What does it mean if P NP?
The statement P=NP means that if a problem takes polynomial time on a non-deterministic TM, then one can build a deterministic TM which would solve the same problem also in polynomial time. So far nobody has been able to show that it can be done, but nobody has been able to prove that it cannot be done, either.
What happens when NP equals P?
If P equals NP, every NP problem would contain a hidden shortcut, allowing computers to quickly find perfect solutions to them. But if P does not equal NP, then no such shortcuts exist, and computers’ problem-solving powers will remain fundamentally and permanently limited.
How do you prove a problem is NP?
The easiest way to prove some problem is in NP is using the certificate definiiton of NP mentioned in other answers. The nondeterministic definition of NP is usually not very useful for showing a problem belongs to NP.
How do you solve NP-hard problems?
Option One: Approximation Algorithms In some cases, you may be able to combat NP-hardness by using an approximation algorithm. For example, a canonical example of an NP-hard problem is the traveling salesman problem. In this problem, you’re given as input a complete graph representing a transportation network.
Is NP-hard harder than NP-complete?
An NP-hard problem can be beyond NP. The polynomial-time reduction from your X to any problem in NP does not necessarily have a polynomial-time inverse. If the inverse is harder, then the verification is harder. An NP-complete problem, on the other hand, is one that is NP-hard and itself in NP.
Is traveling salesman NP-complete?
Traveling Salesman Optimization(TSP-OPT) is a NP-hard problem and Traveling Salesman Search(TSP) is NP-complete. However, TSP-OPT can be reduced to TSP since if TSP can be solved in polynomial time, then so can TSP-OPT(1).
Can you explain P NP NP completeness & NP-hard briefly?
What are NP, P, NP-complete and NP-Hard problems? P is set of problems that can be solved by a deterministic Turing machine in Polynomial time. NP is set of decision problems that can be solved by a Non-deterministic Turing Machine in Polynomial time. Therefore, NP-Complete set is also a subset of NP-Hard set.
Why is Sudoku called Sudoku?
The name “sudoku” is abbreviated from the Japanese suuji wa dokushin ni kagiru, which means “the numbers (or digits) must remain single.”
Who really invented Sudoku?
The modern Sudoku was most likely designed anonymously by Howard Garns, a 74-year-old retired architect and freelance puzzle constructor from Connersville, Indiana, and first published in 1979 by Dell Magazines as Number Place (the earliest known examples of modern Sudoku).
Is Sudoku from Japan?
The game first appeared in Japan in 1984 where it was given the name “Sudoku,” which is short for a longer expression in Japanese – “Sūji wa dokushin ni kagiru” – which means, “the digits are limited to one occurrence.” Sudoku continues to be highly popular in Japan, where people buy over 600,000 Sudoku magazines per …
What is the trick to Sudoku?
There are more than a few techniques to solve a Sudoku puzzle, but per Conceptis Puzzles, the easiest way to a Sudoku solution is to, “Scan rows and columns within each triple-box area, eliminating numbers or squares and finding situations where only a single number can fit into a single square.” If you’re looking to …