Largest Perimeter Triangle

Largest Perimeter Triangle

1. What is this problem about?

The Largest Perimeter Triangle coding problem asks you to find the largest possible perimeter of a triangle that can be formed using three lengths from a given array of positive integers. If it is impossible to form a triangle of non-zero area with any three lengths, you must return 0. To form a valid triangle, the sum of any two side lengths must be strictly greater than the third side length (the Triangle Inequality Theorem).

2. Why is this asked in interviews?

This question is a staple at companies like Tesla and Meta because it tests a candidate's ability to combine mathematical properties with sorting. It's a classic example of a problem where a brute-force approach (checking all combinations of three sides) is inefficient, while a greedy approach based on sorted data is optimal. It evaluates your efficiency in algorithm design and your understanding of basic geometric constraints.

3. Algorithmic pattern used

This problem utilizes the Array, Math, Sorting, and Greedy interview pattern. To maximize the perimeter, we should try to use the largest available side lengths. By sorting the array in descending order, we can greedily check triplets of adjacent elements (A[i], A[i+1], A[i+2]). The first triplet that satisfies the Triangle Inequality (A[i+1] + A[i+2] > A[i]) will automatically yield the largest possible perimeter.

4. Example explanation

Consider the lengths: [3, 6, 2, 3].

1. Sort descending: [6, 3, 3, 2].
2. Check first triplet: (6, 3, 3).
   • 3 + 3 > 6? (6 > 6 is False). Not a valid triangle.
3. Check second triplet: (3, 3, 2).
   • 3 + 2 > 3? (5 > 3 is True). Valid triangle!
4. Perimeter: 3 + 3 + 2 = 8. The largest perimeter is 8.

5. Common mistakes candidates make

The most frequent error is attempting to use a triple-nested loop to check every combination, which results in O(N³) complexity and fails for large inputs. Another mistake is forgetting the strict inequality in the Triangle Inequality Theorem (a+b must be strictly greater than c, not equal). Some candidates also forget to return 0 if no valid triangle is found.

6. Interview preparation tip

When you see a "maximize" or "minimize" requirement with "Array, Greedy interview pattern", always consider if sorting the data first simplifies the decision-making process. Sorting often transforms a complex combinatorial problem into a simple linear scan.