Certainly! To generate test cases for the problem "Cat Going Straight II", we need to create a function that generates random valid inputs according to the given constraints. Here's the test case generator:

```python
import random

def generate_dataset():
    # Number of pillars (3 ≤ C ≤ 100)
    C = random.randint(3, 100)
    
    # Number of walls (3 ≤ W ≤ 300)
    W = random.randint(3, 300)
    
    # Generating unique coordinates for the pillars
    pillars = set()
    while len(pillars) < C:
        x = random.randint(-1000, 1000)
        y = random.randint(-1000, 1000)
        pillars.add((x, y))
    
    pillars = list(pillars)
    
    # Generating walls
    walls = set()
    while len(walls) < W:
        s = random.randint(1, C)
        t = random.randint(1, C)
        if s != t:
            wall = (min(s, t), max(s, t))
            walls.add(wall)
    
    walls = list(walls)
    
    # Constructing the dataset as a string
    dataset = f"{C} {W}\n"
    dataset += "\n".join(f"{x} {y}" for x, y in pillars)
    dataset += "\n"
    dataset += "\n".join(f"{s} {t}" for s, t in walls)
    
    return dataset

def tcgen():
    # Generate multiple datasets
    num_datasets = random.randint(1, 50)
    test_cases = []
    
    for _ in range(num_datasets):
        test_cases.append(generate_dataset())
    
    # Add the terminating "0 0" at the end
    test_cases.append("0 0")
    
    return "\n\n".join(test_cases)

# Example usage:
print(tcgen())
```

This function `tcgen` generates multiple datasets (up to 50) and appends the end-of-input marker `0 0` at the end. Each dataset consists of a number of pillars and walls, with randomly generated coordinates for the pillars and randomly generated connections (walls) between the pillars.

**Key Points:**
- The number of pillars \(C\) is between 3 and 100.
- The number of walls \(W\) is between 3 and 300.
- Each pillar has unique coordinates within the range \([-1000, 1000]\).
- Each wall connects two different pillars.

This generator ensures that the generated datasets conform to the constraints provided in the problem statement.