Implement Trie (Prefix Tree)

Implement Trie (Prefix Tree) - Problem

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.

Input & Output

Example 1 — Basic Trie Operations

$ Input: operations = ["Trie", "insert", "search", "search", "startsWith", "insert", "search"], values = ["", "apple", "apple", "app", "app", "app", "app"]

› Output: [null, null, true, false, true, null, true]

💡 Note: Create trie, insert "apple", search "apple" (found), search "app" (not found), check prefix "app" (exists), insert "app", search "app" (now found)

Example 2 — Multiple Words with Shared Prefix

$ Input: operations = ["Trie", "insert", "insert", "search", "startsWith"], values = ["", "car", "card", "care", "car"]

› Output: [null, null, null, false, true]

💡 Note: Insert "car" and "card", search "care" (not found), but "car" is a valid prefix

Example 3 — Single Character Operations

$ Input: operations = ["Trie", "insert", "search", "startsWith"], values = ["", "a", "a", "a"]

› Output: [null, null, true, true]

💡 Note: Edge case with single character: insert "a", search "a" (found), "a" starts with "a"

Constraints

1 ≤ word.length, prefix.length ≤ 2000
word and prefix consist only of lowercase English letters
At most 3 × 10⁴ calls in total will be made to insert, search, and startsWith

Visualization

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Asked in

G Google 45 a Amazon 38 M Microsoft 32 🍎 Apple 25

The key insight is to use a tree structure where each path represents a word prefix, allowing efficient sharing of common prefixes. The optimal approach uses a trie with nodes containing character children and end markers. Time: O(m) per operation, Space: O(ALPHABET_SIZE × N × M) for the tree structure.

Common Approaches

✓ Greedy

⏱️ Time: N/A Space: N/A

Dp 1d

⏱️ Time: N/A Space: N/A

Array/List Storage

⏱️ Time: O(n*m) Space: O(n*m)

Use a basic array or list to store all inserted words. For search and prefix operations, iterate through all stored words to check for matches.

Trie Data Structure

⏱️ Time: O(m) Space: O(ALPHABET_SIZE × N × M)

Build a tree where each node contains children for each possible character. Each path from root to a marked node represents a complete word. This allows sharing of common prefixes.

Algorithm Steps — Algorithm Steps

Code -

solution.c — C

Time & Space Complexity

Time Complexity

⏱️

✓ Linear Growth

Space Complexity

✓ Linear Space

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Smart Actions

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