37. Sudoku Solver (Graph; WFS)

class Solution {
public:
    void solveSudoku(vector<vector<char>> &board) {
        backtracking(board,0);
    }
    bool backtracking(vector<vector<char>> &board,int line)
    {
        //find first empty cell
        for(int i = line; i<9; i++)
        {
           for(int j = 0; j<9; j++)
            {
                if(board[i][j]!=‘.‘) continue;
               
                //first empty cell is found
                for(int k = 1; k<=9; k++) //回溯法求该空单元中应该填的数字
                {
                    if(!isValid(board,i,j,k+‘0‘)) continue;
                    board[i][j] = k+‘0‘;
                    if(backtracking(board,i)) return true;
                }
                board[i][j] = ‘.‘;
                return false; //if no valid value is found
            }
        }
        return true; //if no empty cell is found
    }

    //为回溯法写一个独立的check函数
    bool isValid(vector<vector<char>> &board, int line, int column, char value)
    {
        //check九宫格的一个格
        int upperBoard = line/3 * 3;
        int leftBoard = column/3 * 3;
        for(int i = 0; i<3; i++)
        {
            for(int j = 0; j<3; j++)
            {
                if(board[upperBoard+i][leftBoard+j] == value) return false;
            }
        }
     
        //check 列
        for(int i = 0; i<9; i++)
        {
            if(board[line][i] == value) return false;
        }
        for(int i = 0; i<9; i++)
        {
            if(board[i][column] == value) return false;
        }
        return true;
    }

};