题目描述

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：

    数字 1-9 在每一行只能出现一次。
    数字 1-9 在每一列只能出现一次。
    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：

提示：

    board.length == 9
    board[i].length == 9
    board[i][j] 是一位数字或者 '.'
    题目数据 保证 输入数独仅有一个解

来源：力扣（LeetCode）
链接：https://leetcode.cn/problems/sudoku-solver
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讲解视频：

让电脑帮我解数独，实现曾经的幻想【Leetcode37.解数独】_哔哩哔哩_bilibili

c++代码

class Solution {
private:
    bool finish;
    bool rowArr[9][10],colArr[9][10],areaArr[9][10];
public:
    void init(vector<vector<char>>& board){//用于初始化三个arr数组
        memset(rowArr,false,sizeof(rowArr));
        memset(colArr,false,sizeof(colArr));
        memset(areaArr,false,sizeof(areaArr));
        for(int i=0;i<9;i++){
            for(int j=0;j<9;j++){
                if(board[i][j]!='.'){
                    rowArr[i][board[i][j]-48]=true;
                    colArr[j][board[i][j]-48]=true;
                    areaArr[getAreaIndex(i,j)][board[i][j]-48]=true;
                }
            }
        }
    }
    int getAreaIndex(int row,int col){
        return 3*(row/3)+col/3;
    }
    void dfs(vector<vector<char>>& board,int index){
        if(index==81){
            finish=true;
            return;
        }
        int row=index/9;
        int col=index%9;
        char val=board[row][col];
        if(val!='.'){
            dfs(board,index+1);
        }else{
            for(int num=1;num<10;++num){
                bool rowTemp=rowArr[row][num];
                bool colTemp=colArr[col][num];
                bool areaTemp=areaArr[getAreaIndex(row,col)][num];
                if(!rowTemp&&!colTemp&&!areaTemp){
                    rowArr[row][num]=true;
                    colArr[col][num]=true;
                    areaArr[getAreaIndex(row,col)][num]=true;
                    board[row][col]=(char)(num+48);
                    dfs(board,index+1);
                    if(finish){
                       return; 
                    }
                    rowArr[row][num]=rowTemp;
                        colArr[col][num]=colTemp;
                        areaArr[getAreaIndex(row,col)][num]=areaTemp;
                        board[row][col]='.';
                }
            }
            
        }
    }
    void solveSudoku(vector<vector<char>>& board) {
        init(board);
        finish=false;
        dfs(board,0);
    }
};