题目

编写一个程序，通过填充空格来解决数独问题。

数独的解法需 遵循如下规则：

1. 数字 1-9 在每一行只能出现一次。
2. 数字 1-9 在每一列只能出现一次。
3. 数字 1-9 在每一个以粗实线分隔的 3x3 宫内只能出现一次。（请参考示例图）

数独部分空格内已填入了数字，空白格用 '.' 表示。

示例 1：

输入：board = [["5","3",".",".","7",".",".",".","."],["6",".",".","1","9","5",".",".","."],[".","9","8",".",".",".",".","6","."],["8",".",".",".","6",".",".",".","3"],["4",".",".","8",".","3",".",".","1"],["7",".",".",".","2",".",".",".","6"],[".","6",".",".",".",".","2","8","."],[".",".",".","4","1","9",".",".","5"],[".",".",".",".","8",".",".","7","9"]]
输出：[["5","3","4","6","7","8","9","1","2"],["6","7","2","1","9","5","3","4","8"],["1","9","8","3","4","2","5","6","7"],["8","5","9","7","6","1","4","2","3"],["4","2","6","8","5","3","7","9","1"],["7","1","3","9","2","4","8","5","6"],["9","6","1","5","3","7","2","8","4"],["2","8","7","4","1","9","6","3","5"],["3","4","5","2","8","6","1","7","9"]]
解释：输入的数独如上图所示，唯一有效的解决方案如下所示：

提示：

• board.length == 9
• board[i].length == 9
• board[i][j] 是一位数字或者 '.'
• 题目数据 保证 输入数独仅有一个解

代码

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

void solveSudoku(char **board, int boardSize, int *boardColSize);
bool isValidSudoku(char **board, int boardSize, int *boardColSize);

int main()
{
    // char b[9][10] = 
    //     {"53..7....",
    //      "6..195...",
    //      ".98....6.",
    //      "8...6...3",
    //      "4..8.3..1",
    //      "7...2...6",
    //      ".6....28.",
    //      "...419..5",
    //      "....8..79"};
    char b[9][10]=
        {"..9748...",
        "7........",
        ".2.1.9...",
        "..7...24.",
        ".64.1.59.",
        ".98...3..",
        "...8.3.2.",
        "........6",
        "...2759.."};
    int t, *te;
    char **board = (char **)malloc(sizeof(char *) * 9);
    for (int i = 0; i < 9; i++)
    {
        board[i] = b[i];
        printf("%s ", b[i]);
    }
    printf("\n");
    solveSudoku(board, t, te);
    for (int i = 0; i < 9; i++)
    {
        printf("%s ", board[i]);
    }
    return 0;
}

void solveSudoku(char **board, int boardSize, int *boardColSize)
{
    int r, c;
    for (int p = 0; p < 9; p++)
    {
        for (int q = 0; q < 9; q++)
        {
            if (board[p][q] == '.')
            {
                r = p;
                c = q;
                continue;
            }
        }
    }
    static int sign = 0;
    for (int i = 0; i < 9; i++)
    {
        for (int j = 0; j < 9; j++)
        {
            if (board[i][j] == '.')
            {
                int p;
                for (p = 1; p <= 9 && sign == 0; p++)
                {
                    board[i][j] = p + '0';
                    if (isValidSudoku(board, boardSize, boardColSize) == 1)
                    {
                        if (i == r && j == c)
                        {
                            sign = 1;
                        }
                        solveSudoku(board, boardSize, boardColSize);
                        if (sign == 1)
                        {
                            return;
                        }
                    }
                    else
                    {
                        sign = 0;
                        continue;
                    }
                }
                if (p == 10)
                {
                    board[i][j] = '.';
                }
                return;
            }
        }
    }
    for (int i = 0; i < 9; i++)
    {
        printf("%s ", board[i]);
    }
    printf("\n");
}

bool isValidSudoku(char **board, int boardSize, int *boardColSize)
{
    int rownums[10], colnums[10];
    memset(rownums, 0, sizeof(rownums));
    memset(colnums, 0, sizeof(colnums));
    for (int i = 0; i < 9; i++)
    {
        for (int j = 0; j < 9; j++)
        {
            if (board[i][j] != '.')
            {
                int number = board[i][j] - '0';
                if (rownums[number] == 0)
                {
                    rownums[number] = 1;
                }
                else
                    return false;
            }
            if (board[j][i] != '.')
            {
                int number = board[j][i] - '0';
                if (colnums[number] == 0)
                {
                    colnums[number] = 1;
                }
                else
                    return false;
            }
        }
        memset(rownums, 0, sizeof(rownums));
        memset(colnums, 0, sizeof(colnums));
    }
    int i = 0, j = 0;
    for (int p = 3; p <= 9; p = p + 3)
    {
        for (int q = 3; q <= 9; q = q + 3)
        {
            i = p - 3;
            for (; i < p; i++)
            {
                j = q - 3;
                for (; j < q; j++)
                {
                    if (board[i][j] != '.')
                    {
                        int number = board[i][j] - '0';
                        if (rownums[number] == 0)
                        {
                            rownums[number] = 1;
                        }
                        else
                            return false;
                    }
                }
            }
            memset(rownums, 0, sizeof(rownums));
        }
    }
    return true;
}