Problem p03136 - Generation 2

Orig Description

Score : 200 points
Problem StatementDetermine if an N-sided polygon (not necessarily convex) with sides of length L_1, L_2, ..., L_N can be drawn in a two-dimensional plane.
You can use the following theorem:
Theorem: an N-sided polygon satisfying the condition can be drawn if and only if the longest side is strictly shorter than the sum of the lengths of the other N-1 sides.
Constraints
All values in input are integers.
3 \leq N \leq 10
1 \leq L_i \leq 100
InputInput is given from Standard Input in the following format:
N
L_1 L_2 ... L_N
OutputIf an N-sided polygon satisfying the condition can be drawn, print Yes; otherwise, print No.
Sample Input 14
3 8 5 1
Sample Output 1Yes
Since 8 < 9 = 3 + 5 + 1, it follows from the theorem that such a polygon can be drawn on a plane.
Sample Input 24
3 8 4 1
Sample Output 2No
Since 8 \geq 8 = 3 + 4 + 1, it follows from the theorem that such a polygon cannot be drawn on a plane.
Sample Input 310
1 8 10 5 8 12 34 100 11 3
Sample Output 3No

Extracted Specification

An integer N (3 ≤ N ≤ 10), representing some quantity or size.
A list of integers L of size N, where each integer is between 1 and 100.

### Example Input:

```
4
3 8 5 1
```

### Function Signature:
Write a function f(N, L) that takes in the input.
def f(N: int, L: List[int]):
    '''
    N: an integer
    L: a list of integers
    '''

Test Case Generator

Sure, here is a test case generator for the given problem statement:

```python
import random

def tcgen(): 
    # Step 1: Generate a random integer N within the given constraints
    N = random.randint(3, 10)
    
    # Step 2: Generate a list of N integers, each within the specified range
    L = [random.randint(1, 100) for _ in range(N)]
    
    return N, L

# Example of generating a random test case
if __name__ == "__main__":
    N, L = tcgen()
    print(N)
    print(' '.join(map(str, L)))
```

### Explanation:

1. **Step 1**: We generate a random integer \(N\) where \(3 \leq N \leq 10\). This ensures that the number of sides of the polygon is within the specified constraints.

2. **Step 2**: We generate a list \(L\) of \(N\) integers where each integer \(L_i\) is between \(1\) and \(100\). This ensures that the length of each side of the polygon is within the specified range.

3. **Output**: The function returns \(N\) and the list \(L\). When executed, it prints \(N\) and the list \(L\) as space-separated integers.

This generator will produce random valid test cases for the problem statement.

Extract Arguments

def extract_arguments(fh):
    N = int(fh.readline().strip())
    L = list(map(int, fh.readline().strip().split()))
    return N, L