Problem p00593 - Generation 1

Orig Description

JPEG Compression
    The fundamental idea in the JPEG compression algorithm is to sort coeffi-
cient of given image by zigzag path and encode it. In this problem, we don’t
discuss about details of the algorithm, but you are asked to make simple pro-
gram. You are given single integer N , and you must output zigzag path on
a matrix where size is N by N . The zigzag scanning is start at the upper-left
corner (0, 0) and end up at the bottom-right corner. See the following Figure
and sample output to make sure rule of the zigzag scanning. For example, if you
are given N = 8, corresponding output should be a matrix shown in right-side
of the Figure. This matrix consists of visited time for each element.
Input
Several test cases are given. Each test case consists of one integer N (0 < N <
10) in a line. The input will end at a line contains single zero.
Output
For each input, you must output a matrix where each element is the visited
time. All numbers in the matrix must be right justified in a field of width 3.
Each matrix should be prefixed by a header “Case x:” where x equals test case
number.
Sample Input
3
4
0
Output for the Sample Input
Case 1:
  1  2  6
  3  5  7
  4  8  9
Case 2:
  1  2  6  7
  3  5  8 13
  4  9 12 14
 10 11 15 16

Extracted Specification

An integer \( N \) (0 < \( N \) < 10) representing some quantity or size, for several test cases. The input ends with a line containing a single zero.

### Example Input:
```
3
4
0
```

### Function Signature:
Write a function `f(inputs)` that takes in a list of tuples containing one integer each. 
```python
def f(inputs: List[Tuple[int]]):
    '''
    inputs: a list of tuples, where each tuple contains a single integer
    '''
```

Test Case Generator

Sure! Let's first understand the zigzag traversal of the matrix and then create a test case generator for the given problem.

### Zigzag Traversal Explanation

For an \(N \times N\) matrix, the traversal starts at the upper-left corner (0, 0) and moves in a zigzag manner until it reaches the bottom-right corner. The order of traversal can be visualized as follows:

For \(N = 3\):
```
1  2  6
3  5  7
4  8  9
```

For \(N = 4\):
```
 1  2  6  7
 3  5  8 13
 4  9 12 14
10 11 15 16
```

### Test Case Generator

The test case generator will create random values for \(N\) in the given range (0 < N < 10) and generate these matrices accordingly. The input will end with a line containing a single zero.

Here's the Python code for the test case generator:

```python
import random

def zigzag_traversal(n):
    matrix = [[0]*n for _ in range(n)]
    i, j = 0, 0
    direction = 1  # 1 for down, -1 for up
    for num in range(1, n*n + 1):
        matrix[i][j] = num
        if direction == 1:
            if j == 0 or i == n - 1:
                direction = -1
                if i == n - 1:
                    j += 1
                else:
                    i += 1
            else:
                i += 1
                j -= 1
        else:
            if i == 0 or j == n - 1:
                direction = 1
                if j == n - 1:
                    i += 1
                else:
                    j += 1
            else:
                i -= 1
                j += 1
    return matrix

def tcgen():
    test_cases = []
    
    # Generate a random number of test cases between 1 and 10
    num_cases = random.randint(1, 10)
    
    for _ in range(num_cases):
        N = random.randint(1, 9)
        test_cases.append(N)
    
    # Append the terminating zero
    test_cases.append(0)
    
    return test_cases

def format_output(test_cases):
    case_number = 1
    output = ""
    for N in test_cases:
        if N == 0:
            break
        output += f"Case {case_number}:\n"
        matrix = zigzag_traversal(N)
        for row in matrix:
            output += " ".join(f"{num:3}" for num in row) + "\n"
        case_number += 1
    return output

# Example usage
test_cases = tcgen()
formatted_output = format_output(test_cases)
print("Sample Input:")
print("\n".join(map(str, test_cases)))

print("\nOutput for the Sample Input:")
print(formatted_output)
```

### Explanation

1. **`zigzag_traversal(n)`**: Generates the zigzag order matrix for a given \(N \times N\).
2. **`tcgen()`**: Generates a random number of test cases, each with a random \(N\) in the range (1, 9). Adds a terminating zero at the end.
3. **`format_output(test_cases)`**: Formats the test cases and their corresponding matrices to match the required output format.

This code first generates random test cases and then formats them to display the required zigzag traversal matrices. The `print` statements demonstrate the sample input and its corresponding output as specified.

Extract Arguments

def extract_arguments(fh):
    inputs = []
    case_number = 1
    while True:
        N = int(fh.readline().strip())
        if N == 0:
            break
        inputs.append((case_number, N))
        case_number += 1
    return inputs