Complexity Classes: P and NP

This lecture covers the complexity classes P and NP, focusing on problems solvable in polynomial time by an algorithm. It explains the difference between P (solvable) and NP (verifiable) problems, using examples like element search and list sorting for P, and factorization for NP. The lecture also introduces NP-complete and NP-hard problems, which are among the most challenging in the NP class. It discusses the difficulty of problems like subset sum and discrete optimization, illustrating the concept of problems that are at least as hard as NP problems but may not belong to NP. The instructor emphasizes the significance of these complexity classes in understanding the computational difficulty of various problems.