Sure, I can help you write a test case generator for the "Non-redundant Drive" problem. Here's a Python function that will generate random test cases based on the input constraints you've provided:

```python
import random

def generate_test_case():
    # Number of cities
    N = random.randint(1, 100000)
    
    # Gasoline amounts for each city
    g = [random.randint(1, 10000) for _ in range(N)]
    
    # List to store roads
    roads = []
    
    # To ensure the graph is connected and has exactly N-1 edges, we use a tree generation approach.
    # We will use a simple sequential connection to ensure it's a valid tree (non-redundant road network).
    for i in range(2, N + 1):
        # Connect each city i to a previous city randomly to ensure it's connected
        a = random.randint(1, i - 1)
        b = i
        d = random.randint(1, 10000)
        roads.append((a, b, d))
    
    return N, g, roads

def print_test_case(N, g, roads):
    print(N)
    print(' '.join(map(str, g)))
    for road in roads:
        print(f"{road[0]} {road[1]} {road[2]}")

# Generate a test case
N, g, roads = generate_test_case()

# Print the generated test case
print_test_case(N, g, roads)
```

This script does the following:
1. Generates a random number of cities \(N\) within the allowed range.
2. Generates a list of gasoline amounts for each city, ensuring each amount is within the specified range.
3. Creates a non-redundant road network (a tree) by sequentially connecting each new city to one of the previously created cities. This ensures that the network is connected and has exactly \(N - 1\) roads.
4. Prints the generated test case in the correct format.

You can run this script to generate random test cases for the "Non-redundant Drive" problem. Make sure to handle the large outputs appropriately, especially since \(N\) can be as large as 100,000.