The Triangle Finding Problem
We present a significant advancement in solving the Triangle Finding Problem. We have developed a novel algorithm with a time complexity of O(n + m), offering a substantial improvement over previous approaches. Furthermore, we have demonstrated the versatility of this algorithm by adapting it to not only identify but also count all triangles within the same optimal O(n + m) time bound. This adaptability highlights the underlying efficiency and robustness of our method. Finally, the implications of this algorithm extend beyond the Triangle Finding Problem itself, opening up promising avenues for applications in various other computational challenges within combinatorial optimization and computational geometry. This suggests that the presented algorithm has the potential to become a valuable tool in addressing a wider range of problems in these fields.