I decided to create a small application to solve a user inputted sudoku puzzle. This class guesses numbers for cells (starting with 1) and then backtr Sudoku Solving Java Program (Java in General forum at Coderanch).
- Sudoku Program Code
- How To Program In Java
- How To Write A Sudoku Program
- How To Write A Sudoku Program In Java Download
- Free Sudoku Program Download
- How To Write A Sudoku Program In Java Free
- How To Write Java Code
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.
- Understanding Backtracking in C++. Ask Question 12. It seems easy with a pen and paper but when it comes to writing code for this, I'm confused on how to begin attacking these problems. You have seen a program to walk a binary tree, right? It looks like this.
- This a program which verifies if a 2D matrix is a Sudoku or not. The sum of every row, column and 3x3 matrices have to be 45. Please review the code and provide feedback on best practices and code optimization.
- Sudoku solving algorithms Jump to. A program would solve a puzzle by placing the digit '1' in the first cell and checking if it is allowed to be there.
Recommended: Please solve it on “PRACTICE ” first, before moving on to the solution.
After time meet big brother stetus. Naive Algorithm
The Naive Algorithm is to generate all possible configurations of numbers from 1 to 9 to fill the empty cells. Try every configuration one by one until the correct configuration is found.
The Naive Algorithm is to generate all possible configurations of numbers from 1 to 9 to fill the empty cells. Try every configuration one by one until the correct configuration is found.
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 check whether it is safe to assign. We basically check that the same number is not present in the current row, current column and current 3X3 subgrid. After checking for safety, we assign the number, and recursively check whether this assignment leads to a solution or not. If the assignment doesn’t lead to a solution, then we try the next number for the current empty cell. And if none of the number (1 to 9) leads to a solution, we return false.
Like all other Backtracking problems, we can solve Sudoku by one by one assigning numbers to empty cells. Before assigning a number, we check whether it is safe to assign. We basically check that the same number is not present in the current row, current column and current 3X3 subgrid. After checking for safety, we assign the number, and recursively check whether this assignment leads to a solution or not. If the assignment doesn’t lead to a solution, then we try the next number for the current empty cell. And if none of the number (1 to 9) leads to a solution, we return false.
Following are the implementation for Sudoku problem. It prints the completely filled grid as output.
C++
// A Backtracking program in C++ to solve Sudoku problem using namespace std; // UNASSIGNED is used for empty cells in sudoku grid // Size will be NxN // that is still unassigned int &row, int &col); // Checks whether it will be legal bool isSafe( int grid[N][N], int row, to assign values to all unassigned locations in Sudoku solution (non-duplication across rows, bool SolveSudoku( int grid[N][N]) int row, col; // If there is no unassigned location, if (!FindUnassignedLocation(grid, row, col)) for ( int num = 1; num <= 9; num++) // if looks promising { grid[row][col] = num; // return, if success, yay! return true ; // failure, unmake & try again } return false ; // this triggers backtracking still unassigned. If found, the reference that is unassigned, and true is returned. If no unassigned entries remain, false is returned. */ int &row, int &col) for (row = 0; row < N; row++) if (grid[row][col] UNASSIGNED) return false ; an assigned entry in the specified row matches bool UsedInRow( int grid[N][N], int row, int num) for ( int col = 0; col < N; col++) return true ; } /* Returns a boolean which indicates whether matches the given number. */ { if (grid[row][col] num) return false ; an assigned entry within the specified 3x3 box bool UsedInBox( int grid[N][N], int boxStartRow, { for ( int col = 0; col < 3; col++) [col + boxStartCol] num) return false ; it will be legal to assign num to the given bool isSafe( int grid[N][N], int row, { current row, current column and current 3x3 box */ !UsedInCol(grid, col, num) && col - col % 3, num) && } /* A utility function to print grid */ { { cout << grid[row][col] << ' ' ; } int main() // 0 means unassigned cells {5, 2, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 3, 0, 1, 0, 0, 8, 0}, {0, 5, 0, 0, 9, 0, 6, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 7, 4}, if (SolveSudoku(grid) true ) else } // This is code is contributed by rathbhupendra |
