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4th.cpp

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+#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;
+}
+
+