Tries

Tries are a type of tree data structure that is used to store a dynamic set of strings, where the keys are usually strings. They are particularly useful for tasks such as autocomplete and spell checking.

Structure of a Trie

A trie consists of nodes, where each node represents a character in a string. The root node represents an empty string, and each path from the root to a node represents a prefix of the strings stored in the trie. Each node contains:

• A list of child nodes, each representing a character.
• A boolean flag indicating whether the node represents the end of a valid string.

Insertion

Walk the key one character at a time, creating a missing child as needed. Mark only the node reached after the entire key as terminal. Intermediate prefixes are not automatically stored keys. Empty strings, if permitted, use the root’s terminal flag.

Deletion

To delete a string from a trie, follow these steps:

1. Start at the root node.
2. For each character in the string:
   • Check if the character exists in the current node’s children.
   • If it does, move to that child node.
   • If it doesn’t, the string is not present in the trie, and no deletion is needed.
   • If you reach the end of the string, set the boolean flag of the last character’s node to false.
   • If the node has no children and is not marked as the end of another string, delete the node and backtrack to remove any empty nodes.

Connections

• Topic index

Obvious technical and formatting errors repaired.