Topic: Data Structures – Trees – Part 4 of 4: Advanced Trees – Red-Black Trees and Trie

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### 1. Introduction

This part covers two advanced and widely used tree data structures:

• Red-Black Trees – balanced search trees
• Trie (Prefix Tree) – efficient string storage and retrieval

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### 2. Red-Black Trees (RBT)

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#### What is a Red-Black Tree?

A Red-Black Tree is a self-balancing Binary Search Tree with extra color property:

* Each node is either red or black
* Root is always black
* Red nodes cannot have red children (no two reds in a row)
* Every path from root to leaves has the same number of black nodes (black-height)

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#### Why Red-Black Trees?

* Guarantees O(log n) time for insert, delete, and search
* Slightly less rigid balancing than AVL but faster insertion/deletion
* Used in many libraries (e.g., C++ STL map/set)

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#### Key Properties Recap

1. Every node is red or black
2. Root is black
3. Red nodes have black children
4. Every path from root to null leaves contains same black nodes count

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#### Basic Operations

* Insertions and deletions are followed by color adjustments and rotations
* Ensures tree remains balanced with Red-Black properties intact

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### 3. Trie (Prefix Tree)

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#### What is a Trie?

A Trie is a tree-like data structure used to store a dynamic set of strings, where:

* Each node represents a character
* Path from root to leaf forms a word
* Used for prefix searches efficiently

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#### Why Use a Trie?

• Fast lookup for words and prefixes
• Auto-complete features
• Spell checking
• IP routing (longest prefix matching)

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#### Trie Node Structure (Python)

class TrieNode:
    def __init__(self):
        self.children = {}
        self.is_end_of_word = False

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#### Basic Operations

Insert Word:

def insert(root, word):
    node = root
    for char in word:
        if char not in node.children:
            node.children[char] = TrieNode()
        node = node.children[char]
    node.is_end_of_word = True

Search Word:

def search(root, word):
    node = root
    for char in word:
        if char not in node.children:
            return False
        node = node.children[char]
    return node.is_end_of_word

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### 4. Example Usage of Trie

root = TrieNode()
insert(root, "hello")
insert(root, "helium")

print(search(root, "hello"))  # True
print(search(root, "hel"))    # False (prefix only)

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### 5. Advantages and Disadvantages

| Data Structure | Advantages | Disadvantages |
| -------------- | -------------------------------------- | ------------------------------- |
| Red-Black Tree | Balanced, efficient search and update | Complex implementation |
| Trie | Fast prefix search and auto-completion | Memory-heavy with many children |

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### 6. Summary

* Red-Black Trees and AVL Trees both keep BSTs balanced but with different balancing rules
* Tries are specialized for string data, enabling efficient prefix operations
* Both structures are essential for advanced algorithms and systems

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### 7. Exercise

• Implement basic Red-Black Tree insertion (research needed)
• Implement delete operation in Trie
• Use Trie to implement a simple autocomplete function
• Compare search time for BST vs Trie on string data sets

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#DSA #RedBlackTree #Trie #AdvancedTrees #DataStructures #Python

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