Orig Description
Problem Statement
Nathan O. Davis is a student at the department of integrated systems.
Today's agenda in the class is audio signal processing.
Nathan was given a lot of homework out.
One of the homework was to write a program to process an audio signal.
He copied the given audio signal to his USB memory and brought it back to his home.
When he started his homework, he unfortunately dropped the USB memory to the floor.
He checked the contents of the USB memory and found that the audio signal data got broken.
There are several characteristics in the audio signal that he copied.
The audio signal is a sequence of $N$ samples.
Each sample in the audio signal is numbered from $1$ to $N$ and represented as an integer value.
Each value of the odd-numbered sample(s) is strictly smaller than the value(s) of its neighboring sample(s).
Each value of the even-numbered sample(s) is strictly larger than the value(s) of its neighboring sample(s).
He got into a panic and asked you for a help.
You tried to recover the audio signal from his USB memory but some samples of the audio signal are broken and could not be recovered.
Fortunately, you found from the metadata that all the broken samples have the same integer value.
Your task is to write a program,
which takes the broken audio signal extracted from his USB memory as its input,
to detect whether the audio signal can be recovered uniquely.
Input
The input consists of multiple datasets.
The form of each dataset is described below.
$N$$a_{1}$ $a_{2}$ ... $a_{N}$
The first line of each dataset consists of an integer, $N (2 \le N \le 1{,}000)$.
$N$ denotes the number of samples in the given audio signal.
The second line of each dataset consists of $N$ values separated by spaces.
The $i$-th value, $a_{i}$, is either a character x or an integer between $-10^9$ and $10^9$, inclusive.
It represents the $i$-th sample of the broken audio signal.
If $a_{i}$ is a character x , it denotes that $i$-th sample in the audio signal is broken.
Otherwise it denotes the value of the $i$-th sample.
The end of input is indicated by a single $0$.
This is not included in the datasets.
You may assume that the number of the datasets does not exceed $100$.
Output
For each dataset, output the value of the broken samples in one line if the original audio signal can be recovered uniquely.
If there are multiple possible values, output ambiguous.
If there are no possible values, output none.
Sample Input
5
1 x 2 4 x
2
x x
2
1 2
2
2 1
2
1000000000 x
4
x 2 1 x
0
Output for the Sample Input
3
none
ambiguous
none
ambiguous
none
Extracted Specification
An integer N (2 ≤ N ≤ 1,000), representing some quantity or size.
A list of N values where each value is either an integer between -10^9 and 10^9 or a character 'x'.
The end of input is indicated by a single 0, which is not included in the datasets.
You may assume that the number of the datasets does not exceed 100.
### Example Input:
```
5
1 x 2 4 x
2
x x
2
1 2
2
2 1
2
1000000000 x
4
x 2 1 x
0
```
### Function Signature:
Write a function f(inputs) that takes in the input.
def f(inputs: List[Tuple[int, List[Union[int, str]]]]):
'''
inputs: a list of tuples, each containing an integer and a list of integers/strings
'''
Test Case Generator
Sure, let's write a test case generator for the given problem statement. We need to generate multiple datasets, each containing an integer \(N\) and a list with \(N\) elements, where some elements might be the character 'x', indicating broken samples, and other elements are integers between \(-10^9\) and \(10^9\). The end of the input is indicated by a single \(0\).
Here is the test case generator:
```python
import random
def generate_test_case():
# Randomly choose a value for N between 2 and 1000
N = random.randint(2, 1000)
# Generate the list with integers or 'x'
audio_signal = []
for _ in range(N):
# Randomly decide if the sample is broken or not
if random.random() < 0.3: # Let's say 30% chance of being broken
audio_signal.append('x')
else:
audio_signal.append(random.randint(-10**9, 10**9))
return N, audio_signal
def tcgen():
test_cases = []
# Randomly decide the number of datasets, not exceeding 100
num_datasets = random.randint(1, 100)
for _ in range(num_datasets):
N, audio_signal = generate_test_case()
test_cases.append((N, audio_signal))
# Append the final 0 to indicate the end of input
test_cases.append(0)
return test_cases
def print_test_cases(test_cases):
for case in test_cases:
if case == 0:
print("0")
else:
N, audio_signal = case
print(N)
print(" ".join(map(str, audio_signal)))
# Generate and print test cases
test_cases = tcgen()
print_test_cases(test_cases)
```
### Explanation:
1. **generate_test_case() function**:
- Randomly chooses \(N\) between 2 and 1000.
- Constructs an audio signal list with \(N\) elements, where each element is either an integer between \(-10^9\) and \(10^9\) or the character 'x'.
- Uses a 30% chance to insert a broken sample ('x').
2. **tcgen() function**:
- Generates a random number of datasets (up to 100).
- Calls generate_test_case() to create each dataset.
- Appends a final 0 to indicate the end of input.
3. **print_test_cases() function**:
- Prints all test cases in the expected format.
By running this code, you will generate test cases that can be used to test the problem of recovering the audio signal from broken samples.
Extract Arguments
def extract_arguments(fh):
datasets = []
while True:
N = int(fh.readline().strip())
if N == 0:
break
A = fh.readline().strip().split()
datasets.append((N, A))
return datasets
# if __name__ == "__main__":
# input_path = sys.argv[1]
# with open(input_path, 'r') as fh:
# datasets = extract_arguments(fh)
# f(datasets)