Sudoku Solver

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本文介绍了一个使用递归回溯算法解决数独问题的C++程序。通过预先填充已知数字，并利用位运算来标记每个单元格可能的数值，该算法能够有效地找到唯一解。

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Write a program to solve a Sudoku puzzle by filling the empty cells.

Empty cells are indicated by the character '.'.

You may assume that there will be only one unique solution.

A sudoku puzzle...

...and its solution numbers marked in red.

class Solution {
public:

	bool process(vector<vector<char> > &board, vector<vector<int> > &flag)
	{
		for (int i = 0; i < 9; ++i)
			for (int j = 0; j < 9; ++j)
			  {
				 if ('.' == board[i][j])
				 {
					for (int k = 0; k < 9; ++k)
					{
						int val = 1 << k;
						if (flag[0][i] & val || flag[1][j] & val || flag[2][(i/3)*3 + j/3] & val)
							continue;
						board[i][j] = k + '1';
						flag[0][i] |= val;
						flag[1][j] |= val;
						flag[2][(i/3)*3 + j/3] |= val;
						if (process(board, flag))
							return true;
						else
						{
							board[i][j] = '.';
							flag[0][i] ^= val;
							flag[1][j] ^= val;
							flag[2][(i/3)*3 + j/3] ^= val;
						}
					}
					return false;
				 }
			   }

		return true;
	}
    void solveSudoku(vector<vector<char> > &board) 
	{
	   vector< vector<int> > flag(3, vector<int>(9, 0));

		for (int i = 0; i < 9; i++)
			for(int j = 0; j < 9; j++)
			{
				if ('.' == board[i][j])
					continue;
				int val = 1 << (board[i][j] - '1');
				flag[0][i] |= val;
				flag[1][j] |= val;
				flag[2][(i/3)*3 + j/3] |= val;
			}
		process(board, flag);
    }
};