Difference Between Binary Tree and Binary Search Tree

Both of these are data structures that work with nodes. In this article, we will take a look into the significant difference between binary tree and binary search tree. Let us know a bit more about them individually before we get into further differences.

What is a Binary Tree?

It is a non-linear type of data structure in which every element can have either 2, 1, or 0 nodes. Every node in this tree acts either like a parent node or a child node. The topmost node of this tree is known as the root node. Every parent node may have only two children (child nodes). Here, we typically name them the left child/ child node and the right child/ child node.

Each node in the binary tree may have three fields, namely:

  • Data Element – It functions as a storage for the data value that the node needs to store.
  • Pointer to the Left Child – It holds the address (or the reference to) the left child node.
  • Pointer to the Right Child – It holds the address (or the reference to) the right child node.

Several nodes combine this way for building a Binary Tree.

What is a Binary Search Tree?

Also known as the BST, the Binary Search Tree is a node-based, non-linear type of data structure of the binary tree. You can utilize it for retrieving, sorting, and searching data. It has its nodes arranged in a particular order, and thus, also called the Ordered Binary Tree. It possesses the following properties:

  • Both the right and left subtree must also be a binary search tree each.
  • A node’s right subtree only contains nodes with keys that are greater than the node’s keys.
  • A node’s left subtree only contains nodes with keys that are lesser than the node’s key.
  • A Binary Search Tree does not allow duplicate nodes.
  • Every node has a unique key.

Difference Between Binary Tree and Binary Search Tree

Parameter Binary Tree Binary Search Tree
Definition A Binary Tree refers to a non-linear type of data structure in which the nodes can have 2, 1, or 0 nodes. Every node individually consists of a right pointer, left pointer, and the data element. The BST or Binary Search Tree is also a Binary Tree that is organized and has structurally organized nodes. Every subtree must be a part of the concerned structure.
Performance of Operations You can perform operations like insertion, deletion, and traversal using the Binary Tree. Since these are sorted types of Binary Trees, they are useful for efficient and fast binary search, deletion, and insertion.
Structure It requires no organized structure of the nodes present in a tree. It has an organized structure. The value of the right subtree should be greater than the node, while that of the left subtree should be lesser.
Types The Binary tree is of several types. The most common among them are the Full Binary Tree, Complete Binary Tree, and Extended Binary Tree. The Binary Search Tree also has various types. The most popular ones among them are the Splay Trees, AVL Trees, T-Trees, Tango Trees, and more.
Duplicate Values The Binary Tree allows duplicate node values. The Binary Search Tree does not allow any duplicate node values.
Time Taken Any operation on a Binary Tree takes a longer time compared to a Binary Search Tree. Thus, the Insert, Search and Delete operations take O(n) time. A Binary Search Tree stays sorted. Thus, it provides faster operation for insert, search, and delete. As a result, it takes almost O(log n) time. Thus, in cases of lookups, a user can mainly deploy the BST (because all the keys stay arranged in sorted order).
Speed Since the Binary tree is unordered, the processes of deletion, insertion, and searching are comparatively slower than that of the Binary Search Tree. Since the Binary Search Tree has ordered characteristics, it performs deletion, insertion, and searching of elements faster.
Hierarchy A Binary Tree is basically a hierarchical data structure. It is present as a collection of elements known as nodes. It is a Binary Tree variant with the nodes arranged in relative order.
Use The Binary Tree works well for efficient and fast lookup of information and data in any tree structure. The Binary Search Tree works well in the cases of deletion, insertion, and searching of the elements.

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