#include<stdio.h>
void output(int a[9][9]);
void complete(int a[9][9], int m, int n);
int check(int a[9][9], int row, int col, int num);
int judge(int a[9][9], int b);
void W(int a[9][9]);

//任务四：判断 数组是否满足定义 并给出完整矩阵 
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} };

	W(board0);
	W(board1);
	W(board2);

}

void output(int a[9][9])//定义函数，按格式打印数组 
{
	for (int i = 0; i < 9; i++)
	{
		printf("|");//每一行的以|开始 
		for (int j = 0; j < 9; j++)
		{
			printf("%d", a[i][j]);
			if ((j + 1) % 3 == 0)
			{
				printf("|");//区分3*3 
				if (j == 8)
				{
					printf("\n");
				}
			}
		}
		if ((i + 1) % 3 == 0 && i != 8)
		{
			printf("|----分割---|\n");
		}//每三行就换一行

	}
}

int check(int a[9][9], int row, int col, int num) 
//检查某数能否放在某位置，在补全数组的函数complete中会被调用
{
	// 对行
	for (int i = 0; i < 9; i++) 
	{
		if (a[row][i] == num) return 0;
	}
	// 对列
	for (int i = 0; i < 9; i++) 
	{
		if (a[i][col] == num) return 0;
	}
	// 对块
	int Row = row - row % 3;
	int Col = col - col % 3;
	for (int i = 0; i < 3; i++) 
	{
		for (int j = 0; j < 3; j++) 
		{
			if (a[i + Row][j + Col] == num) return 0;
		}
	}
	return 1;
}
void complete(int a[9][9], int m, int n) 
{
	// 如果到达最后一行最后一列，返回成功
	if (m == 9&&n==9) 
	{
		printf("The solution of Sudoku matrix:\n");
		output(a);
		return;
	}

	// 移动到下一个位置
	if (n == 9) 
	{
		m++;
		n = 0;
	}
	// 如果当前位置已经有数字，移动到下一个位置
	if (a[m][n] != 0) 
	{
		complete(a, m, n + 1);
		return;
	}
	// 填数
	for (int i = 1; i <= 9; i++) 
	{
		if (check(a, m, n, i)) 
		{
			a[m][n] = i;
			complete(a, m, n + 1);
			
			if (m == 9) return;
			a[m][n] = 0; 
		}
	}
}

int judge(int a[9][9], int b)//判断数独是否满足定义，并返回判断值，返还值为0意味这数独满足定义 
{
	int c = 0;//c=0意味数独满足定义 
	//b=0说明不打印，只判断；b=1，则该函数会打印语句 

	//判断是否每一行不出现多次 
	for (int i = 0; i < 9; i++)
	{
		int times[9] = { 0 };
		for (int j = 0; j < 9; j++)//统计第i行每个数字的出现次数 
		{
			if(a[i][j]>=1)times[a[i][j] - 1]++;
		}

		for (int j = 0; j < 9; j++)
		{
			if (times[j] > 1)
			{
				c = 1;
				if (b == 1) 
				{ printf("False:Invalid initial Sudoku matrix!\nThe number %d in the row %d has been used!\n", j + 1, i + 1); }
				break;
			}
		}

		if (c) { break; }

	}

	if (c == 0)
	{
		//判断是否每一列不出现多次 
		for (int j = 0; j < 9; j++)
		{
			int times[9] = { 0 };
			for (int i = 0; i < 9; i++)//统计第j列每个数字的出现次数 
			{
				if (a[i][j] >= 1)times[a[i][j] - 1]++;
			}
			for (int i = 0; i < 9; i++)
			{
				if (times[i] > 1)
				{
					c = 1;
					if (b == 1) 
					{ printf("False:Invalid initial Sudoku matrix!\nThe number %d in the col %d has been used!\n", i + 1, j + 1); }
					break;
				}
			}
			if (c) { break; }
		}
	}
	if (c == 0)
	{

		//判断每一块是否不出现多次 
		for (int i = 0; i < 3; i++)
		{
			for (int j = 0; j < 3; j++)
			{
				int times[9] = { 0 };
				for (int m = 3 * i; m <= 3 * i + 2; m++)
				{
					for (int n = 3 * j; n <= 3 * j + 2; n++)
					{
						if (a[m][n] >= 1)times[a[m][n] - 1]++;
					}
				}
				for (int i = 0; i < 9; i++)
				{
					if (times[i] > 1)
					{
						c = 1;
						if (b == 1)
						 { printf("False:Invalid initial Sudoku matrix!\nThe number %d in the block %d has been used!\n", i + 1, i + j + 1); }
						break;
					}
				}
				if (c) { break; }
			}
			if (c) { break; }
		}
	}

	return c;
}
void W(int a[9][9])//本代码文件最重要的函数 
{
	printf("The original Sudoku matrix:\n");
	output(a);
	if (judge(a, 0) == 1)
	{
		judge(a, 1);
		printf("No solution！\n");
	}
	else
	{
		printf("True:Valid initial Sudoku matrix!\n");
		complete(a, 0, 0);//进行填充数独的操作 
		int judgee = 1;
		for (int i = 0; i < 9; i++)
		{
			for (int j = 0; j < 9; j++)
			{
				if (a[i][j] == 0)
				{
					printf("No solution！\n");
					judgee = 0;
					break;
				}
			}
			if (judgee == 0){break;}
		}
	}

	return;
}