🍋 P, NP, NPComplete | Data Structures & Algorithms

#ComputerScience #Algorithms #ComplexityTheory #PvsNP This video provides an introduction to computational complexity theory, focusing on the famous P vs. NP problem. Presented by Hayden Smith, this lecture explains how computer scientists categorize problems based on how difficult they are to solve. 🤔 Solving vs. Verifying We can think about a problem's difficulty in two ways: * Solving: How hard is it to find a correct answer from scratch? * Verifying: If someone gives you a potential answer, how hard is it to check if it's correct? For example, a completed Sudoku puzzle is very easy to verify, but finding the solution in the first place can be very hard. 🅿️ The "P" Class (Polynomial Time) P stands for Polynomial time. This class contains all the problems that are considered "easy" to solve. An algorithm is in P if its runtime is polynomial (e.g., O(n), O(n²)), meaning it can be solved efficiently by a standard computer. Examples include sorting a list or finding a spanning tree. 🅾️ The "NP" Class (Non-deterministic Polynomial Time) NP stands for Non-deterministic Polynomial time. This class contains all the problems for which a potential solution is "easy" to verify. This includes all problems in P, but also many "hard" problems like the Hamiltonian Path problem and Sudoku. While we can check an answer quickly, finding an answer for these hard problems can take an exponential amount of time. ❓ The P vs. NP Problem The P versus NP problem is one of the biggest unsolved questions in computer science. It asks: If a solution to a problem can be verified quickly (i.e., it's in NP), can it also be solved quickly (i.e., is it also in P)? In other words, does P = NP? 💥 NP-Complete NP-Complete problems are a special set of the "hardest" problems in NP. They are all related in such a way that if a fast (polynomial time) algorithm is ever found for just one NP-Complete problem, it would mean a fast algorithm exists for all NP problems, proving that P = NP. View the full playlist: https://www.youtube.com/playlist?list=PLi2pCZz5m6GEftzPIxVH1ylwytux9WOGN