Orig Description
11 Puzzle
Taro-kun is very good at the 8 puzzle and often plays with his friends during break time by having them rearrange the tiles. At such a time, his friend asked him, "Can you solve a more complex puzzle?" but he had never tried any other puzzles. It seemed that his friend had created an 11 puzzle himself. The puzzle is in the shape shown below.
The 11 puzzle is played with 11 square cards and a frame shaped like the one in Figure 1. First, put the 11 cards in the frame. Then, two spaces will be left empty, and you can move the cards adjacent to these spaces. Repeat this process to neatly arrange the cards and complete the puzzle as shown in Figure 2.
Taro-kun decided to challenge this puzzle. However, he easily solved the 11 puzzle. So his friend said, "Solve it with the fewest number of moves!" and asked him to create a program to output the minimum number of steps to solve the 11 puzzle before he challenged it. At this time, although there are two places where you can move, consider moving one number one space as one step.
Create a program that takes the initial state of the 11 puzzle as input and outputs the minimum number of steps to solve the 11 puzzle. However, if it takes more than 20 steps to solve the puzzle, output "NA". The state of the puzzle is input in order from the first line of information, and the number 0 represents an empty space. For example, the input that represents the state in Figure 1 is as follows:
6
2 1 3
10 5 7 0 8
9 4 11
0
Input
A sequence of multiple datasets is given as input. The end of the input is indicated by a single line with -1. Each dataset is given in the following format.
p1
p2 p3 p4
p5 p6 p7 p8 p9
p10 p11 p12
p13
The information for the i-th row of the puzzle, pi (0 ≤ pi ≤ 11), is given separated by spaces on the i-th line.
There are no more than 100 datasets.
Output
For each dataset, output the minimum number of steps or NA on one line.
Sample Input
2
1 0 3
4 5 6 7 8
9 0 11
10
0
1 2 3
4 5 6 7 8
9 10 11
0
0
11 10 9
8 7 6 5 4
3 2 1
0
-1
Output for the Sample Input
2
0
NA
Extracted Specification
An integer (0 ≤ integer ≤ 11).
Three integers on the next line (0 ≤ integer ≤ 11).
Five integers on the next line (0 ≤ integer ≤ 11).
Three integers on the next line (0 ≤ integer ≤ 11).
An integer (0 ≤ integer ≤ 11).
Repeat the above format for multiple datasets.
The end of the input is indicated by a single line with -1.
There are no more than 100 datasets.
### Example Input:
```
2
1 0 3
4 5 6 7 8
9 0 11
10
0
1 2 3
4 5 6 7 8
9 10 11
0
0
11 10 9
8 7 6 5 4
3 2 1
0
-1
```
### Function Signature:
Write a function f(inputs) that processes the input datasets.
```python
def f(inputs: List[Tuple[int, List[int], List[int], List[int], int]]):
'''
inputs: a list of tuples, where each tuple represents a dataset and contains:
- an integer
- a list of three integers
- a list of five integers
- a list of three integers
- an integer
'''
```
Test Case Generator
Sure, I can help you create a test case generator for the "11 Puzzle" problem. The generator will create random configurations of the puzzle and ensure that the constraints are respected. Here is a possible implementation of the test case generator:
```python
import random
def generate_random_puzzle():
puzzle = list(range(12))
random.shuffle(puzzle)
# Convert the flat list into the 11-puzzle format
return [
[puzzle[0]], # First row
puzzle[1:4], # Second row
puzzle[4:9], # Third row
puzzle[9:], # Fourth row
]
def puzzle_to_string(puzzle):
# Convert the 11-puzzle format into a string
return "\n".join(" ".join(map(str, row)) for row in puzzle)
def tcgen():
num_datasets = random.randint(1, 100)
datasets = []
for _ in range(num_datasets):
puzzle = generate_random_puzzle()
datasets.append(puzzle_to_string(puzzle))
# Append the termination line
datasets.append("-1")
return "\n\n".join(datasets)
# Example of generating test cases
if __name__ == "__main__":
print(tcgen())
```
### Explanation:
1. **generate_random_puzzle()**: This function creates a shuffled list of integers from 0 to 11 and arranges them in the format required by the 11-puzzle problem.
2. **puzzle_to_string()**: This function converts the puzzle from a list of lists to a formatted string as needed for the input.
3. **tcgen()**: This function generates a random number of datasets (between 1 and 100), converts each dataset to the string format, and then appends the termination line `"-1"`.
### Sample Output:
The generated test cases will look similar to the following:
```
6
5 1 2
3 0 7 9 4
11 8 10
0
0
1 2 3
4 5 6 7 8
9 10 11
0
3
0 9 7
8 1 5 10 4
6 11 2
0
-1
```
With this test case generator, you can create diverse and random configurations of the 11-puzzle to thoroughly test your solution.
Extract Arguments
def extract_arguments(fh):
datasets = []
while True:
p1 = int(fh.readline().strip())
if p1 == -1:
break
p2 = list(map(int, fh.readline().strip().split()))
p3 = list(map(int, fh.readline().strip().split()))
p4 = list(map(int, fh.readline().strip().split()))
p5 = list(map(int, fh.readline().strip().split()))
p6 = int(fh.readline().strip())
dataset = (p1, p2, p3, p4, p5, p6)
datasets.append(dataset)
return datasets
# Example usage:
# with open('input.txt', 'r') as fh:
# inputs = extract_arguments(fh)
# for dataset in inputs:
# print(dataset)