Problem p03904 - Generation 1

Orig Description

Score : 1000 points
Problem StatementYou are given a string S consisting of digits between 1 and 9, inclusive.
You will insert at most K commas (,) into this string to separate it into multiple numbers.
Your task is to minimize the maximum number among those produced by inserting commas. Find minimum possible such value.
Constraints
0 ≦ K < |S| ≦ 100,000
S consists of digits between 1 and 9, inclusive.
Partial Scores
In the test set worth 100 points, |S| ≦ 2.
In the test set worth another 100 points, |S| ≦ 16.
In the test set worth another 200 points, |S| ≦ 100.
In the test set worth another 200 points, |S| ≦ 2,000.
InputThe input is given from Standard Input in the following format:
K
S
OutputPrint the minimum possible value.
Sample Input 12
15267315
Sample Output 1315
When the string is separated into 152, 67 and 315, the maximum among these is 315, which is the minimum possible value.
Sample Input 20
12456174517653111
Sample Output 212456174517653111
12456174517653111 itself is the answer.
Sample Input 38
127356176351764127645176543176531763517635176531278461856198765816581726586715987216581
Sample Output 35317635176

Extracted Specification

An integer K (0 ≤ K < 100,000), representing some quantity or size.
A string S of digits of length |S|, where each digit is between 1 and 9.

### Example Input:

```
2
15267315
```

### Function Signature:
Write a function f(K, S) that takes in the input. 
```python
def f(K: int, S: str):
    ''' 
    K: an integer 
    S: a string of digits
    '''
```

Test Case Generator

Sure! Below is a Python function that generates test cases for the problem statement you provided. This function will randomly generate values for \( K \) and \( S \) within the specified constraints.

```python
import random

def tcgen():
    # Length of the string S
    length = random.randint(1, 100000)
    
    # Generate a random string S of digits between 1 and 9
    S = ''.join(random.choice('123456789') for _ in range(length))
    
    # Generate a random integer K such that 0 ≤ K < |S|
    K = random.randint(0, length - 1)
    
    return K, S

# Example usage
for _ in range(5):
    K, S = tcgen()
    print(f'K: {K}\nS: {S}\n')
```

### Explanation:
1. **Length of \( S \)**: The length of the string \( S \) is randomly chosen between 1 and 100,000.
2. **String \( S \)**: The string \( S \) is generated by randomly selecting digits between '1' and '9' for each position in the string.
3. **Value of \( K \)**: \( K \) is randomly chosen such that \( 0 \leq K < \text{length of } S \).

This function ensures that the generated test cases adhere to the constraints provided in the problem statement.

### Example Output:
The example usage shows how you can generate multiple test cases and print them. Each output will have a random \( K \) and a corresponding random string \( S \).

```plaintext
K: 5123
S: 918273645918273645...

K: 23456
S: 123456789123456789...

K: 99999
S: 987654321987654321...

...
```

Feel free to run the function and adjust it as needed for your specific testing needs.

Extract Arguments

def extract_arguments(fh):
    K = int(fh.readline().strip())
    S = fh.readline().strip()
    return K, S