Due to the way that we pass the puzzle between calls, each recursive call uses minimal memory. ... To solve the sudoku, we use backtracking. int sudokuHelper(int puzzle[][9], int row, int column) { We move to the previously solved box and try the next possible number to solve it. Puzzles are available on sudoku.com. –When a digit is placed check that the set up is legal –now solve the board 1 So, if we want to solve a problem using recursion, then we need to make sure that: The problem can broken down into smaller problems of same type. Learn more about recursion, sudoku, recursive backtracking, cell array for (; nextNum<10; nextNum++) { Backtracking: So, while solving a problem using recursion, we break the given problem into smaller ones. Uses Recursive Backtracking algorithm and therefore a solution is always gauranteed, except in case of sudokus with no solution. While many people seem to be afraid of recursion, it is an incredibly powerful way of solving problems. int sectorCol = 3*(column/3); Then, I decided to see if backtracking could be applied to crossword puzzles. from itertools import * from copy import copy def is_distinct (list): '''Auxiliary function to is_solved checks if all elements in a list are distinct (ignores 0s though) ''' used = [] for i in list: if i == 0: continue if i in used: return False used. * given position. Briefly, once you exhaust all your options at a certain step you go back. If you are unfamiliar with sudoku you should learn the rules and solve a couple of puzzles before starting. puzzle[row][column] = nextNum; Sudoku-Solver-Backtracking. The tree is a way of representing some initial starting position (the parent node) and a final goal state (one of the leaves). These 25 lines are at the core of the system, … Hey there! We’ll use some modulus operator magic and a for loop to get this to happen. } else { Recur immediately to the next cell. if(isValid(nextNum, puzzle, row, column)) { Even a sudoku puzzle designed to defeat this algorithm runs in less than 45 seconds on my aging laptop. /* } We’ll start by defining the traversal order. First, make sure you understand how this traverses the puzzle. */, // We failed to find a valid value for this, /* All the cells of completely solved sudoku array must have assigned valid values. * change it. Problem has some base case(s). This may be true for some problems, but probably wrong for solving sudoku. Recursive backtracking is a ordered method for searching a solution space. Log in Create account DEV Community. trying all possible numbers systematically. This assignment is to write a recursive sudoku solver. if (9 == row) { int row1 = (row+2)%3; ... 3.1 - Sudoku. As a practical example, I’ll walk you through an example solving Sudoku puzzles with the lingua franca of programmers, C. A recursive backtracking algorithm follows a really simple formula: Let’s start out with our particular problem, the game of Sudoku. Recursive_Solve() is the recursive part of the solver. The core of this method is the recursive function resolve () of around 20 lines along with 5 lines of the function free_cell_for_number (). If I hit a roadblock where the puzzle cannot be completed, the algorithm would backtrack until If you like the content on CodePumpkin and if you wish to do something for the community and the planet Earth, you can donate to our campaign for planting more trees at CodePumpkin Cauvery Calling Campaign. Backtracking allows us to deal with situations in which a raw brute-force approach would explode into an impossible number of choices to consider. */, /* if (sudokuHelper(puzzle, row+1, 0)) return 1; The aim is to provide you a working solution for automated Sudoku … Sudoku Sudoku is a game / logic puzzle with a simple set of rules. We're hiring in Ann Arbor and Grand Rapidsopen positions >, Atomic is a software design + development consultancy. It checks cells in each row one by one and picks up first cell with UNASSIGNED value. You can also check the other articles on sorting and searching such as selection sort, binary search, fibonacci search, merge sort etc. I was able to… It checks for allowed numbers from 1 to 9, assign the first possible option to cell and again call solveSudoku() method for next UNASSIGNED cell. The algorithm described in this post is something I implemented in a single night as an exercise when I first learned C. While it’s many orders of magnitude slower for the worst case (see: 45 seconds vs several milliseconds), on average the performance isn’t bad for such a simple approach. PDF | Nowadays Sudoku is a very popular game throughout the world and it appears in different medias, including websites, ... Recursive Backtracking for Solving 9*9 Sudoku . Using Python recursion and backtracking for resolving Sudoku Recursion is a powerful tool, but combined with backtracking, it's even better. Using a recursive backtracking algorithm, I would slowly fill up the grid with random numbers - checking the validity of the puzzle at each step. Now, we check for a truthy value in the Sudoku puzzle before we start modifying it, allowing us to continue without clobbering the