While running these algorithms on some test puzzles, I found that DFS does decently well onĮasy and medium difficulty puzzles, while struggles on the harder ones with very large numbers of steps.īFS works fine on the 4x4 puzzles, but is incredibly slow otherwise because it checks every intermediate possibilityĪll the way to the solution. I will still attempt to make functional solvers, however I think that I will favour the use of stack safe solvers This function is essentially the same as the earlier recursive function, just without the recursion. Linear Programming for Sudoku (Image by Author) In the case of Sudoku, we need to identify a feasible solution to solve it. These are simple algorithms, they can really just start looking on the very first empty cell in the grid, starting from theĬonst solve2 = isBfs => grid => When deciding what value to put in each cell, we first have to decide which cell we want to try filling first. Also, because the Sudoku grid is anĪcyclic graph where every move we take will lead to a uniqueīoard state, we can omit keeping a record of discovered cells that are separate from We willĪctually use this to our advantage and make a single function able to use either algorithm viaĬurrying.
#Pseudocode for solving sudoku movie#
Whereas a queue being the opposite of it is a "First In, First Out" order (like a queue to buy movie tickets). The gist of it is items stored in a stack are retrieved in a "Last In, First Out" order (like a stack of plates), There are several possible algorithms to automatically solve Sudoku boards the most notable is the backtracking algorithm, that takes a brute-force approach to. The nodes it will expand, whereas BFS uses a queue. When looking at the pseudocode on Wikipedia for both algorithms, they are extremely similar with only one key difference:ĭFS uses a stack data structure to store the order of
Search path sufficiently to go back and expand other paths. Both algorithms make use ofīacktracking once they have explored a branch in their
The two most basic methods of search are Depth First(DFS) andīreadth First Search(BFS). The generated Sudoku grid should have enough clues (numbers in cells) to be solvable resulting in a unique solution.The simplest way to solve a Sudoku puzzle would be to simply search for the answer one cell at a time. The Backtracking approach may not always be the most effective but is used in this challenge to demonstrate how a backtracking algorithm behaves and how it can be implemented using Python.Īn extra challenge would be to design an algorithm used to create a Sudoku Grid. Note that there are other approaches that could be used to solve a Sudoku puzzle. A recursive function is a function that calls itself until a condition is met. Every time you reach a dead-end, you backtrack to try another path untill you find the exit or all path have been explored.īacktracking algorithms can be used for other types of problems such as solving a Magic Square Puzzle or a Sudoku grid.īacktracking algorithms rely on the use of a recursive function. The typical scenario where a backtracking algorithm is when you try to find your way out in a maze. Each time a path is tested, if a solution is not found, the algorithm backtracks to test another possible path and so on till a solution is found or all paths have been tested. A Sudoku puzzle is a partially completed grid, which for a well-posed puzzle has a single solution.Ī 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. The objective of a Sudoku puzzle is to fill a 9×9 grid with digits so that each column, each row, and each of the nine 3×3 subgrids that compose the grid (also called “boxes”) contains all of the digits from 1 to 9. The purpose of this Python challenge is to demonstrate the use of a backtracking algorithm to solve a Sudoku puzzle.
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