37. 解数独

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

  1. 数字 1-9 在每一行只能出现一次。
  2. 数字 1-9 在每一列只能出现一次。
  3. 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:

复制代码
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
cpp 复制代码
class Solution {
public:
    bool isvaild(int row,int col,char val,vector<vector<char>>& board){
        //row
        for(int i = 0;i < 9;i++){
            if(board[row][i] == val) return false;
        }
        //col
        for(int j = 0;j < 9;j++){
            if(board[j][col] == val) return false;
        }
        //九宫格
        int startx = (row/3)*3; // 假如在第一个九宫格,row/3=0,再*3=0;
        int starty = (col/3)*3; //假如在第二个九宫格,row/3=1,再*3=3; 我直呼nb
        for(int i = startx;i < startx+3;i++){
            for(int j = starty;j < starty+3;j++){
                if(board[i][j] == val) return false;
            }
        }
        return true;
    }
    bool backtracking(vector<vector<char>>& board){
        for(int i = 0;i < board.size();i++){
            for(int j = 0;j < board[0].size();j++){
                //遇到空格
                if(board[i][j] == '.'){
                    for(char a = '1';a <= '9';a++){
                        //判断这里应该填入啥数字合法
                        if(isvaild(i,j,a,board)){
                            board[i][j] = a;
                            //得将这个状态一直返回
                            if(backtracking(board) == true) return true;
                            board[i][j] = '.'; // 回溯
                        }
                    }
                    return false; //填入0-9都不对,都不合法,填错了。
                }
            }
        }
        return true; //填完且填正确了。
    }
    void solveSudoku(vector<vector<char>>& board) {
        backtracking(board);
    }
};
相关推荐
刚入门的大一新生几秒前
归并排序延伸-非递归版本
算法·排序算法
独好紫罗兰5 分钟前
洛谷题单3-P1980 [NOIP 2013 普及组] 计数问题-python-流程图重构
开发语言·python·算法
独好紫罗兰10 分钟前
洛谷题单3-P1009 [NOIP 1998 普及组] 阶乘之和-python-流程图重构
开发语言·python·算法
曦月逸霜21 分钟前
蓝桥杯高频考点——高精度(含C++源码)
c++·算法·蓝桥杯
ゞ 正在缓冲99%…31 分钟前
leetcode152.乘积最大子数组
数据结构·算法·leetcode
敲上瘾38 分钟前
高并发内存池(二):Central Cache的实现
linux·服务器·c++·缓存·哈希算法
闯闯爱编程1 小时前
数组与特殊压缩矩阵
数据结构·算法·矩阵
秋风战士1 小时前
通信算法之255:无人机频谱探测设备技术详解
算法·无人机
SNAKEpc121381 小时前
在MFC中使用Qt(五):MFC和Qt的共存和交互
c++·qt·mfc
我们的五年2 小时前
【Linux系统】进程间通信-System V消息队列
linux·运维·服务器·c++