Trie (a.k.a. prefix tree) is an ordered tree data structure that is used to store an associative array where the keys are usually strings. All the descendants of a node have a common prefix of the string associated with that node, and the root is associated with the empty string.
Reference: Wikipedia

• Looking up keys is faster. Looking up a key of length key takes O(|key|) time
• Looking up prefixes is faster. Looking up a prefix takes O(|prefix|) time
• Removing takes O(|key|) time

Trie trie = ["star", "start", "stack", "stop", "stay", "key"];

          {root}
            /\
           s  k
          /    \
         t      e
        / \      \
      a    o     [y]
    / | \    \
  [r][y] c   [p]
  /       \
[t]       [k]

where [char] -- is end of word

The library provides two implementations of the trie data structure:

• Trie : ICollection<string>, this is a set which stores unique strings
• TrieDictionary<TValue> : IDictionary<string, TValue>, this is a key-value-pair collection

TrieDictionary initialization:

// Initialization
TrieDictionary<int> trie = [];

// or using constructor with comparer
IEqualityComparer<char> comparer = ...; // specify the comparer
TrieDictionary<int> trieWithComparer = new(comparer);

Adding items to trie

trie.Add("key", 17);

The Add method throws ArgumentNullException if a value with the specified key already exists, however setting the Item property overwrites the old value. In other words, TrieDictionary<TValue> has the same behavior as Dictionary<TKey, TValue>.

The main advantage of trie is really fast prefix lookup. To find all items of TrieDictionary<TValue> which have keys with given prefix use StartsWith method which returns IEnumerable<KeyValuePair<string, TValue>>:

var result = trie.StartsWith("abc");

Another handy method is Matches(IReadOnlyList<Character> pattern)

var result = trie.Matches([Character.Any, 'c', Character.Any, Character.Any, 't']);

which will return all words that match this regex: ^.c.{2}t$, e.g.: octet, scout, scoot.

There are two overloads of the StartsWith method:

• StartsWith(string value)
• StartsWith(IReadOnlyList<Character> pattern)

For performance tests I used 370105 English words (from: https://github.com/dwyl/english-words).

© Kirill Polishchuk