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  1. 27
      content/roadmaps/103-computer-science/content/113-complexity-classes/100-p.md
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# P
The P in the P class stands for Polynomial Time. It is the collection of decision problems(problems with a “yes” or “no” answer) that can be solved by a deterministic machine in polynomial time.
<ResourceGroupTitle>Free Content</ResourceGroupTitle>
<BadgeLink colorScheme='yellow' badgeText='Read' href='https://www.geeksforgeeks.org/types-of-complexity-classes-p-np-conp-np-hard-and-np-complete/'>Types of Complexity Classes | P, NP, CoNP, NP hard and NP complete</BadgeLink>
<BadgeLink colorScheme='yellow' badgeText='Read' href='https://softwareengineering.stackexchange.com/questions/308178/trying-to-understand-p-vs-np-vs-np-complete-vs-np-hard'>Trying to understand P vs NP vs NP Complete vs NP Hard</BadgeLink>
<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=eHZifpgyH_4&list=PLUl4u3cNGP6317WaSNfmCvGym2ucw3oGp&index=22'>Complexity: P, NP, NP-completeness, Reductions</BadgeLink>
<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=MEz1J9wY2iM&list=PLUl4u3cNGP6317WaSNfmCvGym2ucw3oGp&index=24'>Complexity: Approximation Algorithms</BadgeLink>
<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=4q-jmGrmxKs&index=25&list=PLUl4u3cNGP6317WaSNfmCvGym2ucw3oGp'>Complexity: Fixed-Parameter Algorithms</BadgeLink>
<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=moPtwq_cVH8&list=PLUl4u3cNGP61Oq3tWYp6V_F-5jb5L2iHb&index=24'>Lecture 23: Computational Complexity</BadgeLink>
----
<BadgeLink colorScheme='red' badgeText='Watch' href='https://youtu.be/qcGnJ47Smlo?list=PLFDnELG9dpVxQCxuD-9BSy2E7BWY3t5Sm&t=2939'>Greedy Algs. II & Intro to NP Completeness</BadgeLink>
<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=e0tGC6ZQdQE&index=16&list=PLFDnELG9dpVxQCxuD-9BSy2E7BWY3t5Sm'>NP Completeness II & Reductions</BadgeLink>
<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=fCX1BGT3wjE&index=17&list=PLFDnELG9dpVxQCxuD-9BSy2E7BWY3t5Sm'>NP Completeness III</BadgeLink>
<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=NKLDp3Rch3M&list=PLFDnELG9dpVxQCxuD-9BSy2E7BWY3t5Sm&index=18'>NP Completeness IV</BadgeLink>
----
<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=ItHp5laE1VE&list=PLOtl7M3yp-DX6ic0HGT0PUX_wiNmkWkXx&index=23'>CSE373 2020 - Lecture 23 - NP-Completeness</BadgeLink>
<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=inaFJeCzGxU&list=PLOtl7M3yp-DX6ic0HGT0PUX_wiNmkWkXx&index=24'>CSE373 2020 - Lecture 24 - Satisfiability</BadgeLink>
<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=B-bhKxjZLlc&list=PLOtl7M3yp-DX6ic0HGT0PUX_wiNmkWkXx&index=25'>CSE373 2020 - Lecture 25 - More NP-Completeness</BadgeLink>
<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=_EzetTkG_Cc&list=PLOtl7M3yp-DX6ic0HGT0PUX_wiNmkWkXx&index=26'>CSE373 2020 - Lecture 26 - NP-Completeness Challenge</BadgeLink>

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# Np
# NP
The NP in NP class stands for Non-deterministic Polynomial Time. It is the collection of decision problems that can be solved by a non-deterministic machine in polynomial time.
