Problem p03890 - Generation 1

Orig Description

Score : 100 points
Problem StatementKode Festival is an anual contest where the hardest stone in the world is determined. (Kode is a Japanese word for "hardness".)
This year, 2^N stones participated. The hardness of the i-th stone is A_i.
In the contest, stones are thrown at each other in a knockout tournament.
When two stones with hardness X and Y are thrown at each other, the following will happen:
When X > Y:
  The stone with hardness Y will be destroyed and eliminated.
  The hardness of the stone with hardness X will become X-Y.
When X = Y:
  One of the stones will be destroyed and eliminated.
  The hardness of the other stone will remain the same.
When X < Y:
  The stone with hardness X will be destroyed and eliminated.
  The hardness of the stone with hardness Y will become Y-X.
The 2^N stones will fight in a knockout tournament as follows:
The following pairs will fight: (the 1-st stone versus the 2-nd stone), (the 3-rd stone versus the 4-th stone), ...
The following pairs will fight: (the winner of (1-st versus 2-nd) versus the winner of (3-rd versus 4-th)), (the winner of (5-th versus 6-th) versus the winner of (7-th versus 8-th)), ...
And so forth, until there is only one stone remaining.
Determine the eventual hardness of the last stone remaining.
Constraints
1 \leq N \leq 18
1 \leq A_i \leq 10^9
A_i is an integer.
InputThe input is given from Standard Input in the following format:
N
A_1
A_2
:
A_{2^N}
OutputPrint the eventual hardness of the last stone remaining.
Sample Input 12
1
3
10
19
Sample Output 17
Sample Input 23
1
3
2
4
6
8
100
104
Sample Output 22

Extracted Specification

An integer N (1 ≤ N ≤ 18), representing some quantity or size.
A list of 2^N integers, each between 1 and 1e9.

### Example Input:

```
2
1
3
2
4
6
8
100
104
```

### Function Signature:
Write a function f(N, A) that takes in the input. 
def f(N: int, A: List[int]): 
    ''' 
    N: an integer
    A: a list of integers
    '''

Test Case Generator

Sure! Here's a test case generator for the given problem statement:

```python
import random

def generate_test_case():
    # Generate a random value for N
    N = random.randint(1, 18)
    
    # Generate 2^N random integers for the hardness values
    A = [random.randint(1, 10**9) for _ in range(2**N)]
    
    return N, A

def print_test_case(N, A):
    print(N)
    for hardness in A:
        print(hardness)

# Example of generating and printing a test case
if __name__ == "__main__":
    N, A = generate_test_case()
    print_test_case(N, A)
```

This script generates a test case for the problem statement involving a knockout tournament of stones with given hardness values. The function `generate_test_case` creates a random value for `N` between 1 and 18, and then generates `2^N` random integers for the hardness values, each between 1 and `10^9`. The function `print_test_case` is used to print the generated test case in the required format.

You can run the script to generate and print a test case. This will help you to test your solution by providing various random inputs.

Extract Arguments

def extract_arguments(fh):
    N = int(fh.readline().strip())
    A = [int(fh.readline().strip()) for _ in range(2 ** N)]
    return N, A