What is the time and space complexity of Implement Trie (Prefix Tree)?

Time complexity: O(L). Space complexity: O(total characters).

Implement Trie (Prefix Tree)

Easy

Concept

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Solution Guide: Implement Trie (Prefix Tree)

Approach

Use nested child pointers under each node. Insert writes each character path and marks the terminal node. Search/startsWith walk the same path and check terminal or complete prefix existence.

Complexity Analysis

Time: O(L)
Space: O(total characters)

Pattern

Trie Construction and Lookup

Why It Works

Shared prefixes are stored once in the tree, and every query touches at most L nodes for an L-length word.

Updated Feb 2026