<ResourceGroupTitle>Free Content</ResourceGroupTitle>
<BadgeLink colorScheme='yellow' badgeText='Read' href='https://www.geeksforgeeks.org/types-of-complexity-classes-p-np-conp-np-hard-and-np-complete/'>Types of Complexity Classes | P, NP, CoNP, NP hard and NP complete</BadgeLink>
<BadgeLink colorScheme='yellow' badgeText='Read' href='https://softwareengineering.stackexchange.com/questions/308178/trying-to-understand-p-vs-np-vs-np-complete-vs-np-hard'>Trying to understand P vs NP vs NP Complete vs NP Hard</BadgeLink>
<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=eHZifpgyH_4&list=PLUl4u3cNGP6317WaSNfmCvGym2ucw3oGp&index=22'>Complexity: P, NP, NP-completeness, Reductions</BadgeLink>
<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=MEz1J9wY2iM&list=PLUl4u3cNGP6317WaSNfmCvGym2ucw3oGp&index=24'>Complexity: Approximation Algorithms</BadgeLink>
<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=4q-jmGrmxKs&index=25&list=PLUl4u3cNGP6317WaSNfmCvGym2ucw3oGp'>Complexity: Fixed-Parameter Algorithms</BadgeLink>
<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=moPtwq_cVH8&list=PLUl4u3cNGP61Oq3tWYp6V_F-5jb5L2iHb&index=24'>Lecture 23: Computational Complexity</BadgeLink>
----
<BadgeLink colorScheme='red' badgeText='Watch' href='https://youtu.be/qcGnJ47Smlo?list=PLFDnELG9dpVxQCxuD-9BSy2E7BWY3t5Sm&t=2939'>Greedy Algs. II & Intro to NP Completeness</BadgeLink>
<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=e0tGC6ZQdQE&index=16&list=PLFDnELG9dpVxQCxuD-9BSy2E7BWY3t5Sm'>NP Completeness II & Reductions</BadgeLink>
<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=fCX1BGT3wjE&index=17&list=PLFDnELG9dpVxQCxuD-9BSy2E7BWY3t5Sm'>NP Completeness III</BadgeLink>
<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=NKLDp3Rch3M&list=PLFDnELG9dpVxQCxuD-9BSy2E7BWY3t5Sm&index=18'>NP Completeness IV</BadgeLink>
----
<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=ItHp5laE1VE&list=PLOtl7M3yp-DX6ic0HGT0PUX_wiNmkWkXx&index=23'>CSE373 2020 - Lecture 23 - NP-Completeness</BadgeLink>
<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=inaFJeCzGxU&list=PLOtl7M3yp-DX6ic0HGT0PUX_wiNmkWkXx&index=24'>CSE373 2020 - Lecture 24 - Satisfiability</BadgeLink>
<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=B-bhKxjZLlc&list=PLOtl7M3yp-DX6ic0HGT0PUX_wiNmkWkXx&index=25'>CSE373 2020 - Lecture 25 - More NP-Completeness</BadgeLink>
<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=_EzetTkG_Cc&list=PLOtl7M3yp-DX6ic0HGT0PUX_wiNmkWkXx&index=26'>CSE373 2020 - Lecture 26 - NP-Completeness Challenge</BadgeLink>

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# Co np
# Co-NP
Co-NP stands for the complement of NP Class. It means if the answer to a problem in Co-NP is No, then there is proof that can be checked in polynomial time.
