A **Binary Search Tree** is a binary tree where each node contains a key and an optional associated value. It allows particularly fast lookup, addition, and removal of items.

The nodes are arranged in a binary search tree according to the following properties: 

* The left subtree of a particular node will always contain nodes with keys less than that node’s key. 

* The right subtree of a particular node will always contain nodes with keys greater than that node’s key. 

* The left and the right subtree of a particular node will also, in turn, be binary search trees. 

# Time Complexity

In average cases, the above mentioned properties enable the insert, search and deletion operations in $O(log n)$ time where *n* is the number of nodes in the tree. However, the time complexity for these operations is $O(n)$ in the worst case when the tree becomes unbalanced. 

# Space Complexity

The space complexity of a binary search tree is $O(n)$ in both the average and the worst cases. 

# Types of Traversals
The Binary Search Tree can be traversed in the following ways:
1. Pre-order Traversal
2. In-order Traversal
3. Post-order Traversal

The *pre-order* traversal will visit nodes in **Parent-LeftChild-RightChild** order.  

The *in-order* traversal will visit nodes in **LeftChild-Parent-RightChild** order. In this way, the tree is traversed in an ascending order of keys.  

The *post-order* traversal will visit nodes in **LeftChild-RightChild-Parent** order. 

What is a Binary Search Tree?

A Binary Search Tree ensures fast lookups, additions, and removals with O(log n) average time complexity, but O(n) in worst-case, and supports pre-, in-, and post-order traversals.