Problem p02954 - Generation 2

Orig Description

Score : 400 points
Problem StatementGiven is a string S consisting of L and R.
Let N be the length of S. There are N squares arranged from left to right, and the i-th character of S from the left is written on the i-th square from the left.
The character written on the leftmost square is always R, and the character written on the rightmost square is always L.
Initially, one child is standing on each square.
Each child will perform the move below 10^{100} times:
Move one square in the direction specified by the character written in the square on which the child is standing. L denotes left, and R denotes right.
Find the number of children standing on each square after the children performed the moves.
Constraints
S is a string of length between 2 and 10^5 (inclusive).
Each character of S is L or R.
The first and last characters of S are R and L, respectively.
InputInput is given from Standard Input in the following format:
S
OutputPrint the number of children standing on each square after the children performed the moves, in order from left to right.
Sample Input 1RRLRL
Sample Output 10 1 2 1 1
After each child performed one move, the number of children standing on each square is 0, 2, 1, 1, 1 from left to right.
After each child performed two moves, the number of children standing on each square is 0, 1, 2, 1, 1 from left to right.
After each child performed 10^{100} moves, the number of children standing on each square is 0, 1, 2, 1, 1 from left to right.
Sample Input 2RRLLLLRLRRLL
Sample Output 20 3 3 0 0 0 1 1 0 2 2 0
Sample Input 3RRRLLRLLRRRLLLLL
Sample Output 30 0 3 2 0 2 1 0 0 0 4 4 0 0 0 0

Extracted Specification

An integer N (2 ≤ N ≤ 10^5), representing some quantity or size.
A string S of length N, consisting of the characters 'L' and 'R'. The first character of S is 'R' and the last character is 'L'.

### Example Input:

```
5
RRLRL
```

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

Test Case Generator

Sure, let's create a test case generator for the given problem. The problem involves generating a string `S` that consists of characters 'L' and 'R', with the constraints that the first character is 'R' and the last character is 'L'. The length of the string can vary between 2 and \(10^5\).

Here's the test case generator:

```python
import random

def generate_test_case():
    # Set the length of the string S between 2 and 10^5
    N = random.randint(2, 10**5)
    
    # The first character must be 'R' and the last character must be 'L'
    S = ['R'] + [random.choice(['L', 'R']) for _ in range(N - 2)] + ['L']
    
    return ''.join(S)

# Example usage:
test_case = generate_test_case()
print(test_case)
```

This function will generate a random valid string `S` according to the given constraints.

### Explanation:
1. **Length Constraint**: `N` is generated randomly between 2 and \(10^5\).
2. **String Generation**: 
   - The first character is set to `'R'`.
   - The last character is set to `'L'`.
   - The characters in between are randomly chosen from `'L'` and `'R'`.

You can run this function multiple times to generate different test cases for your problem.

Extract Arguments

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