P AND NP PROBLEMS
P AND NP PROBLEMS - THEORY OF COMPUTATION
#theoryofcomputation #P #NP #NPHARD #NPCOMPLETE #KRUSKALS #TRAVELLINGSALESMAN #finiteautomata #regularexpressions #pcp #postcorrespondenceproblem #regularlanguages #toc #computerscience
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This tutorial will give you a full introduction into the P AND NP PROBLEMS • P AND NP PROBLEMS
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TOPIC - P AND NP PROBLEM • P AND NP PROBLEMS
What are P problems?
The problems that can be solved in a polynomial time by deterministic turing machine.
Example: a) Kruskals Algorithm b) Decidable Problem
What are NP problems?
The problems that can be solved in a non-deterministic polynomial time by non deterministic
turing machine.
Example: a)Travelling Salesman Problem b)Undecidable Problem
The NP problems can be classified into NP-complete and NP-hard.
NP-complete: A problem is NP-complete if it belongs to class NP and every problem in NP can also be solved in polynomial time.
NP-hard: A problem is said to be NP-hard if an algorithm for solving it can be translated into a problem which is NP problem.
Thus NP-hard is an algorithm for a problem which is at least as hard as any NP problem.
Example - Sum of subset problem, travelling salesman problem.
All NP-complete problems are NP-hard but all NP-hard problems cannot be NP-complete.
Example for P-class Problem: Kruskal’s Algorithm
In Kruskal’s algorithm, the minimum weight is obtained.
Circuit should not be formed.
Each time, the edge of minimum weight has to be selected from the graph.
It is not necessary to have edges of minimum weights to be adjacent.
Example for NP-class Problem: Travelling Salesman Problem
This problem can be stated as “Given set of cities and cost to travel between each pair of cities, determine whether there is a path that visits every city once and returns to the first city.”
Such that the cost travelled is less.
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