37 Sudoku Solver

Write a program to solve a Sudoku puzzle by filling the empty cells.

A sudoku solution must satisfy all of the following rules:

1. Each of the digits 1-9 must occur exactly once in each row.
2. Each of the digits 1-9 must occur exactly once in each column.
3. Each of the digits 1-9 must occur exactly once in each of the 9 3x3 sub-boxes of the grid.

The '.' character indicates empty cells.

Example 1:

Input: 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"]]
Output: [["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"]]
Explanation: The input board is shown above and the only valid solution is shown below:

Constraints:

• board.length == 9
• board[i].length == 9
• board[i][j] is a digit or '.'.
• It is guaranteed that the input board has only one solution.

class Solution {
public:
    void solveSudoku(vector<vector<char>>& board) {
        help(board);
        return;
    }
    //回溯 
    bool help(vector<vector<char>>& board){
        for(int i=0;i<board.size();i++){
            for(int j=0;j<board[i].size();j++){
                //最后没有数字要填，退出递归
                if(board[i][j] == '.'){
                    for(char k='1';k<='9';k++){
                        //先判定有效再填入
                        if(isValid(board,i,j,k)){
                            board[i][j] = k;
                            if(help(board)) return true;
                            else board[i][j] = '.';
                        }
                    }
                    //所有数字都填了
                    return false;
                }
                //没有数字要填了，退出返回true
            }
        }
        return true;
    }
        
private:
    //填入的c(1-9)在该行、该列、以及该box中是否有效，有效才填入，无效换下一个数
    bool isValid(vector<vector<char>>& board,int row,int col,char c){
        for(int i=0;i<9;i++){
            if(c == board[row][i]) return false;
            if(c == board[i][col]) return false;
            int x = i/3+row/3*3;
　　　　　　　//不好想到
            int y = i%3+col/3*3;
            if(c == board[x][y]) return false;
        }
        return true;
    }
};