Triplet Counting

Imagine you have been given an array of integers, and a query number k. Your task is to write a function that finds all the triplets in the array that sum up to the query number k.

Let’s illustrate this with some examples:

Example 1:

Input:

nums = [1, 2, 3, 4, 5]
k = 6

Output:

count_triplets(nums, k) -> 1

In this case, there is only one triplet that sums up to 6: (1, 2, 3).

Example 2:

Input:

nums = [10, 10, 20, 30, 40]
k = 60

Output:

count_triplets(nums, k) -> 3

In this case, there are three triplets that sum up to 60: (10, 10, 40), (10, 20, 30), and (10, 20, 30). The value 10 can be retrieved as nums[0] or nums[1], therefore resulting in two triplets with the same value.