Problem p01699 - Generation 3

Orig Description

Elevator Hall Number
JAG (Japanese Alumni Group) is a mysterious organization located in a high-rise building somewhere in Tokyo. The building has $N$ elevators, and the $i$-th elevator stops at each floor from $low_i$ to $high_i$ ($1 \le i \le N$).
X, a new member of JAG, has arrived at the elevator hall of the building to visit the headquarters. While waiting for the elevator after pressing the button, X noticed that the display showing the current floor of the elevator is a little different. When the $i$-th elevator is on the $a_i$-th floor, the display shows a single number obtained by concatenating $a_1,a_2,\dots,a_N$ in order without leading zeros or spaces. For example, if $N=3$ and the elevators are on the 10th, 2nd, and 11th floors, then "10211" is displayed.
X is curious about how many possible numbers can be displayed on the screen. Your task is to create a program that calculates this.
Input:
The input consists of multiple datasets. Each dataset has the following format:
  $N$
  $low_1$ $high_1$
  $\dots$
  $low_N$ $high_N$
The first line of each dataset contains an integer $N$ ($2 \leq N \leq 6$) that represents the number of elevators. The $i$-th of the following $N$ lines contains two integers $low_i$ and $high_i$ ($1 \leq low_i \leq high_i \leq 99$), which represent the range of floors that the $i$-th elevator can reach.
The input ends with a line containing a single zero.
Output:
For each dataset, output the number of possible numbers that can be displayed on the screen in a single line.
Sample Input:
2
1 11
1 11
3
10 10
2 2
11 11
4
89 91
1 12
1 12
89 91
5
1 8
2 76
10 19
6 16
33 42
6
10 59
20 69
30 79
40 89
50 99
50 99
0
Sample Output:
120
1
1278
659520
15625000000

Extracted Specification

An integer N (2 ≤ N ≤ 6), representing some quantity or size.
A list of N tuples, each containing two integers (low_i, high_i), where 1 ≤ low_i ≤ high_i ≤ 99.
The input ends with a line containing a single zero.

### Example Input:

```
2
1 11
1 11
0
```

### Function Signature:
Write a function f(inputs) that takes in the input.
```python
def f(inputs: List[Tuple[int, List[Tuple[int, int]]]]):
    ''' 
    inputs: a list of tuples where each tuple contains an integer and a list of tuples of integers
    '''
```

Test Case Generator

Sure! Below is a test case generator for the "Elevator Hall Number" problem described in your prompt. This generator will create random valid inputs based on the constraints provided.

```python
import random

def tcgen():
    # Generate a random number of elevators, N
    N = random.randint(2, 6)
    
    # Generate ranges for each elevator
    floors = []
    for _ in range(N):
        low = random.randint(1, 99)
        high = random.randint(low, 99)  # Ensure high is at least as large as low
        floors.append((low, high))
    
    return N, floors

def generate_test_cases(num_cases):
    test_cases = []
    for _ in range(num_cases):
        N, floors = tcgen()
        test_case = f"{N}\n"
        for low, high in floors:
            test_case += f"{low} {high}\n"
        test_cases.append(test_case.strip())
    
    # End the input with a zero line
    test_cases.append("0")
    
    return test_cases

# Example usage:
num_cases = 5
test_cases = generate_test_cases(num_cases)
for test_case in test_cases:
    print(test_case)
    print()
```

### Explanation:

1. **tcgen Function**: This function generates a single test case for the problem:
   - `N` is randomly chosen between 2 and 6.
   - For each elevator, `low` is randomly chosen between 1 and 99, and `high` is chosen between `low` and 99 to ensure the constraint `low ≤ high`.

2. **generate_test_cases Function**: This function generates a specified number of test cases and formats them according to the problem's input requirements. After generating the specified number of test cases, it adds a final line with a single zero to indicate the end of inputs.

3. **Example Usage**: The `generate_test_cases` function is called with `num_cases` set to 5, and the generated test cases are printed.

You can modify `num_cases` to generate as many test cases as you need. Each test case is generated randomly while respecting the constraints specified in the problem statement.

Extract Arguments

def extract_arguments(fh):
    datasets = []
    while True:
        N = int(fh.readline().strip())
        if N == 0:
            break
        elevators = []
        for _ in range(N):
            low, high = map(int, fh.readline().strip().split())
            elevators.append((low, high))
        datasets.append((N, elevators))
    return datasets