Upstart may evaluate collections of numeric features where valid three-value combinations must satisfy a strict relationship. Given a list of positive integers representing potential triangle side lengths, count how many combinations of three distinct indices can form a non-degenerate triangle.
A triplet of side lengths a, b, and c forms a triangle if the sum of every pair is greater than the remaining side. Equivalently, after sorting the triplet so that a <= b <= c, only a + b > c must be checked.
Return the number of valid index combinations. The order of elements in a combination does not matter, and duplicate values at different indices count as separate choices.
nums, a list of n positive integers.def count_triangles(nums):