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 integers A of size 2^N, where each integer is between 1 and 10^9.
### 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! Below is a Python function to generate test cases for the given problem statement.
```python
import random
def tcgen():
# Generate the value of N
N = random.randint(1, 18)
# The number of stones is 2^N
num_stones = 2 ** N
# Generate the hardness values for the stones
A = [random.randint(1, 10**9) for _ in range(num_stones)]
return N, A
# Example usage
N, A = tcgen()
print(N)
for hardness in A:
print(hardness)
```
### Explanation:
1. **N** is randomly selected between 1 and 18, inclusive.
2. **num_stones** is calculated as \(2^N\), which gives the number of stones participating in the contest.
3. **A** is a list of integers where each integer represents the hardness of a stone. The hardness is randomly selected between 1 and \(10^9\), inclusive.
4. The function returns \(N\) and the list \(A\).
### Example Output:
Here's an example of what the generated output might look like:
```
3
154315
999999999
472472
354354
832498
9999999
483483
675767
```
You can use this function to generate various test cases for your problem. Each time you run `tcgen()`, it will produce a new set of 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