Orig Description
Score : 700 points
Problem StatementWe have N cards numbered 1, 2, ..., N.
Card i (1 \leq i \leq N) has an integer A_i written in red ink on one side and an integer B_i written in blue ink on the other side.
Initially, these cards are arranged from left to right in the order from Card 1 to Card N, with the red numbers facing up.
Determine whether it is possible to have a non-decreasing sequence facing up from left to right (that is, for each i (1 \leq i \leq N - 1), the integer facing up on the (i+1)-th card from the left is not less than the integer facing up on the i-th card from the left) by repeating the operation below. If the answer is yes, find the minimum number of operations required to achieve it.
Choose an integer i (1 \leq i \leq N - 1).
Swap the i-th and (i+1)-th cards from the left, then flip these two cards.
Constraints
1 \leq N \leq 18
1 \leq A_i, B_i \leq 50 (1 \leq i \leq N)
All values in input are integers.
InputInput is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
B_1 B_2 ... B_N
OutputIf it is impossible to have a non-decreasing sequence, print -1.
If it is possible, print the minimum number of operations required to achieve it.
Sample Input 13
3 4 3
3 2 3
Sample Output 11
By doing the operation once with i = 1, we have a sequence [2, 3, 3] facing up, which is non-decreasing.
Sample Input 22
2 1
1 2
Sample Output 2-1
After any number of operations, we have the sequence [2, 1] facing up, which is not non-decreasing.
Sample Input 34
1 2 3 4
5 6 7 8
Sample Output 30
No operation may be required.
Sample Input 45
28 15 22 43 31
20 22 43 33 32
Sample Output 4-1
Sample Input 55
4 46 6 38 43
33 15 18 27 37
Sample Output 53
Extracted Specification
Canonicalized Input Description:
An integer N (1 ≤ N ≤ 18), representing some quantity or size.
Two lists of integers A and B, each of size N, where each integer is between 1 and 50.
### Example Input:
```
3
3 4 3
3 2 3
```
### Function Signature:
Write a function f(N, A, B) that takes in the input.
def f(N: int, A: List[int], B: List[int]):
'''
N: an integer
A: a list of integers
B: a list of integers
'''
Test Case Generator
Sure, I can write a test case generator for the given problem. Here's a Python function that generates random test cases following the constraints specified in your problem statement:
```python
import random
def tcgen():
# Generate a random integer N (1 ≤ N ≤ 18)
N = random.randint(1, 18)
# Generate two lists A and B of size N with integers between 1 and 50
A = [random.randint(1, 50) for _ in range(N)]
B = [random.randint(1, 50) for _ in range(N)]
return N, A, B
# Example usage:
for _ in range(5): # Generate 5 test cases
N, A, B = tcgen()
print(f"{N}")
print(" ".join(map(str, A)))
print(" ".join(map(str, B)))
print()
```
### Explanation:
1. **N**: The number of cards (1 ≤ N ≤ 18).
2. **A**: A list of integers of size N representing the integers written in red ink on one side of the cards (each integer between 1 and 50).
3. **B**: A list of integers of size N representing the integers written in blue ink on the other side of the cards (each integer between 1 and 50).
The `tcgen` function generates random values for these according to the constraints and returns them. The example usage prints out 5 randomly generated test cases in the required format.
You can run the given code to generate test cases for the problem.
Extract Arguments
def extract_arguments(fh):
N = int(fh.readline().strip())
A = list(map(int, fh.readline().strip().split()))
B = list(map(int, fh.readline().strip().split()))
return N, A, B
# if __name__ == "__main__":
# input_path = sys.argv[1]
# with open(input_path, 'r') as fh:
# N, A, B = extract_arguments(fh)
# f(N, A, B)