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

• C++
• Java
• JavaScript
• Python
• Ruby

• 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)