问题
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.
例子
A sudoku puzzle...
...and its solution numbers marked in red.
分析
backtracking，从左上到右下，枚举每个空白格子的数字（1-9），然后使用Valid Sudoku的方法验证数独的正确性：如果正确，继续枚举后面的格子；如果不正确，回溯到上一个状态，继续枚举。
要点
backtracking，每一步枚举之后都验证一次，用以剪枝。
时间复杂度
O(9^m)，但是由于可以边枚举边验证，实际的复杂度要远远小于这个量级。
空间复杂度
O(1)
代码
class Solution {
public:
void solveSudoku(vector<vector<char>>& board) {
if (board.empty()) return;
solve(board);
}
private:
bool solve(vector<vector<char>>& board) {
for (int i = 0; i < board.size(); i++) {
for (int j = 0; j < board[0].size(); j++) {
if (board[i][j] == '.') {
for (char c = '1'; c <= '9'; c++) {
if (isValid(board, i, j, c)) {
board[i][j] = c;
if (solve(board))
return true;
else
board[i][j] = '.';
}
}
return false;
}
}
}
return true;
}
bool isValid(const vector<vector<char>>& board, int row, int col, int c) {
for (int i = 0; i < 9; i++) {
if (board[row][i] == c ||
board[i][col] == c ||
board[3 * (row / 3) + i / 3][3 * (col / 3) + i % 3] == c) return false;
}
return true;
}
};
