#include <stdio.h>
int correct(int board[9][9]){
	int col[9]={0},row[9]={0},block[9]={0};
	int i,j;
	for(i=0;i<9;++i){
		for(j=0;j<9;j++){
			int index=1<<(board[i][j]-1);
			int blockindex=i/3*3+j/3;
			if(board[i][j]!=0){
				if(row[i]&index){
					printf("False:Invalid initial Sudoku matrix!\n");
					printf("The number %d in the row %d has been used!",board[i][j],i+1);
					return 0;
				}
				row[i]=index;
				if(col[j]&index){
					printf("False:Invalid initial Sudoku matrix!\n");
					printf("The number %d in the rol %d has been used!",board[i][j],j+1);
					return 0;
				}
				col[j]=index;
				if(block[blockindex]&index){
					printf("False:Invalid initial Sudoku matrix!\n");
					printf("The number %d in the block %d has been used!",board[i][j],blockindex+1);
					return 0;
				}
				block[blockindex]=index;
			}
			
			
			
		}
	}
	printf("True:Valid initial Sudoku matrix!\n");
	return 1;
	
}
int isSafe(int board[9][9], int row, int col, int num) {
	int x,i,j;
	for (x = 0; x <= 8; x++)
        if (board[row][x] == num)
            return 0;
    for (x = 0; x <= 8; x++)
        if (board[x][col] == num)
            return 0;
    int sRow = row - row % 3, sCol = col - col % 3;
    for (i = 0; i < 3; i++)
        for (j = 0; j < 3; j++)
            if (board[i + sRow][j + sCol] == num)
                return 0;
    return 1;
}
int solve(int board[9][9]){
	int num;
	int i=0,j=0;
	for(i=0;i<9;i++){
		for(j=0;j<9;j++){
			if(board[i][j]==0){
				for(num=1;num<=9;++num){
					if(isSafe(board,i,j,num)){
						board[i][j]=num;
						if(solve(board)){
							return 1;
						}
						board[i][j]=0;
					}
					
				}
				return 0;
			}
		}
	}
	return 1;
}
void print(int board[9][9]){
	printf("|---|---|---|---|---|---|\n");
	int i=0,j=0,s=0,k=0;
	for(i=0;i<9;++i){
		for(j=0;j<9;j++){
			while(j%3==0){
				printf("| ");
				break;
			}
			printf("%d ",board[i][j]);
		}
		printf("|\n");
		while((i+1)%3==0){
			printf("|---|---|---|---|---|---|\n");
			break;
		}
	}
}
int main(){
	int board1[9][9]={{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}};
	printf("The original Sudoku matrix:\n");
	print(board1);
	if(correct(board1)){
		if(solve(board1)){
			printf("The solution of Sudoku matrix:\n");
			print(board1);
		}else{
			printf("No solutions!\n");
		}
		
	}
	
	return 0;
}