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)