Problem p01957 - Generation 2

Orig Description

Tournament Chart
  In 21XX, an annual programming contest, Japan Algorithmist GrandPrix (JAG) has become one of the most popular mind sports events.
  JAG is conducted as a knockout tournament. This year, $N$ contestants will compete in JAG. A tournament chart is represented as a string. '[[a-b]-[c-d]]' is an easy example. In this case, there are 4 contestants named a, b, c, and d, and all matches are described as follows:
Match 1 is the match between a and b.
Match 2 is the match between c and d.
Match 3 is the match between [the winner of match 1] and [the winner of match 2].
  More precisely, the tournament chart satisfies the following BNF:
 ::=  | "["  "-"  "]"
 ::= "a" | "b" | "c" | ... | "z"
  You, the chairperson of JAG, are planning to announce the results of this year's JAG competition. However, you made a mistake and lost the results of all the matches. Fortunately, you found the tournament chart that was printed before all of the matches of the tournament. Of course, it does not contains results at all. Therefore, you asked every contestant for the number of wins in the tournament, and got $N$ pieces of information in the form of "The contestant $a_i$ won $v_i$ times".
Now, your job is to determine whether all of these replies can be true.
Input
  The input consists of a single test case in the format below.
$S$
$a_1$ $v_1$
:
$a_N$ $v_N$
$S$ represents the tournament chart. $S$ satisfies the above BNF. The following $N$ lines represent the information of the number of wins. The ($i+1$)-th line consists of a lowercase letter $a_i$ and a non-negative integer $v_i$ ($v_i \leq 26$) separated by a space, and this means that the contestant $a_i$ won $v_i$ times. Note that $N$ ($2 \leq N \leq 26$) means that the number of contestants and it can be identified by string $S$. You can assume that each letter $a_i$ is distinct. It is guaranteed that $S$ contains each $a_i$ exactly once and doesn't contain any other lowercase letters.
Output
Print 'Yes' in one line if replies are all valid for the tournament chart. Otherwise, print 'No' in one line.
Sample Input 1
[[m-y]-[a-o]]
o 0
a 1
y 2
m 0
Output for Sample Input 1
Yes
Sample Input 2
[[r-i]-[m-e]]
e 0
r 1
i 1
m 2
Output for Sample Input 2
No

Extracted Specification

An integer N (2 ≤ N ≤ 26), representing some quantity or size.
A string S that follows a specific format containing exactly N unique lowercase letters.
A list of tuples of the form (char, int), where char is a unique lowercase letter from the string S and int (0 ≤ int ≤ 26) represents some quantity associated with the letter.

### Example Input:

```
[[m-y]-[a-o]]
o 0
a 1
y 2
m 0
```

### Function Signature:
Write a function f(S, inputs) that takes in the input.
```python
def f(S: str, inputs: List[Tuple[str, int]]):
    '''
    S: a string
    inputs: a list of tuples
    '''
```

Test Case Generator

Sure, I can help you write a test case generator for the "Tournament Chart" problem. Here is a Python function that generates random test cases for this problem:

```python
import random
import string

def generate_tournament_chart(contestants):
    """
    Generates a balanced tournament chart for a given list of contestants.
    """
    if len(contestants) == 1:
        return contestants[0]
    mid = len(contestants) // 2
    left_chart = generate_tournament_chart(contestants[:mid])
    right_chart = generate_tournament_chart(contestants[mid:])
    return f"[{left_chart}-{right_chart}]"

def tcgen():
    N = random.randint(2, 26)  # Number of contestants (2 ≤ N ≤ 26)
    
    # Generate unique contestants
    contestants = random.sample(string.ascii_lowercase, N)
    
    # Generate tournament chart
    S = generate_tournament_chart(contestants)
    
    # Generate win counts for each contestant
    wins = {contestant: random.randint(0, N - 1) for contestant in contestants}
    
    # Format the output
    result = [S]
    for contestant in contestants:
        result.append(f"{contestant} {wins[contestant]}")
    
    return "\n".join(result)

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

### Explanation

1. **generate_tournament_chart(contestants):**
   This recursive function generates a balanced tournament chart for a given list of contestants. It splits the list into two halves, recursively generates the tournament chart for each half, and then combines them into the required format.

2. **tcgen():**
   - **N:** Randomly chooses the number of contestants between 2 and 26.
   - **contestants:** Randomly samples `N` unique lowercase letters to represent the contestants.
   - **S:** Uses the `generate_tournament_chart` function to create the tournament chart.
   - **wins:** Randomly generates a win count for each contestant.
   - **result:** Formats the output as required by the problem statement.

You can run the `tcgen()` function to generate a random test case for the "Tournament Chart" problem. The function prints the tournament chart followed by the win counts for each contestant.

Extract Arguments

def extract_arguments(fh):
    S = fh.readline().strip()
    N = S.count('-') + 1
    wins = {}
    for _ in range(N):
        line = fh.readline().strip().split()
        contestant = line[0]
        wins[contestant] = int(line[1])
    return S, wins