Following are the rules of Suduku for a player.
- In all 9 sub matrices 3×3 the elements should be 1-9, without repetition.
- In all rows there should be elements between 1-9 , without repetition.
- In all columns there should be elements between 1-9 , without repetition.
The task is to generate a 9 x 9 Suduku grid that is valid, i.e., a player can fill the grid following above set of rules.
A simple naive solution can be.
- Randomly take any number 1-9.
- Check if it is safe to put in the cell.(row , column and box)
- If safe, place it and increment to next location and go to step 1.
- If not safe, then without incrementing go to step 1.
- Once matrix is fully filled, remove k no. of elements randomly to complete game.
Improved Solution : We can improve the solution, if we understand a pattern in this game. We can observe that all 3 x 3 matrices, which are diagonally present are independent of other 3 x 3 adjacent matrices initially, as others are empty.
3 8 5 0 0 0 0 0 0 9 2 1 0 0 0 0 0 0 6 4 7 0 0 0 0 0 0 0 0 0 1 2 3 0 0 0 0 0 0 7 8 4 0 0 0 0 0 0 6 9 5 0 0 0 0 0 0 0 0 0 8 7 3 0 0 0 0 0 0 9 6 2 0 0 0 0 0 0 1 4 5
(We can observe that in above matrix, the diagonal matrices are independent of other empty matrices initially). So if we fill them first, then we will only have to do box check and thus column/row check not required.
Secondly, while we fill rest of the non-diagonal elements, we will not have to use random generator, but we can fill recursively by checking 1 to 9.
Following is the improved logic for the problem. 1. Fill all the diagonal 3x3 matrices. 2. Fill recursively rest of the non-diagonal matrices. For every cell to be filled, we try all numbers until we find a safe number to be placed. 3. Once matrix is fully filled, remove K elements randomly to complete game.
/* Java program for Sudoku generator */import java.lang.*; public class Sudoku { int[] mat[]; int N; // number of columns/rows. int SRN; // square root of N int K; // No. Of missing digits // Constructor Sudoku(int N, int K) { this.N = N; this.K = K; // Compute square root of N Double SRNd = Math.sqrt(N); SRN = SRNd.intValue(); mat = new int[N][N]; } // Sudoku Generator public void fillValues() { // Fill the diagonal of SRN x SRN matrices fillDiagonal(); // Fill remaining blocks fillRemaining(0, SRN); // Remove Randomly K digits to make game removeKDigits(); } // Fill the diagonal SRN number of SRN x SRN matrices void fillDiagonal() { for (int i = 0; i<N; i=i+SRN) // for diagonal box, start coordinates->i==j fillBox(i, i); } // Returns false if given 3 x 3 block contains num. boolean unUsedInBox(int rowStart, int colStart, int num) { for (int i = 0; i<SRN; i++) for (int j = 0; j<SRN; j++) if (mat[rowStart+i][colStart+j]==num) return false; return true; } // Fill a 3 x 3 matrix. void fillBox(int row,int col) { int num; for (int i=0; i<SRN; i++) { for (int j=0; j<SRN; j++) { do { num = randomGenerator(N); } while (!unUsedInBox(row, col, num)); mat[row+i][col+j] = num; } } } // Random generator int randomGenerator(int num) { return (int) Math.floor((Math.random()*num+1)); } // Check if safe to put in cell boolean CheckIfSafe(int i,int j,int num) { return (unUsedInRow(i, num) && unUsedInCol(j, num) && unUsedInBox(i-i%SRN, j-j%SRN, num)); } // check in the row for existence boolean unUsedInRow(int i,int num) { for (int j = 0; j<N; j++) if (mat[i][j] == num) return false; return true; } // check in the row for existence boolean unUsedInCol(int j,int num) { for (int i = 0; i<N; i++) if (mat[i][j] == num) return false; return true; } // A recursive function to fill remaining // matrix boolean fillRemaining(int i, int j) { // System.out.println(i+" "+j); if (j>=N && i<N-1) { i = i + 1; j = 0; } if (i>=N && j>=N) return true; if (i < SRN) { if (j < SRN) j = SRN; } else if (i < N-SRN) { if (j==(int)(i/SRN)*SRN) j = j + SRN; } else { if (j == N-SRN) { i = i + 1; j = 0; if (i>=N) return true; } } for (int num = 1; num<=N; num++) { if (CheckIfSafe(i, j, num)) { mat[i][j] = num; if (fillRemaining(i, j+1)) return true; mat[i][j] = 0; } } return false; } // Remove the K no. of digits to // complete game public void removeKDigits() { int count = K; while (count != 0) { int cellId = randomGenerator(N*N); // System.out.println(cellId); // extract coordinates i and j int i = (cellId/N); int j = cellId%9; if (j != 0) j = j - 1; // System.out.println(i+" "+j); if (mat[i][j] != 0) { count--; mat[i][j] = 0; } } } // Print sudoku public void printSudoku() { for (int i = 0; i<N; i++) { for (int j = 0; j<N; j++) System.out.print(mat[i][j] + " "); System.out.println(); } System.out.println(); } // Driver code public static void main(String[] args) { int N = 9, K = 20; Sudoku sudoku = new Sudoku(N, K); sudoku.fillValues(); sudoku.printSudoku(); } } |
Output: [0 means not filled]
2 3 0 4 1 5 0 6 8 0 8 0 2 3 6 5 1 9 1 6 0 9 8 7 2 3 4 3 1 7 0 9 4 0 2 5 4 5 8 1 2 0 6 9 7 9 2 6 0 5 8 3 0 1 0 0 0 5 0 0 1 0 2 0 0 0 8 4 2 9 0 3 5 9 2 3 7 1 4 8 6
This article is contributed by Ankur Trisal (ankur.trisal@gmail.com). If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
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