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
To generate test cases for the given problem statement, we need to follow the constraints and the theorem provided. Here's a test case generator function that adheres to the problem constraints and ensures valid random input based on the conditions:
```python
import random
def tcgen():
# Number of sides for the polygon
N = random.randint(3, 10)
# List of side lengths
L = [random.randint(1, 100) for _ in range(N)]
return N, L
# Function to format the test case for easy use
def format_test_case(N, L):
return f"{N}\n{' '.join(map(str, L))}"
# Example usage
if __name__ == "__main__":
N, L = tcgen()
test_case = format_test_case(N, L)
print(test_case)
```
### Explanation:
1. **N**: We randomly generate the number of sides \(N\) for the polygon, ensuring it is between 3 and 10 (inclusive) as per the problem constraints.
2. **L**: We generate a list of \(N\) side lengths, each being a random integer between 1 and 100 (inclusive).
3. **format_test_case**: This helper function formats the test case in the way it is expected for input, making it easier to visualize and use directly.
### Example Output:
Here is what an example output could look like when you run the test case generator:
```
7
14 56 23 45 67 89 12
```
### Running the Generator:
Every time you run the `tcgen` function, it will produce a new random test case that you can use to test your solution.
This generator ensures that the test cases are within the constraints and can be used to validate the implementation of the solution effectively.
Extract Arguments
def extract_arguments(fh):
N = int(fh.readline().strip())
L = list(map(int, fh.readline().strip().split()))
return N, L
# if __name__ == "__main__":
# input_path = sys.argv[1]
# with open(input_path, 'r') as fh:
# N, L = extract_arguments(fh)
# f(N, L)