Sure! Below is a Python test case generator for the given bamboo problem.

```python
import random

def tcgen():
    # Constraints
    N = random.randint(3, 8)
    A = random.randint(1, 1000)
    B = random.randint(1, A - 1)
    C = random.randint(1, B - 1)
    
    # Ensure l_i values are within the given constraints
    lengths = [random.randint(1, 1000) for _ in range(N)]
    
    return N, A, B, C, lengths

def format_test_case(N, A, B, C, lengths):
    test_case = f"{N} {A} {B} {C}\n" + "\n".join(map(str, lengths))
    return test_case

# Example usage
for _ in range(5):  # Generate 5 random test cases
    N, A, B, C, lengths = tcgen()
    print(format_test_case(N, A, B, C, lengths))
    print()
```

This function `tcgen` generates test cases for the problem, ensuring that all constraints are met. It then formats the output to match the expected input format for the problem. You can adjust the number of test cases generated by changing the range in the example usage.

Let's break down what the generator does:
1. **N:** Randomly selects the number of bamboos between 3 and 8.
2. **A, B, C:** Randomly selects the lengths of the desired bamboos ensuring \(C < B < A \leq 1000\).
3. **lengths:** Generates a list of N random bamboo lengths, each between 1 and 1000.

The `format_test_case` function takes these values and formats them into the standard input format for the problem, which is then printed out.

Feel free to use and modify this generator as needed for your testing purposes!