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 $O(1)$.

Python3

class Solution:
    def triangleType(self, nums: List[int]) -> str:
        nums.sort()
        if nums[0] + nums[1] <= nums[2]:
            return "none"
        if nums[0] == nums[2]:
            return "equilateral"
        if nums[0] == nums[1] or nums[1] == nums[2]:
            return "isosceles"
        return "scalene"

Java

class Solution {
    public String triangleType(int[] nums) {
        Arrays.sort(nums);
        if (nums[0] + nums[1] <= nums[2]) {
            return "none";
        }
        if (nums[0] == nums[2]) {
            return "equilateral";
        }
        if (nums[0] == nums[1] || nums[1] == nums[2]) {
            return "isosceles";
        }
        return "scalene";
    }
}

C++

class Solution {
public:
    string triangleType(vector<int>& nums) {
        sort(nums.begin(), nums.end());
        if (nums[0] + nums[1] <= nums[2]) {
            return "none";
        }
        if (nums[0] == nums[2]) {
            return "equilateral";
        }
        if (nums[0] == nums[1] || nums[1] == nums[2]) {
            return "isosceles";
        }
        return "scalene";
    }
};

Go

func triangleType(nums []int) string {
	sort.Ints(nums)
	if nums[0]+nums[1] <= nums[2] {
		return "none"
	}
	if nums[0] == nums[2] {
		return "equilateral"
	}
	if nums[0] == nums[1] || nums[1] == nums[2] {
		return "isosceles"
	}
	return "scalene"
}

TypeScript

function triangleType(nums: number[]): string {
    nums.sort((a, b) => a - b);
    if (nums[0] + nums[1] <= nums[2]) {
        return 'none';
    }
    if (nums[0] === nums[2]) {
        return 'equilateral';
    }
    if (nums[0] === nums[1] || nums[1] === nums[2]) {
        return 'isosceles';
    }
    return 'scalene';
}

C#

public class Solution {
    public string TriangleType(int[] nums) {
        Array.Sort(nums);
        if (nums[0] + nums[1] <= nums[2]) {
            return "none";
        }
        if (nums[0] == nums[2]) {
            return "equilateral";
        }
        if (nums[0] == nums[1] || nums[1] == nums[2]) {
            return "isosceles";
        }
        return "scalene";
    }
}