37. Sudoku Solver

problem：

该问题是数独求解问题，采用方法是深度搜索优先算法。

class Solution {private:      bool isOver;  //是否已经找到一个正确解。    public:    void dfs(vector<vector<char>>& board, int i, int j, int n)    {        if(j >= n)        {            dfs(board, i+1, 0, n);        }        else if(i == n)        {            this->isOver = true;             return;        }        else if(board[i][j] != '.')        {            dfs(board, i, j+1, n);        }        else        {            for (int k = 1; k <= n; ++k)            {                board[i][j] = (char)('0' + k);                if (isValid(board, i, j, n)){                      dfs(board, i, j+1 , n);                  }                if(this->isOver)                     return;  //找到一个解救跳出，防止遍历整个search tree                  board[i][j] = '.';                }        }    }    bool isValid(vector<vector<char>> &board, int i , int j, int n)     {          for (int index = 0; index < n; ++index)        {              if (index != j && board[i][index] == board[i][j])             {                  return false;              }          }            for (int index = 0; index < n; ++index)        {              if (index != i && board[index][j] == board[i][j])             {                  return false;              }          }            int index_i = i / 3;          int index_j = j / 3;                    for (int x = index_i * 3; x < index_i * 3 + 3; ++x)         {              for (int y = index_j * 3; y < index_j * 3 + 3; ++y)             {                  if ((x!=i || y != j) && board[x][y] == board[i][j])                 { //注意这里逻辑是"或"||，不是"与"                      return false;                  }              }          }          return true;      }      void solveSudoku(vector<vector<char>>& board)     {        if (board.size() == 0 || board[0].size() == 0) return; //简洁的方式去验证输入合法性          this->isOver = false;          dfs(board, 0, 0, 9);      }};