Finding efficient ways to analyze pairs in data sets is crucial in various fields, from computer science to social sciences. As data continues to grow exponentially, the need for effective algorithms that can efficiently process and analyze this data becomes increasingly important. The concept of good pairs is particularly relevant in combinatorial problems, where the objective is often to determine certain relationships between elements in a set. In many applications, identifying pairs that meet specific criteria can help in decision-making processes, whether it be in market research, social network analysis, or even in scientific research. By understanding how to define and find these “good pairs,” researchers and analysts can derive…