Problem p01055 - Generation 3

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 ≤ 1000), representing some dimension.
An integer W (1 ≤ W ≤ 1000), representing some dimension.
A list of N integers Li (1 ≤ Li ≤ 100), representing sizes.
A list of N lists of tuples (pxij, pyij), where each tuple contains two integers (0 ≤ pxij < W, 0 ≤ pyij < H).

### Example Input:
```
3
10
10
2 3 4
[(0, 0), (1, 1)]
[(2, 2), (3, 3), (4, 4)]
[(5, 5), (6, 6), (7, 7), (8, 8)]
```

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

Test Case Generator

Certainly! Based on the given partial problem statement for "Bomb Removal," here is a more complete problem statement along with a test case generator:

### Problem Statement: Bomb Removal

**Description**

You are given a grid of height \( H \) and width \( W \) with \( N \) bombs, each connected by a fuse cord. Each fuse cord follows a specific path consisting of \( L_i \) squares, and the bomb is located at the last square of the path. The goal is to determine the final positions of all bombs after the paths are traced.

**Input**

1. An integer \( H \) (1 ≤ \( H \) ≤ 100), representing the height of the grid.
2. An integer \( W \) (1 ≤ \( W \) ≤ 100), representing the width of the grid.
3. An integer \( N \) (1 ≤ \( N \) ≤ 10), representing the number of bombs.
4. For each bomb, an integer \( L_i \) (1 ≤ \( L_i \) ≤ 20), representing the length of the path.
5. For each bomb's path, a list of \( L_i \) tuples \((px_{i,j}, py_{i,j})\) representing the coordinates of the path squares in the grid, where \( 1 ≤ px_{i,j} ≤ H \) and \( 1 ≤ py_{i,j} ≤ W \).

**Output**

For each bomb, print the final position \((px_{i,L_i}, py_{i,L_i})\).

**Examples**

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

_Output_
```
3 3
2 2
```

**Explanation**

In the example, there are two bombs:
1. The first bomb's path is \((1,1) \rightarrow (2,2) \rightarrow (3,3)\). The final position is \((3,3)\).
2. The second bomb's path is \((5,5) \rightarrow (4,4) \rightarrow (3,3) \rightarrow (2,2)\). The final position is \((2,2)\).

**Note**

This problem tests your ability to handle multiple sequences of movements on a grid and extracting the final positions from those paths.

### Test Case Generator

Here is the test case generator for the "Bomb Removal" problem:

```python
import random

def tcgen():
    H = random.randint(1, 100)
    W = random.randint(1, 100)
    N = random.randint(1, 10)
    
    bomb_paths = []
    for _ in range(N):
        L = random.randint(1, 20)
        path = []
        for _ in range(L):
            px = random.randint(1, H)
            py = random.randint(1, W)
            path.append((px, py))
        bomb_paths.append(path)
    
    return H, W, N, bomb_paths

# Generate a test case
test_case = tcgen()
H, W, N, bomb_paths = test_case

# Print the test case in the required format
print(H)
print(W)
print(N)
for path in bomb_paths:
    print(len(path))
    for px, py in path:
        print(px, py)
```

This generator function creates random values for the height \( H \), width \( W \), and the number of bombs \( N \). For each bomb, it generates a random path of length \( L \) with coordinates within the grid's boundaries.

Extract Arguments

def extract_arguments(fh):
    N, H, W = map(int, fh.readline().strip().split())
    fuse_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))
        fuse_paths.append(path)
    return N, H, W, fuse_paths

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