37. Sudoku Solver

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

Empty cells are indicated by the character '.'.

You may assume that there will be only one unique solution.

A sudoku puzzle...

...and its solution numbers marked in red.

class Solution {public:   bool isValid(vector<vector<char> > &board, int x, int y)      {          int i, j;          for (i = 0; i < 9; i++)              if (i != x && board[i][y] == board[x][y])                  return false;          for (j = 0; j < 9; j++)              if (j != y && board[x][j] == board[x][y])                  return false;          for (i = 3 * (x / 3); i < 3 * (x / 3 + 1); i++)              for (j = 3 * (y / 3); j < 3 * (y / 3 + 1); j++)                  if (i != x && j != y && board[i][j] == board[x][y])                      return false;          return true;      }      bool solveSudoku(vector<vector<char> > &board)      {          for (int i = 0; i < 9; ++i)              for (int j = 0; j < 9; ++j)              {                  if ('.' == board[i][j])                  {                      for (int k = 1; k <= 9; ++k)                      {                          board[i][j] = '0' + k;                          if (isValid(board, i, j) && solveSudoku(board))                              return true;                          board[i][j] = '.';                      }                      return false;                  }              }          return true;      }};