Complexity theory classifies computational problems by difficulty from "summary" of Code by Charles Petzold
Complexity theory deals with how difficult it is to compute a solution to a problem. It's not just about whether a problem can be solved by a computer, but also about how much time and resources are needed to find a solution. In complexity theory, problems are classified according to how much time it takes to solve them. The time complexity of a problem is often expressed in terms of the number of steps a computer needs to take to solve it. The classification of computational problems by difficulty is important because it helps us understand the limits of what can be computed efficiently. Some problems may be so difficult that it would take an unreasonable amount of time to find a solution. Complexity theory helps us identify these problems so that we can focus our efforts on finding efficient solutions to more tractable problems. Complexity theory also helps us understand the relationships between different types of problems. For example, some problems are known to be equivalent in terms of difficulty, which means that if one problem can be solved efficiently, then so can the other. This kind of insight can be invaluable in designing algorithms and solving practical problems. In complexity theory, problems are often classified into different classes based on their difficulty. One common classification is the class of NP problems, which are problems that can be verified efficiently but for which finding a solution is difficult. Another class is the class of P problems, which are problems that can be solved efficiently using a deterministic algorithm. Understanding the relationships between these classes can help us better understand the nature of computational problems and design better algorithms.- Complexity theory provides a framework for understanding the difficulty of computational problems and helps us identify efficient algorithms for solving them. By classifying problems based on their difficulty, complexity theory guides us in focusing our efforts on solving tractable problems efficiently and effectively.
