SRM 700 DIV II 450

My DFS solution during contest, which passed all system tests except TLE for one. As a result, I received zero points.
This is not the first time that I am tempted to use a brutal force solution for a 450 / 500 problem that seemingly work but
ultimately fail due to inefficiency.

class XMarksTheSpot {
    int result;
public:
    void dfs(vector<string> board, int i, int j, int rs, int cs) {
        if (i == rs - 1 && j == cs - 1) {
            if (board[i][j] == '?') {
                board[i][j] = 'O';
                compute(board);
                board[i][j] = '.';
                compute(board);
            } else {
                compute(board);
            }
            return;
        }
        int ni, nj;
        if (j + 1 < cs) {
            ni = i;
        } else {
            ni = i + 1;
        }
        nj = (j + 1) % cs;
        
        if (board[i][j] == '.' || board[i][j] == 'O') {
            dfs(board, ni, nj, rs, cs);
        } else {
            board[i][j] = '.';
            dfs(board, ni, nj, rs, cs);
            board[i][j] = 'O';
            dfs(board, ni, nj, rs, cs);
        }
    }
    
    void compute(vector<string> board) {
        int rs = (int)board.size();
        int cs = (int)board[0].size();
        int t = INT_MAX, b = INT_MIN, l = INT_MAX, r = INT_MIN;
        for (int i = 0; i < rs; ++i) {
            for (int j = 0; j < cs; ++j) {
                if (board[i][j] == '.') continue;
                t = std::min(i, t);
                b = std::max(i, b);
                l = std::min(j, l);
                r = std::max(j, r);
            }
        }

        for (int i = t; i <= b; ++i) {
            for (int j = l; j <= r; ++j) {
                ++result;
            }
        }
    }
    
    int countArea(vector<string> board) {
        result = 0;
        int rs = (int)board.size();
        int cs = (int)board[0].size();
        dfs(board, 0, 0, rs, cs);
        return result;
    }
}

Actually even with brutal force, there is better approaches without recursing (which is the root of many evils of time outs during contest).
We can just iterate through all the states explicitly and calculate the results at higher level while iterating. Here is a good example on how to do so.