#include <stdio.h>
int correct(int board[9][9]){//判断是否合法 
	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++){//遍历 
			int index=1<<(board[i][j]-1);//设置初始位掩码 
			int blockindex=i/3*3+j/3;//分块 
			if(board[i][j]!=0){//需要判断的位置 
				if(row[i]&index){//行合法 
					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;//判断一个条件不成立即可 所以位掩码恢复 
				if(col[j]&index){//列合法 
					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){//块合法 
					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");//以上都通过 成立 
	return 1;
	
}
int isSafe(int board[9][9],int row,int col,int num){//判断是否合法的函数 
	int x,i,j;
	for (x=0;x<=8;x++)//遍历行合法 
    	if(board[row][x]==num)
            return 0;
    for (x=0;x<= 8;x++)//遍历列合法 
        if(board[x][col]==num)
            return 0;
    int sRow=row-row%3,sCol=col-col%3;//初始化块的起始行与列 
    for(i=0;i<3;i++)
        for(j=0;j<3;j++)//遍历每个块 
            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){//需要填空的部分 
				for(num=1;num<=9;++num){
					if(isSafe(board,i,j,num)){//填空中也要满足数独的定义 
						board[i][j]=num;
						if(solve(board)){//函数嵌套 
							return 1;
						}
						board[i][j]=0;
					}
					
				}
				return 0;//遍历后无法填出正确答案 
			}
		}
	}
	//return 1;
}
void print(int board[9][9]){//格式化输出 
	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, 2, 0, 0, 7, 0, 0, 0, 0},//初始化矩阵 
			   {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);//格式化输出原矩阵 
	if(correct(board1)){//判断是否合法 
		if(solve(board1)){//是否有解 
			printf("The solution of Sudoku matrix:\n");
			print(board1);//格式化输出解 
		}else{
			printf("No solutions!\n");//无解 
		}
		
	}
	
	return 0;
}