Problem p03942 - Generation 2

Orig Description

Score : 1500 points
Problem Statement
Shik's job is very boring. At day 0, his boss gives him a string S_0 of length N which consists of only lowercase English letters. In the i-th day after day 0, Shik's job is to copy the string S_{i-1} to a string S_i. We denote the j-th letter of S_i as S_i[j].
Shik is inexperienced in this job. In each day, when he is copying letters one by one from the first letter to the last letter, he would make mistakes. That is, he sometimes accidentally writes down the same letter that he wrote previously instead of the correct one. More specifically, S_i[j] is equal to either S_{i-1}[j] or S_{i}[j-1]. (Note that S_i[1] always equals to S_{i-1}[1].)
You are given the string S_0 and another string T.
Please determine the smallest integer i such that S_i could be equal to T. If no such i exists, please print -1.
Constraints
1 \leq N \leq 1,000,000
The lengths of S_0 and T are both N.
Both S_0 and T consist of lowercase English letters.
InputThe input is given from Standard Input in the following format:
N
S_0
T
OutputPrint the smallest integer i such that S_i could be equal to T. If no such i exists, print -1 instead.
Sample Input 15
abcde
aaacc
Sample Output 12
S_0 = abcde, S_1 = aaccc and S_2 = aaacc is a possible sequence such that S_2 = T.
Sample Input 25
abcde
abcde
Sample Output 20
Sample Input 34
acaa
aaca
Sample Output 32
Sample Input 45
abcde
bbbbb
Sample Output 4-1

Extracted Specification

An integer N (1 ≤ N ≤ 1,000,000), representing some quantity or size.
A string S_0 of length N consisting of lowercase English letters.
A string T of length N consisting of lowercase English letters.

### Example Input:

```
5
abcde
aaacc
```

### Function Signature:
Write a function f(N, S_0, T) that takes in the input. 
def f(N: int, S_0: str, T: str): 
    ''' 
    N: an integer 
    S_0: a string of length N
    T: a string of length N
    '''

Test Case Generator

Sure, let's write a test case generator for the given problem statement.

The task is to generate test cases for the problem, which involves generating random strings \( S_0 \) and \( T \) of a given length \( N \). Here’s a Python function to generate such test cases:

```python
import random
import string

def tcgen():
    # Step 1: Generate a random N within the given constraints
    N = random.randint(1, 10**6)
    
    # Step 2: Generate a random string S_0 of length N
    S_0 = ''.join(random.choices(string.ascii_lowercase, k=N))
    
    # Step 3: Generate a random string T of length N
    T = ''.join(random.choices(string.ascii_lowercase, k=N))
    
    return N, S_0, T

# Example usage:
N, S_0, T = tcgen()
print(N)
print(S_0)
print(T)
```

Explanation:

1. **Step 1**: We generate a random integer \( N \) within the range [1, 1,000,000] using `random.randint`.

2. **Step 2**: We generate a random string \( S_0 \) of length \( N \) using `random.choices` with `string.ascii_lowercase` to get lowercase English letters.

3. **Step 3**: We generate another random string \( T \) of length \( N \), following the same approach as for \( S_0 \).

The function `tcgen()` will return a tuple containing the generated values \( N \), \( S_0 \), and \( T \).

This generator can be used to create various test cases for competitive programming problems by calling the function and printing or using its output as needed.

Extract Arguments

def extract_arguments(fh):
    N = int(fh.readline().strip())
    S_0 = fh.readline().strip()
    T = fh.readline().strip()
    return N, S_0, T