P vs NP: Complexity Theory

This lecture covers the fundamental concepts of complexity theory, focusing on the P vs NP problem. It explores the classification of problems based on the efficiency of algorithms, discussing the classes P and NP, and the challenges in solving NP problems efficiently. The instructor explains the difference between problems that can be solved in polynomial time and those whose solutions can be verified in polynomial time. Through examples like the Traveling Salesman and Knapsack problems, the lecture illustrates the complexity hierarchy and the implications of NP-completeness. The importance of efficient algorithms in practical computing tasks is emphasized, highlighting the significance of understanding the computational complexity of problems.