0976 - Largest Perimeter Triangle (Easy)

Problem Link

https://leetcode.com/problems/largest-perimeter-triangle/

Problem Statement

Given an integer array nums, return the largest perimeter of a triangle with a non-zero area, formed from three of these lengths. If it is impossible to form any triangle of a non-zero area, return 0.

Example 1:

Input: nums = [2,1,2]
Output: 5

Example 2:

Input: nums = [1,2,1]
Output: 0

Constraints:

• 3 <= nums.length <= 10^4
• 1 <= nums[i] <= 10^6

Approach 1: Sort

In order to form a valid triangle, the side lengths of the triangle must satisfy $a + b > c$ where $a \leq b \leq c$. Therefore, we can sort the array and try each $(a,b,c)$ tuples to see if it is satisfied. If so, return the sum of three lengths. Else return 0 at the end.

class Solution {
public:
    int largestPerimeter(vector<int>& nums) {
        // sort it first
        sort(nums.begin(), nums.end());
        // try the largest one
        for (int i = nums.size() - 1; i >= 2; i--) {
            // check if a + b > c is satisfied
            if (nums[i - 2] + nums[i - 1] > nums[i]) {
                // valid! non-zero area
                return nums[i] + nums[i - 1] + nums[i - 2];
            }
        }
        return 0;
    }
};