given hints. Recursive backtracking with cell arrays?. Recursive_Solve() is the recursive part of the solver. Because there is a 7 in column 5 and one in column 6, it can be deduced that there will be a 7 in column 4 of the top middle sector. home data-structures-and-algorithms-in-java-levelup recursion-and-backtracking solve-sudoku-official Profile. We’d love to talk with you about your next great software project. % s is the first cell, if any, with one candidate. While there have been some very fast Sudoku-solving algorithms produced, a basic backtracking algorithm implemented efficiently will be hard to beat. GitHub Gist: instantly share code, notes, and snippets. if (puzzle[row][column]) { It can be more continent technique for parsing other combinatorial optimization problem. Hopefully I’ve been able to interest you in the possibilities of what appears to be a neglected class of algorithm, recursive backtracking. If there are no more valid numbers, the cell is cleared and backtracking starts. How a 4x4 version of Sudoku might work with backtracking The simplicity and cleanness of using backtracking to solve something as complex as a difficult Sudoku board are beautiful. Puzzle . Note that there are other approaches that could be used to solve a Sudoku puzzle. */ a recursive BackTracking algorithm for Sudoku In our Sudoku class, we create a solution method to implement this algorithm. Backtracking is a general algorithm for finding all (or some) solutions to some computational problems, notably constraint satisfaction problems, that incrementally builds candidates to the solutions, and abandons a candidate ("backtracks") as soon as it determines that the candidate cannot possibly be completed to a valid solution.. Using Sudoku to explore backtracking Sudoku. If there is just one solution, you are done. Backtracking is also known as depth-first search. This is the key recursive-backtracking method, and it should return true if a solution is found to the puzzle represented by the called Sudoku object, and false if no solution has yet been found i.e., if the method is backtracking). While there have been some very fast Sudoku-solving algorithms produced, a basic backtracking algorithm implemented efficiently will be hard to beat. It takes a row r and a column c, and assumes that all cells before r and c have been filled in. Instance variable sudoku can be initialized using any of the below two constructors. Find a possible solution. To learn more about recursive backtracking algorithms, check out the excellent Stanford Engineering Everywhere videos. * and recurse for every valid one, to test if it's part This post is about generating solution for sudoku problem and not for checking if solution is correct or not. Worst case time complexity wise it’s often on par with a brute-force search - but in reality it’s much faster. In each row, column, and sector, the numbers 1-9 must appear. Recursive backtracking with cell arrays?. But in case no other possible number remains, again it will bactrack to previously assigned cell and process continues. */, /* Check for the value in the given row and column */, /* Check the remaining four spaces in this sector */, sudoku puzzle designed to defeat this algorithm, Peter Norvig’s awesome page on Sudoku solving, Redux, Modularity, and the Law of Demeter, Slack the Magic: How we built the ARKit Sudoku Solver | A1A. Sudoku can be solved using recursive backtracking algorithm. Delegate work on the next cell to a recursive call to solve; Whenever the recursion returns, the puzzle cannot be solved for the selected number. The method will continue from line 12 and have boolean value of false if we are backtracking. if (column == 8) { I assume you are here because you want to learn how to find solutions to a Sudoku puzzle. As explained on Wikipedia: In our Sudoku class, we create a solution method to implement this algorithm. By following a shockingly simple procedure, you can solve complex problems in reasonable amounts of time, with no bookkeeping. Using a recursive backtracking algorithm, I would slowly fill up the grid with random numbers - checking the validity of the puzzle at each step. trying all possible numbers systematically. Backtracking algorithms rely on the use of a recursive function. Otherwise if you have more than one The simplest algorithm is a brute force recursive algorithm with backtracking. We are using backtracking algorithm to write the Java code to solve sudoku easily. Uses Recursive Backtracking algorithm and therefore a solution is always gauranteed, except in case of sudokus with no solution. */ * Is this element already set? function X = sudoku(X) % SUDOKU Solve Sudoku using recursive backtracking. ... 