Problem p00235 - Generation 2

Orig Description

Sergeant Ryan
Under the orders to "rescue Sergeant Ryan", the rescue team of the Aizu army was engaged in a fierce battle with enemy forces in the water city of Germany. They safely joined forces with Sergeant Ryan, but there were many enemy tanks and they were unable to call for rescue helicopters. So, they decided to execute a plan to blow up all the bridges in the city to confuse the enemy tanks.
The plan was immediately relayed to headquarters and preparations for the rescue helicopter were underway. To fly the rescue helicopter, it is necessary to predict when all the bridges will be blown up. Your task as a programmer in the military is to calculate the time required for the rescue team to blow up all the bridges.
The water city consists of N islands, and there are bridges between each island. All islands are connected like a tree (see diagram below). There is only one route from one island to another. Crossing each bridge takes a certain amount of time, and it is possible to cross the bridge in both directions in that time.
The rescue team has no means of moving on water, so they have no choice but to cross the bridges to move between islands. The rescue team can blow up the necessary bridges in the island where they are currently located in an instant. What is the minimum time required for the rescue team to blow up all the bridges? However, the time required to move within the island is not considered.
Create a program that takes the number of islands and the information on each bridge as input and outputs the minimum time required to blow up all the bridges. Each island is represented by a number from 1 to N. There are N-1 bridges. Bridge information consists of the numbers of two islands adjacent to the bridge (a, b) and the time required to cross the bridge t. The rescue team starts from island number 1.
Input
A sequence of multiple data sets is given as input. The end of the input is indicated by a single zero line. Each data set is given in the following format.
N
a1 b1 t1
a2 b2 t2
:
aN-1 bN-1 tN-1
All input is given as integers. The number of islands N (2 ≤ N ≤ 20) is given on the first line.
For the following N-1 lines, information on the i-th bridge is given. ai, bi, and ti (1 ≤ ti ≤ 500) represent that it is possible to travel between island ai and island bi in time ti by passing through the i-th bridge.
The number of data sets does not exceed 100.
Output
For each data set, output a line with the minimum time required to blow up all the bridges.
Sample Input
7
1 2 5
2 3 2
3 4 3
2 5 3
5 6 3
5 7 8
0
Output for the Sample Input
12

Extracted Specification

An integer N (2 ≤ N ≤ 20), representing some quantity or size.
A list of tuples of the form (a, b, t) of size N-1, where each tuple consists of three integers: 
- a (1 ≤ a ≤ N), an integer representing one part of a pair,
- b (1 ≤ b ≤ N), an integer representing the other part of the pair,
- t (1 ≤ t ≤ 500), an integer representing a time or weight.

The input ends with a single line containing zero.

### Example Input:

```
7
1 2 5
2 3 2
3 4 3
2 5 3
5 6 3
5 7 8
0
```

### Function Signature:
Write a function f(inputs) that takes in the input.
```python
def f(inputs: List[Tuple[int, List[Tuple[int, int, int]]]]):
    '''
    inputs: a list of tuples, where each tuple contains:
        - an integer N
        - a list of N-1 tuples (a, b, t)
    '''
```

Test Case Generator

Certainly! Below is a test case generator for the "Sergeant Ryan" problem. This generator will create random test cases following the constraints described in the problem statement.

```python
import random

def tcgen():
    # Generate a random number of islands N (2 ≤ N ≤ 20)
    N = random.randint(2, 20)

    bridges = []
    for i in range(2, N+1):
        # Connect the island i to a random previously created island
        a = random.randint(1, i-1)
        b = i
        t = random.randint(1, 500)
        bridges.append((a, b, t))

    return N, bridges

def generate_multiple_datasets(num_datasets=100):
    datasets = []
    for _ in range(num_datasets):
        N, bridges = tcgen()
        dataset = [N] + bridges
        datasets.append(dataset)
    return datasets

def format_datasets(datasets):
    formatted_data = ""
    for dataset in datasets:
        formatted_data += f"{dataset[0]}\n"
        for bridge in dataset[1:]:
            formatted_data += f"{bridge[0]} {bridge[1]} {bridge[2]}\n"
    formatted_data += "0\n"
    return formatted_data

# Generate test cases
datasets = generate_multiple_datasets(100)
formatted_output = format_datasets(datasets)
print(formatted_output)
```

### Explanation:
1. **`tcgen` Function**: This function generates a random test case:
   - It first picks a random number of islands \( N \) between 2 and 20.
   - For each island from 2 to \( N \), it connects it to a randomly selected previously created island, ensuring the tree structure.
   - Each bridge is assigned a random travel time \( t \) between 1 and 500.

2. **`generate_multiple_datasets` Function**: This function leverages `tcgen` to generate multiple datasets (up to 100 in this case).

3. **`format_datasets` Function**: This function formats the datasets to match the input format specified in the problem statement, with each dataset ending in a line with a `0`.

4. **Main Execution**: The code generates 100 datasets and prints them in the required format.

This script will produce a random but valid set of test cases that you can use to test your solution to the problem.

Extract Arguments

def extract_arguments(fh):
    data_sets = []
    while True:
        N = int(fh.readline().strip())
        if N == 0:
            break
        bridges = []
        for _ in range(N-1):
            a, b, t = map(int, fh.readline().strip().split())
            bridges.append((a, b, t))
        data_sets.append((N, bridges))
    return data_sets