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 indicating the end of input, which is always -1.
A sequence of multiple datasets is given as input. Each dataset is represented as follows:
An integer X (0 ≤ X ≤ 11).
Three integers Y1, Y2, Y3 (0 ≤ Yi ≤ 11).
Five integers Z1, Z2, Z3, Z4, Z5 (0 ≤ Zi ≤ 11).
Three integers W1, W2, W3 (0 ≤ Wi ≤ 11).
An integer V (0 ≤ V ≤ 11).
There are no more than 100 datasets.
### Example Input:
```
6
2 1 3
10 5 7 0 8
9 4 11
0
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(datasets) that takes in a list of datasets. Each dataset is a tuple of integers.
def f(datasets: List[Tuple[int, List[int, int, int], List[int, int, int, int, int], List[int, int, int], int]]):
'''
datasets: a list of tuples representing each dataset
'''
Test Case Generator
Certainly! Here is a test case generator for the "11 Puzzle" problem statement.
```python
import random
def tcgen():
# Generate a single dataset for the 11 puzzle
def generate_dataset():
# Create a list of numbers from 0 to 11
numbers = list(range(12))
random.shuffle(numbers)
# Format the numbers into the specific layout
dataset = [
[numbers[0]],
numbers[1:4],
numbers[4:9],
numbers[9:12],
[numbers[12]]
]
# Convert the dataset into a format suitable for input
formatted_dataset = []
for row in dataset:
formatted_dataset.append(' '.join(map(str, row)))
return formatted_dataset
# Generate multiple datasets (up to 100)
num_datasets = random.randint(1, 100)
datasets = []
for _ in range(num_datasets):
datasets.append(generate_dataset())
# Add the end-of-input indicator
datasets.append(["-1"])
# Convert the dataset list into a single string with proper line breaks
test_case = '\n'.join(['\n'.join(dataset) for dataset in datasets])
return test_case
# Print a generated test case for demonstration
print(tcgen())
```
### Explanation:
1. **Dataset Generation**:
- The function `generate_dataset` creates a shuffled list of numbers from 0 to 11 and formats them into the specific layout required by the problem.
- This dataset is then converted into strings suitable for input.
2. **Multiple Datasets**:
- Up to 100 datasets are generated.
- Each dataset is appended to a list `datasets`.
3. **End-of-Input Indicator**:
- After generating datasets, `-1` is appended to indicate the end of input.
4. **Formatting**:
- The datasets are joined with line breaks to form a single input string suitable for the problem's input format.
This generator will output a string that can be directly used as the input for the "11 Puzzle" problem, containing multiple datasets and the final `-1` to indicate the end.
Extract Arguments
def extract_arguments(fh):
datasets = []
while True:
p1 = 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 = (int(p1), p2, p3, p4, int(p5[0]), p5[1:], p6)
datasets.append(dataset)
return datasets