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The idea is to sort the array in non-decreasing order and try to form the triangle starting from the largest possible sides. If the largest sides satisfy the triangle inequality, they will produce the largest perimeter. Iterate from the end of the sorted array and check for the triangle inequality condition for the last three elements. If the condition is satisfied, those three can form a triangle, otherwise keep checking the next set of three largest sides.
Time Complexity: O(n log n) due to sorting the array. Space Complexity: O(1) as no additional space is used apart from auxiliary variables.
1def largestPerimeter(nums):
2 nums.sort()
3 for i in range(len(nums) - 3, -1, -1):
4 if nums[i] + nums[i + 1] > nums[i + 2]:
5 return nums[i] + nums[i + 1] + nums[i + 2]
6 return 0This Python function begins by sorting the input array. It then iterates backward from the third last element, checking if the current element and the next two largest elements can form a triangle using the triangle inequality rule. If they can, it returns their sum as the largest perimeter.
This approach involves checking all possible combinations of three lengths from the array to see if they form a triangle. If they do, we calculate the perimeter and update the maximum perimeter found so far. This approach is less efficient due to its combinatorial nature but demonstrates the basic principle of checking all potential solutions.
Time Complexity: O(n^3), as it evaluates all combinations of three elements. Space Complexity: O(1), requiring constant additional space.
1This JavaScript function uses three nested loops to check all possible triplets from the array for the triangle inequality and updates the maximum perimeter found.