Given an array of integers, nums, determine the number of unique triplets that can be selected from the array such that the selected values can form the sides of a valid triangleA triangle is valid if the sum of the lengths of any two smaller sides is strictly greater than the length of the third largest side. For three sides a, b, c (such that a ≤ b ≤ c), the condition to form a valid triangle is a + b > c.. Return this count as the result.

Constraints:

• $1 <=$ nums.length $<= 1000$

• $0 <=$ nums[i] $<= 1000$

The solution uses the sort and search pattern to count the number of valid triangles formed from a given set of numbers. The ...