What is the problem complexity of Sudoku?

A Sudoku puzzle's complexity is defined by the order of the puzzle as well as the number of clues given; as the order increase and the number of clues decrease, the complexity of the puzzle increase. As the complexity of the puzzle increase, the likelihood of finding a solution within a reasonable time decrease.

What type of problem is Sudoku?

Sudoku is a logic-based puzzle. It is a type of constraint satisfaction problem, where the solver is given a finite number of objects (the numerals 1-9) and a set of conditions stating how the objects must be placed in relation to one another.

Is Sudoku a NP problem?

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.

What is the complexity of Sudoku in backtracking?

Time Complexity: The backtracking algorithm takes O(9^m) time complexity in the worst case since for every unfilled cell there are 9 possibilites to explore and there are m unfilled cells in the sudoku. For Brute force approach: Worst Case Time Complexity: O(9^m)

What is the problem strategy for Sudoku?

The most common strategies for solving sudoku involve scanning rows and columns inside each triple-box region, removing numbers or squares, and identifying circumstances where just a single number can fit into a single square is the simplest approach to begin a sudoku problem.

Sudoku (Visualisation) | Backtracking | Set 7 | GeeksforGeeks

What is the 45 rule in Sudoku?

The 45 rule is a basic solving-technique in Killer Sudoku. Each house (row, column, nonet) must add to 45 (the sum of the digits 1 through 9).

What is the logic for solving Sudoku puzzles?

The most basic strategy to solve a Sudoku puzzle is to first write down, in each empty cell, all possible entries that will not contradict the One Rule with respect to the given cells. If a cell ends up having only one possible entry, it is a "forced" entry that you should fill in.

What is the best time complexity to solve Sudoku?

Mathematics of Sudoku explains this pretty well: The general problem of solving Sudoku puzzles on n^2×n^2 grids of n×n blocks is known to be NP-complete. The runtime complexity of any algorithm solving Sudoku is thus at least exponential in n. For a normal Sudoku (n = 3) this means O(N^3) is perfectly reasonable.

What is the most efficient algorithm to solve Sudoku?

Backtracking algorithm is the fastest algorithm to solve sudoku puzzles, It is by far the fastest compared to the other two methods. Also, let's note that each algorithm was faster with harder problems than with easier problems.

What is the best data structure for Sudoku?

The Sudoku Puzzle is a 9x9 grid, so an array is the right data structure.

Is a 9x9 Sudoku NP-complete?

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

Is there math behind Sudoku?

To solve a Sudoku puzzle, one needs to use a combination of logic and trial-and-error. More math is involved behind the scenes: combinatorics used in counting valid Sudoku grids, group theory used to describe ideas of when two grids are equivalent, and computational complexity with regards to solving Sudokus.

Is Sudoku an optimization problem?

Sudoku is a puzzle where the player assigns digits to squares (see Wikipedia for a complete description). The puzzle can be formulated as a mathematical optimization problem and solved in a few milliseconds on a decent laptop.

Are there unsolvable Sudoku puzzles?

Realistically, no! There are 6,670,903,752,021,072,936,960 possible solvable Sudoku grids that yield a unique result (that's 6 sextillion, 670 quintillion, 903 quadrillion, 752 trillion, 21 billion, 72 million, 936 thousand, 960 in case you were wondering). That's way more than the number of stars in the universe.

What are the 3 rules of Sudoku?

Can Sudoku have 2 solutions?

A well-formed Sudoku puzzle is one that has a unique solution. A Sudoku puzzle can have more than one solution, but in this case the kind of logical reasoning we described while discussing solving strategies may fall short. There are examples of rank-3 Sudoku puzzles with 17 givens that are well-formed.

What is the smartest way to play Sudoku?

What is the swordfish technique in Sudoku?

The Sudoku Swordfish strategy is a single-candidate technique that uses 3 rows and 3 columns. This means the player only needs to focus on one digit. The grid must contain 3 rows or 3 columns where the digit is a candidate to only 2 or 3 cells.

What is the fewest number to solve Sudoku?

The fewest clues required for a proper Sudoku is 17, but not all completed grids can be reduced to a proper 17 clue Sudoku. About 49,000 unique (non-equivalent) Sudokus with 17 clues have been found. (A proper Sudoku has only one solution).

How long does it take the average person to solve a Sudoku puzzle?

It is believed that the average Sudoku player spends approximately 20 minutes solving a typical Sudoku puzzle. For very hard puzzles, that number can be much higher. While the game itself can be challenging and complex, several strategies can be used successfully to find the solution.

How long does it take the average person to solve a hard Sudoku puzzle?

The average person takes more than a few minutes to solve a Sudoku. It requires patience, time, and attention. If you're not very patient by nature, you will likely find yourself very disappointed and annoyed with the game.

How long does it take the average person to solve expert Sudoku?

I generally take around 3-5 minutes for expert level. Anyway, it's not hard. Don't complicate it and just enjoy the game. How many fields in a 9x9 sudoku puzzle have to be revealed in order to lead to a unique solution?

What is Sudoku rule of 1?

Rule 1 - Each row must contain the numbers from 1 to 9, without repetitions. The player must focus on filling each row of the grid while ensuring there are no duplicated numbers. The placement order of the digits is irrelevant. Every puzzle, regardless of the difficulty level, begins with allocated numbers on the grid.

What is the L rule in Sudoku?

The L pattern exists when there is a wall that has one populated cell adjacent to it. The wall and the adjacent cell must be in the same box.

Is 6 minutes good for Sudoku?

5 minutes is more than enough time to jump start your brain, re-evaluate your Sudoku strategy, and develop a new perspective on how to view the Sudoku grid. So “take 5” and give yourself a new chance at solving Sudoku puzzles!