Problem p03974 - Generation 3

Orig Description

Score : 1100 points
Problem StatementThere are N strings of lowercase alphabet only. The i-th string is S_i. Every string is unique.
Provide answers for the Q queries below. The i-th query has the following format:
Query: An integer k_i and a string p_{i,1}p_{i,2}...p_{i,26} that results from permuting {a,b,...,z} are given. Output the sequence of the string S_{k_i} among the N strings in lexicographical order when the literal sequence is p_{i,1}
                

Extracted Specification

An integer N (1 ≤ N ≤ 100,000), representing some quantity or size.
N strings, each consisting of lowercase alphabet characters. Each string is unique.
An integer Q (1 ≤ Q ≤ 100,000), representing some quantity or size.
Q pairs, each consisting of an integer k (1 ≤ k ≤ N) and a permutation of the lowercase alphabet characters.

### Example Input:

```
5
aa
abbaa
abbba
aaab
aaaaaba
5
1 abcdefghijklmnopqrstuvwxyz
2 bacdefghijklmnopqrstuvwxyz
3 abcdefghijklmnopqrstuvwxyz
4 bacdefghijklmnopqrstuvwxyz
5 abcdefghijklmnopqrstuvwxyz
```

### Function Signature:
Write a function f(N, strings, Q, queries) that takes in the input.
```
def f(N: int, strings: List[str], Q: int, queries: List[Tuple[int, str]]):
    '''
    N: an integer
    strings: a list of strings
    Q: an integer
    queries: a list of tuples, each containing an integer and a string
    '''
```

Test Case Generator

Sure, I can help you write a test case generator for the given problem statement. Here is a Python function that generates random test cases for the described problem:

```python
import random
import string

def generate_random_string(length):
    return ''.join(random.choices(string.ascii_lowercase, k=length))

def generate_unique_strings(N, max_total_length):
    unique_strings = set()
    current_length = 0
    
    while len(unique_strings) < N:
        length = random.randint(1, min(100, max_total_length - current_length))
        new_string = generate_random_string(length)
        if new_string not in unique_strings:
            unique_strings.add(new_string)
            current_length += length
    
    return list(unique_strings)

def tcgen():
    N = random.randint(1, 100000)
    max_total_length = 400000
    strings = generate_unique_strings(N, max_total_length)
    
    Q = random.randint(1, 100000)
    queries = []
    
    for _ in range(Q):
        k = random.randint(1, N)
        perm = ''.join(random.sample(string.ascii_lowercase, 26))
        queries.append((k, perm))
    
    return N, strings, Q, queries

def format_test_case(N, strings, Q, queries):
    result = [str(N)]
    result.extend(strings)
    result.append(str(Q))
    for k, perm in queries:
        result.append(f"{k} {perm}")
    return "\n".join(result)

# Generate a test case
N, strings, Q, queries = tcgen()
test_case = format_test_case(N, strings, Q, queries)
print(test_case)
```

### Explanation

1. **generate_random_string(length)**: Generates a random string of lowercase letters of the specified length.
2. **generate_unique_strings(N, max_total_length)**: Generates `N` unique strings of lowercase letters such that the sum of the lengths does not exceed `max_total_length`.
3. **tcgen()**: Generates the test case parameters:
   - `N`: Number of unique strings.
   - `strings`: List of `N` unique strings.
   - `Q`: Number of queries.
   - `queries`: List of tuples where each tuple contains a query in the form `(k, perm)`, where `k` is an integer and `perm` is a permutation of the alphabet.
4. **format_test_case(N, strings, Q, queries)**: Formats the generated test case into the specified input format.

Run the provided script to generate and print a test case. This will give you random yet valid inputs that adhere to the constraints described in the problem statement.

Extract Arguments

def extract_arguments(fh):
    N = int(fh.readline().strip())
    S = [fh.readline().strip() for _ in range(N)]
    Q = int(fh.readline().strip())
    queries = []
    for _ in range(Q):
        k_p = fh.readline().strip().split()
        k = int(k_p[0])
        p = k_p[1]
        queries.append((k, p))
    return N, S, Q, queries