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：
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：
class Solution { public: void solveSudoku(vector<vector<char>>& board) { solve(board); } private : bool solve1(vector<vector<char>>&board, int m,int n,char k)//判断加入的数字是否合法 { for(int i=0;i<9;i++) { if(board[m][i]==k) //列判断 return false; if(board[i][n]==k) //行判断 return false; //九宫格判断 if(board[i/3+m/3*3][i%3+n/3*3]==k) return false; } return true; } private: //遍历图表 用1到9的数字分别填入观察哪个合适 bool solve(vector<vector <char >> &board) { for(int i=0;i<9;i++) { for(int j=0;j<9;j++) { if(board[i][j]=='.') { //当board[i][j]=='.'时 进行判断 for(char k='1';k<='9';k++) //用char类型是因为有数字，'.'判断 { if(solve1(board,i,j,k)) //如果当前数字符合条件 { board[i][j]=k; //进行赋值 if(solve(board)) //循环里面有回溯 { return true; } board[i][j]='.'; //如果上未找出正确答案 在这个点初始化为'.' } } return false; //循环结束未找到返回false } } } return true; } };
