Hello, coding enthusiast! On our journey to master programming and problem-solving, we've embraced an exciting challenge today. We’re going to delve into combinatorial problems using Kotlin's distinct features. Our focus is on efficiently solving these problems with large datasets containing multiple pairs of numbers. Throughout this lesson, you'll discover how to implement efficient solutions using Kotlin's powerful data structures like HashMap and avoid time-consuming operations like iterating over large collections. Excited? Let's dive in!

• Input: You are given a list of pairs where each pair consists of distinct, positive integers. The list can contain up to 1,000,000 pairs, and no two pairs are element-wise identical.

• Output: The goal is to find the number of index pairs (i, j) (where i ≠ j) such that the i-th pair does not share a common member with the j-th pair.

• Explanation:

  • A pair (a, b) is considered non-common with another pair (c, d) if they do not share any member, meaning none of a or is equal to or .