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 ≤ \(N\) ≤ 1000), representing some quantity or size.
A list of \(N\) values where each value is either a character 'x' or an integer between \(-10^9\) and \(10^9\).
The end of input is indicated by a single 0, which is not included in the datasets.
### 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.
```python
def f(inputs: List[Tuple[int, List[Union[int, str]]]]):
'''
inputs: a list of tuples, where each tuple contains:
- an integer N: the size
- a list of N values: a mix of integers and characters
'''
```
Test Case Generator
Sure, let's create a test case generator for the given problem statement. The generator will create datasets with varying lengths and broken samples following the specified rules.
Here's a test case generator for the problem:
```python
import random
def tcgen():
datasets = []
# Number of datasets
num_datasets = random.randint(1, 100)
for _ in range(num_datasets):
# Random length of the audio signal (N)
N = random.randint(2, 1000)
# Create the audio signal array with a mix of integers and 'x' (broken samples)
audio_signal = []
for i in range(N):
if random.random() < 0.3: # 30% chance that a sample is broken
audio_signal.append('x')
else:
audio_signal.append(random.randint(-10**9, 10**9))
# Append the generated dataset to datasets list
datasets.append((N, audio_signal))
return datasets
# Function to print the datasets in the required format
def print_datasets(datasets):
for dataset in datasets:
N, audio_signal = dataset
print(N)
print(" ".join(map(str, audio_signal)))
print(0)
# Generate and print the datasets
datasets = tcgen()
print_datasets(datasets)
```
This Python script creates a function `tcgen` that generates multiple datasets according to the given constraints. The `print_datasets` function prints these datasets in the required format.
Here is a step-by-step explanation of the script:
1. **Generating the Number of Datasets**: We randomly determine the number of datasets (1 to 100).
2. **Generating Each Dataset**:
- We randomly determine the length \( N \) of the audio signal for each dataset (2 to 1000).
- We construct the audio signal array with a mix of integers and 'x' (broken samples). There is a 30% chance that any given sample is broken.
3. **Printing the Datasets**: We print each dataset followed by a zero to indicate the end of input.
You can run this script to generate multiple test cases for the given problem.
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)