Sure, I can create a test case generator for the given problem statement "There is No Alternative". The test case generator will produce random inputs based on the constraints provided in the problem statement.

Here's a Python function to generate random test cases:

```python
import random

def tcgen():
    # Generate N: Number of islands
    N = random.randint(3, 500)
    
    # Generate M: Number of possible bridges
    M = random.randint(N-1, min(50000, N * (N - 1) // 2))
    
    bridges = set()
    while len(bridges) < M:
        S = random.randint(1, N - 1)
        D = random.randint(S + 1, N)
        C = random.randint(1, 10000)
        bridges.add((S, D, C))

    bridges = list(bridges)
    
    # Format the output
    test_case = f"{N} {M}\n"
    for S, D, C in bridges:
        test_case += f"{S} {D} {C}\n"
        
    return test_case.strip()

# Example of generating a test case
print(tcgen())
```

### Explanation:

1. **N Generation**:
    - `N` is generated randomly between 3 and 500 (inclusive), which represents the number of islands.

2. **M Generation**:
    - `M` is generated randomly between `N-1` and `min(50000, N * (N - 1) // 2)` (inclusive), representing the number of possible bridges. This ensures there are enough bridges to potentially connect all islands.

3. **Bridges Generation**:
    - A set of bridges is generated to ensure no duplicates. Each bridge is represented by a tuple `(S, D, C)` where:
        - \( S \) is a starting island (randomly chosen between 1 and \( N-1 \)).
        - \( D \) is a destination island (randomly chosen between \( S+1 \) and \( N \)).
        - \( C \) is the cost of building the bridge (randomly chosen between 1 and 10000).
    - This loop continues until we have `M` unique bridges.

4. **Output Formatting**:
    - The output is formatted as a single string with the first line containing `N` and `M`.
    - Each subsequent line contains `S`, `D`, and `C` for each bridge.

This generator will create various test cases that can be used to thoroughly test the solution for the given problem, ensuring that it handles a wide range of inputs within the specified constraints.