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C++11 Trie Implementation

This is a C++ implementation of compressed prefix trie.

To use it, you don't need to clone the repository. You only need to download one single file, trie.h. All the implementation is in one header.

This implementation depends on C++11

When to use

Using trie is beneficial when have a lot of very long strings having the common prefix (e.g. urls, file paths) and you want to use them as keys for set or map. Trie will provide you with performance, close to the one of hash table (still worse on average, however), but with some benefits, like partial search (currently by prefix substring).

How long is very long? Is would say that the real difference will only become noticeable when the average length is greater then CPU cache line (usually 64 bytes). Below that I would not expect benefit in performance over the normal map operations.

In future, I plan to implement fast pattern matching and edit distance search, which cannot be implemented efficiently with hash table.

Trie is also theoretically is more space efficient then just regular map/unordered_map. In practice that heavily depends on the nature of strings you have.

Motivation

First, a minute of being honest, the real motivation behind this project is to get myself familiar with new C++11 features. That's why, you will probably find excessive use of lambda expressions, unnecessary templates, usage of and keyword instead of && etc. Having said that, I'm going to use this implementation in some small projects of mine.

I am going to work on this to make it a really usable library. My goal is to do at least one improvement/bug fix per week.

Related work

For simple prefix-tree implementation it makes sense to use boost::spirit::qi::tst_map

Really good library for practical purposes is patl. In fact this library has much more then just trie implementation. If you need to use something in your project, please consider this library. This is a very solid implementation, but I am not sure whether it's supported anymore.

Simple Usage Examples

The trie implementation has some caveats which should be mentioned from the beginning.

As Regular Map

{
    typedef trie::trie_map<char, int> TestMap;
    TestMap tmap;

    tmap.insert("105", 105);
    tmap.insert("104", 104);
    tmap.insert("2093", 2093);
    tmap.insert("2097", 2097);

    std::cout << tmap["105"] << " ";
    std::cout << tmap["104"] << " ";
    std::cout << tmap["2093"] << " ";
    std::cout << tmap["2097"] << " ";
    std::cout << std::endl;
}

1 2 3 4

As Regular Set

Since there is no additional cost involved, the trie can be used as multiset. In order to do that the value type should be specified as trie::SetCounter. Note, that specifying SetCounter as value type is different then just specifying int. Internally, SetCounter provides different node implementation, which is more efficient. It is very similar to int, but uses 0 as a special value to distinguish between leaf and non-leaf nodes.

{
    typedef trie::trie_map<char, trie::SetCounter> TestSet;
    TestSet tset;

    tset.insert("10.0.0.1");
    tset.insert("10.0.17.8");
    tset.insert("192.168.0.1");
    tset.insert("192.168.0.2");

    std::cout << tset.contains("10.0.0.1") << " ";
    std::cout << tset.contains("10.0.17.8") << " ";
    std::cout << tset.contains("10.0.17.2") << " ";
    std::cout << tset.contains("10.0.1.1") << " ";
    std::cout << std::endl;
}

1 1 0 0

It's not recommended to use find() or find_prefix() to look for key in set, because the iterator they return is very heavy. Function contains() does a much more efficient lookup.

Iterating Over Trie

Trie is a different from the map when it comes to iterating over objects. The reason for that difference is that it does not really store keys, so dereferencing the iterator does not return pair<key, value>, instead it only returns the reference to the value. To obtain key, we call key() method of the iterator, which reconstructs the key (thus, somewhat slow).

Also note, that iterator itself is very heavy, since we store the whole path to the current node in the tree. One can think of that as a drawback, but on the other hand, we don't have to store parent node reference this way.

{
    typedef trie::trie_map<char, int> TestMap;
    TestMap tmap;

    tmap.insert("10.0.0.1",    1);
    tmap.insert("10.0.17.8",   2);
    tmap.insert("192.168.0.1", 3);
    tmap.insert("192.168.0.2", 4);

    for (auto it = tmap.begin(); it != tmap.end(); ++it) {
        std::cout << *it << " ";
    }

    for (auto it = tmap.begin(); it != tmap.end(); ++it) {
        std::cout << it.key() << " ";
    }
}

1 2 4 3 10.0.0.1 10.0.17.8 192.168.0.2 192.168.0.1

From the perspective of ordering, trie is somewhat in the middle between map and unordered_map. The only order, which is guaranteed during iteration is that any string appears later then any of its prefix substring. However, strict ordering can be achieved, it just requires a more sophisticated iterator (TBD).

Subtrie Iterator

There is a special kind of iterator, which is subtrie iterator. It is returned by find_prefix() method. After the subtrie is traversed (regular ++ operator), the iterator becomes equal to the end iterator. So, end iterator is universal for trie and any of its subtries.

{
    typedef trie::trie_map<char, int> TestMap;
    TestMap tmap;

    tmap.insert("/home/user1/audio", 10);
    tmap.insert("/home/user1/video", 11);
    tmap.insert("/home/user2/audio", 20);
    tmap.insert("/home/user2/video", 21);

    for (auto it = tmap.find_prefix("/home/user1"); it != tmap.end(); ++it) {
        std::cout << it.key() << " ";
        std::cout << *it << ";\n";
    }
}

/home/user1/video 11;
/home/user1/audio 10;

Implementation Details

Wiki to read on subject:

Testing

TBD

Performance

TBD

Theoretical

TBD

Real Evaluations

I am only comparing this library to standard map. If anyone wants to do comparison against existing trie implementations (like boost::tst or PATL), I'd be glad to help with that. My expectation is they are going to be a little faster.

TBD

Future Plans

Small Improvements.

Big Changes