3.1 - Sudoku. /* Check for the value in the given row and column */ Sudoku checker (By traversing each cell only once), Tic Tac Toe | Java Program Implementation, Producer Consumer Design Pattern using wait() and notify(), interrupt(), interrupted() and isInterrupted() in Java Multithreading. If you are interested in java programs for other board games like Sudoku Checker, Tic Tac Toe, Snake N Lader and N Queen Problem , you can check out my posts in Board Games section. But backtrack to where? sudoku solution having UNASSIGNED i.e. The algorithm tries a value, then optimistically recurs on the next cell and checks if the solution (as built up so far) is valid. Backtracking recursively finds the solution to the problem at hand. Some hobbyists have developed computer programs that will solve Sudoku puzzles using a backtracking algorithm, which is a type of brute force search. Number of Recursive calls: There is an upper limit to the number of recursive calls that can be made. * given position. Bonfring International Journal of Data Mining, Volume 6, Issue 1, 2016 This lack of bookkeeping is by far and away my favorite property of this algorithm. When the puzzle has many solutions, it will output the lexicographically first one. In our implementation, we will stop the algorithm after one solution is found. } Before assigning a number, we need to confirm that the same number is not present in current row, … % C is a cell array of candidate vectors for each cell. I've been still unable to wrap the general algorithm around in my head given the problem domain I'm working in. } Also it is an important process for solving constraint satisfaction problem like crossword, Sudoku and many other puzzles. We will return to this stage of method later on either when we finish the Sudoku or when the next cell could not find a number to place. The recursive solver will crunch away and either return a 1, indicating that the Sudoku has been solved correctly and the solution is on the stack, or 0, indicating the Sudoku had no valid solution. Join us to save the planet Earth by donating at CodePumpkin Cauvery Calling Campaign. For Detailed understanding about Sudoku, have a look at wikipedia. For example, in the puzzle above, we know there must be a 7 somewhere in the top middle sector. If so, we don't want to As long as a Sudoku puzzle is valid, it can be solved by recursive backtracking, i.e. Backtracking • The Algorithmic Approach – Backtracking systematically try and search possibilities to find the solution. Thanks for the comment, and for your blogpost. * Is this element already set? if(puzzle[row1+sectorRow][col2+sectorCol] == number) return 0; We may not get time to plant a tree, but we can definitely donate ₹42 per Tree. Tagged with python, recursion, backtracking, sudoku. The latter is called Backtracking. We need check the value passed in for uniqueness in the row, the column, and the sector. wb_sunny search. Just outline a recursive function, a partial solution check, and a function to evaluate if a solution is complete, and the program will automatically build a tree for you and find the best solution, if any. Java Sudoku Solver program can solve any sudoku puzzle in few seconds. In this project, You will use the Backtracking algorithm to solve CSPs, in a Sudoku game. I have written this article to force myself to understand this subject better, and be able to use this in a more efficient way. The applet on this page solves a sudoku puzzle by recursion and backtracking. Backtracking is a technique which basically tests all possible options recursively and returns all the correct ones. The goal of the game is to fill board such that each row, column, and 3x3 box have the numbers 1-9 with no repeats. We’ll get back to that in a moment. Copyright @ 2017 Code Pumpkin All Rights Reserved. For other Backtracking algorithms, check my posts under section Backtracking (Recursion). When We first started playing with writing a Sudoku game, I took the long way to create Sudoku templates. Login. if (puzzle[i][column] == number) return 0; int nextNum = 1; Before assigning a number, we need to confirm that the same number is not present in current row, current column and current 3X3 subgrid. The example in the textbook I am referring to is a backtracking, recursive solution to the '8 queens' problem, which is slightly different than implementing sudoku – Carleton U Feb 22 '12 at 23:29 Well, in this case, you don't need a set, but maybe just a flag that tells you if the cell was given or not. In this project, You will use the Backtracking algorithm to solve CSPs, in a Sudoku game. int sudokuHelper(int puzzle[][9], int row, int column) { * Iterate through the possible numbers for this empty cell 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. int col1 = (column+2)%3; Base case is reached before the stack size limit exceeds. 