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+# Tree Examples
+
+## 1. Binary Tree
+
+### Example
+  1
+ / \
+2   3
+/\5
+4
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+
+### Operations
+- **Inorder Traversal**: 4, 2, 5, 1, 3
+- **Preorder Traversal**: 1, 2, 4, 5, 3
+- **Postorder Traversal**: 4, 5, 2, 3, 1
+
+## 2. Binary Search Tree (BST)
+
+### Example
+  10
+ /  \
+5   15
+/\
+    7
+3   \
+    20
+
+
+### Operations
+- **Insertion**: Adding 6 to the BST
+- **Search**: Finding 7 in the BST
+- **Deletion**: Removing 15 from the BST
+
+
+### Operations
+- **Insertion**: Adding the word "cat" to the Trie
+- **Search**: Checking if "rat" exists in the Trie
+- **Deletion**: Removing the word "cat"
+
+## 8. Segment Trees
+- **Definition**: A binary tree used for storing intervals or segments and allows querying the intervals efficiently.
+- **Operations**:
+  - **Query**: Finding information over a range of indices.
+  - **Update**: Modifying elements in the array.
+
+### Example (Range Minimum Query)
+- **Array**: [2, 3, 1, 4, 5]
+- **Segment Tree**:
+
+      [1]
+     /   \
+   [1]   [4]
+  /  \   / \
+ [2] [1] [4] [5]
+
+
+
+### Operations
+- **Query**: Minimum value in range [1, 3]
+- **Update**: Change value at index 2 to 6
+
+## 9. Fenwick Trees (Binary Indexed Trees)
+- **Definition**: A data structure that provides efficient methods for cumulative frequency tables.
+- **Operations**:
+  - **Update**: Adding a value to an element.
+  - **Query**: Calculating prefix sums.
+
+### Example
+- **Array**: [3, 2, 4, 5, 1]
+- **Fenwick Tree**:
+    [3]
+   /  \
+ [5]   [4]
+/  \    / \
+[3] [4] [5] [1]
+
+
+### Operations
+- **Update**: Add 3 to the value at index 2
+- **Query**: Sum of elements from index 1 to 3
+
+## 10. N-ary Trees
+- **Definition**: A tree in which a node can have at most N children.
+- **Properties**: Generalizes binary trees.
+
+### Example
+    1
+   /|\ 
+  2 3 4
+ / \
+5   6
+
+### Operations
+- **Traversal**: Depth-First Search (DFS)
+- **Traversal**: Breadth-First Search (BFS)
+
+## 11. Tree Traversal Algorithms
+- **Depth-First Search (DFS)**:
+  - **Inorder**: Traverses left subtree, visits node, traverses right subtree.
+  - **Preorder**: Visits node, traverses left subtree, traverses right subtree.
+  - **Postorder**: Traverses left subtree, traverses right subtree, visits node.
+- **Breadth-First Search (BFS)**: Traverses level by level from the root.
+
+## 12. Applications of Trees
+- **Expression Trees**: Used in compilers to parse mathematical expressions.
+- **Syntax Trees**: Represents the structure of a program or expression.
+- **Decision Trees**: Used in machine learning for classification and regression.
+
+## 13. Advanced Topics
+- **Suffix Trees**: Used for efficient string matching and substring search.
+- **Generalized Trees**: Extensions of traditional tree structures.
+- **Tree Isomorphism**: Determining if two trees are structurally identical.
+
+## 14. Complexity Analysis
+- **Time Complexity**: Measures the time required for operations in terms of input size.
+- **Space Complexity**: Measures the memory used by the tree data structure.
+
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+# Trees in Data Structures
+
+## 1. Introduction to Trees
+- Definition and Terminology
+- Types of Trees
+
+## 2. Binary Trees
+- Definition
+- Properties
+- Types of Binary Trees
+  - Full Binary Tree
+  - Complete Binary Tree
+  - Perfect Binary Tree
+  - Balanced Binary Tree
+  - Degenerate (or pathological) Tree
+
+## 3. Binary Search Trees (BST)
+- Definition
+- Properties
+- Operations
+  - Insertion
+  - Deletion
+  - Search
+  - Traversal (Inorder, Preorder, Postorder)
+
+## 4. AVL Trees
+- Definition
+- Rotations
+  - Single Rotation
+  - Double Rotation
+- Insertion
+- Deletion
+- Balancing
+
+## 5. Red-Black Trees
+- Definition
+- Properties
+- Rotations
+  - Left Rotation
+  - Right Rotation
+- Insertion
+- Deletion
+- Balancing
+
+## 6. B-Trees
+- Definition
+- Properties
+- Operations
+  - Insertion
+  - Deletion
+  - Search
+
+## 7. Trie (Prefix Tree)
+- Definition
+- Operations
+  - Insertion
+  - Search
+  - Deletion
+
+## 8. Segment Trees
+- Definition
+- Operations
+  - Query
+  - Update
+
+## 9. Fenwick Trees (Binary Indexed Trees)
+- Definition
+- Operations
+  - Update
+  - Query
+
+## 10. N-ary Trees
+- Definition
+- Properties
+- Traversal Methods
+
+## 11. Tree Traversal Algorithms
+- Depth-First Search (DFS)
+  - Inorder
+  - Preorder
+  - Postorder
+- Breadth-First Search (BFS)
+
+## 12. Applications of Trees
+- Expression Trees
+- Syntax Trees
+- Decision Trees
+
+## 13. Advanced Topics
+- Suffix Trees
+- Generalized Trees
+- Tree Isomorphism
+
+## 14. Complexity Analysis
+- Time Complexity
+- Space Complexity