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).
A list of integers A of size 2^N, where each integer is 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.
```python
def f(N: int, A: List[int]):
'''
N: an integer
A: a list of integers
'''
```
Test Case Generator
Certainly! Here is a Python function to generate test cases for the given "Kode Festival" problem statement.
```python
import random
def tcgen():
N = random.randint(1, 18)
A = [random.randint(1, 10**9) for _ in range(2**N)]
return N, A
# Example usage:
if __name__ == "__main__":
N, A = tcgen()
print(N)
for a in A:
print(a)
```
This function `tcgen()` generates a random value for \(N\) within the range [1, 18] and then generates \(2^N\) random integers within the range [1, 10^9] for the array \(A\). The generated values are printed in the format specified by the problem statement.
You can run this script to generate random test cases to use for testing your solution to the problem.
Extract Arguments
def extract_arguments(fh):
N = int(fh.readline().strip())
A = []
for _ in range(2 ** N):
A.append(int(fh.readline().strip()))
return N, A