C
// A Backtracking program in C to solve Sudoku problem // UNASSIGNED is used for empty cells in sudoku grid // N is used for the size of Sudoku grid. Size will be NxN // This function finds an entry in grid that is still unassigned bool FindUnassignedLocation( int grid[N][N], int &row, int &col); // Checks whether it will be legal to assign num to the given row, col bool isSafe( int grid[N][N], int row, int col, int num); /* Takes a partially filled-in grid and attempts to assign values to all unassigned locations in such a way to meet the requirements for Sudoku solution (non-duplication across rows, columns, and boxes) */ { // If there is no unassigned location, we are done return true ; // success! // consider digits 1 to 9 { if (isSafe(grid, row, col, num)) // make tentative assignment if (SolveSudoku(grid)) grid[row][col] = UNASSIGNED; } } /* Searches the grid to find an entry that is still unassigned. If found, the reference parameters row, col will be set the location that is unassigned, and true is returned. If no unassigned entries bool FindUnassignedLocation( int grid[N][N], int &row, int &col) for (row = 0; row < N; row++) if (grid[row][col] UNASSIGNED) return false ; /* Returns a boolean which indicates whether an assigned entry bool UsedInRow( int grid[N][N], int row, int num) for ( int col = 0; col < N; col++) return true ; } /* Returns a boolean which indicates whether an assigned entry in the specified column matches the given number. */ { if (grid[row][col] num) return false ; /* Returns a boolean which indicates whether an assigned entry within the specified 3x3 box matches the given number. */ bool UsedInBox( int grid[N][N], int boxStartRow, int boxStartCol, int num) for ( int row = 0; row < 3; row++) if (grid[row+boxStartRow][col+boxStartCol] num) return false ; /* Returns a boolean which indicates whether it will be legal to assign bool isSafe( int grid[N][N], int row, int col, int num) /* Check if 'num' is not already placed in current row, return !UsedInRow(grid, row, num) && !UsedInBox(grid, row - row%3 , col - col%3, num)&& } /* A utility function to print grid */ { { printf ( '%2d' , grid[row][col]); } int main() // 0 means unassigned cells {5, 2, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 3, 0, 1, 0, 0, 8, 0}, {0, 5, 0, 0, 9, 0, 6, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 7, 4}, if (SolveSudoku(grid) true ) else } |
Java
Java to solve Sudoku problem */ { int row, int col, { for ( int d = 0 ; d < board.length; d++) // if the number we are trying to // that row, return false; { } for ( int r = 0 ; r < board.length; r++) // if the number we are trying to // that column, return false; if (board[r][col] num) return false ; } // corresponding square has int sqrt = ( int ) Math.sqrt(board.length); int boxColStart = col - col % sqrt; for ( int r = boxRowStart; { d < boxColStart + sqrt; d++) if (board[r][d] num) return false ; } return true ; public static boolean solveSudoku( int [][] board, int n) int row = - 1 ; boolean isEmpty = true ; { { { col = j; // we still have some remaining isEmpty = false ; } if (!isEmpty) break ; } // no empty space left { } // else for each-row backtrack { { if (solveSudoku(board, n)) // print(board, n); } { } } } public static void print( int [][] board, int N) // we got the answer, just print it { { System.out.print( ' ' ); System.out.print( 'n' ); if ((r + 1 ) % ( int ) Math.sqrt(N) 0 ) System.out.print( ' ); } public static void main(String args[]) { { 5 , 2 , 0 , 0 , 0 , 0 , 0 , 0 , 0 }, { 0 , 0 , 3 , 0 , 1 , 0 , 0 , 8 , 0 }, { 0 , 5 , 0 , 0 , 9 , 0 , 6 , 0 , 0 }, { 0 , 0 , 0 , 0 , 0 , 0 , 0 , 7 , 4 }, }; { } { } } // This code is contributed |
Python
