Confronting the unsolvable NP-hard problems
In previous sections, we explored various rates of growth and learned how to describe them using formal representations, particularly asymptotic notations. While studying these growth rates, we encountered problems that appeared highly challenging, yet we did not address their solvability. In this section, we will focus on problems that go beyond our computational capabilities, discussing NP-hard problems that are inherently difficult, if not impossible, to solve efficiently.
In computer science, there exists a category that challenges our ability to find efficient solutions. These problems, known as NP-hard problems, represent some of the most complex and difficult challenges in computer science. Before exploring NP-hard problems, it is essential to understand why some problems cannot be solved efficiently, or in some cases, at all:
- Inherent complexity: Certain problems are intrinsically complex, requiring an astronomical number...
