What is backtracking algorithm in Sudoku?
What is backtracking algorithm in Sudoku?
A backtracking algorithm is a recursive algorithm that attempts to solve a given problem by testing all possible paths towards a solution until a solution is found.
How do you solve recursion with Sudoku?
Approach for solving sudoku using recursive backtracking algorithm
- Like all other Backtracking problems, we can solve Sudoku by one by one assigning numbers to empty cells.
- Before assigning a number, we need to confirm that the same number is not present in current row, current column and current 3X3 subgrid.
Can Sudoku have multiple solutions?
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. It is important to note that this is not the same as stating that if a Sudoku of rank n has n2-1 distinct digits in the givens, then it is well-formed.
Can Sudoku be solved mathematically?
In fact, mathematical thinking in the form of logical deduction is very useful in solving Sudokus. 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.
How the backtracking approach is working to solve the Sudoku problem?
A Sudoku (top) being solved by backtracking. Each cell is tested for a valid number, moving “back” when there is a violation, and moving forward again until the puzzle is solved.
Can every Sudoku be solved without guessing?
All Sudoku puzzles are solvable only through logical deductions, with no guessing. Some hard Sudoku puzzles may require deductive techniques that you don’t know. Some very hard Sudoku puzzles may require techniques that are so complicated that no human can do them without taking extensive notes.
When to use backtracking in Sudoku?
Backtracking is particularly helpful when solving constraint satisfaction problems such as crosswords, verbal arithmetic, and Sudoku. In general, backtracking algorithms can be applied to the following three types of problems: In this article, I will be demonstrating the backtracking strategy by solving a popular problem known as the Sudoku Solver.
How do you solve the Sudoku problem?
One digit cannot be repeated in one row, one column or in one 3 x 3 box. Using the backtracking algorithm, we will try to solve the Sudoku problem. When some cell is filled with a digit, it checks whether it is valid or not. When it is not valid, it checks for other numbers.
How many grids are there in a Sudoku puzzle?
Although it has been established that approximately 6.67 x 1021 final grids exist, a brute force algorithm can be a practical method to solve Sudoku puzzles. A brute force algorithm visits the empty cells in some order, filling in digits sequentially, or backtracking when the number is found to be not valid.
What is the time complexity of Sudoku?
Time complexity: O (9^ (n*n)). For every unassigned index there are 9 possible options so the time complexity is O (9^ (n*n)). Space Complexity: O (n*n). To store the output array a matrix is needed. Method 2: Backtracking. Like all other Backtracking problems, Sudoku can be solved by one by one assigning numbers to empty cells.
