Prefixfák

Prefixfák, also known as prefix trees or radix trees, are a type of tree data structure used for storing a dynamic set of strings. They are particularly efficient for operations that involve searching for strings based on their prefixes. In a prefix tree, each node represents a common prefix of the strings stored within the tree. The root node represents an empty string, and each child node represents a single character appended to the prefix represented by its parent.

The path from the root to a particular node spells out a prefix. If a node marks the end of a complete string, it is typically distinguished from other nodes, often by a flag or by storing the complete string at that node. When searching for a string, one traverses the tree character by character. If at any point the required character does not have a corresponding child node, the string is not present in the prefix tree.

Prefix trees offer several advantages, including fast search, insertion, and deletion times, which are typically proportional to the length of the string being operated on, rather than the total number of strings stored. This makes them ideal for applications like autocomplete systems, spell checkers, and IP routing tables. Variations of prefix trees exist, such as compressed prefix trees (radix trees) where nodes with only one child are merged, reducing space complexity.