README updated

Binary_Search_Tree/README.md

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-# Binary Search Tree
-- Differ from a regular Binary Tree because of one key property: Nodes must be arranged in order
-  - the node's left subtree must have values less than the node
-  - the node's right subtree must have values greater than the node
-  - this is going based on that every value in the BST must be unique
-
-# Functions Implemented
-- Init
-  - tree = BST(1,None,None) _creates a tree with one node_
-  - A basic constructor that creates a BST with three parameters
-  - BST(value,left_subtree,right_subtree)
-- Add
-  - tree.add(4) _adds 4 to our previous tree created, giving a right child_
-  - Maintains BST properties by adding to either subtree depending on the value
-  - returns a string telling if insertion was or wasn't successful
-- Remove
-  - tree.remove(1) _removes 1 from our current tree, resulting 4 to be the sole node_
-  - Maintains BST properties by restructuring the tree when we remove the value
-  - returns a string telling if deletion was or wasn't successful
+
+#    Binary Search Tree (BST) Implementation in Python
+![Alt text](https://i.pinimg.com/originals/e7/f5/b6/e7f5b60413ff4bedebfd2805f97d8de7.jpg)  
+
+##   Overview
+A **Binary Search Tree (BST)** is a special kind of **Binary Tree** with one key property:  
+- The **left subtree** of a node contains values **less than** the node’s value.  
+- The **right subtree** of a node contains values **greater than** the node’s value.  
+- **All values in a BST must be unique**.
+
+This project provides a **Python implementation** of a BST, allowing you to **insert**, **remove**, **search**, and **traverse** nodes while maintaining the BST property.
+
+---
+
+##   Features
+-   **Initialization** — Create a BST with a given root node and optional left/right subtrees.
+-   **Add** — Insert a new value while keeping the BST property intact.
+-   **Remove** — Delete a value and restructure the tree if needed.
+-   **Search** — Find if a value exists in the tree.
+-   **Traversal** — Inorder, Preorder, and Postorder printing.
+
+---
+
+##   BST Property Rule  
+
+For any node N:  
+  All values in N's left subtree  <  N.value  
+  All values in N's right subtree >  N.value  
+```python
+from bst import BST  # assuming file is bst.py
+
+#   Initialize the BST
+tree = BST(1, None, None)  
+print("Initial Tree:")
+tree.print_inorder()  # Output: 1
+
+#  Add elements
+print(tree.add(4))  # Adds 4 as the right child
+print(tree.add(0))  # Adds 0 as the left child
+tree.print_inorder()  # Output: 0 1 4
+
+#   Remove elements
+print(tree.remove(1))  # Removes 1, restructures tree
+tree.print_inorder()  # Output: 0 4
+
+#   Search
+print(tree.search(4))  # True
+print(tree.search(10)) # False
+# Initial Insertion: 1, 4, 0
+    1
+   / \
+  0   4
+# After Removing 1:
+    4
+   /
+  0
+#Time Complexity
+
+| Operation  | Average Case | Worst Case |
+| ---------- | ------------ | ---------- |
+| **Search** | O(log n)     | O(n)       |
+| **Insert** | O(log n)     | O(n)       |
+| **Delete** | O(log n)     | O(n)       |
+
+
+
+
 # Author
 [Tomas Urdinola](https://github.com/tomurdi)