#include using namespace std; //enter a sudoku to be solved or leave it for default input #define n 9 int board[n][n] = {{5,3,0,0,7,0,0,0,0}, {6,0,0,1,9,5,0,0,0}, {0,9,8,0,0,0,0,6,0}, {8,0,0,0,6,0,0,0,3}, {4,0,0,8,0,3,0,0,1}, {7,0,0,0,2,0,0,0,6}, {0,6,0,0,0,0,2,8,0}, {0,0,0,4,1,9,0,0,5}, {0,0,0,0,8,0,0,7,9}}; bool inrow(int row,int x) //function to check if the row contains the same element { for(int i = 0;i < n;i++) if(board[row][i] == x) return true; return false; } bool incol(int col,int x) //function to check if the column contains the same element { for(int i = 0;i < n;i++) if(board[i][col] == x) return true; return false; } bool ingrid(int row,int col,int x) //function to check if the grid (3×3) contains the same element { int r = row - row%3, c = col - col%3; for(int i = r;i < r+3;i++) for(int j = c;j < c+3;j++) if(board[i][j] == x) return true; return false; } bool issafe(int row,int col,int x)//checks for sudoku codition { return !inrow(row,x) && !incol(col,x) && !ingrid(row,col,x); } bool solve() { for(int i = 0;i < n;i++) { for(int j = 0;j < n;j++) { if(board[i][j] == 0)//check if the block at which we are writing is empty { for(int x = 1;x <= n;x++) { if(issafe(i,j,x))//check for sudoku condition { board[i][j] = x;//write the number if(solve()) return true; else board[i][j] = 0; //line 46-49 is called backtracing //it tracks the element entered, if wrong, rewrites it to 0 } } return false;//statement which reports that the element entered is wrong } } } return true; } int main() { for(int i = 0;i < n;i++) for(int j = 0;j < n;j++) cin >> board[i][j];//initialization of matrix for(int i = 0;i < n;i++) {for(int j = 0;j < n;j++) cout << board[i][j] << " ";//printing the initial matrix cout << "\n"; } solve(); cout << "\n\n"; for(int i = 0;i < n;i++) {for(int j = 0;j < n;j++) cout << board[i][j] << " ";//printing the solved matrix cout << "\n"; } return 0; }

Sudoku using backtracking