Why do we want to use Binary Search Tree?

A Binary Search Tree (BST) is a specialized type of binary tree that offers several advantages for organizing and managing data efficiently. Here are the key reasons why one might want to use a Binary Search Tree:

1. Efficient Searching

• Time Complexity: BSTs allow for efficient searching operations with an average time complexity of $$O(\log n)$$ when the tree is balanced. This is because each comparison during the search operation reduces the search space by half, similar to binary search on a sorted array[3][4][6].
• Ordered Structure: The inherent ordering of elements in a BST (left child values are less than the parent node, and right child values are greater) facilitates quick lookups and range queries[4][7].

2. Dynamic Insertion and Deletion

• Insertion and Deletion: BSTs support dynamic insertion and deletion of elements while maintaining the sorted order. These operations also have an average time complexity of $$O(\log n)$$ when the tree is balanced[3][4][6].
• No Shifting Required: Unlike arrays, BSTs do not require shifting elements in memory during insertion or deletion, making these operations more efficient[3].

3. Versatility and Applications

• Data Storage: BSTs are used for storing data in a hierarchical manner, which is useful in various applications such as databases, file systems, and indexing[4][11].
• Sorting and Range Queries: BSTs can be used to sort elements and perform range queries efficiently, which is beneficial in applications like databases and search engines[4][11].
• Abstract Data Types: BSTs can implement abstract data types such as dynamic sets, lookup tables, and priority queues[17].

4. Space Efficiency

• Space Complexity: BSTs are space-efficient as they only store key values and pointers to child nodes. The space complexity is $$O(n)$$, where $$n$$ is the number of nodes in the tree[9][11].

5. Self-Balancing Variants

• Balanced BSTs: Variants like AVL trees and Red-Black trees ensure that the tree remains balanced, maintaining the $$O(\log n)$$ time complexity for operations even in the worst case[5][17]. This makes BSTs robust and reliable for various applications.

6. Simplicity and Ease of Implementation

• Simple Structure: The structure of a BST is straightforwa...