Largest Perimeter Triangle

Problem Description

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.

Key Insights

• A valid triangle can be formed if the sum of the lengths of any two sides is greater than the length of the third side.
• To maximize the perimeter, we should consider the longest side lengths first.
• Sorting the array in descending order allows us to easily check the triangle inequality condition.

Space and Time Complexity

Time Complexity: O(n log n) - due to the sorting of the array. Space Complexity: O(1) - no additional space is required other than a few variables.

Solution

To solve the problem, we can follow these steps:

1. Sort the given array in descending order.
2. Iterate through the sorted array, checking groups of three consecutive lengths to see if they can form a triangle.
3. The first valid triangle found will have the largest perimeter since we are checking from largest to smallest.
4. If no valid triangle is found, return 0.

The data structure used is an array, and the algorithm employed is a greedy approach utilizing sorting.

Code Solutions