Problem p02238 - Generation 1

Orig Description

Depth First Search
  Depth-first search (DFS) follows the strategy to search ”deeper” in the graph whenever possible. In DFS, edges are recursively explored out of the most recently discovered vertex $v$ that still has unexplored edges leaving it. When all of $v$'s edges have been explored, the search ”backtracks” to explore edges leaving the vertex from which $v$ was discovered.
  This process continues until all the vertices that are reachable from the original source vertex have been discovered. If any undiscovered vertices remain, then one of them is selected as a new source and the search is repeated from that source.
  DFS timestamps each vertex as follows:
$d[v]$ records when $v$ is first discovered.
$f[v]$ records when the search finishes examining $v$’s adjacency list.
  Write a program which reads a directed graph $G = (V, E)$ and demonstrates DFS on the graph based on the following rules:
$G$ is given in an adjacency-list. Vertices are identified by IDs $1, 2,... n$ respectively.
IDs in the adjacency list are arranged in ascending order.
The program should report the discover time and the finish time for each vertex.
When there are several candidates to visit during DFS, the algorithm should select the vertex with the smallest ID.
The timestamp starts with 1.
Input
  In the first line, an integer $n$ denoting the number of vertices of $G$ is given. In the next $n$ lines, adjacency lists of $u$ are given in the following format:
$u$ $k$ $v_1$ $v_2$ ... $v_k$
$u$ is ID of the vertex and $k$ denotes its degree. $v_i$ are IDs of vertices adjacent to $u$.
Output
  For each vertex, print $id$, $d$ and $f$ separated by a space character in a line. $id$ is ID of the vertex, $d$ and $f$ is the discover time and the finish time respectively. Print in order of vertex IDs.
Constraints
$1 \leq n \leq 100$
Sample Input 1
4
1 1 2
2 1 4
3 0
4 1 3
Sample Output 1
1 1 8
2 2 7
3 4 5
4 3 6
Sample Input 2
6
1 2 2 3
2 2 3 4
3 1 5
4 1 6
5 1 6
6 0
Sample Output 2
1 1 12
2 2 11
3 3 8
4 9 10
5 4 7
6 5 6
  This is example for Sample Input 2 (discover/finish)
Reference
Introduction to Algorithms, Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. The MIT Press.

Extracted Specification

An integer \( n \) (1 ≤ \( n \) ≤ 100), representing some quantity or size.
A list of \( n \) lines, each line containing:
  1. An integer \( u \) (1 ≤ \( u \) ≤ 100), an identifier.
  2. An integer \( k \) (0 ≤ \( k \) ≤ 100), representing some quantity or size.
  3. \( k \) integers \( v_1, v_2, ..., v_k \) (1 ≤ \( v_i \) ≤ 100), representing identifiers.

### Example Input:

```
4
1 1 2
2 1 4
3 0
4 1 3
```

### Function Signature:
Write a function f(n, adjacency_list) that takes in the input.
def f(n: int, adjacency_list: List[Tuple[int, int, List[int]]]):
    '''
    n: an integer
    adjacency_list: a list of tuples, where each tuple contains an integer, an integer, and a list of integers
    '''

Test Case Generator

Sure, I can help you create a test case generator for the Depth First Search (DFS) problem.

Here's a Python function to generate test cases for the given problem statement:

```python
import random

def generate_graph(n):
    graph = []
    for u in range(1, n + 1):
        k = random.randint(0, n - 1)  # Number of adjacent vertices
        adj_vertices = random.sample(range(1, n + 1), k)
        adj_vertices.sort()  # Ensure IDs are in ascending order
        graph.append([u, k] + adj_vertices)
    return graph

def tcgen():
    n = random.randint(1, 100)
    graph = generate_graph(n)
    
    return n, graph

def format_test_case(n, graph):
    formatted_graph = "\n".join(" ".join(map(str, line)) for line in graph)
    return f"{n}\n{formatted_graph}"

# Generate a test case
n, graph = tcgen()
print(format_test_case(n, graph))
```

### Explanation:

1. **`generate_graph(n)`**: This function generates a random graph with `n` vertices. Each vertex `u` has a randomly determined number of adjacent vertices `k`, and we ensure that the adjacent vertices are listed in ascending order as required.

2. **`tcgen()`**: This function generates a random integer `n` (number of vertices) and calls `generate_graph(n)` to create the graph. It then returns the number of vertices and the adjacency list.

3. **`format_test_case(n, graph)`**: This utility function formats the generated test case into the required input format for the problem.

4. **Generate and print a test case**: The last part of the code generates a test case and prints it in the required format.

You can run the script to generate a random test case each time. The generated test cases will adhere to the constraints and format specified in the problem statement.

Extract Arguments

def extract_arguments(fh):
    n = int(fh.readline().strip())
    adjacency_list = []
    for _ in range(n):
        parts = list(map(int, fh.readline().strip().split()))
        u = parts[0]
        k = parts[1]
        v = parts[2:]
        adjacency_list.append((u, k, v))
    return n, adjacency_list

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