not best, but 8ms - beats 77.99% of cpp submissions.

fast-sudoku.cc

class Solution {
private:
    int flags[3][3] = {{0}};
    int rows[9] = {0};
    int cols[9] = {0};
    int count = 0;
    deque<pair<int, int>> s;

public:
    void solveSudoku(vector<vector<char>>& board) {
        for (int row = 0; row < 9; row ++) {
            for (int col = 0; col < 9; col++) {
                char sym = board[row][col];
                if (sym == '.') {
                    s.push_front(make_pair(row, col));
                } else {
                    int num = sym - '0';
                    int rowi = row / 3;
                    int coli = col / 3;
                    int mask = 1 << num;
                    flags[rowi][coli] |= mask;
                    rows[row] |= mask;
                    cols[col] |= mask;
                    count ++;
                }
            }
        }

        if (count == 81) {
            return;
        }

        dfs(board);
    }

    void dfs(vector<vector<char>>& board) {
        if (!s.empty()) {
            auto pair = s.back();
            s.pop_back();
            int row = pair.first;
            int col = pair.second;
            int rowi = row / 3;
            int coli = col / 3;
            int a = flags[rowi][coli];
            int b = rows[row];
            int c = cols[col];
            
            for (int i = 1; i < 10; i ++) {
                int mask = 1 << i;
                if (!((rows[row] | cols[col] | flags[rowi][coli]) & mask)) {
                    board[row][col] = '0' + (char)i;
                    count ++;
                    flags[rowi][coli] = a | mask;
                    rows[row] = b | mask;
                    cols[col] = c | mask;
                    dfs(board);
                    if (count == 81) {
                        return;
                    }
                    flags[rowi][coli] = a;
                    rows[row] = b;
                    cols[col] = c;
                }
            }

            board[row][col] = '.';
            count --;
            s.push_back(pair);
        }
    }
};