Problem p01055 - Generation 2

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 H (1 ≤ H ≤ 10^3), representing some quantity or size.
An integer W (1 ≤ W ≤ 10^3), representing some quantity or size.
An integer N (1 ≤ N ≤ 10^3), representing some quantity or size.
A list of N integers L, where each integer (1 ≤ L[i] ≤ 10^3) represents some quantity or size.
A list of N lists of tuples, where each tuple contains two integers (1 ≤ x, y ≤ 10^3).

### Example Input:

```
5
5
3
2 3 4
[(1, 2), (3, 4)]
[(1, 1), (2, 2), (3, 3)]
[(2, 3), (3, 4), (4, 5), (5, 6)]
```

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

Test Case Generator

Certainly! It looks like your problem statement got cut off. However, I can help you create a test case generator based on a common scenario in competitive programming involving grids, paths, and bombs.

Here’s a complete problem statement based on what you've provided and a test case generator for it:

### Problem Statement: Bomb Removal

**Description**

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 \( L_i \) squares, with the \( j \)-th square of the path specified by coordinates \( (px_{ij}, py_{ij}) \). Each bomb is located at the last square of its path \( (px_{iL_i}, py_{iL_i}) \).

**Input**

1. Two integers \( H \) and \( W \) (1 ≤ \( H, W \) ≤ 1000), representing the height and width of the grid.
2. An integer \( N \) (1 ≤ \( N \) ≤ 100), representing the number of fuse cords.
3. For each fuse cord:
   - An integer \( L_i \) (1 ≤ \( L_i \) ≤ 100), representing the length of the path of the \( i \)-th fuse cord.
   - \( L_i \) pairs of integers \( (px_{ij}, py_{ij}) \) (1 ≤ \( px_{ij} \) ≤ \( H \), 1 ≤ \( py_{ij} \) ≤ \( W \)), representing the coordinates of the path for the \( i \)-th fuse cord.

**Output**

Print the grid after all bombs have been placed.

**Example**

_Input_
```
5 5
2
3
1 1 2 2 3 3
2
4 1 5 5
```

_Output_
```
B . . . .
. B . . .
. . B . .
. . . . .
. . . . B
```

In the example, there are 2 fuse cords with bombs. The first fuse cord has a path of length 3 ending at (3,3), and the second fuse cord has a path of length 2 ending at (5,5). Bombs are placed at these positions on the grid.

### Test Case Generator

Here is a Python function to automatically generate test cases for the problem:

```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():
    H = random.randint(1, 1000)
    W = random.randint(1, 1000)
    N = random.randint(1, 100)
    
    test_case = []
    test_case.append(f"{H} {W}")
    test_case.append(f"{N}")
    
    for _ in range(N):
        L = random.randint(1, 100)
        path = generate_path(H, W, L)
        path_str = ' '.join(f"{x} {y}" for (x, y) in path)
        test_case.append(f"{L} {path_str}")
    
    return '\n'.join(test_case)

# Example usage
print(tcgen())
```

This function generates a random grid height and width, a random number of fuse cords, and for each fuse cord, it generates a random path of specified length within the grid. The output is formatted as a string that matches the input specification of the problem.

Extract Arguments

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