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

void printMatrix(int matrix[9][9]) {
    for (int i = 0; i < 9; i++) {
        if (i == 0 || i == 3 || i == 6) {
            printf("|-----------------------|\n");
        }
        for (int j = 0; j < 9; j++) {
            if (j == 0 || j == 3 || j == 6) {
                printf("| ");
            }
            if (matrix[i][j] == 0) {
                printf(". ");
            }
            else {
                printf("%d ", matrix[i][j]);
            }
            printf("|\n");
        }
        printf("|-----------------------|\n");
    }
}

// 检查行中数字1 - 9是否最多出现一次
bool checkRows(int matrix[9][9]) {
    for (int i = 0; i < 9; i++) {
        int count[9] = {0};
        for (int j = 0; j < 9; j++) {
            if (matrix[i][j] > 0 && matrix[i][j] <= 9) {
                int num = matrix[i][j] - 1;
                if (count[num] > 0) {
                    return false;
                }
                count[num]++;
            }
        }
    }
    return true;
}

// 检查列中数字1 - 9是否最多出现一次
bool checkColumns(int matrix[9][9]) {
    for (int j = 0; j < 9; j++) {
        int count[9] = {0};
        for (int i = 0; i < 9; i++) {
            if (matrix[i][j] > 0 && matrix[i][j] <= 9) {
                int num = matrix[i][j] - 1;
                if (count[num] > 0) {
                    printf("The number %d in the col %d has been used!\n", matrix[i][j], j);
                    return false;
                }
                count[num]++;
            }
        }
    }
    return true;
}

// 检查3x3子矩阵中数字1 - 9是否最多出现一次
bool checkSubMatrices(int matrix[9][9]) {
    for (int row = 0; row < 9; row += 3) {
        for (int col = 0; col < 9; col += 3) {
            int count[9] = {0};
            for (int i = row; i < row + 3; i++) {
                for (int j = col; j < col + 3; j++) {
                    if (matrix[i][j] > 0 && matrix[i][j] <= 9) {
                        int num = matrix[i][j] - 1;
                        if (count[num] > 0) {
                            printf("The number %d in the block %d has been used!\n", matrix[i][j], (row / 3) * 3 + col / 3);
                            return false;
                        }
                        count[num]++;
                    }
                }
            }
        }
    }
    return true;
}

// 判断矩阵是否满足数独矩阵的定义
bool isSudokuMatrix(int matrix[9][9]) {
    if (!checkRows(matrix)) {
        return false;
    }
    if (!checkColumns(matrix)) {
        return false;
    }
    return checkSubMatrices(matrix);
}

int main() {
    printf("The original Sudoku matrix: \n");
    int matrix[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}
    };
    printMatrix(matrix);
    bool result = isSudokuMatrix(matrix);
    if (result) {
        printf("True:Valid initial Sudoku matrix!\n");
    } else {
        printf("False:Invalid initial Sudoku matrix!\n");
    }
    return 0;
}