[LeetCode] 3024. Type of Triangle

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

三角形类型。

给你一个下标从 0 开始长度为 3 的整数数组 nums ，需要用它们来构造三角形。

如果一个三角形的所有边长度相等，那么这个三角形称为 equilateral 。
如果一个三角形恰好有两条边长度相等，那么这个三角形称为 isosceles 。
如果一个三角形三条边的长度互不相同，那么这个三角形称为 scalene 。

如果这个数组无法构成一个三角形，请你返回字符串 “none” ，否则返回一个字符串表示这个三角形的类型。

思路

首先做排序，对 nums 进行升序排序，保证 nums[0] ≤ nums[1] ≤ nums[2]，这样只需检查一次三角不等式。

关于三角不等式：判断 nums[0] + nums[1] > nums[2]。若不满足，则无效三角，返回 “none”。

分类：

• 全等边：若 nums[0] == nums[1] && nums[1] == nums[2]，返回 “equilateral”。
• 等腰三角：若 nums[0] == nums[1] || nums[1] == nums[2]，返回 “isosceles”。
• 其他情况，返回 “scalene”

复杂度

时间O(1)
空间O(1)

代码

Java实现

class Solution {
    /**
     * 根据三条边的长度分类三角形类型
     * @param nums 长度为 3 的边长数组
     * @return "equilateral"、"isosceles"、"scalene" 或 "none"
     */
    public String triangleType(int[] nums) {
        // 1. 排序
        Arrays.sort(nums);

        // 2. 检查三角不等式
        if (nums[0] + nums[1] <= nums[2]) {
            return "none";
        }

        // 3. 分类
        if (nums[0] == nums[2]) {
            // 三条边相等
            return "equilateral";
        }
        if (nums[0] == nums[1] || nums[1] == nums[2]) {
            // 任意两条边相等
            return "isosceles";
        }
        // 三条边皆不相等
        return "scalene";
    }
}