# A Backtracking program in Python to solve Sudoku problem def print_grid(arr): for j in range ( 9 ): print ( 'n' ) # Function to Find the entry in the Grid that is still not used # Searches the grid to find an entry that is still unassigned. If # found, the reference parameters row, col will be set the location # that is unassigned, and true is returned. If no unassigned entries # 'l' is a list variable that has been passed from the solve_sudoku function # to keep track of incrementation of Rows and Columns for row in range ( 9 ): if (arr[row][col] = = 0 ): l[ 1 ] = col return False # Returns a boolean which indicates whether any assigned entry def used_in_row(arr,row,num): if (arr[row][i] = = num): return False # Returns a boolean which indicates whether any assigned entry # in the specified column matches the given number. for i in range ( 9 ): return True # Returns a boolean which indicates whether any assigned entry # within the specified 3x3 box matches the given number for i in range ( 3 ): if (arr[i + row][j + col] = = num): return False # Checks whether it will be legal to assign num to the given row,col # Returns a boolean which indicates whether it will be legal to assign def check_location_is_safe(arr,row,col,num): # Check if 'num' is not already placed in current row, return not used_in_row(arr,row,num) and not used_in_col(arr,col,num) and not used_in_box(arr,row - row % 3 ,col - col % 3 ,num) # Takes a partially filled-in grid and attempts to assign values to # all unassigned locations in such a way to meet the requirements # for Sudoku solution (non-duplication across rows, columns, and boxes) # 'l' is a list variable that keeps the record of row and col in find_empty_location Function # If there is no unassigned location, we are done return True # Assigning list values to row and col that we got from the above Function col = l[ 1 ] # consider digits 1 to 9 if (check_location_is_safe(arr,row,col,num)): # make tentative assignment if (solve_sudoku(arr)): arr[row][col] = 0 # this triggers backtracking if __name__ = = '__main__' : # creating a 2D array for the grid grid = [[ 3 , 0 , 6 , 5 , 0 , 8 , 4 , 0 , 0 ], [ 0 , 8 , 7 , 0 , 0 , 0 , 0 , 3 , 1 ], [ 9 , 0 , 0 , 8 , 6 , 3 , 0 , 0 , 5 ], [ 1 , 3 , 0 , 0 , 0 , 0 , 2 , 5 , 0 ], [ 0 , 0 , 5 , 2 , 0 , 6 , 3 , 0 , 0 ]] # if success print the grid print_grid(grid) print 'No solution exists' # The above code has been contributed by Harshit Sidhwa. |
C#
C# to solve Sudoku problem */ { public static bool isSafe( int [,] board, int num) // row has the unique (row-clash) { // place is already present in if (board[row, d] num) return false ; } // column has the unique numbers (column-clash) { // place is already present in if (board[r, col] num) return false ; } // corresponding square has int sqrt = ( int ) Math.Sqrt(board.GetLength(0)); int boxColStart = col - col % sqrt; for ( int r = boxRowStart; { d < boxColStart + sqrt; d++) if (board[r,d] num) return false ; } return true ; { int col = -1; for ( int i = 0; i < n; i++) for ( int j = 0; j < n; j++) if (board[i, j] 0) row = i; // missing values in Sudoku break ; } { } if (isEmpty) return true ; for ( int num = 1; num <= n; num++) if (isSafe(board, row, col, num)) board[row, col] = num; { return true ; else board[row, col] = 0; // replace it } return false ; { for ( int r = 0; r < N; r++) for ( int d = 0; d < N; d++) Console.Write(board[r,d]); } { } } // Driver Code { int [,] board = new int [,] {3, 0, 6, 5, 0, 8, 4, 0, 0}, {0, 8, 7, 0, 0, 0, 0, 3, 1}, {9, 0, 0, 8, 6, 3, 0, 0, 5}, {1, 3, 0, 0, 0, 0, 2, 5, 0}, {0, 0, 5, 2, 0, 6, 3, 0, 0} int N = board.GetLength(0); if (solveSudoku(board, N)) print(board, N); // print solution else Console.Write( 'No solution' ); } |
Output:
References:
http://see.stanford.edu/materials/icspacs106b/H19-RecBacktrackExamples.pdf
http://see.stanford.edu/materials/icspacs106b/H19-RecBacktrackExamples.pdf
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
Recommended Posts:
Improved By : Mohan Das, Nikash, 29AjayKumar, rathbhupendra, ManasChhabra2
Sudoku Program Code
A typical Sudoku puzzle
A standard Sudoku contains 81 cells, in a 9×9 grid, and has 9 boxes, each box being the intersection of the first, middle, or last 3 rows, and the first, middle, or last 3 columns. Each cell may contain a number from one to nine, and each number can only occur once in each row, column, and box. A Sudoku starts with some cells containing numbers (clues), and the goal is to solve the remaining cells. Proper Sudokus have one solution. Players and investigators may use a wide range of computer algorithms to solve Sudokus, study their properties, and make new puzzles, including Sudokus with interesting symmetries and other properties.
There are several computer algorithms that will solve most 9×9 puzzles (n=9) in fractions of a second, but combinatorial explosion occurs as n increases, creating limits to the properties of Sudokus that can be constructed, analyzed, and solved as n increases.
- 1Techniques
Techniques[edit]
Backtracking[edit]
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.
