37. Sudoku Solver (Array;Back-Track)

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:
    void solveSudoku(vector<vector<char>> &board) {
        int line=0,column=-1;
        findNextEmpty(board,line,column);
        backtracking(board,line,column);
    }
    
    bool backtracking(vector<vector<char>> &board,int line, int column)
    {
        int i=line, j = column;
        for(int k = 1; k<=9; k++)
        {
            if(!isValid(board,line,column,k+'0')) continue;
            board[line][column] = k+'0';
            
            if(!findNextEmpty(board,line,column)) return true; //if no empty cell is found
            if(backtracking(board,line,column)) return true;
            
            //backTracking
            line = i;
            column = j;
        }
        
        //backTracking
        board[line][column] = '.';
        return false; //if no valid number 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;
        }
        
        //check行
        for(int i = 0; i<9; i++)
        {
            if(board[i][column] == value) return false;
        }
        return true;
    }
    
    bool findNextEmpty(vector<vector<char>> &board, int &line, int &column){
        int i,j;
        for(j = column+1; j < 9; j++){
            if(board[line][j]!='.') continue;
            
            column=j;
            return true;
        }
        
        for(i = line+1; i < 9; i++){
            for(j = 0; j < 9; j++){
                if(board[i][j]!='.') continue;
            
                line = i;
                column=j;
                return true;
            }
        }
        
        return false;
    }

};