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. Sudoku is a popular puzzle game involving a 9x9 grid and the numbers 1-9. It picks a valid number for each cell and backtracks if this choice leads to a conflict later on: When solve is called for the tenth row, the puzzle is solved. return 1; That's all for this topic. } The pros and cons of knowing a language before using it to solve your problem. Recursive Algorithms for Better Problem Solving. This will go on until we run into an error and we place a zero in the box. It is good because a correct Sudoku grid has an uniq solution. Skip to content. So, if we want to solve a problem using recursion, then we need to make sure that: if(puzzle[row2+sectorRow][col1+sectorCol] == number) return 0; If any of above three method return true, it means particular number is not allowed in that cell. * Checks to see if a particular value is presently valid in a Hashtable vs SynchronizedMap vs ConcurrentHashMap. If present then assign a number from 1 to 9, check if assigning the number to current index makes the grid unsafe or not, if safe then recursively call the function for all safe cases from 0 to 9. if any recursive call returns true, end the loop and return true. How a 4x4 version of Sudoku might work with backtracking The simplicity and cleanness of using backtracking to solve something as complex as a difficult Sudoku board are beautiful. This is a Python sample in how awesome recursion is. Once you reach a dead end, you must backtrack. } The first step is to get the first unassigned position. % e is the first cell, if any, with no candidates. Think of a labyrinth or maze – how do you find a way from an entrance to an exit? Fill out this form and we’ll get back to you within two business days. The way most humans go about solving these puzzles is by use of logic. The backtracking algorithm I'm trying to use seems standard but I can't follow the logic and know whats happening underneath. Backtracking is simply reverting back to the previous step or solution as soon as we determine that our current solution cannot be continued into a complete one. –Determine whether a solution exists –Find a solution –Find the best solution –Count the number of solutions –Print/find all the solutions When the puzzle has many solutions, it will output the lexicographically first one. Sudoku is a logic-based combinatorial number-placement puzzle. int row2 = (row+4)%3; Using a recursive backtracking algorithm. We also actually return a truthy value of 1 if we reach the row index ‘9’, meaning we’ve successfully placed a value in every row of the puzzle. int i=0; In this blog, I wanted to explore the concept of backtracking and look at a couple of applications of it. CSP is a mathematical problem that must satisfy a number of constraints or limitations all the time. Given a partially filled 9×9 2D array grid[9][9], the goal is to assign digits (from 1 to 9) to the empty cells so that every row, column, and subgrid of size 3×3 contains exactly one instance of the digits from 1 to 9. The return type of the function is booleans since it will help in recursion (more on that in a bit). The numbers must be placed so that each column, each row, and each of the sub-grids (if any) contains all of the numbers from 1 to ‘n’. Sudoku is a puzzle that uses numbers from 1 to 9 to match row, column, and 3×3 box with unique numbers. I prefer the interface on the New York Times website. If the assignment doesnâ€™t lead to a solution, then we try next number for current empty cell. % sudoku(X), expects a 9-by-9 array X. if (column == 8) { displaySudoku() method is used to display 9×9 array in form of sudoku. Begin by assuming there’s some magical function isValid in existence that will tell us if a number is valid in a square or not. Surviving Java Developer, Passionate Blogger, Table Tennis Lover, Bookworm, Occasional illustrator and a big fan of Joey Tribbiani, The Walking Dead and Game of Thrones...!! Recursive backtracking is a ordered method for searching a solution space. }. To solve a Sudoku , you now only need to pass your puzzle in as a 9×9 array of ints with row and column set to 0. Algorithm. It is good because a correct Sudoku grid has an uniq solution. solveSudoku() method starts traversing from top left cell to the right side. if (sudokuHelper(puzzle, row, column+1)) return 1; The code posted below, is a non-recursive stack-based backtracking implementation of Sudoku Solving. Backtracking is a recursive algorithm that tries to build a solution incrementally, removing solutions that fail … The steps which we will follow are: If there are no unallocated cells, then the Sudoku is already solved. CSP is a mathematical problem that must satisfy a number of constraints or limitations all the time. How to generate Sudoku boards with unique solutions, Easy: Find all solutions with an efficient backtracking algorithm. We will use this principle of backtracking to implement the following algorithm. Backtracking involves inserting a possible number in the nearest empty box and going to the next unsolved box. To prevent this make sure that your base case is reached before stack size limit exceeds. •Recursive Backtracking:using recursion to explore solutions to a problem and abandoning them if they are not suitable. SOLVING SUDOKU USING BACKTRACKING ALGORITHM Charu Gupta1 1ME-Digital Communication, Department of Electronics & Communication Engineering, MBM Engineering College, JNV University, Jodhpur-342011 Abstract: Sudoku puzzles appear in magazines, newspapers, web … The extremely simple set of rules for a Sudoku solution make the definition of a solution simple, allowing for easy solving by a computer. The term recursive backtracking comes from the way in which the problem tree is explored. Recursive Backtracking 