Certainly! Let's create a test case generator for the problem "A Light Road". The generator will produce random test cases based on the given constraints.

Here's the test case generator function in Python:

```python
import random

def tcgen():
    N = random.randint(2, 100)
    M = random.randint(2, 100)
    A = random.randint(0, 10)
    
    # Initialize grid with empty spaces
    grid = [['.' for _ in range(M)] for _ in range(N)]
    
    # Place obstacles randomly
    num_obstacles = random.randint(0, N * M // 4)  # At most 25% of the grid can be obstacles
    for _ in range(num_obstacles):
        x, y = random.randint(0, N-1), random.randint(0, M-1)
        grid[x][y] = '#'
    
    # Place the laser generator
    while True:
        laser_x, laser_y = random.randint(0, N-1), random.randint(0, M-1)
        if grid[laser_x][laser_y] == '.':
            grid[laser_x][laser_y] = 'S'
            break
    
    # Place the creature
    while True:
        creature_x, creature_y = random.randint(0, N-1), random.randint(0, M-1)
        if grid[creature_x][creature_y] == '.' and (creature_x != laser_x or creature_y != laser_y):
            grid[creature_x][creature_y] = 'G'
            break
    
    # Convert grid to required input format
    grid_str = "\n".join("".join(row) for row in grid)
    
    return f"{N} {M} {A}\n{grid_str}"

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

This function generates a random test case adhering to the constraints of the problem statement. Here's how it works:

1. Randomly select the grid dimensions \(N\) and \(M\) within the given constraints.
2. Randomly determine the number of type P and type Q mirrors \(A\).
3. Initialize an empty grid of dimensions \(N \times M\).
4. Randomly place obstacles in the grid.
5. Randomly place the laser generator (`S`) in an empty cell.
6. Randomly place the evil creature (`G`) in an empty cell that is not occupied by the laser generator.
7. Convert the grid to the required input string format.

You can call this function to generate test cases for the problem. Each call to `tcgen()` will produce a new random test case.