Sure, let's create a test case generator for the given problem statement. We'll need to generate random values for \(N\), the array \(A\), and the connections between devices \(U\) and \(V\). Here's a Python script that can generate such test cases:

```python
import random

def tcgen():
    # Generate a random N (number of devices) within the constraints
    N = random.randint(1, 5000)
    
    # Generate the array A of size N with values between -10^9 and 10^9, non-zero
    A = [random.randint(1, 10**9) * random.choice([-1, 1]) for _ in range(N)]
    
    # Generate the N-1 cables (edges) ensuring they form a valid tree
    edges = []
    for i in range(2, N + 1):
        # Connect each new node to any of the previous nodes
        edges.append((i, random.randint(1, i - 1)))

    return N, A, edges

def print_test_case():
    N, A, edges = tcgen()
    print(N)
    print(" ".join(map(str, A)))
    for u, v in edges:
        print(u, v)

# Example of generating and printing a test case
print_test_case()
```

### Explanation:
1. **Generating N**: We randomly choose \(N\) within the given constraints (1 ≤ \(N\) ≤ 5000).
2. **Generating A**: We create an array \(A\) of size \(N\) with each element being a non-zero integer within the range \([-10^9, 10^9]\).
3. **Generating edges**: We form a tree by connecting each new node \(i\) (from 2 to \(N\)) to any of the previous nodes (1 to \(i-1\)). This ensures the tree structure is maintained, meaning the graph is connected and acyclic.
4. **Printing the test case**: The function `print_test_case` prints the generated test case in the required format.

This script will produce random test cases each time it is run, which can be used to test the competitive programming problem.