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

// 打印数独矩阵
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]);
            }
            if (j == 8) {
                printf("|\n");
            }
        }
        if (i == 8) {
            printf("|-----------------------|\n");
        }
    }
}

// 判断数字是否在某行中出现
int isInRow(int matrix[9][9], int row, int num) {
    for (int i = 0; i < 9; i++) {
        if (matrix[row][i] == num) {
            return 1;
        }
    }
    return 0;
}

// 判断数字是否在某 3x3 子矩阵中出现
int isInGroup(int matrix[9][9], int startRow, int startCol, int num) {
    for (int i = 0; i < 3; i++) {
        for (int j = 0; j < 3; j++) {
            if (matrix[startRow + i][startCol + j] == num) {
                return 1;
            }
        }
    }
    return 0;
}

// 判断数字是否在某行中已被使用
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;
}

// 判断数字是否在某列中已被使用
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;
}

// 判断数字是否在某 3x3 子矩阵中已被使用
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;
}

// 判断在特定位置放置特定数字是否安全
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);
}

// 查找空位置
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;
}

// 解决数独问题
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;
}

// 检查行是否符合数独规则
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;
}

// 检查列是否符合数独规则
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;
}

// 检查 3x3 子矩阵是否符合数独规则
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;
}

// 判断整个矩阵是否是有效的数独矩阵
bool isSudokuMatrix(int matrix[9][9]) {
    return checkRows(matrix) && checkColumns(matrix) && checkSubMatrices(matrix);
}

int main() {
    printf("The original Sudoku matrix: \n");
    srand(time(NULL));
    int matrix[9][9] = { 0 };
    int numbers[9] = { 1, 2, 3, 4, 5, 6, 7, 8, 9 };

    for (int group = 0; group < 3; group++) {
        int usedNumbers[9] = { 0 };
        for (int i = 0; i < 9; i++) {
            usedNumbers[i] = numbers[i];
        }

        for (int i = 0; i < 9; i++) {
            int idx = rand() % (9 - i);
            int temp = usedNumbers[idx];
            usedNumbers[idx] = usedNumbers[8 - i];
            usedNumbers[8 - i] = temp;
        }

        for (int row = 0; row < 3; row++) {
            int count = 0;
            while (count < 3) {
                int num;
                do {
                    int idx = rand() % 9;
                    num = usedNumbers[idx];
                } while (num == 0 || isInRow(matrix, group * 3 + row, num) || isInGroup(matrix, group * 3, 0, num));

                int pos;
                do {
                    pos = rand() % 9;
                } while (matrix[group * 3 + row][pos] != 0);

                matrix[group * 3 + row][pos] = num;
                count++;
            }
        }
    }

    for (int row = 0; row < 9; row++) {
        int uniqueNumbers[9] = { 0 };
        int uniqueCount = 0;
        for (int i = 0; i < 9; i++) {
            if (matrix[row][i] != 0 && !uniqueNumbers[matrix[row][i] - 1]) {
                uniqueNumbers[matrix[row][i] - 1] = 1;
                uniqueCount++;
            }
        }
        if (uniqueCount > 3) {
            while (uniqueCount > 3) {
                int idx = rand() % 9;
                if (matrix[row][idx] != 0 && uniqueNumbers[matrix[row][idx] - 1]) {
                    matrix[row][idx] = 0;
                    uniqueCount--;
                }
            }
        }
        else if (uniqueCount < 3) {
            while (uniqueCount < 3) {
                int num;
                do {
                    num = rand() % 9 + 1;
                } while (uniqueNumbers[num - 1]);
                int idx;
                do {
                    idx = rand() % 9;
                } while (matrix[row][idx] != 0);
                matrix[row][idx] = num;
                uniqueNumbers[num - 1] = 1;
                uniqueCount++;
            }
        }
    }

    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;
}