Problem p01699 - Generation 2

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 pairs of integers (low, high), where each integer is between 1 and 99, inclusive.

### Example Input:

```
2
1 11
1 11
```

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

Test Case Generator

Sure, I can help you write a test case generator for the "Elevator Hall Number" problem. Below is the Python code for the test case generator:

```python
import random

def tcgen():
    # Generate a random number of elevators N (2 ≤ N ≤ 6)
    N = random.randint(2, 6)
    
    # Generate random low and high floor ranges for each elevator
    ranges = []
    for _ in range(N):
        low = random.randint(1, 99)
        high = random.randint(low, 99)
        ranges.append((low, high))
    
    return N, ranges

def generate_multiple_test_cases(num_cases):
    test_cases = []
    for _ in range(num_cases):
        N, ranges = tcgen()
        test_case = f"{N}\n"
        for low, high in ranges:
            test_case += f"{low} {high}\n"
        test_cases.append(test_case.strip())
    return test_cases

def main():
    num_cases = 5  # You can specify the number of test cases you want to generate
    test_cases = generate_multiple_test_cases(num_cases)
    for test_case in test_cases:
        print(test_case)
        print()  # Print a blank line between test cases

if __name__ == "__main__":
    main()
```

Explanation:
1. **`tcgen` Function**: This function generates a single test case.
    - It randomly selects the number of elevators \(N\) within the range [2, 6].
    - For each elevator, it generates a random floor range with `low` and `high` values such that \(1 \leq \text{low} \leq \text{high} \leq 99\).

2. **`generate_multiple_test_cases` Function**: This function generates multiple test cases.
    - It calls `tcgen` multiple times to create the specified number of test cases.
    - It formats each test case as a string and stores them in a list.

3. **`main` Function**: This function controls the overall execution.
    - It sets the number of test cases to generate.
    - It prints each test case, followed by a blank line for separation.

To use the generator, simply run the `main` function. You can adjust the `num_cases` variable to generate the desired number of test cases.

Extract Arguments

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

# Example usage:
# with open('input.txt', 'r') as fh:
#     inputs = extract_arguments(fh)
#     for input_tuple in inputs:
#         f(input_tuple)