feat: Implement comprehensive Trie (Prefix Tree) data structure in Java

Java/data_structures/trees/README.md

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+# Tree Data Structures in Java
+
+This directory contains implementations of various tree data structures in Java, showcasing different tree-based algorithms and their practical applications.
+
+## 📁 Available Implementations
+
+### 1. Trie (Prefix Tree) - `Trie.java`
+**Description**: A tree-like data structure for efficient storage and retrieval of strings, commonly used for prefix-based operations.
+
+**Key Features**:
+- Insert, search, and delete words
+- Prefix checking and counting
+- Auto-complete functionality
+- Memory-efficient string storage
+- Comprehensive statistics
+
+**Time Complexity**:
+- Insert: O(m) where m is word length
+- Search: O(m) where m is word length  
+- Delete: O(m) where m is word length
+- Prefix operations: O(p) where p is prefix length
+
+**Space Complexity**: O(ALPHABET_SIZE × N × M) where N is number of words, M is average length
+
+**Applications**:
+- Auto-complete/Auto-suggestion systems
+- Spell checkers and word validators
+- IP routing tables (Longest Prefix Matching)
+- T9 predictive text input
+- Word games (Scrabble, Boggle)
+- Search engines and indexing
+
+**Code Highlights**:
+```java
+Trie trie = new Trie();
+trie.insert("hello");
+trie.insert("help");
+trie.insert("hero");
+
+// Search operations
+boolean exists = trie.search("hello");           // true
+boolean hasPrefix = trie.startsWith("hel");      // true
+
+// Advanced operations
+List<String> words = trie.getWordsWithPrefix("he"); // [hello, help, hero]
+int count = trie.countWordsWithPrefix("hel");       // 2
+String commonPrefix = trie.getLongestCommonPrefix(); // "he"
+```
+
+## 🚀 How to Run
+
+### Compile and Run Trie
+```bash
+# Compile
+javac Trie.java
+
+# Run
+java Trie
+```
+
+### Program Modes
+1. **Interactive Mode**: Enter your own words and perform operations
+2. **Demonstration Mode**: See predefined examples and test cases
+
+## 📊 Performance Comparison
+
+| Operation | Trie | HashMap | Array |
+|-----------|------|---------|-------|
+| Insert | O(m) | O(m) | O(n) |
+| Search | O(m) | O(m) | O(n×m) |
+| Prefix Search | O(p) | O(n×p) | O(n×m×p) |
+| Memory | High | Medium | Low |
+| Cache Locality | Good | Poor | Excellent |
+
+## 🎯 When to Use Trie
+
+**✅ Use Trie When**:
+- You need frequent prefix-based operations
+- Implementing auto-complete features
+- Working with large dictionaries
+- Need memory-efficient string storage
+- Implementing spell checkers
+- Building search suggestions
+
+**❌ Don't Use Trie When**:
+- Only doing exact string matches (use HashMap)
+- Memory is extremely limited
+- Working with very long strings
+- Need range queries on strings
+
+## 🔧 Customization Options
+
+The Trie implementation can be easily extended:
+
+1. **Different Alphabets**: Modify `ALPHABET_SIZE` and character mapping
+2. **Case Sensitivity**: Remove toLowerCase() calls
+3. **Unicode Support**: Use HashMap<Character, TrieNode> instead of array
+4. **Weighted Trie**: Add frequency counts for auto-complete ranking
+5. **Compressed Trie**: Implement path compression for space optimization
+
+## 📚 Educational Value
+
+This implementation demonstrates:
+- **Tree Traversal**: Depth-first search patterns
+- **Recursive Algorithms**: Clean recursive deletion and traversal
+- **Memory Management**: Efficient node creation and cleanup
+- **String Processing**: Character-by-character manipulation
+- **Data Structure Design**: Balancing time vs space complexity
+
+## 🤝 Contributing
+
+Feel free to contribute additional tree implementations:
+- Binary Search Tree (BST)
+- AVL Tree (Self-balancing BST)
+- Red-Black Tree
+- B-Tree / B+ Tree
+- Segment Tree
+- Fenwick Tree (Binary Indexed Tree)
+- Suffix Tree
+- Radix Tree (Compressed Trie)
+
+## 📖 References
+
+- [Trie Data Structure - GeeksforGeeks](https://www.geeksforgeeks.org/trie-insert-and-search/)
+- [Introduction to Algorithms - CLRS](https://mitpress.mit.edu/books/introduction-algorithms)
+- [Data Structures and Algorithms in Java - Goodrich](https://www.wiley.com/en-us/Data+Structures+and+Algorithms+in+Java%2C+6th+Edition-p-9781118771334)
+
+---
+
+**Author**: Abhijit  
+**Hacktoberfest 2025**: ✅  
+**Language**: Java  
+**Category**: Data Structures - Trees