Am searching for an efficient algorithm for generating solved Sudoku given the size(rows and column) of the board as input.

i have written a program but its performing badly when the number of rows and column exceeds 40 (ie 40 x 40 matrix ).

```
import java.util.Scanner;
public class Main {
public static int [][]board;
public static int n=0;
public static int m=0;
public static boolean isValid(int row,int matrix,int value){
// Checks vertically
for(int i=0;i<n;i++){
if(board[i][0]==value)
return false;
else if(board[i][0]==0){
i=n;
}
}
//No need to check horizontally
//checks the m x m blocks
for(int i=matrix;i<matrix+m;i++){
for(int j=0;j<m;j++)
if(board[i][j]==value)
return false;
else if(board[i][j]==0){
j=m;
i=n;
}
}
return true;
}
private static void fillData(int row, int j) {
for(int i=0;i<n;i++){
board[row][i]=j%(n+1)+(j/(n+1));
j++;
}
}
public static void main(String[] args) {
Scanner sc=new Scanner(System.in);
int matrix=0;
int count=0;
m=sc.nextInt();
n=(int) Math.pow(m, 2);
board=new int[n][n];
for(int i=0;i<n;i++){
count++;
/* For a 9x9 board , matrix values will be 0,3,6 which are the row index of the 3x3 boxes */
if(count==(m+1)){
count=1;
matrix+=m;
}
for(int j=1;j<=n;j++){
if(isValid(i,matrix,j)){
fillData(i,j);
j=n+1;
}
}
}
for (int k = 0; k < n; k++) {
for(int j=0;j<n;j++)
System.out.print(board[k][j]+" ");
System.out.println();
}
}
}
```

Let me know if there are any optimizations that i can make or any algorithm that performs well