added 3024 lc solution

dsa-solutions/lc-solutions/3000-3099/3024-Type-of-Triangle.md

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+---
+id: type-of-triangle
+title: Type of Triangle (LeetCode)
+sidebar_label: 3024-TypeOfTriangle
+tags:
+  - Triangle
+  - Array
+description: Determine the type of triangle that can be formed by an array of integers representing the sides of the triangle.
+sidebar_position: 3024
+---
+
+## Problem Description
+
+| Problem Statement | Solution Link | LeetCode Profile |
+| :---------------- | :------------ | :--------------- |
+| [Type of Triangle](https://leetcode.com/problems/type-of-triangle/) | [Type of Triangle Solution on LeetCode](https://leetcode.com/problems/type-of-triangle/solutions/) | [vaishu_1904](https://leetcode.com/u/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
+
+```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++
+```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
+```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.