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#include<stdio.h>
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void output(int a[9][9]);
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void complete(int a[9][9], int m, int n);
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int check(int a[9][9], int row, int col, int num);
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int judge(int a[9][9], int b);
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void W(int a[9][9]);
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//任务四：判断 数组是否满足定义 并给出完整矩阵
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int main()
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{
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int board0[9][9] = { {5, 3, 0, 0, 7, 0, 0, 0, 0},
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{6, 0, 0, 1, 9, 5, 0, 0, 0},
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{0, 9, 8, 0, 0, 0, 0, 6, 0},
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{8, 0, 0, 0, 6, 0, 0, 0, 3},
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{4, 0, 0, 8, 0, 3, 0, 0, 1},
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{7, 0, 0, 0, 2, 0, 0, 0, 6},
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{0, 6, 0, 0, 0, 0, 2, 8, 0},
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{0, 0, 0, 4, 1, 9, 0, 0, 5},
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{0, 0, 0, 0, 8, 0, 0, 7, 9} };
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int board1[9][9] = { {8, 3, 0, 0, 7, 0, 0, 0, 0},
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{6, 0, 0, 1, 9, 5, 0, 0, 0},
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{0, 9, 8, 0, 0, 0, 0, 6, 0},
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{8, 0, 0, 0, 6, 0, 0, 0, 3},
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{4, 0, 0, 8, 0, 3, 0, 0, 1},
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{7, 0, 0, 0, 2, 0, 0, 0, 6},
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{0, 6, 0, 0, 0, 0, 2, 8, 0},
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{0, 0, 0, 4, 1, 9, 0, 0, 5},
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{0, 0, 0, 0, 8, 0, 0, 7, 9} };
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int board2[9][9] = { {5, 2, 0, 0, 7, 0, 0, 0, 0},
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{6, 0, 0, 1, 9, 5, 0, 0, 0},
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{0, 9, 8, 0, 0, 0, 0, 6, 0},
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{8, 0, 0, 0, 6, 0, 0, 0, 3},
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{4, 0, 0, 8, 0, 3, 0, 0, 1},
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{7, 0, 0, 0, 2, 0, 0, 0, 6},
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{0, 6, 0, 0, 0, 0, 2, 8, 0},
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{0, 0, 0, 4, 1, 9, 0, 0, 5},
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{0, 0, 0, 0, 8, 0, 0, 7, 9} };
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W(board0);
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W(board1);
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W(board2);
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}
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void output(int a[9][9])//定义函数，按格式打印数组
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{
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for (int i = 0; i < 9; i++)
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{
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printf("|");//每一行的以|开始
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for (int j = 0; j < 9; j++)
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{
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printf("%d", a[i][j]);
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if ((j + 1) % 3 == 0)
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{
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printf("|");//区分3*3
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if (j == 8)
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{
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printf("\n");
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}
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}
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}
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if ((i + 1) % 3 == 0 && i != 8)
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{
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printf("|----分割---|\n");
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}//每三行就换一行
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}
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}
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int check(int a[9][9], int row, int col, int num)
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//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
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{
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// 对行
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for (int i = 0; i < 9; i++)
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{
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if (a[row][i] == num) return 0;
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}
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// 对列
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for (int i = 0; i < 9; i++)
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{
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if (a[i][col] == num) return 0;
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}
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// 对块
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int Row = row - row % 3;
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int Col = col - col % 3;
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for (int i = 0; i < 3; i++)
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{
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for (int j = 0; j < 3; j++)
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{
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if (a[i + Row][j + Col] == num) return 0;
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}
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}
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return 1;
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}
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void complete(int a[9][9], int m, int n)
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{
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// 如果到达最后一行最后一列，返回成功
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if (m == 9&&n==9)
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{
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printf("The solution of Sudoku matrix:\n");
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output(a);
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return;
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}
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// 移动到下一个位置
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if (n == 9)
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{
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m++;
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n = 0;
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}
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// 如果当前位置已经有数字，移动到下一个位置
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if (a[m][n] != 0)
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{
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complete(a, m, n + 1);
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return;
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}
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// 填数
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for (int i = 1; i <= 9; i++)
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{
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if (check(a, m, n, i))
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{
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a[m][n] = i;
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complete(a, m, n + 1);
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if (m == 9) return;
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a[m][n] = 0;
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}
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}
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}
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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
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{
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int c = 0;//c=0意味数独满足定义
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//b=0说明不打印，只判断；b=1，则该函数会打印语句
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//判断是否每一行不出现多次
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for (int i = 0; i < 9; i++)
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{
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int times[9] = { 0 };
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for (int j = 0; j < 9; j++)//统计第i行每个数字的出现次数
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{
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if(a[i][j]>=1)times[a[i][j] - 1]++;
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}
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for (int j = 0; j < 9; j++)
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{
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if (times[j] > 1)
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{
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c = 1;
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if (b == 1)
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{ printf("False:Invalid initial Sudoku matrix!\nThe number %d in the row %d has been used!\n", j + 1, i + 1); }
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break;
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}
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}
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if (c) { break; }
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}
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if (c == 0)
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{
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//判断是否每一列不出现多次
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for (int j = 0; j < 9; j++)
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{
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int times[9] = { 0 };
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for (int i = 0; i < 9; i++)//统计第j列每个数字的出现次数
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{
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if (a[i][j] >= 1)times[a[i][j] - 1]++;
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}
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for (int i = 0; i < 9; i++)
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{
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if (times[i] > 1)
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{
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c = 1;
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if (b == 1)
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{ printf("False:Invalid initial Sudoku matrix!\nThe number %d in the col %d has been used!\n", i + 1, j + 1); }
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break;
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}
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}
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if (c) { break; }
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}
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}
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if (c == 0)
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{
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//判断每一块是否不出现多次
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for (int i = 0; i < 3; i++)
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{
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for (int j = 0; j < 3; j++)
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{
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int times[9] = { 0 };
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for (int m = 3 * i; m <= 3 * i + 2; m++)
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{
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for (int n = 3 * j; n <= 3 * j + 2; n++)
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{
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if (a[m][n] >= 1)times[a[m][n] - 1]++;
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}
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}
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for (int i = 0; i < 9; i++)
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{
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if (times[i] > 1)
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{
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c = 1;
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if (b == 1)
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{ printf("False:Invalid initial Sudoku matrix!\nThe number %d in the block %d has been used!\n", i + 1, i + j + 1); }
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break;
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}
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}
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if (c) { break; }
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}
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if (c) { break; }
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}
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}
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return c;
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}
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void W(int a[9][9])//本代码文件最重要的函数
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{
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printf("The original Sudoku matrix:\n");
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output(a);
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if (judge(a, 0) == 1)
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{
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judge(a, 1);
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printf("No solution！\n");
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}
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else
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{
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printf("True:Valid initial Sudoku matrix!\n");
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complete(a, 0, 0);//进行填充数独的操作
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int judgee = 1;
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for (int i = 0; i < 9; i++)
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{
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for (int j = 0; j < 9; j++)
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{
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if (a[i][j] == 0)
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{
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printf("No solution！\n");
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judgee = 0;
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break;
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}
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}
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if (judgee == 0){break;}
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}
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}
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return;
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}
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