80 lines
2.9 KiB
Markdown
Executable File
80 lines
2.9 KiB
Markdown
Executable File
# What is a Binary search Tree, and how Does it Differ from a Regular Binary Tree?
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### **Binary Search Tree (BST):**
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A **Binary Search Tree (BST)** is a type of binary tree where nodes are organized based on their key values to maintain a specific order. It adheres to the following properties:
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1. **Left Subtree Rule**: For any node, all values in its left subtree are less than the value of the node.
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2. **Right Subtree Rule**: For any node, all values in its right subtree are greater than the value of the node.
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3. **Uniqueness**: Typically, BSTs do not allow duplicate values (though this can vary depending on implementation).
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These properties ensure that a **BST is sorted**, which allows for efficient searching, insertion, and deletion operations.
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---
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### **Binary Tree (General Definition):**
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A **Binary Tree** is a tree data structure where each node has at most two children. It does not impose any ordering constraints on the values of the nodes.
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- **Structure**: Each node can have a **left child**, a **right child**, or both (or no children).
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- **No Value Order**: The values in a binary tree are not arranged in any specific order.
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---
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### **Key Differences Between Binary Tree and Binary Search Tree:**
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|**Aspect**|**Binary Tree**|**Binary Search Tree**|
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|---|---|---|
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|**Node Value Order**|No specific order for node values.|Nodes are organized by the BST property (left < root < right).|
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|**Searching Efficiency**|Searching is linear in worst case (O(n)).|Searching is efficient (O(log n)) if balanced.|
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|**Insertion Rule**|Nodes can be added in any order.|Nodes are inserted based on their value to maintain the BST property.|
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|**Duplicates**|Allows duplicates freely.|May or may not allow duplicates, depending on implementation.|
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|**Applications**|Used for general tree structures.|Used for sorted collections or when efficient searching is required.|
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---
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### **Example:**
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#### Binary Tree:
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A binary tree with no ordering constraints:
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```
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10
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/ \
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20 30
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/
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40
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```
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- Node values are not in any specific order.
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#### Binary Search Tree:
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A binary search tree:
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```
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10
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/ \
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5 20
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/ \ / \
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2 7 15 25
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```
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- For every node:
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- Left subtree values < Node value.
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- Right subtree values > Node value.
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---
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### **Advantages Of BST Over a General Binary Tree:**
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1. **Efficient Searching**: Searching in a BST takes $O(h)$, where $h$ is the height of the tree. In a balanced BST, $h=O(logn)$.
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2. **Ordered Traversal**: In-order traversal of a BST produces the nodes in sorted order.
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3. **Efficient Range Queries**: BSTs can efficiently find all elements within a specific range.
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### **Disadvantages Of BST:**
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1. If unbalanced (e.g., when nodes are inserted in sorted order), the BST can degrade to a linked list, resulting in $O(n)$ time for operations.
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2. Maintaining balance (e.g., in AVL or Red-Black Trees) adds complexity.
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