What is a trie and how is it different from a prefix tree?

A trie, also known as a prefix tree or digital tree, is a specialized tree-based data structure that is primarily used for efficient retrieval of strings or words. It is particularly useful when dealing with large sets of strings or when there is a need to perform prefix-based searches.

In a trie, each node represents a single character, and the edges of the tree represent the possible characters that can follow the current character. The root node represents an empty string, and each path from the root to a leaf node represents a complete word. The leaf nodes typically indicate the end of a word.

One key difference between a trie and a prefix tree lies in their implementation. A trie is typically implemented using a collection of linked nodes, where each node contains a character and a set of child nodes. On the other hand, a prefix tree is often implemented using a collection of linked nodes as well, but each node contains a character and a set of child nodes, along with a flag indicating whether the current node represents the end of a word.

Another difference lies in the way they handle prefixes. In a trie, all words with a common prefix share the same path until the point where they diverge. This makes it efficient to search for words with a specific prefix, as we can simply traverse the trie until we reach the desired prefix. In contrast, a prefix tree explicitly marks the end of each word, making it easier to determine if a given string is a complete word or just a prefix.

Additionally, a trie can be more memory-efficient compared to a prefix tree when dealing with a large number of words with common prefixes. This is because a trie avoids storing redundant information by sharing common prefixes among multiple words.

In summary, a trie and a prefix tree are similar in concept and purpose, but they differ in their implementation and the way they handle prefixes. A trie is a more memory-efficient data structure that allows for efficient prefix-based searches, while a prefix tree explicitly marks the end of each word, making it easier to determine if a string is a complete word or just a prefix.