matrix/task 4.c

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

#define SIZE 9

// 打印数独矩阵
void printSudoku(int board[SIZE][SIZE]) {
	int row,col; 
    for (row = 0; row < SIZE; row++) {
        for (col = 0; col < SIZE; col++) {
            printf("%d ", board[row][col]);
        }
        printf("\n");
    }
}

// 检查当前位置是否安全
bool isSafe(int board[SIZE][SIZE], int row, int col, int num) {
    // 检查行
    int x;
    for (x = 0; x < SIZE; x++) {
        if (board[row][x] == num) {
            return false;
        }
    }

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

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

    return true;
}

// 解决数独的回溯算法
bool solveSudoku(int board[SIZE][SIZE]) {
    // 遍历整个数独矩阵
    int row,col;
    for (row = 0; row < SIZE; row++) {
        for (col = 0; col < SIZE; col++) {
            // 如果当前位置是空的
            if (board[row][col] == 0) {
                // 尝试填充 1 到 9
                int num;
                for (num = 1; num <= 9; num++) {
                    if (isSafe(board, row, col, num)) {
                        // 放置数字
                        board[row][col] = num;

                        // 递归调用解决数独
                        if (solveSudoku(board)) {
                            return true;
                        }

                        // 如果失败，回溯
                        board[row][col] = 0;
                    }
                }

                // 如果 1 到 9 都不能放置，返回 false
                return false;
            }
        }
    }

    // 如果所有位置都填充完毕，返回 true
    return true;
}

// 检查数独矩阵的有效性
bool isValidSudoku(int board[SIZE][SIZE]) {
    // 检查行和列是否有重复的数字
    int row,col;
    for (row = 0; row < SIZE; row++) {
        int rowSet[10] = {0};
        int colSet[10] = {0};
        for (col = 0; col < SIZE; col++) {
            int num = board[row][col];
            if (num != 0) {
                if (rowSet[num]) {
                    printf("Row %d has duplicate number %d\n", row, num);
                    return false;
                }
                rowSet[num] = 1;

                if (colSet[num]) {
                    printf("Column %d has duplicate number %d\n", col, num);
                    return false;
                }
                colSet[num] = 1;
            }
        }
    }

    // 检查 3x3 子网格是否有重复的数字
    int block;
    for (block = 0; block < 9; block++) {
        int blockSet[10] = {0};
        int startRow = block / 3 * 3;
        int startCol = block % 3 * 3;
        int i,j;
        for (i = 0; i < 3; i++) {
            for (j = 0; j < 3; j++) {
                int num = board[startRow + i][startCol + j];
                if (num != 0) {
                    if (blockSet[num]) {
                        printf("3x3 block starting at (%d, %d) has duplicate number %d\n", startRow, startCol, num);
                        return false;
                    }
                    blockSet[num] = 1;
                }
            }
        }
    }

    return true;
}

int main() {
    int board[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");
    printSudoku(board);

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

    return 0;
}