Complexity Classes | P, NP, NP-Hard, NP-Complete Explained | Class 11 Computer Science | Ch 3 | L 5

Social Media Links: ______/❤ All Students are requested to Follow Me on Social Media!! ❤\________  Instagram:➜ https://www.instagram.com/digitaleduc...  Twitter:➜ https://twitter.com/shahbaz_ali101  Facebook Page:➜ https://www.facebook.com/digitalEduca...  Whatsapp:➜ https://chat.whatsapp.com/GqLGyGuZyNp...  Youtube:➜ https://bit.ly/32hA7C4?sub_confirmati... 0:50 Complexity classes 2:49 Class p 3:35 Class NP 6:45 NP Complete 11:50 Class NP Hard 3.3.2 Complexity Classes (P, NP, NP-hard, NP-complete) Understanding the complexity of problems involves classifying them into different categories based on their solvability and the time required to solve them. 3.3.2.1 Class P Class P refers to a category of problems that can be solved efficiently by a computer. In simpler terms, these are problems where a computer can find a solution quickly, even as the size of the problem grows: problem grows. Example: Let's consider a simple problem: sorting a list of numbers. Suppose you have the following list:[4, 1, 3, 2, 5]The goal is to arrange these numbers in ascending order:[1, 2, 3, 4, 5]The time required to sort the list grows at a manageable rate as the list size increases. For example, going from 5 numbers to 10 numbers will increase the time, but it remains within a reasonable limit. 3.3.3.2 Class NP Class NP refers to a category of problems for which, if a solution is given, it can be checked quickly by a computer. These are problems where verifying a proposed solutions easy, but finding that solution might be difficult and time-consuming. Example: Consider a common example of solving a Sudoku puzzle. In Sudoku, you fill a 9 x 9 grid with numbers so that each row, column, and 3 x 3 sub grid contains all digits from 1 to 9exactly once as shown in Figure 3.3. Class NP and Sudoku 3.3.3.3ClassNP-Hard NP-hard Problems are a class of problems that are at least as difficult as the hardest problems in Non-deterministic Polynomial time (NP). Solving an NP-hard problem is\challenging, and no efficient algorithm is known for finding a solution6:54 .Example: A well-known example of an NP-hard problem is the Traveling Salesman Problem (TSP),we discussed in Section 3.3.2.3.3.3.4 NP- Complete -Complete problems are a special subset of NP problems that are both in NP and as hard as the hardest problems in NP. This means that these problems are particularly challenging, and if you can solve one NP-Complete problem efficiently, you can solve all problems in NP efficiently. Example: A classic example of an NP-Complete problem is the Knapsack Problem. The Knapsack Problem in the Knapsack Problem, you have a knapsack with a maximum weight capacity and asset of items, each with a weight and a value. The goal is to determine the most valuable combination of items to put in the knapsack without exceeding its weight capacity. #DigitalEducation #DigitalEducationLatestNews #DigitalEducationShahbazAli #11thComputerScience #Class11CS #ComputerScience11 #CSClass11 #Class11ComputerScience #ComputerScienceFundamentals #CS11th #LearnComputerScience #DigitalEducationCS #DigitalEducation #11thComputerScience #ComplexityClasses #PvsNP #NPComplete #NPHard #ComputationalComplexity #Sudoku #KnapsackProblem #TravelingSalesmanProblem Computer Science 11th class Lecturer of Computer Science By Sir Shahbaz Ali For any query or private tutoring contact (0309-0334424) shahbazalicp@gmail.com