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

#define SIZE 9

// 函数声明
bool isSafe(int grid[SIZE][SIZE], int row, int col, int num);
bool solveSudoku(int grid[SIZE][SIZE]);
void findInvalidReason(int grid[SIZE][SIZE]);
void print(int matrix[SIZE][SIZE]);

// 主函数
int main() {
    int sudoku[SIZE][SIZE] = {  {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}};

    printf("The original Sudoku matrix: \n");
    print(sudoku);

    if (solveSudoku(sudoku)) {
        printf("True:Valid initial Sudoku matrix!\n");
        printf("The solution of Sudoku matrix:\n");
        print(sudoku);
    } else {
        printf("False:Invalid initial Sudoku matrix!\n");
        findInvalidReason(sudoku);
        printf("No solution!\n");
    }

    return 0;
}



// 检查在给定的数独矩阵中，数字 num 能否放在位置 (row, col)
bool isSafe(int grid[SIZE][SIZE], int row, int col, int num) {
    int x, i, j;
    // 检查行
    for (x = 0; x < SIZE; x++)
        if (grid[row][x] == num)
            return false;

    // 检查列
    for (x = 0; x < SIZE; x++)
        if (grid[x][col] == num)
            return false;

    // 检查 3x3 宫格
    int startRow = row - row % 3, startCol = col - col % 3;
    for (i = 0; i < 3; i++)
        for (j = 0; j < 3; j++)
            if (grid[i + startRow][j + startCol] == num)
                return false;

    return true;
}

// 解决数独问题的递归函数
bool solveSudoku(int grid[SIZE][SIZE]) {
    int row, col, num;
    // 查找空白格
    for (row = 0; row < SIZE; row++)
        for (col = 0; col < SIZE; col++)
            if (grid[row][col] == 0) {
                for (num = 1; num <= 9; num++) {
                    if (isSafe(grid, row, col, num)) {
                        grid[row][col] = num;
                        if (solveSudoku(grid))
                            return true;
                        grid[row][col] = 0; // 回溯
                    }
                }
                return false; // 触发回溯
            }
    return true; // 解决了数独
}

// 查找不满足数独定义的原因
void findInvalidReason(int grid[SIZE][SIZE]) {
    int row, col, num, blockRow, blockCol;
    for (row = 0; row < SIZE; row++) {
        for (col = 0; col < SIZE; col++) {
            if (grid[row][col] != 0) {
                for (num = 1; num <= 9; num++) {
                    if (grid[row][col] == num && !isSafe(grid, row, col, num)) {
                        blockRow = row - row % 3;
                        blockCol = col - col % 3;
                        printf("The number %d is duplicated in row %d, column %d, or block %d.\n", num, row + 1, col + 1, (blockRow / 3) * 3 + (blockCol / 3) + 1);
                        return;
                    }
                }
            }
        }
    }
}

// 格式化输出数独矩阵
void print(int matrix[SIZE][SIZE]) {
    int i, j;
    printf("|-----------------------------|\n");
    for (i = 0; i < SIZE; i++) {
        printf("|");
        for (j = 0; j < SIZE; j++) {
            printf("%2d ", matrix[i][j]);
            if ((j + 1) % 3 == 0 ) printf("|");
        }
        printf("\n");
        if ((i + 1) % 3 == 0 && i < SIZE-1) {
            printf("|-----------------------------|\n");
        }        
    }
    printf("|-----------------------------|\n");

}