Largest Perimeter Triangle

Published: Oct 20, 2022

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.

Constraints:

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

Examples

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

Example 2
Input: nums = [1,2,1,10]
Output: 0

Analysis

This problem requires trigonometry knowledge. To form a triangle, 3 sides a, b, c should have the length, a + b > c, where c is the longest side. The first step is to sort the given array, and test three elements from the biggest ones as c, b, a. If the condition, a + b > c, satisfies, the perimeter is a + b + c. If not, shift the values to take the next biggest ones since the biggest value is too big to form a triangle. After repeating this, we’ll get the answer.

Solution

class LargestPerimeterTriangle:
    def largestPerimeter(self, nums: List[int]) -> int:
        nums.sort()
        for i in range(len(nums) - 3, -1, -1):
            if nums[i] + nums[i + 1] > nums[i + 2]:
                return nums[i] + nums[i + 1] + nums[i + 2]
        return 0

# @param {Integer[]} nums
# @return {Integer}
def largest_perimeter(nums)
  nums.sort!
  (nums.length-3).downto(0) do |i|
    if nums[i] + nums[i+1] > nums[i+2]
      return [nums[i], nums[i+1], nums[i+2]].sum
    end
  end
  0
end

Complexities

• Time: O(nlog(n))
• Space: O(1)