrusion route of the unidentified creature does not include the vertices of the polygon or the intersection with other polygons. In addition, the unidentified creature does not invade along the edge of the polygon.
Input
The input is given in the following format.
Number of polygonsNumber of polygon verticesx-coordinate y-coordinatex-coordinate y-coordinate...Number of polygon verticesx-coordinate y-coordinatex-coordinate y-coordinate...Number of occurrence points and important facility datax-coordinate of the occurrence position y-coordinate of the occurrence position x-coordinate of the important facility y-coordinate of the important facilityx-coordinate of the occurrence position y-coordinate of the occurrence position x-coordinate of the important facility y-coordinate of the important facility...
Constraints
The coordinates included in the input are integers with absolute values up to 1,000.
The number of polygons is 1 to 5.
The number of polygon vertices is 3 to 5.
The number of data for the occurrence point and important facility is 1 to 100.
A polygon refers to a polygon that can be created by connecting the given vertices in order, and has no self-intersection.
Neither the occurrence point nor the important facility is on the vertex or the edge of the polygon.
Output
Output the minimum damage that the unidentified creature will receive when invading the important facility for each pair of occurrence point and important facility data on a separate line.
Sample Input 1
2
4
0 4
1 1
3 1
4 4
3
6 0
10 0
8 7
1
2 3 9 1
Output for the Sample Input 1
2
One point of damage is inflicted when leaving the first polygon, and another one when entering the second polygon.
Sample Input 2
1
4
0 0
10 0
10 10
0 10
2
15 5 5 5
5 5 15 5
Output for the Sample Input 2
1
1
Damage occurs when the unidentified creature enters the polygon in the first data.
Damage occurs when the unidentified creature leaves the polygon in the second data.
Sample Input 3
2
4
0 0
10 0
10 10
0 10
4
10 0
20 0
20 10
10 10
1
5 5 15 5
Output for the Sample Input 3
0
Since there is no change in concentration when the unidentified creature moves from the first polygon to the second polygon, damage cannot be inflicted.
Sample Input 4
2
3
0 0
10 0
5 10
3
5 0
15 0
10 10
1
5 5 10 5
Output for the Sample Input 4
2
The areas of the occurrence point and important facility contact at a point, but the unidentified creature does not invade through this point.
Sample Input 5
2
4
0 0
10 0
10 10
0 10
4
0 0
10 0
10 10
0 10
2
15 5 5 5
5 5 15 5
Output for the Sample Input 5
2
2

Extracted Specification

Canonicalized Input Description: 

An integer T (1 ≤ T ≤ 5), representing some quantity or size.
For each of T items:
    An integer N (3 ≤ N ≤ 5), representing some quantity or size.
    N pairs of integers, each pair representing some data point (-1000 ≤ x, y ≤ 1000).
An integer M (1 ≤ M ≤ 100), representing some quantity or size.
For each of M items:
    Four integers, each representing some data point (-1000 ≤ x, y ≤ 1000).

### Example Input:

```
2
4
0 4
1 1
3 1
4 4
3
6 0
10 0
8 7
1
2 3 9 1
```

### Function Signature:

Write a function f(T, polygons, points) that takes in the input.

```python
def f(T: int, polygons: List[Tuple[int, List[Tuple[int, int]]]], points: List[Tuple[int, int, int, int]]):
    '''
    T: an integer
    polygons: a list of tuples, where each tuple contains an integer and a list of integer pairs
    points: a list of tuples, where each tuple contains four integers
    '''
```

Test Case Generator

Here's a test case generator function for "The Last Line of Defense" problem. This generator will create random valid test cases based on the given constraints.

```python
import random

def generate_polygon():
    num_vertices = random.randint(3, 5)
    vertices = []
    for _ in range(num_vertices):
        x = random.randint(-1000, 1000)
        y = random.randint(-1000, 1000)
        vertices.append((x, y))
    return num_vertices, vertices

def generate_occurrence_facility_data():
    x1 = random.randint(-1000, 1000)
    y1 = random.randint(-1000, 1000)
    x2 = random.randint(-1000, 1000)
    y2 = random.randint(-1000, 1000)
    return (x1, y1, x2, y2)

def tcgen():
    num_polygons = random.randint(1, 5)
    polygons = []
    
    for _ in range(num_polygons):
        num_vertices, vertices = generate_polygon()
        polygons.append((num_vertices, vertices))
        
    num_occ_facility_data = random.randint(1, 100)
    occ_facility_data = []
    
    for _ in range(num_occ_facility_data):
        occ_facility_data.append(generate_occurrence_facility_data())
        
    return num_polygons, polygons, num_occ_facility_data, occ_facility_data

# Example usage
if __name__ == "__main__":
    num_polygons, polygons, num_occ_facility_data, occ_facility_data = tcgen()
    
    # Print the generated test case
    print(num_polygons)
    for num_vertices, vertices in polygons:
        print(num_vertices)
        for x, y in vertices:
            print(x, y)
    
    print(num_occ_facility_data)
    for x1, y1, x2, y2 in occ_facility_data:
        print(x1, y1, x2, y2)
```

### Explanation:
1. **generate_polygon()**:
   - Randomly generates the number of vertices (between 3 and 5) for a polygon.
   - Generates vertex coordinates with values between -1000 and 1000.
   
2. **generate_occurrence_facility_data()**:
   - Generates random coordinates for the occurrence and facility points.
   
3. **tcgen()**:
   - Generates the number of polygons (between 1 and 5).
   - Generates the vertices for each polygon using `generate_polygon`.
   - Generates the number of occurrence and facility data points (between 1 and 100).
   - Generates the data points using `generate_occurrence_facility_data`.
   
4. **Main Usage**:
   - Calls `tcgen` to generate a test case and prints it in the required format.

This generator ensures that all generated test cases adhere to the problem constraints and provide diverse scenarios for thorough testing.

Extract Arguments

def extract_arguments(fh):
    import sys
    input = sys.stdin.read
    data = input().split()
    
    index = 0
    
    num_polygons = int(data[index])
    index += 1
    
    polygons = []
    for _ in range(num_polygons):
        num_vertices = int(data[index])
        index += 1
        
        vertices = []
        for _ in range(num_vertices):
            x = int(data[index])
            y = int(data[index + 1])
            vertices.append((x, y))
            index += 2
        polygons.append(vertices)
    
    num_occurrences = int(data[index])
    index += 1
    
    occurrences = []
    for _ in range(num_occurrences):
        ox = int(data[index])
        oy = int(data[index + 1])
        fx = int(data[index + 2])
        fy = int(data[index + 3])
        occurrences.append((ox, oy, fx, fy))
        index += 4
        
    return polygons, occurrences

# Example usage:
# with open('input.txt', 'r') as fh:
#     polygons, occurrences = extract_arguments(fh)