Is Solving Sudoku An NP problem?

Introduction. The generalised Sudoku problem is an NP-complete problem which, effectively, requests a Latin square that satisfies some additional constraints. In addition to the standard requirement that each row and column of the Latin square contains each symbol precisely once, Sudoku also demands block constraints.

Can Sudoku be solved in polynomial time?

No. First of all, solving 4×4 Sudoku is a Polynomial-time problem. Any 4×4 Sudoku puzzle can be solved in less than one trillion years. Since there is a constant upper bound on the time, the problem is O(1), which is polynomial.

Can an NP problem be solved in polynomial time?

If an NP-complete problem can be solved in polynomial time then all problems in NP can be solved in polynomial time. If a problem in NP cannot be solved in polynomial time then all problems in NP-complete cannot be solved in polynomial time. Note that an NP-complete problem is one of those hardest problems in NP.

Is 9×9 Sudoku NP-complete?

Sudoku is NP-complete when generalized to a n × n grid however a standard 9 × 9 Sudoku is not NP- complete.

Are NP-hard problems NP-complete?

NP-Hard problems are as hard as NP-Complete problems. NP-Hard Problem need not be in NP class. A problem is NP-Complete if it is a part of both NP and NP-Hard Problem. A non-deterministic Turing machine can solve NP-Complete problem in polynomial time.

Will P vs NP ever be solved?

Although one-way functions have never been formally proven to exist, most mathematicians believe that they do, and a proof of their existence would be a much stronger statement than P ≠ NP. Thus it is unlikely that natural proofs alone can resolve P = NP.

How does Sudoku algorithm work?

Briefly, a program would solve a puzzle by placing the digit “1” in the first cell and checking if it is allowed to be there. If there are no violations (checking row, column, and box constraints) then the algorithm advances to the next cell and places a “1” in that cell.

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.

Is there a polynomial-time algorithm for solving Sudoku puzzles?

Because the generalized Sudoku problem (with n 2 × n 2 grids) is NP-hard, if there were a known polynomial-time algorithm for solving Sudoku puzzles, it would prove P = NP. That would be a huge deal. Something to keep in mind is that Sudoku puzzles as we know them are all 9 × 9 grids.

Is Sudoku an NP-complete problem?

From the research I’ve done, Sudoku is an NP-Complete problem (which is required for the project), and I’ve found a few ways of creating algorithms for it. I’m planning on doing a brute force solving method, and I need to do two other methods.

What is an NP-complete problem?

• NP-complete problems is class of “hardest” problems in NP. • If an NP-complete problem can be solved in polynomial time, then all problems in NP can be, and thus P = NP. 16 Possible Worlds

How to reduce Sudoku to graph-coloring problem?

It is also really easy to reduce sudoku to graph-coloring problem (each cell is represented by a node of a graph, nodes are connected according to the rules of sudoku, in order not to have the same color. Prefilled nodes are grounded to some color).