Problem p01055 - Generation 1

Orig Description

Bomb Removal
Problem
There are N fuse cords and bombs, each with one bomb, on a grid of height H and width W. Each fuse cord and bomb are placed on a path consisting of Li squares, with the j-th square of the path (pxij, pyij). Each bomb is located at the last square (pxiLi, py<

Extracted Specification

Canonicalized Input Description:

An integer N (1 ≤ N ≤ 10^3), representing some quantity or size.
An integer H (1 ≤ H ≤ 10^3), representing some dimension or height.
An integer W (1 ≤ W ≤ 10^3), representing some dimension or width.
A list of N integers L, where each integer represents a size (1 ≤ L[i] ≤ 10^3).
A list of N lists of tuples of integers (pxij, pyij), where each tuple represents coordinates (0 ≤ pxij < W, 0 ≤ pyij < H).

### Example Input:

```
2
5
5
3 4
[(0, 1), (1, 2), (2, 3)]
[(1, 1), (2, 2), (3, 3), (4, 4)]
```

### Function Signature:
Write a function f(N, H, W, L, paths) that takes in the input.
```python
def f(N: int, H: int, W: int, L: List[int], paths: List[List[Tuple[int, int]]]): 
    ''' 
    N: an integer
    H: an integer
    W: an integer
    L: a list of integers
    paths: a list of lists of tuples of integers
    '''
```

Test Case Generator

Sure, let's write a test case generator for the given problem statement "Bomb Removal". However, it seems like the problem statement is not complete. Based on the partial description provided, I will make some reasonable assumptions to complete the problem statement. If you have more details, please add them to refine the generator.

### Assumptions:
1. **Input**
   - An integer \( N \) (1 ≤ \( N \) ≤ 1000), representing the number of fuse cords and bombs.
   - An integer \( H \) (1 ≤ \( H \) ≤ 1000), representing the height of the grid.
   - An integer \( W \) (1 ≤ \( W \) ≤ 1000), representing the width of the grid.
   - \( N \) lists of integers where the \( i \)-th list represents the path of the \( i \)-th fuse cord with \( L_i \) squares. Each path contains \( L_i \) pairs of integers (pxij, pyij) indicating the x and y coordinates of the j-th square.

2. **Output**
   - The output will be dependent on the problem's requirements, which are not entirely clear from the statement. For now, we will focus on generating the input.

### Test Case Generator:
```python
import random

def generate_path(H, W, L):
    path = []
    for _ in range(L):
        x = random.randint(1, H)
        y = random.randint(1, W)
        path.append((x, y))
    return path

def tcgen():
    N = random.randint(1, 1000)
    H = random.randint(1, 1000)
    W = random.randint(1, 1000)
    
    paths = []
    for _ in range(N):
        L = random.randint(1, min(H, W))  # Reasonable assumption for path length
        path = generate_path(H, W, L)
        paths.append(path)
    
    return N, H, W, paths

# Example usage
N, H, W, paths = tcgen()
print(f"{N} {H} {W}")
for path in paths:
    print(len(path), " ".join(f"{x} {y}" for x, y in path))
```

### Explanation:
1. **generate_path(H, W, L)**: Generates a path of length \( L \) with coordinates within the grid dimensions \( H \) and \( W \).
2. **tcgen()**: Generates the entire input:
   - Randomly selects \( N \), \( H \), and \( W \) within the specified ranges.
   - For each fuse cord, generates a path of random length \( L \) (with a reasonable assumption that \( L \leq \min(H, W) \)).
   - Returns the generated values.

This should provide a good starting point for generating test cases for the "Bomb Removal" problem. You can adjust the specifics of the grid or path generation as necessary based on additional problem details.

Extract Arguments

def extract_arguments(fh):
    N = int(fh.readline().strip())
    H, W = map(int, fh.readline().strip().split())
    paths = []
    for _ in range(N):
        Li = int(fh.readline().strip())
        path = []
        for _ in range(Li):
            pxij, pyij = map(int, fh.readline().strip().split())
            path.append((pxij, pyij))
        paths.append(path)
    return N, H, W, paths

# if __name__ == "__main__":
#     input_path = sys.argv[1]
#     with open(input_path, 'r') as fh: 
#         N, H, W, paths = extract_arguments(fh)
#     f(N, H, W, paths)