Encode and Decode TinyURL — C++

// Time:  O(1)
// Space: O(n)

class Solution {
public:
    Solution() : gen_((random_device())()) {
    }

    // Encodes a URL to a shortened URL.
    string encode(string longUrl) {
        string key = getRand();
        while (lookup_.count(key)) {
            key = getRand();
        }
        lookup_[key] = longUrl;
        return "http://tinyurl.com/" + key;
    }

    // Decodes a shortened URL to its original URL.
    string decode(string shortUrl) {
        return lookup_[shortUrl.substr(tiny_url.length())];
    }

private:
    string getRand() {
        string random;
        for (int i = 0; i < random_length; ++i) {
            random += alphabet_[uniform_int_distribution<int>{0, alphabet_.length() - 1}(gen_)];
        }
        return random;
    }

    const int random_length = 6;
    const string tiny_url = "http://tinyurl.com/";
    const string alphabet_ = "0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ";
    default_random_engine gen_;
    unordered_map<string, string> lookup_;
};

// Your Solution object will be instantiated and called as such:
// Solution solution;
// solution.decode(solution.encode(url));