#include <stdio.h>
#include <stdbool.h>

// 打印数独函数
void x1(int m[9][9])
{
  int i,j;
  for(i=0;i<9;i++)
  {
    if(i%3==0)printf("-------------\n");
    for(j=0;j<9;j++)
    {
      if(j%3==0)printf("|");
      printf("%d",m[i][j]);
    }
    printf("|\n");
  }
  printf("-------------\n");
}

// 检查行是否有效
bool hang(int m[9][9], int i, int num) {
    for (int j = 0; j < 9; j++) {
        if (m[j][i] == num) {
            return false;
        }
    }
    return true;
}

// 检查列是否有效
bool lie(int m[9][9], int j, int num) {
    for (int i = 0; i < 9; i++) {
        if (m[i][j] == num) {
            return false;
        }
    }
    return true;
}

// 检查3x3子矩阵是否有效
bool o3(int board[9][9], int starti, int startj, int num) {
    for (int i = 0; i < 3; i++) {
        for (int j = 0; j < 3; j++) {
            if (board[starti + i][startj + j] == num) {
                return false;
            }
        }
    }
    return true;
}

// 检查某个位置是否可以放置某个数字
bool check(int m[9][9], int i, int j, int num) {
    return hang(m, i, j) &&
           lie(m, i, j) &&
           o3(m, i - i % 3, j - j % 3, num);
}

// 解数独
bool solve(int m[9][9]) {
    for (int i = 0; i < 9; i++) {
        for (int j = 0; j < 9; j++) {
            if (m[i][j] == 0) {
                for (int num = 1; num <= 9; num++) {
                    if (check(m, i, j, num)) {
                        m[i][j] = num;
                        if (solve(m)) {
                            return true;
                        }
                        m[i][j] = 0; // 回溯
                    }
                }
                return false; // 无法填充，回溯
            }
        }
    }
    return true; // 数独已解
}

// 检查整个数独矩阵是否有效
bool judge(int m[9][9]) {
    for (int i = 0; i < 9; i++) {
        for (int j = 0; j < 9; j++) {
            if (m[i][j] != 0) {
                int num = m[i][j];
                m[i][j] = 0;
                if (!check(m, i, j, num)) {
                    printf("The number %d in the row %d has been used!\n", num, i + 1);
                    m[i][j] = num;
                    return false;
                }
                m[i][j] = num;
            }
        }
    }
    return true;
}

int main() {
    int m[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}};

    printf("The original Sudoku matrix:\n");
    x1(m);

    if (judge(m)) {
        printf("True: Valid initial Sudoku matrix!\n");
        if (solve(m)) {
            printf("The solution of Sudoku matrix:\n");
            x1(m);
        } else {
            printf("No solution!\n");
        }
    } else {
        printf("False: Invalid initial Sudoku matrix!\n");
        printf("No solution!\n");
    }

    return 0;
}