# Program for Sudoku Generator

Background:

Following are the rules of Suduku for a player.

1. In all 9 sub matrices 3×3 the elements should be 1-9, without repetition.
2. In all rows there should be elements between 1-9 , without repetition.
3. 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.

1. Randomly take any number 1-9.
2. Check if it is safe to put in the cell.(row , column and box)
3. If safe, place it and increment to next location and go to step 1.
4. If not safe, then without incrementing go to step 1.
5. 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.

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

 /* 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; ii==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=N && 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

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

Matrix Matrix