3024. Type of Triangle

You are given a 0-indexed integer array nums of size 3 which can form the sides of a triangle.

• A triangle is called equilateral if it has all sides of equal length.
• A triangle is called isosceles if it has exactly two sides of equal length.
• A triangle is called scalene if all its sides are of different lengths.

Return a string representing the type of triangle that can be formed or "none" if it cannot form a triangle.

Example 1:

Input: nums = [3,3,3]
Output: "equilateral"
Explanation: Since all the sides are of equal length, therefore, it will form an equilateral triangle.

Example 2:

Input: nums = [3,4,5]
Output: "scalene"
Explanation:
nums[0] + nums[1] = 3 + 4 = 7, which is greater than nums[2] = 5.
nums[0] + nums[2] = 3 + 5 = 8, which is greater than nums[1] = 4.
nums[1] + nums[2] = 4 + 5 = 9, which is greater than nums[0] = 3.
Since the sum of the two sides is greater than the third side for all three cases, therefore, it can form a triangle.
As all the sides are of different lengths, it will form a scalene triangle.

def triangleType(self, nums: List[int]) -> str:
	if not (nums[0] + nums[1] > nums[2] and nums[1] + nums[2] > nums[0] and nums[2] + nums[0] > nums[1]):
		return "none"
	if nums[0] == nums[1] == nums[2]:
		return "equilateral"
	elif nums[0] == nums[1] or nums[1] == nums[2] or nums[2] == nums[0]:
		return "isosceles"
	else:
		return "scalene"