Finding good pairs in a dataset is a fundamental problem in various fields, including computer science and data analysis. Good pairs typically refer to combinations of elements that meet specific criteria or satisfy certain conditions. Understanding how to efficiently identify these pairs is crucial for optimizing algorithms and improving performance in applications such as social network analysis, recommendation systems, and statistical data interpretation. This topic encompasses a range of methodologies that can be employed to analyze and extract meaningful relationships from datasets. These methods can vary in complexity, from straightforward brute-force approaches to more sophisticated techniques that utilize hashing, sorting, and mathematical insights. The choice of method often depends on…