Trie

The last preceding node where there was a key or a bifurcation, a fork in the path, is a parent node in the type of trie shown here, where only unique string prefixes are represented as paths in the trie.

The result of such compression may look similar to trying to transform the trie into a directed acyclic graph (DAG), because the reverse transform from a DAG to a trie is obvious and always possible.

This works best under the following conditions: * The trie is mostly static (key insertions to or deletions from a pre-filled trie are disabled).

Additional information will have to be associated with each key to indicate the population count or original order of any duplicate keys in a trie-based radix sort if keeping track of that information is important for a particular application.

A depth-first traversal of a trie starting from the root node will visit each key in order.

A post-order traversal is used to process the contents of a trie in descending order.

A pre-order traversal is used to process the contents of a trie in ascending order.

Compressing tries Compressing the trie and merging the common branches can sometimes yield large performance gains.

E.g., a string of n bytes can alternatively be regarded as a string of 2n four-bit units and stored in a trie with sixteen pointers per node.

For example, if Bashful is inserted into the trie, then the predecessor is the null string in the parent node, which is the root node in this case.

For example, if Grumpy were the last key inserted into the trie, then the computer would have a choice of trying to find either the predecessor, Dopey, or the successor, Happy, with a depth-first search starting from the parent node of Grumpy.

Implementation strategies A trie implemented as a doubly chained tree : vertical arrows are child pointers, dashed horizontal arrows are next pointers.

In particular, a bitwise trie is keyed on the individual bits making up any fixed-length binary datum, such as an integer or memory address.

In such a case, the trie is keyed by the bit element position within the full set.

Maintaining the trie structure also makes it possible to insert new keys into the set incrementally or delete keys from the set incrementally while maintaining sorted order in O(k) time, in a time that is independent of the total number of keys.

Performing a radix sort with the buckets is like creating a trie and then discarding the non-leaf nodes.

Such applications take advantage of a trie's ability to quickly search for, insert, and delete entries; however, if storing dictionary words is all that is required (i.

Term indexing A discrimination tree term index stores its information in a trie data structure.

This is because a DAFSA can compress identical branches from the trie which correspond to the same suffixes (or parts) of different words being stored.

This structure will be called a circularly threaded trie.