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🌳 Tries: Implement Trie (Prefix Tree)

📝 Problem Description

Implement a Trie class with insert, search, and startsWith methods.

Real-World Application

Tries are the backbone of modern text processing: - Autocomplete: Efficiently suggesting word completions. - Spell Checkers: Storing dictionaries for rapid word validation. - IP Routing: Longest prefix matching in network routers.

🛠️ Constraints & Edge Cases

  • \(1 \le \text{word.length} \le 2000\)
  • Words consist of lowercase English letters.
  • Edge Cases to Watch:
    • Inserting empty strings.
    • Searching prefixes that don't exist.
    • Repeated insertion of the same word.

🧠 Approach & Intuition

The Aha! Moment

Instead of storing strings directly, represent the dataset as a tree of characters where each node holds a map/array of its children. This allows for \(O(L)\) lookups regardless of the number of strings in the trie.

🐢 Brute Force (Naive)

Storing all words in an array or a standard HashSet. Checking if a word exists is \(O(L)\), but checking if a prefix exists requires scanning all strings (\(O(N \cdot L)\)), leading to Time Limit Exceeded for large dictionaries.

🐇 Optimal Approach

Use a tree structure where each node represents a character. 1. TrieNode: Contains a hash map of children nodes and a boolean is_end. 2. insert: Iterate through characters, creating nodes as needed. Mark last as is_end. 3. search: Traverse down; if any path is missing, return false. Return is_end at the target node. 4. startsWith: Same as search, but return true immediately after the loop.

🧩 Visual Tracing

graph TD
    Root((root)) -->|a| A((a))
    A -->|p| P1((p))
    P1 -->|p| P2((p))
    P2 -->|l| L((l))
    L -->|e| E((e))
    style E fill:#ccf,stroke:#333

💻 Solution Implementation

(Implementation details need to be added...)

⏱️ Complexity Analysis

  • Time Complexity: \(\mathcal{O}(L)\) where \(L\) is the length of the string, for all operations.
  • Space Complexity: \(\mathcal{O}(N \cdot L)\) in the worst case (where no words share prefixes), where \(N\) is the number of words.

🎤 Interview Toolkit

  • Harder Variant: Use compressed Tries (Radix Tree) if memory is tight and strings are long.
  • Alternative Data Structures: Hash Map (good for search, bad for prefix matching).