Finding efficient ways to identify good pairs in various contexts has become increasingly relevant in today’s data-driven world. Whether in mathematics, computer science, or even social sciences, the concept of pairing elements based on specific criteria can lead to significant insights and optimizations. Good pairs can refer to elements that complement each other in problem-solving scenarios, such as in algorithms, partnerships in business, or even friendships in social networks. The challenge lies in developing methods that not only accurately identify these pairs but do so efficiently, minimizing computational costs and time. With the rapid growth of data, traditional methods may become inefficient, prompting the need for innovative approaches. Moreover, understanding…