10 Major Differences between BST and Binary Tree

ByIshita Juneja
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BST and binary trees are concepts that aggravate the interest of every programmer in one way or the other!

Both forms an integral part of data structure, but did you know the key differences between them?

For starters, we can say that a Binary search tree is a sorted version of a binary tree, where the value of the right children nodes is greater than the left children nodes and as left subtrees as well. 

But there are certain notable differences between these concepts that you should know.

So let’s get started but besides this, we will also be discussing unique paths and the largest BST in binary tree. 

 

 Major differences between BST and Binary Tree

From Usage to structural differences we have covered it all regarding a Binary Search Tree (BST) and a Binary Tree:

  • Definition

A Binary Tree can be defined as a non-linear structural element where each node of the tree leads to one or two nodes at maximum. 

BST can be defined as a structurally organized binary Tree that has been pre-sorted. Here the value of the right children nodes is always greater than the value of the left children nodes. 

  • Usage

On one hand, we have the Binary Tree which is used for deriving solutions to problems such as deletion, insertion, and traversal. 

On the other hand, we have the BST which is used to derive the solutions to problems related to the binary Tree itself since it is the sorted version of a Binary Tree. 

  • Structure

In order to understand and navigate the nodes of a Binary Tree, we do not require to follow a definite structure. 

On the other hand, the BST is already structured. And it goes on to say that the value of the left nodes is always lower than the right in a Binary Search Tree. 

  • Types

The most common types of a Binary Tree are- Extended Binary Tree, Complete Binary Tree, and, Full Binary Tree. 

As for the Binary Search Tree, we have the most common types as Tango Trees, T- Trees, AVL Trees, and Splay Trees. 

  • Speed

When it comes to solving problems of deletion, insertion, and traversal on a Binary Tree you will find that the procedure is rather slow. 

While on the Binary Search Tree we can perform the same procedures of deletion, insertion, and traversal way faster. 

  • Hierarchy

If you have observed the structure of a Binary Tree before you would know that the Tree follows a hierarchical order, from the root node to the left nodes of the tree.

On the other hand, since the Binary Search Tree is an already sorted structure, it loses its hierarchical order. 

  • Time required

Any operation that you perform on the Binary Tree will always require you to go through the longer route or the lengthier procedure. 

This problem is not relevant to the Binary Search Tree because you will be able to navigate through the problems relatively easily. 

  • Duplicate values

In the case of a Binary Tree, the nodes are allowed to have duplicate values in more than one node. 

While in the case of the Binary Search Tree, having duplicate node values is not tolerated. 

  • Area of Excellence

When it comes to navigation you will find that using the Binary Tree provides greater efficiency than the Binary Search Tree. 

But, when it comes to solving problems related to deletion, insertion, and traversal you will find that using the Binary Search Tree attains better results and with efficiency. 

  • Order of arrangement

On a structured Binary Tree, you will find that the value of the nodes is fragmented in ascending order. 

While on the other hand we have the Binary Search Tree where the value of the nodes is completely sorted due to which it does not follow an ascending path. 

Now that we have covered the major differences between a Binary Tree and a Binary Search Tree let’s move on to the next section and discuss Unique Paths. 

 

Unique Paths

This set of problems is the most common type that you will encounter in the case of a Binary Tree. 

In order to solve the problems related to unique paths in a Binary Tree you can assume that for every Tree that has N number of nodes, the formula for deriving its unique path will be to use:

 

N*(N-1) /2

 

By applying the above formula to any given Binary Tree you will be able to derive its unique path. 

If you head over to the problem-solving websites or YouTube channels you will find plenty of practice problems that you can solve in order to test your knowledge so far. 

 

With that cleared out, we head into the final section of this blog which is discussing the largest BST in Binary Tree. 

 

Largest BST in Binary Tree

A Tree will be considered to be a Binary Search Tree if the following two clauses seem fit for the structure of the Tree:

Let us assume that we have a Binary Tree with N node values. 

  • The value of N should always be greater than the value of the smallest node in the right part of the sub Tree. 
  • The value of N should always be smaller than the value of the largest node in the left part of the sub Tree. 

Finally, in order to find if the above statements are true for the given structure of your Binary Tree, you must navigate the Tree from its left node i.e. bottoms up. 

 

Conclusion

Binary Tree and Binary Search Tree are two of the most interesting concepts when it comes to studying data structure once you are familiar with their properties. 

Before you start learning about these approaches you should familiarize yourself with the different terms that we use in the context of the Binary Tree and the Binary Search Tree. 

In this blog, you will find that we have presented you with a plethora of facts about the two. We have also incorporated the procedures for solving problems related to, finding out the largest BST in Binary Tree and its unique path.