Find Polygon With the Largest Perimeter

lcpy gen -n 2971   # by problem number
lcpy gen -s find_polygon_with_the_largest_perimeter   # by problem name

Input: nums = [5,5,5]
Output: 15
Explanation: The only possible polygon that can be made from nums has 3 sides: 5, 5, and 5. The perimeter is 5 + 5 + 5 = 15.

Input: nums = [1,12,1,2,5,50,3]
Output: 12
Explanation: The polygon with the largest perimeter which can be made from nums has 5 sides: 1, 1, 2, 3, and 5. The perimeter is 1 + 1 + 2 + 3 + 5 = 12.
We cannot have a polygon with either 12 or 50 as the longest side because it is not possible to include 2 or more smaller sides that have a greater sum than either of them.
It can be shown that the largest possible perimeter is 12.

Input: nums = [5,5,50]
Output: -1
Explanation: There is no possible way to form a polygon from nums, as a polygon has at least 3 sides and 50 > 5 + 5.

class Solution:
    # Time: O(n log n)
    # Space: O(n)
    def largest_perimeter(self, nums: list[int]) -> int:
        sides = sorted(nums)
        total = sum(sides)
        for i in range(len(sides) - 1, 1, -1):
            if total - sides[i] > sides[i]:
                return total
            total -= sides[i]
        return -1