#include <stdio.h>
#include <stdbool.h>
#include <stdlib.h>
#include <time.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");
    }
}


bool usedInRow(int matrix[9][9], int row, int num) {
    for (int col = 0; col < 9; col++) {
        if (matrix[row][col] == num) {
            return true;
        }
    }
    return false;
}
bool usedInCol(int matrix[9][9], int col, int num) {
    for (int row = 0; row < 9; row++) {
        if (matrix[row][col] == num) {
            return true;
        }
    }
    return false;
}

bool usedInBox(int matrix[9][9], int boxStartRow, int boxStartCol, int num) {
    for (int row = 0; row < 3; row++) {
        for (int col = 0; col < 3; col++) {
            if (matrix[row + boxStartRow][col + boxStartCol] == num) {
                return true;
            }
        }
    }
    return false;
}bool isSafe(int matrix[9][9], int row, int col, int num) {
    return!usedInRow(matrix, row, num) &&!usedInCol(matrix, col, num) &&!usedInBox(matrix, row - row % 3, col - col % 3, num);
}
bool findEmptyLocation(int matrix[9][9], int *row, int *col) {
    for (*row = 0; *row < 9; (*row)++) {
        for (*col = 0; *col < 9; (*col)++) {
            if (matrix[*row][*col] == 0) {
                return true;
            }
        }
    }
    return false;
}

bool solveSudoku(int matrix[9][9]) {
    int row, col;
    if (!findEmptyLocation(matrix, &row, &col)) {
        return true; // 数独已解决
    }
    for (int num = 1; num <= 9; num++) {
        if (isSafe(matrix, row, col, num)) {
            matrix[row][col] = num;
            if (solveSudoku(matrix)) {
                return true;
            }
            matrix[row][col] = 0; // 回溯
        }
    }
    return false;
}

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;
}

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) {
                    return false;
                }
                count[num]++;
            }
        }
    }
    return true;
}

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) {
                            return false;
                        }
                        count[num]++;
                    }
                }
            }
        }
    }
    return true;
}

bool isSudokuMatrix(int matrix[9][9]) {
    return checkRows(matrix) && checkColumns(matrix) && 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 valid = isSudokuMatrix(matrix);
    if (valid) {
        printf("True:Valid initial Sudoku matrix!\n");
        if (solveSudoku(matrix)) {
            printf("The solution of Sudoku matrix:\n");
            printMatrix(matrix);
        } else {
            printf("No solution!\n");
        }
    } else {
        printf("False:Invalid initial Sudoku matrix!\n");
        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);
                        break;
                    }
                    count[num]++;
                }
            }
        }
        printf("No solution!\n");
    }
    return 0;
}