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Type of Triangle

Difficulty: Easy

Problem Description

You are given a 0-indexed integer array nums of size 3 which can form the sides of a triangle. Return a string representing the type of triangle that can be formed or "none" if it cannot form a triangle.

Key Insights

  • A triangle is equilateral if all sides are equal.
  • A triangle is isosceles if exactly two sides are equal.
  • A triangle is scalene if all sides are of different lengths.
  • To determine if three sides can form a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Space and Time Complexity

Time Complexity: O(1)
Space Complexity: O(1)

Solution

To solve this problem, we will first check if the three sides can form a triangle using the triangle inequality theorem. If they can, we will then classify the triangle based on the lengths of its sides. We will use a simple comparison of the side lengths to determine the type: equilateral, isosceles, or scalene.

Code Solutions

def triangle_type(nums):
    # Check if the sides can form a triangle
    if nums[0] + nums[1] <= nums[2] or nums[0] + nums[2] <= nums[1] or nums[1] + nums[2] <= nums[0]:
        return "none"
    
    # Check for equilateral
    if nums[0] == nums[1] == nums[2]:
        return "equilateral"
    
    # Check for isosceles
    if nums[0] == nums[1] or nums[1] == nums[2] or nums[0] == nums[2]:
        return "isosceles"
    
    # If none of the above, it must be scalene
    return "scalene"
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