C programming - Sodoku Solution using Backtracking

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write a program that receives from the user sodoku board dimenstion(N) (can be any number for example: 3,4,5...) [not constant we must recieve it for the user]

and after that the sodoku board (we can fill elemnt a[i][j] with numbers from 1 to N and if it doesn't flled with a number then it is 0). [recieve from the user] after this the program must check if the board has solution then to print it, if not to print (NO solution!).

the rules: 1) to fill the board with numbers from 1 to N [we can assume that the user insert correct numbers no need to check it he inserts a number more than N] 2) two identical numbers must not appear on the same row

3) two identical numbers must not appear on the same colum

4) for this solution there is no limit for two identical numbers appearing in the same sub matrix(block) (for example: id it is 9x9 sodoku then number 1 for example can appear more than once in the sub matrix 3*3) [I provided an example]

5)the programm must be effective to finish in few seconds

6) must use backtracking *please run the program before giving me the solution.

I have a code that works really good in every board , the problem is when i put 9x9 board with no solution it doesn't work(I would like from you to make it more effective)

#include

int n;

// function to print matrix void print(int a[n][n]) { printf(" Your sodoku solution is: "); int i, j; for(i=0; i

// function to check if a number x can be placed at a given cell int isValid(int x, int i, int j, int a[n][n]) { int k; for(k=0; k

// recursive function to solve sudoku board using backtracking int backtrack(int a[n][n], int i, int j) { // base case if(i >= n) return 1;

int k, ans; // skip if the cell is filled if(a[i][j] != 0) { // move to next cell // check end of row if((j+1) >= n) ans = backtrack(a, i+1, 0); else ans = backtrack(a, i, j+1);

if(ans == 1) return 1; return 0; }

// try to fill the cell of a number from 1 to n for(k=1; k= n) ans = backtrack(a, i+1, 0); else ans = backtrack(a, i, j+1);

if(ans == 1) return 1;

// backtrack if unsuccessful a[i][j] = 0; } } // no solution found return 0 return 0; }

int main() { // loop variables int i, j; // input n printf("Please enter your sodoku size:"); scanf("%d", &n); // input matrix int a[n][n];

// input the n*n matrix printf(" Please insert your sodoku board: "); for(i=0; i

// call the backtracking function if(backtrack(a, 0, 0) == 1) // print solution print(a); else printf("No solution ");

return 0; }

input output 9 710000609 200003000 000150008 007000090 006000 700 020000400 1000 29000 000300004 905000086 712438 659 291763 845 36 4152978 457816392 5 8 6 941723 82 35 97461 148629537 679385214 935274186 No Solution! 9 710000619 200003000 000150008 007000090 006000700 020000400 1000 29000 000300004 905000086<>

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