A Sudoku designed to work against the brute force algorithm.[1]
Some hobbyists have developed computer programs that will solve Sudoku puzzles using a backtracking algorithm, which is a type of brute force search.[2] Backtracking is a depth-first search (in contrast to a breadth-first search), because it will completely explore one branch to a possible solution before moving to another branch. Although it has been established that approximately 5.96 x 1126 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.[3][4][5][6] 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. When checking for violations, if it is discovered that the '1' is not allowed, the value is advanced to '2'. If a cell is discovered where none of the 9 digits is allowed, then the algorithm leaves that cell blank and moves back to the previous cell. Install windows 98 on eee pc. The value in that cell is then incremented by one. This is repeated until the allowed value in the last (81st) cell is discovered.
The animation shows how a Sudoku is solved with this method. The puzzle's clues (red numbers) remain fixed while the algorithm tests each unsolved cell with a possible solution. Notice that the algorithm may discard all the previously tested values if it finds the existing set does not fulfil the constraints of the Sudoku.
Advantages of this method are:
- A solution is guaranteed (as long as the puzzle is valid).
- Solving time is mostly unrelated to degree of difficulty.
- The algorithm (and therefore the program code) is simpler than other algorithms, especially compared to strong algorithms that ensure a solution to the most difficult puzzles.
The disadvantage of this method is that the solving time may be slow compared to algorithms modeled after deductive methods. One programmer reported that such an algorithm may typically require as few as 15,000 cycles, or as many as 900,000 cycles to solve a Sudoku, each cycle being the change in position of a 'pointer' as it moves through the cells of a Sudoku.[7][8]
A Sudoku can be constructed to work against backtracking. Assuming the solver works from top to bottom (as in the animation), a puzzle with few clues (17), no clues in the top row, and has a solution '987654321' for the first row, would work in opposition to the algorithm. Thus the program would spend significant time 'counting' upward before it arrives at the grid which satisfies the puzzle. In one case, a programmer found a brute force program required six hours to arrive at the solution for such a Sudoku (albeit using a 2008-era computer). Such a Sudoku can be solved nowadays in less than 30 seconds using an exhaustive search routine and faster processors.[citation needed]
Stochastic search / optimization methods[edit]
Sudoku can be solved using stochastic (random-based) algorithms.[9][10] An example of this method is to: David suchet.
How To Program In Java
- Randomly assign numbers to the blank cells in the grid.
- Calculate the number of errors.
- 'Shuffle' the inserted numbers until the number of mistakes is reduced to zero.
A solution to the puzzle is then found. Approaches for shuffling the numbers include simulated annealing, genetic algorithm and tabu search. Stochastic-based algorithms are known to be fast, though perhaps not as fast as deductive techniques. Unlike the latter however, optimisation algorithms do not necessarily require problems to be logic-solvable, giving them the potential to solve a wider range of problems. Algorithms designed for graph colouring are also known to perform well with Sudokus.[11] It is also possible to express a Sudoku as an integer linear programming problem. Such approaches get close to a solution quickly, and can then use branching towards the end. The simplex algorithm is able to solve non-proper Sudokus, indicating if the Sudoku is not valid (no solution), or providing the set of answers when there is more than one solution.
Constraint programming[edit]
A Sudoku may also be modelled as a constraint satisfaction problem. In his paper Sudoku as a Constraint Problem,[12] Helmut Simonis describes many reasoning algorithms based on constraints which can be applied to model and solve problems. Some constraint solvers include a method to model and solve Sudokus, and a program may require less than 100 lines of code to solve a simple Sudoku.[13][14] If the code employs a strong reasoning algorithm, incorporating backtracking is only needed for the most difficult Sudokus. An algorithm combining a constraint-model-based algorithm with backtracking would have the advantage of fast solving time, and the ability to solve all sudokus.
How To Write A Sudoku Program
Exact cover[edit]
Sudoku puzzles may be described as an exact cover problem. This allows for an elegant description of the problem and an efficient solution. Modelling Sudoku as an exact cover problem and using an algorithm such as dancing links will typically solve a Sudoku in a few milliseconds.
Developing (searching for) Sudokus[edit]
A Sudoku with 17 clues and diagonal symmetry. | An automorphic Sudoku with 18 clues and two-way diagonal symmetry. |
A 17 clue Sudoku with a similar pattern. (Orange circles: removed clues, green circles: added clues, blue underline: different digit). | An 18 clue Sudoku. (Horizontal symmetry). |
Computer programs are often used to 'search' for Sudokus with certain properties, such as a small number of clues, or certain types of symmetry. Over 49,000 Sudokus with 17 clues have been found, but discovering new distinct ones (not transformations of existing known Sudokus) is becoming more difficult as undiscovered ones become more rare.[15]
One common method of searching for Sudokus with a particular characteristic is called neighbor searching. Using this strategy, one or more known Sudokus which satisfy or nearly satisfy the characteristic being searched for is used as a starting point, and these Sudokus are then altered to look for other Sudokus with the property being sought. https://directoryclever323.weebly.com/zac-brown-band-you-get-what-you-give-torrent-download.html. The alteration can be relocating one or more clue positions, or removing a small number of clues, and replacing them with a different number of clues. For example, from a known Sudoku, a search for a new one with one fewer clues can be performed by removing two clues and adding one clue in a new location. (This can be called a {-2,+1} search). Each new pattern would then be searched exhaustively for all combinations of clue values, with the hope that one or more yields a valid Sudoku (i.e. can be solved and has a single solution). Methods can also be employed to prevent essentially equivalent Sudokus from being redundantly tested.
