Algorithms / Tries Prefix Search
Least You Need to Know: Tries, Prefix Search, and Shared Prefix Structure
A **trie** stores strings by characters along root-to-node paths. It is useful when many words share prefixes and the interview task asks about prefix lookup, autocomplete, or word-search branching.
The least you need to know
- Each edge in a trie represents one character choice, and each node corresponds to a prefix.
- Shared prefixes are stored once, which is why tries are good for prefix-heavy workloads.
- A terminal marker distinguishes a full stored word from a prefix that is only part of a longer word.
- Searching for a prefix follows one character at a time; failure happens as soon as a needed edge is missing.
- Tries trade extra pointer-heavy structure for predictable prefix operations.
Key notation
root
empty-prefix start node
terminal / end-of-word
marker that a full dictionary word ends here
path label
string formed by characters along a root-to-node path
Tiny worked example
- Insert `to`, `tea`, and `ten`.
- The root has a `t` edge, then a shared `e` edge for `tea` and `ten`, while `to` branches at the second character.
- The node for path `te` is a prefix node, not yet a complete word unless a terminal marker is also present.
- This is why prefix lookup can reuse structure instead of scanning every word separately.
Common mistakes
- Students often forget that a prefix node and a complete word are different unless a terminal marker is set.
- Students may think each node stores a whole substring; it really stores position in a prefix tree.
- Students sometimes choose tries when only exact membership of a few words is needed and a hash set would be simpler.
How to recognize this kind of problem
- If the prompt asks for many prefix queries or autocomplete behavior, think trie.
- If many candidate strings share long common prefixes, a trie may compress repeated traversal work.
- If the task branches by characters one step at a time, a prefix tree is often the right abstraction.
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