<ResourceGroupTitle>Free Content</ResourceGroupTitle>
<BadgeLink colorScheme='yellow' badgeText='Read' href='https://www.geeksforgeeks.org/types-of-complexity-classes-p-np-conp-np-hard-and-np-complete/'>Types of Complexity Classes | P, NP, CoNP, NP hard and NP complete</BadgeLink>
<BadgeLink colorScheme='yellow' badgeText='Read' href='https://softwareengineering.stackexchange.com/questions/308178/trying-to-understand-p-vs-np-vs-np-complete-vs-np-hard'>Trying to understand P vs NP vs NP Complete vs NP Hard</BadgeLink>
<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=eHZifpgyH_4&list=PLUl4u3cNGP6317WaSNfmCvGym2ucw3oGp&index=22'>Complexity: P, NP, NP-completeness, Reductions</BadgeLink>
<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=MEz1J9wY2iM&list=PLUl4u3cNGP6317WaSNfmCvGym2ucw3oGp&index=24'>Complexity: Approximation Algorithms</BadgeLink>
<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=4q-jmGrmxKs&index=25&list=PLUl4u3cNGP6317WaSNfmCvGym2ucw3oGp'>Complexity: Fixed-Parameter Algorithms</BadgeLink>
<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=moPtwq_cVH8&list=PLUl4u3cNGP61Oq3tWYp6V_F-5jb5L2iHb&index=24'>Lecture 23: Computational Complexity</BadgeLink>
----
<BadgeLink colorScheme='red' badgeText='Watch' href='https://youtu.be/qcGnJ47Smlo?list=PLFDnELG9dpVxQCxuD-9BSy2E7BWY3t5Sm&t=2939'>Greedy Algs. II & Intro to NP Completeness</BadgeLink>
<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=e0tGC6ZQdQE&index=16&list=PLFDnELG9dpVxQCxuD-9BSy2E7BWY3t5Sm'>NP Completeness II & Reductions</BadgeLink>
<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=fCX1BGT3wjE&index=17&list=PLFDnELG9dpVxQCxuD-9BSy2E7BWY3t5Sm'>NP Completeness III</BadgeLink>
<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=NKLDp3Rch3M&list=PLFDnELG9dpVxQCxuD-9BSy2E7BWY3t5Sm&index=18'>NP Completeness IV</BadgeLink>
----
<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=ItHp5laE1VE&list=PLOtl7M3yp-DX6ic0HGT0PUX_wiNmkWkXx&index=23'>CSE373 2020 - Lecture 23 - NP-Completeness</BadgeLink>
<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=inaFJeCzGxU&list=PLOtl7M3yp-DX6ic0HGT0PUX_wiNmkWkXx&index=24'>CSE373 2020 - Lecture 24 - Satisfiability</BadgeLink>
<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=B-bhKxjZLlc&list=PLOtl7M3yp-DX6ic0HGT0PUX_wiNmkWkXx&index=25'>CSE373 2020 - Lecture 25 - More NP-Completeness</BadgeLink>
<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=_EzetTkG_Cc&list=PLOtl7M3yp-DX6ic0HGT0PUX_wiNmkWkXx&index=26'>CSE373 2020 - Lecture 26 - NP-Completeness Challenge</BadgeLink>

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content/roadmaps/103-computer-science/content/113-complexity-classes/103-np-hard.md
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# Np hard
# NP-Hard
An NP-hard problem is at least as hard as the hardest problem in NP and it is the class of the problems such that every problem in NP reduces to NP-hard.
<ResourceGroupTitle>Free Content</ResourceGroupTitle>
<BadgeLink colorScheme='yellow' badgeText='Read' href='https://www.geeksforgeeks.org/types-of-complexity-classes-p-np-conp-np-hard-and-np-complete/'>Types of Complexity Classes | P, NP, CoNP, NP hard and NP complete</BadgeLink>
<BadgeLink colorScheme='yellow' badgeText='Read' href='https://softwareengineering.stackexchange.com/questions/308178/trying-to-understand-p-vs-np-vs-np-complete-vs-np-hard'>Trying to understand P vs NP vs NP Complete vs NP Hard</BadgeLink>
<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=eHZifpgyH_4&list=PLUl4u3cNGP6317WaSNfmCvGym2ucw3oGp&index=22'>Complexity: P, NP, NP-completeness, Reductions</BadgeLink>
<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=MEz1J9wY2iM&list=PLUl4u3cNGP6317WaSNfmCvGym2ucw3oGp&index=24'>Complexity: Approximation Algorithms</BadgeLink>
<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=4q-jmGrmxKs&index=25&list=PLUl4u3cNGP6317WaSNfmCvGym2ucw3oGp'>Complexity: Fixed-Parameter Algorithms</BadgeLink>
<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=moPtwq_cVH8&list=PLUl4u3cNGP61Oq3tWYp6V_F-5jb5L2iHb&index=24'>Lecture 23: Computational Complexity</BadgeLink>
