Implement Trie (Prefix Tree)

LeetCode 208 | Difficulty: Medium

Medium

Problem Description

A trie (pronounced as "try") or prefix tree is a tree data structure used to efficiently store and retrieve keys in a dataset of strings. There are various applications of this data structure, such as autocomplete and spellchecker.

Implement the Trie class:

- `Trie()` Initializes the trie object.

- `void insert(String word)` Inserts the string `word` into the trie.

- `boolean search(String word)` Returns `true` if the string `word` is in the trie (i.e., was inserted before), and `false` otherwise.

- `boolean startsWith(String prefix)` Returns `true` if there is a previously inserted string `word` that has the prefix `prefix`, and `false` otherwise.

Example 1:

Input
["Trie", "insert", "search", "search", "startsWith", "insert", "search"]
[[], ["apple"], ["apple"], ["app"], ["app"], ["app"], ["app"]]
Output
[null, null, true, false, true, null, true]

Explanation
Trie trie = new Trie();
trie.insert("apple");
trie.search("apple");   // return True
trie.search("app");     // return False
trie.startsWith("app"); // return True
trie.insert("app");
trie.search("app");     // return True

Constraints:

- `1 <= word.length, prefix.length <= 2000`

- `word` and `prefix` consist only of lowercase English letters.

- At most `3 * 10^4` calls **in total** will be made to `insert`, `search`, and `startsWith`.

Topics: Hash Table, String, Design, Trie

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Approach

Hash Map

Use a hash map for O(1) average lookups. Store seen values, frequencies, or indices. The key question: what should I store as key, and what as value?

When to use

Need fast lookups, counting frequencies, finding complements/pairs.

Trie (Prefix Tree)

Build a tree where each edge represents a character, and paths from root represent prefixes. Enables O(L) prefix lookups where L is the word length.

When to use

Prefix matching, autocomplete, word search, longest common prefix.

Design

Choose the right data structures to meet the required time complexities for each operation. Consider hash maps for O(1) access, doubly-linked lists for O(1) insertion/deletion, and combining structures for complex requirements.

When to use

Implementing a data structure or system with specific operation time requirements.

String Processing

Consider character frequency counts, two-pointer approaches, or building strings efficiently. For pattern matching, think about KMP or rolling hash. For palindromes, expand from center or use DP.

When to use

Anagram detection, palindrome checking, string transformation, pattern matching.

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Solutions

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Complexity Analysis

Approach	Time	Space
Hash Map	$O(n)$	$O(n)$
Trie	$O(L × n)$	$O(L × n)$

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Interview Tips

Key Points

• Discuss the brute force approach first, then optimize. Explain your thought process.
• Hash map gives O(1) lookup — think about what to use as key vs value.
• Clarify the expected time complexity for each operation before choosing data structures.