976. Largest Perimeter Triangle

// Approach: Sort descending; the first consecutive triple satisfying the triangle inequality gives the maximum perimeter.
// Time: O(n log n) Space: O(1)

public class Solution
{
    public int LargestPerimeter(int[] nums)
    {
        // Sort the array in ascending order to easily check triangle validity
        Array.Sort(nums);

        // Iterate from the largest elements to find the maximum perimeter
        // Start from the end and check consecutive triplets
        for (int i = nums.Length - 1; i >= 2; i--)
        {
            // Get the sum of the two smaller sides
            int sumOfTwoSmallerSides = nums[i - 1] + nums[i - 2];

            // Check triangle inequality: sum of two smaller sides must be greater than the largest side
            // If valid triangle is found, return its perimeter
            if (sumOfTwoSmallerSides > nums[i])
                return sumOfTwoSmallerSides + nums[i];
        }

        // No valid triangle found, return 0
        return 0;
    }
}