Type of Triangle (LeetCode)

Problem Description

Problem Statement	Solution Link	LeetCode Profile
Type of Triangle	Type of Triangle Solution on LeetCode	vaishu_1904

Problem 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

Approach

To determine the type of triangle that can be formed by the given sides, we need to:

1. Check if the given sides can form a valid triangle using the triangle inequality theorem.
2. If the sides form a valid triangle, check if the triangle is equilateral, isosceles, or scalene based on the lengths of the sides.

Solution Code

Python

class Solution:
    def triangleType(self, nums: List[int]) -> str:
        a, b, c = sorted(nums)
        
        if a + b <= c:
            return "none"
        if a == b == c:
            return "equilateral"
        if a == b or b == c or a == c:
            return "isosceles"
        
        return "scalene"

C++

#include <vector>
#include <string>
#include <algorithm>
using namespace std;

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

Java

import java.util.Arrays;

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

Conclusion

The solutions use a simple sorting approach to determine the type of triangle that can be formed by the given sides. This ensures that the problem is solved in a straightforward and efficient manner across different programming languages.