解数独

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：

思路

看了代码随想录

递归方式发生了很大改变，这个是最关键的

“`c++
class Solution {
public:
bool judge_elem_position(vector<vector<char>>& board, char elem, int row, int column)
{
//判断行
for(int j = 0; j < 9; ++j)
{
if(board[row][j] == elem) return false;
}
//判断列
for(int i = 0; i < 9; ++i)
{
if(board[i][column] == elem) return false;
}
//判断3*3宫内
int row_begin = (row / 3) * 3 ;
int column_begin = (column / 3) * 3;
for(int i = row_begin; i < row_begin + 3; ++i)
{
for(int j = column_begin; j < column_begin + 3; ++j)
{
if(board[i][j] == elem) return false;
}
}
return true;
}
bool solveSudokuAux(vector<vector<char>>& board, int row, int column)
{
for(int i = row; i < 9; ++i)
{
for(int j = column; j < 9; ++j)
{
if(board[i][j] != '.') continue;
for(char k = '1'; k <= '9'; ++k)
{
if(!judge_elem_position(board, k, i , j)) continue;
board[i][j] = k;
if(j + 1 == 9)
{
row++;
column = 0;
}
if(solveSudokuAux(board, row, column)) return true;
board[i][j] = '.';
}
return false;
}
}
return true;
}
void solveSudoku(vector<vector<char>>& board) {
solveSudokuAux(board, 0, 0);
}
};
“`