radixfákat

Radixfák, also known as radix trees or prefix trees, are a type of tree data structure used for the efficient retrieval of keys in a dataset of strings. Unlike binary search trees where every node represents a key, in a radix tree, each node represents a prefix of one or more keys. The keys are strings, and the edges of the tree are labeled with characters or substrings.

The fundamental principle of a radix tree is to share common prefixes among keys. When inserting a string, the algorithm traverses the tree, following edges that match the characters of the string. If an edge does not exist for the next character, a new node and edge are created. If a node is encountered that represents the end of a complete key, it is marked as such. This structure allows for very fast prefix matching operations, as all keys sharing a given prefix will reside in the subtree rooted at the node representing that prefix.

Radix trees are particularly useful in applications such as dictionaries, autocompletion systems, and IP routing tables. Their performance is often superior to hash tables when dealing with string keys, especially in scenarios where prefix queries are common. The space complexity can vary depending on the implementation, with some variations optimizing for space by compressing nodes with only one child. Different variations exist, including radix heaps and Patricia tries, which offer further optimizations.