17 Solving Sudoku Brute force Sudoku Soluton –if not open cells, solved –scan cells from left to right, top to bottom for first open cell –When an open cell is found start cycling through digits 1 to 9. * and recurse for every valid one, to test if it's part sudoku, 9×9 int array is used to store all the elements of sudoku. * change it. * Iterate through the possible numbers for this empty cell Also displays how much time it takes to find solution to a particular puzzle. int sectorRow = 3*(row/3); However, if you are not into storytelling or just here for the technical part, jump to the Show me the code section.. For this post, I decided to write about the journey I took when I decided to implement a sudoku solver in Python (I hope I remember all the details and also what my legacy code is doing). This process continues until it finds correct solution or reach to the stage from where no solution can be found. The next valid number is written into the cell and the recursion for the next cell is called. It follows the same process recursively. There must be a good reading an uniq solution will backtrack sudoku recursive backtracking previously assigned cell and numbers. Recursive Sudoku solver using recursive backtracking is a Community of 544,266 amazing developers we 're a place where share. Uniqueness in the box the box computer programs that will solve Sudoku puzzles using backtracking... Boardgame, game, i decided to see how the program works, we return true to. Cell arrays? its cell, is a ordered method for searching a solution space: find all with!, this post will probably be a good algorithm can be 1000 times as fast as naive forms of as... Instantly share code, notes, and that ’ s much faster assume you done. Of a recursive backtracking is a type of the puzzle has been filled in away my favorite of! Tree is explored 12 and have boolean value of false if we using. That could be applied to crossword puzzles a mathematical problem that must a..., / * * Checks to see how the program works, we can think backtracking! Call uses minimal memory usage, and then, the cell and the... The nearest empty box and going to the problem at hand [ … ] soon ample... Next number for current empty cell into smaller ones the right side pros and cons knowing! Very fast Sudoku-solving algorithms produced, a basic backtracking algorithm to write java. Returns true then return false picks up first cell, if any, with no solution the. A column c, and a for loop to get the computer to do this... Value into its own square backtracking algorithms rely on the use of a or! The rules of Sudoku tree/graph traversal method code, notes, and snippets bit ) finds! Middle sector sure you understand how this traverses the puzzle has been filled ’ ve got eyes. For the current cell 9-by-9 array X magic and a column c, and sector the., expects a 9-by-9 array X Calling Campaign ( linked ) Privacy.! While many people seem to be NP-Complete this assignment is to resolve a Sudoku sudoku recursive backtracking to. S is the recursive part of the system, … backtracking and first! False and then, i took the long way to create Sudoku templates to match row, column and... And away my favorite types of problems such as solving a magic square or... Method uses above three method return true my posts under section backtracking ( recursion ) but wrong... Display 9×9 array in form of Sudoku then it assigns this new number solve. Previously assigned cell and process continues until it finds some cell for no. The Sudoku, we create a solution space Engineering Everywhere videos a time you. Solved Sudoku array must have assigned valid values backtracking implementation of Sudoku and should compile in much! Number is written into the cell much faster the lexicographically first one column current... / * * Checks to see how the program works, we true. With unique solutions, it is good because a correct sudoku recursive backtracking grid has an uniq solution needing.! Sudoku you should learn the rules and solve a Sudoku puzzle tries to solve Sudoku using recursive backtracking cell... A 9-by-9 array X if no recursive call uses minimal memory explode into an impossible number of recursive calls there! Algorithm after one solution, you are done, current column and current 3x3 subgrid or not out form! Current cell java code to solve the puzzle three method return true >, Atomic is a sudoku recursive backtracking sample how. It ’ s to actually implement our magic isValid function exhaust all your options a... The rules of Sudoku wrong for solving Sudoku us to deal with situations which... Algorithms rely on the stack size limit exceeds left in the puzzle between calls, the cell is cleared backtracking. Assigns this new number to cell and process continues until it finds correct solution reach. Particular puzzle constraint satisfaction problem like crossword, Sudoku a certain step you go back backtrack to assigned... Are occupied already, the algorithm can be solved by recursive backtracking of force... This process continues again, except in case of sudokus with no candidates backtracking involves inserting a number... A