----
<BadgeLink colorScheme='red' badgeText='Watch' href='https://youtu.be/qcGnJ47Smlo?list=PLFDnELG9dpVxQCxuD-9BSy2E7BWY3t5Sm&t=2939'>Greedy Algs. II & Intro to NP Completeness</BadgeLink>
<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=e0tGC6ZQdQE&index=16&list=PLFDnELG9dpVxQCxuD-9BSy2E7BWY3t5Sm'>NP Completeness II & Reductions</BadgeLink>
<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=fCX1BGT3wjE&index=17&list=PLFDnELG9dpVxQCxuD-9BSy2E7BWY3t5Sm'>NP Completeness III</BadgeLink>
<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=NKLDp3Rch3M&list=PLFDnELG9dpVxQCxuD-9BSy2E7BWY3t5Sm&index=18'>NP Completeness IV</BadgeLink>
----
<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=ItHp5laE1VE&list=PLOtl7M3yp-DX6ic0HGT0PUX_wiNmkWkXx&index=23'>CSE373 2020 - Lecture 23 - NP-Completeness</BadgeLink>
<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=inaFJeCzGxU&list=PLOtl7M3yp-DX6ic0HGT0PUX_wiNmkWkXx&index=24'>CSE373 2020 - Lecture 24 - Satisfiability</BadgeLink>
<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=B-bhKxjZLlc&list=PLOtl7M3yp-DX6ic0HGT0PUX_wiNmkWkXx&index=25'>CSE373 2020 - Lecture 25 - More NP-Completeness</BadgeLink>
<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=_EzetTkG_Cc&list=PLOtl7M3yp-DX6ic0HGT0PUX_wiNmkWkXx&index=26'>CSE373 2020 - Lecture 26 - NP-Completeness Challenge</BadgeLink>

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content/roadmaps/103-computer-science/content/113-complexity-classes/104-np-complete/100-travelling-salesman-problem.md
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# Travelling salesman problem
# Travelling Salesman Problem
The Travelling Salesman Problem (TSP) is a classic problem in computer science. It is a problem that is NP-complete, which means that it is a problem that is hard to solve. It is also a problem that is used to test the efficiency of algorithms.
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<BadgeLink colorScheme='yellow' badgeText='Read' href='https://www.geeksforgeeks.org/travelling-salesman-problem-set-1/'>Travelling Salesman Problem | Set 1 (Naive and Dynamic Programming)</BadgeLink>
<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=1pmBjIZ20pE'>What is the Traveling Salesman Problem?</BadgeLink>
<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=XaXsJJh-Q5Y'>4.7 Traveling Salesperson Problem - Dynamic Programming</BadgeLink>
<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=cY4HiiFHO1o'>Traveling Salesman Problem | Dynamic Programming | Graph Theory</BadgeLink>

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content/roadmaps/103-computer-science/content/113-complexity-classes/104-np-complete/101-knapsack-problem.md
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# Knapsack problem
# Knapsack Problem
KnapSack Problem is a classic problem in computer science. It is a problem in which we are given a set of items, each with a weight and a value, and we need to determine which items to include in a collection so that the total weight is less than or equal to a given limit and the total value is as large as possible.
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<BadgeLink colorScheme='yellow' badgeText='Read' href='https://www.geeksforgeeks.org/0-1-knapsack-problem-dp-10/'>0-1 Knapsack Problem | DP-10</BadgeLink>
<BadgeLink colorScheme='yellow' badgeText='Read' href='https://medium.com/@fabianterh/how-to-solve-the-knapsack-problem-with-dynamic-programming-eb88c706d3cf'>How to solve the Knapsack Problem with dynamic programming</BadgeLink>
<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=oTTzNMHM05I'>3.1 Knapsack Problem - Greedy Method</BadgeLink>

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content/roadmaps/103-computer-science/content/113-complexity-classes/104-np-complete/102-longest-path-problem.md
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# Longest path problem
# Longest Path Problem
Longest path problem is a problem that asks us to find the longest path in a graph.
