题目：

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.

思路：

利用NP的思想完成，为了加快运算速度，我利用了三个数组来保存横列、纵列、方形中的数字重复。

代码：

class Solution {
public:
    bool num[3][9][9];
    void solveSudoku(vector<vector<char> > &board) {
        for(int i=0;i<3;i++)
        {
            for(int j=0;j<9;j++)
            {
                for(int k=0;k<9;k++)
                {
                    num[i][j][k]=true;
                }
            }
        }
        for(int i=0;i<9;i++)
        {
            for(int j=0;j<9;j++)
            {
                if(isInteger(board[i][j]))
                {
                    num[0][i][board[i][j]-'1'] = false;
                    num[1][j][board[i][j]-'1'] = false;
                    num[2][i/3*3+j/3][board[i][j]-'1'] = false;
                }
            }
        }
        fillValidSudoku(0,0,board);
    }
    
    bool fillValidSudoku(int i,int j,vector<vector<char> > &board)
    {
        if(j==9)
        {
            i++;
            j=0;
        }
        if(i==9&&j==0)
        {
            return true;
        }
        else if(isInteger(board[i][j]))
        {
            return fillValidSudoku(i,j+1,board);
        }
        else
        {
            for(int k=1;k<=9;k++)
            {
                if(num[0][i][k-1]&&num[1][j][k-1]&&num[2][i/3*3+j/3][k-1])
                {
                    board[i][j]='0'+k;
                    num[0][i][k-1] = false;
                    num[1][j][k-1] = false;
                    num[2][i/3*3+j/3][k-1] = false;
                    if(fillValidSudoku(i,j+1,board))
                    {
                        return true;
                    }
                    else
                    {
                        num[0][i][k-1] = true;
                        num[1][j][k-1] = true;
                        num[2][i/3*3+j/3][k-1] = true;
                        board[i][j]='.';
                    }
                }
            }
            return false;
        }
        
    }

    bool isInteger(char c)
    {
        if(c-'0'>=1&&c-'0'<=9)
        {
            return true;
        }
        return false;
    }
};