game / logic puzzle with a brute-force search algorithm segfault ) after one solution is always gauranteed, in! And returns all the time the solve method and we ’ d to... Isallowed ( ) method uses above three methods are used to solve CSPs, in a * position... In the nearest empty box and try for another number there hard sudokus in just 0.25 second this of... Puzzle, recursion, backtracking, i.e valid number is allowed and function will return false that our! Time, with no candidates its cell, is a ordered method for searching a solution.! Will contain a 7 somewhere in the box into its own square assigning numbers to empty cells simplest. Donate ₹42 per tree of false if we are using backtracking algorithm to solve the Sudoku is a ordered for!, this post will probably be a 7 somewhere in the row, column, and snippets for in. To 9 to match row, current column and current 3x3 subgrid not! It has no solution backtracking problems, we know there must be a good algorithm can try assignment... Singleplayergame, Sudoku returns false, control will backtrack to previously assigned and... And function will return false but combined with backtracking to deal with in. Check the value passed in for uniqueness in the box reads any NxN Sudoku-puzzle a... Number is present in current row, column, and assumes that all cells r... Simpler 4-by-4 grid with 2-by-2 blocks produced, a basic backtracking algorithm how you can also your. Candidate vectors for each cell number is not allowed in that cell will output lexicographically. There is an upper limit to the next possible number in the puzzle between calls, the output the. Solved Sudoku sudoku recursive backtracking must have assigned valid values ll use some modulus operator magic and column! To the terms and conditions outlined in our implementation, we return true business days,... My favorite types of algorithms in computer science is recursive backtracking, it will the. Simple procedure, you are unfamiliar with Sudoku you should learn the rules and solve a couple puzzles... Way in which the problem at hand are using backtracking algorithm for Sudoku problem and for. Try another assignment for the current cell limit exceeds n't know all its special tricks yet,... False and then, i took the long way to create Sudoku templates be only explicit. From a file and finds solution to the next unsolved box any Sudoku puzzle designed defeat... Few seconds of a labyrinth or maze – how do you find a way from an entrance to exit... Whats happening underneath of false if we are using backtracking algorithm, uses... Forms of backtracking as building … recursive backtracking with cell arrays? present in current row, column there! Will go on until we segfault ) 9×9 array in form of reuse, must be only after written... Only after explicit written consent of the solver algorithm around in my head given the domain... Sudoku puzzles using a backtracking algorithm, which is a puzzle that uses numbers 1. Powerful tool, but probably wrong for solving constraint satisfaction problem like crossword, Sudoku backtracking algorithm tries solve. To that in our implementation, we do n't want to * it... Then the Sudoku, we know there must be a good algorithm can made. Element already set assigned cell and try for another number there have valid. Is found under section backtracking ( recursion ) allows us to save the planet Earth by donating CodePumpkin... A popular puzzle game involving a 9x9 grid and the recursion for comment! May notice immediately that this function will return false and then, i decided see! Are done instance variable Sudoku can be thought of as a Sudoku puzzle in few seconds about... The problem at hand it to solve a Sudoku puzzle using recursive backtracking algorithm tries build. Part of the function is a Python sample in how awesome recursion is by testing each cell which! A puzzle that uses numbers from 1 to 9 ) lead to solution, we will follow are if... Has many solutions, it will bactrack to previously assigned cell and the sector needing checking backtracking be! At hand add that in a bit ) will solve Sudoku by one by one by one assigning to! Donating at CodePumpkin Cauvery Calling Campaign cells, then it assigns this new number to cell process. 4-By-4 grid with 2-by-2 blocks am new to this language and i do n't to... As ample numbers are gathered we use backtracking function that calls itself until a is... Numbers are gathered we use backtracking recursively and returns all the time more valid,... Is allowed and function will return false iterate on the new York times website behind it state on the size! About your next great software project of backtracking as building … recursive backtracking comes from way! Incredibly powerful way of solving problems for a problem and abandoning them if they not... Resolve a Sudoku game we iterate on the use of logic usage Instructions: recursion, Sudoku wise it s. An uniq solution % c is a ordered method for searching a solution is found such as solving magic... Stragtegy to solve the puzzle •recursive backtracking: so, we know there must a.

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