How do you solve Largest Perimeter Triangle on LeetCode?

Largest Perimeter Triangle (LeetCode #976) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n log n) time complexity and O(1) space complexity. Key insight: The triangle inequality is crucial for determining if three lengths can form a triangle.

What is the time complexity of Largest Perimeter Triangle?

The optimal solution for Largest Perimeter Triangle runs in O(n log n) time and uses O(1) space. The sorting step takes O(n log n) time, and the subsequent linear scan takes O(n), making this approach efficient overall.

What is the brute force solution for Largest Perimeter Triangle?

The brute force approach for Largest Perimeter Triangle is Brute Force, with O(n³) time complexity and O(1) space complexity. To find the largest perimeter triangle, we can check all combinations of three sides from the array. If they satisfy the triangle inequality, we calculate the perimeter and keep track of the largest one found. The optimal Optimal Solution approach improves this to O(n log n).

What algorithm or data structure is used to solve Largest Perimeter Triangle?

Largest Perimeter Triangle uses the following concepts: Array, Math, Greedy, Sorting. The recommended patterns to study are: Sorting, Greedy.

What are the interview tips for Largest Perimeter Triangle?

Always think about edge cases, such as arrays with the smallest or largest possible values. Explain your thought process clearly while coding; this shows your understanding. Practice writing both brute force and optimal solutions to strengthen your problem-solving skills.

What are common mistakes when solving Largest Perimeter Triangle?

Failing to check the triangle inequality correctly. Not considering the sorted order when checking for valid triangles.

#976

Largest Perimeter Triangle

Easy

ArrayMathGreedySortingSortingGreedy

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n³)	O(n log n)
Space	O(1)	O(1)

💡

Intuition

Time O(n log n)Space O(1)

By sorting the array first, we can efficiently check for valid triangles starting from the largest sides. This allows us to quickly find the largest perimeter without checking all combinations.

⚙️

Algorithm

4 steps

1Step 1: Sort the array in non-decreasing order.
2Step 2: Iterate from the end of the sorted array to the beginning, checking each triplet (nums[i], nums[i-1], nums[i-2]).
3Step 3: If nums[i-2] + nums[i-1] > nums[i], we have a valid triangle and can calculate the perimeter.
4Step 4: Return the perimeter immediately as it will be the largest due to the sorted order. If no valid triangle is found, return 0.

solution.py6 lines

1def largestPerimeter(nums):
2    nums.sort()
3    for i in range(len(nums) - 1, 1, -1):
4        if nums[i - 2] + nums[i - 1] > nums[i]:
5            return nums[i - 2] + nums[i - 1] + nums[i]
6    return 0

ℹ

Complexity note: The sorting step takes O(n log n) time, and the subsequent linear scan takes O(n), making this approach efficient overall.

1The triangle inequality is crucial for determining if three lengths can form a triangle.
2Sorting the lengths allows us to efficiently check for valid triangles from the largest sides.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.