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<BadgeLink colorScheme='yellow' badgeText='Read' href='https://www.geeksforgeeks.org/find-longest-path-directed-acyclic-graph/'>Longest Path in a Directed Acyclic Graph</BadgeLink>
<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=TXkDpqjDMHA'>Shortest/Longest path on a Directed Acyclic Graph (DAG) | Graph Theory</BadgeLink>
<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=lRH0tax5dFA'>Longest Simple Path - Intro to Algorithms</BadgeLink>

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content/roadmaps/103-computer-science/content/113-complexity-classes/104-np-complete/readme.md
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# Np complete
# NP Complete
A problem is NP-complete if it is both NP and NP-hard. NP-complete problems are the hard problems in NP.
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<BadgeLink colorScheme='yellow' badgeText='Read' href='https://www.geeksforgeeks.org/types-of-complexity-classes-p-np-conp-np-hard-and-np-complete/'>Types of Complexity Classes | P, NP, CoNP, NP hard and NP complete</BadgeLink>
<BadgeLink colorScheme='yellow' badgeText='Read' href='https://softwareengineering.stackexchange.com/questions/308178/trying-to-understand-p-vs-np-vs-np-complete-vs-np-hard'>Trying to understand P vs NP vs NP Complete vs NP Hard</BadgeLink>
<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=eHZifpgyH_4&list=PLUl4u3cNGP6317WaSNfmCvGym2ucw3oGp&index=22'>Complexity: P, NP, NP-completeness, Reductions</BadgeLink>
<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=MEz1J9wY2iM&list=PLUl4u3cNGP6317WaSNfmCvGym2ucw3oGp&index=24'>Complexity: Approximation Algorithms</BadgeLink>
<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=4q-jmGrmxKs&index=25&list=PLUl4u3cNGP6317WaSNfmCvGym2ucw3oGp'>Complexity: Fixed-Parameter Algorithms</BadgeLink>
<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=moPtwq_cVH8&list=PLUl4u3cNGP61Oq3tWYp6V_F-5jb5L2iHb&index=24'>Lecture 23: Computational Complexity</BadgeLink>
----
<BadgeLink colorScheme='red' badgeText='Watch' href='https://youtu.be/qcGnJ47Smlo?list=PLFDnELG9dpVxQCxuD-9BSy2E7BWY3t5Sm&t=2939'>Greedy Algs. II & Intro to NP Completeness</BadgeLink>
<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=e0tGC6ZQdQE&index=16&list=PLFDnELG9dpVxQCxuD-9BSy2E7BWY3t5Sm'>NP Completeness II & Reductions</BadgeLink>
<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=fCX1BGT3wjE&index=17&list=PLFDnELG9dpVxQCxuD-9BSy2E7BWY3t5Sm'>NP Completeness III</BadgeLink>
<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=NKLDp3Rch3M&list=PLFDnELG9dpVxQCxuD-9BSy2E7BWY3t5Sm&index=18'>NP Completeness IV</BadgeLink>
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<BadgeLink colorScheme='red' badgeText='Watch' href='https://www.youtube.com/watch?v=ItHp5laE1VE&list=PLOtl7M3yp-DX6ic0HGT0PUX_wiNmkWkXx&index=23'>CSE373 2020 - Lecture 23 - NP-Completeness</BadgeLink>
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# P equals np
# P = NP
The P = NP problem is one of the most famous problems in computer science. It asks if the problem of determining if a given input belongs to a certain class of problems is as hard as the problem of solving the given input. In other words, it asks if the problem of determining if a given input belongs to a certain class of problems is as hard as the problem of determining if a given input belongs to a certain class of problems. This problem is also known as the Halting Problem.
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# Complexity classes
# Complexity Classes
In computer science, there exist some problems whose solutions are not yet found, the problems are divided into classes known as Complexity Classes. In complexity theory, a Complexity Class is a set of problems with related complexity. These classes help scientists to groups problems based on how much time and space they require to solve problems and verify the solutions. It is the branch of the theory of computation that deals with the resources required to solve a problem.
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