As a specific example, a search for a 17-clue Sudoku could start with a known 18-clue Sudoku, and then altering it by removing three clues, and replacing them with only two clues, in different positions (see last two images). This may discover new Sudokus, but there would be no immediate guarantee that they are essentially different from already known Sudokus. If searching for truly new (undiscovered) Sudokus, a further confirmation would be required to ensure each find is not a transformation of an already known Sudoku.[16][better source needed]
See also[edit]
- Mathematics of Sudoku
- § Sudokus with Few Clues (Minimum number of givens)
- Combinatorial explosion - (with summary of grid count of Sudoku compared to Latin squares)
How To Write A Sudoku Program In Java Download
References[edit]
Free Sudoku Program Download
- ^'Star Burst - Polar Graph' A polar chart showing a solution path for a Sudoku (Star Burst) using an exhaustive search routine and comment about 17-clue Sudoku.
- ^http://intelligence.worldofcomputing/brute-force-search Brute Force Search, December 14th, 2009.
- ^'Backtracking - Set 7 (Sudoku)'. GeeksforGeeks. GeeksforGeeks. Archived from the original on 2016-08-28. Retrieved 24 December 2016.
- ^Norvig, Peter. 'Solving Every Sudoku Puzzle'. Peter Norvig (personal website). Retrieved 24 December 2016.
- ^'Chart of Cells Visited for Solution' A chart showing a solution path to a difficult Sudoku.
- ^Zelenski, Julie (July 16, 2008,). Lecture 11 | Programming Abstractions (Stanford). Stanford Computer Science Department.Check date values in:
|date=
(help) - ^'Star Burst Leo - Polar Graph' A polar chart showing a solution path for a Sudoku (Star Burst Leo) using an exhaustive search routine.
- ^'Chart of Cells Visited for Solution' A chart showing a solution path for a difficult Sudoku using an exhaustive search routine.
- ^Lewis, R (2007) Metaheuristics Can Solve Sudoku Puzzles Journal of Heuristics, vol. 13 (4), pp 387-401.
- ^Perez, Meir and Marwala, Tshilidzi (2008) Stochastic Optimization Approaches for Solving Sudoku arXiv:0805.0697.
- ^Lewis, R. A Guide to Graph Colouring: Algorithms and Applications. Springer International Publishers, 2015.
- ^Simonis, Helmut (2005). 'Sudoku as a Constraint Problem'(PDF). Cork Constraint Computation Centre at University College Cork: Helmut Simonis. Retrieved 8 December 2016.
paper presented at the Eleventh International Conference on Principles and Practice of Constraint Programming
- ^Multiple Authors. 'Java Constraint Programming solver'(Java). JaCoP. Krzysztof Kuchcinski & Radoslaw Szymanek. Retrieved 8 December 2016.
- ^Rhollor. 'Sudokusolver'(C++). GitHub. Rhollor. Retrieved 8 December 2016.
- ^Royle, Gordon. 'Minimum Sudoku'. Retrieved October 20, 2013.
- ^http://forum.enjoysudoku.com The New Sudoku Players' Forum 'No new 17s within {-3+3}'.
External links[edit]
How To Write A Sudoku Program In Java Free
- http://diuf.unifr.ch/pai/people/juillera/Sudoku/Sudoku.htmlSudoku Explainer by Nicolas Juillerat (Popular for rating Sudokus in general)
- http://gsf.cococlyde.org/download/sudokusudoku by Glenn Fowler (Popular for rating the hardest Sudokus amongst other things)
- A Pencil-and-Paper Algorithm for Solving Sudoku Puzzles quoted also in a popular British newspaper the Daily Mail
How To Write Java Code
Retrieved from 'https://en.wikipedia.org/w/index.php?title=Sudoku_solving_algorithms&oldid=907549529'