#include <stdio.h>

void print(int board[9][9]){
	printf("|-----------------------|\n");
	int i,j;
	for(i=0;i<9;i++){
		printf("| ");
		for(j=0;j<9;j++){
			if(board[i][j]==0) printf(". ");
			else printf("%d ",board[i][j]);
			if(j%3==2) printf("| ");
		}
		printf("\n");
		if(i%3==2){
			printf("|-----------------------|\n");
		}
	}
}

void check(int board[9][9]){
	printf("The original Sudoku matrix:\n");
	print(board);
	int i,j,k;
	
	//判断每一行数字是否重复 
	for(i=0;i<9;i++){
		int cnt[10]={}; //统计每个数字出现次数 
		for(j=0;j<9;j++){
			cnt[board[i][j]]++;
		}
		for(j=1;j<=9;j++){
			if(cnt[j]>1){
				printf("False:Invalid initial Sudoku matrix!\n");
				printf("The number %d in the col %d has been used!\n",j,i+1);
				return;
			}
		}
	}
	
	//判断每一列数字是否重复 
	for(i=0;i<9;i++){
		int cnt[10]={}; //统计每个数字出现次数
		for(j=0;j<9;j++){
			cnt[board[j][i]]++;
		}
		for(j=1;j<=9;j++){
			if(cnt[j]>1){
				printf("False:Invalid initial Sudoku matrix!\n");
				printf("The number %d in the row %d has been used!\n",j,i+1);
				return;
			}
		}
	}
	
	//判断每个九宫格数字是否重复 
	for(k=0;k<9;k++){
		int cnt[10]={}; //统计每个数字出现次数
		//起始行为k/3*3 
		for(i=k/3*3;i<k/3*3+3;i++){
			//起始列为k%3*3 	
			for(j=k%3*3;j<k%3*3+3;j++){
				cnt[board[i][j]]++;
			}
		}
		for(j=1;j<=9;j++){
			if(cnt[j]>1){
				printf("False:Invalid initial Sudoku matrix!\n");
				printf("The number %d in the block %d has been used!\n",j,k+1);
				return;
			}
		}
	}
	printf("True:Valid initial Sudoku matrix!\n");
	return;
}

//定义check_plus函数，判断是否为数独矩阵 
int check_plus(int board[9][9]){
	int i,j,k;
	for(i=0;i<9;i++){
		int cnt[10]={};
		for(j=0;j<9;j++){
			cnt[board[i][j]]++;
		}
		for(j=1;j<=9;j++){
			if(cnt[j]>1){
				return 0;
			}
		}
	}
	for(i=0;i<9;i++){
		int cnt[10]={};
		for(j=0;j<9;j++){
			cnt[board[j][i]]++;
		}
		for(j=1;j<=9;j++){
			if(cnt[j]>1){
				return 0;
			}
		}
	}
	for(k=0;k<9;k++){
		int cnt[10]={};
		for(i=k/3*3;i<k/3*3+3;i++){	
			for(j=k%3*3;j<k%3*3+3;j++){
				cnt[board[i][j]]++;
			}
		}
		for(j=1;j<=9;j++){
			if(cnt[j]>1){
				return 0;
			}
		}
	}
	return 1;
}

int solve(int board[9][9]){
	int i,j;
    for(i=0;i<9;i++){
        for(j=0;j<9;j++){
            if(board[i][j]==0){ //找到待填的位置 
				int num; //遍历填写1~9
				for(num=1;num<=9;num++){
					board[i][j]=num;
					//若可以填，则继续递归求解新数独 
					if(check_plus(board)){
                        if(solve(board)){
                            return 1; //成功填写，找到一组解 
                        }
                    }
                    board[i][j]=0; //无解，继续尝试下一个数
                }
                return 0; //若不管填几都无法满足，说明无解 
            }
        }
    }
}

void final_step(int board[9][9]){
	check(board);
    if(solve(board)){
        printf("The solution of Sudoku matrix:\n");
        print(board);
    }
	else printf("No solution！\n");
}

int main(){
	int board0[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}};
	int board1[9][9] = {{8, 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}};
	int board2[9][9] = {{5, 2, 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}};

    final_step(board0);
    final_step(board1);
    final_step(board2);

    return 0;
}