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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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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"

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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";
    }
}

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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";
    }
};

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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"
}

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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';
}

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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";
    }
}

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