3024. Type of Triangle
Description
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.
Constraints:
nums.length == 3
1 <= nums[i] <= 100
Solutions
Solution 1: Sorting + Case Discussion
First, we sort the array, and then we can classify and discuss according to the definition of a triangle.
- If the sum of the smallest two numbers is less than or equal to the largest number, then it cannot form a triangle, return "none".
- If the smallest number is equal to the largest number, then it is an equilateral triangle, return "equilateral".
- If the smallest number is equal to the middle number or the middle number is equal to the largest number, then it is an isosceles triangle, return "isosceles".
- Otherwise, return "scalene".
The time complexity is $O(1)$, and the space complexity is $O(1)$.
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