Orig Description
All Numbers Lead to 6174
Perform the following operation on a four-digit number N consisting of digits 0 to 9.
Arrange the numbers in each digit of N in descending order, and let L be the resulting number.
Arrange the numbers in each digit of N in ascending order, and let S be the resulting number.
Set the difference L-S as the new N (one operation completed)
Repeat from 1. for the new N
In this case, it is known that every four-digit number eventually becomes 6174 except for numbers where all digits are the same (such as 0000, 1111, etc.). For example, when N = 2012,
1st operation (N = 2012): L = 2210, S = 0122, L-S = 2088
2nd operation (N = 2088): L = 8820, S = 0288, L-S = 8532
3rd operation (N = 8532): L = 8532, S = 2358, L-S = 6174
and 6174 is reached in three operations.
Write a program that calculates the number of operations required to reach 6174 from a four-digit number consisting of digits 0 to 9.
Input
The input consists of multiple datasets. The end of input is indicated by a line containing only 0000. Each dataset is given in the following format.
N
The dataset consists of one line, and N (1 ≤ N ≤ 9999) represents a four-digit number. If N < 1000, the upper digits are filled with 0s.
The number of datasets does not exceed 10,000.
Output
For each dataset, output the number of operations required to reach 6174 on one line. However, if a number is given as input where all digits are the same, output NA.
Sample Input
6174
2012
3333
0000
Sample Output
0
3
NA
Extracted Specification
An integer N (1 ≤ N ≤ 9999), representing some quantity or size. If N < 1000, the upper digits are filled with 0s.
### Example Input:
```
6174
2012
3333
0000
```
### Function Signature:
Write a function f(inputs) that takes in the input.
def f(inputs: List[int]):
'''
inputs: a list of integers
'''
Test Case Generator
Sure! To generate test cases for the "All Numbers Lead to 6174" problem, we need to generate valid four-digit numbers (including those with leading zeros). We also need to handle the special case where all digits are the same, which should result in an output of "NA".
Here's a Python test case generator for this problem:
```python
import random
def generate_four_digit_number():
return random.randint(0, 9999)
def format_number(N):
return f"{N:04}"
def tcgen(num_datasets=10):
datasets = []
for _ in range(num_datasets):
N = generate_four_digit_number()
datasets.append(format_number(N))
# Adding the end of input line '0000'
datasets.append("0000")
return datasets
# Example usage
if __name__ == "__main__":
test_cases = tcgen(10)
for case in test_cases:
print(case)
```
This generator creates a specified number of test cases (default is 10) where each test case is a four-digit number formatted as a string with leading zeros if necessary. It also appends the terminating line "0000".
### Explanation:
- `generate_four_digit_number`: Generates a random integer between 0 and 9999.
- `format_number`: Formats the number to ensure it is a four-digit string by adding leading zeros if needed.
- `tcgen`: Generates a list of test cases and appends the terminating "0000" line.
Feel free to adjust the number of datasets by passing a different value to the `tcgen` function when you call it. This will give you a variety of four-digit numbers to test the solution for the given problem.
Extract Arguments
def extract_arguments(fh):
datasets = []
while True:
line = fh.readline().strip()
if line == '0000':
break
datasets.append(int(line))
return datasets
# if __name__ == "__main__":
# input_path = sys.argv[1]
# with open(input_path, 'r') as fh:
# inputs = extract_arguments(fh)
# f(inputs)