Programs

# Binary Tree vs Binary Search Tree: Difference Between Binary Tree and Binary Search Tree

Data analysis is essential today, where the produced data is enormous and contains valuable information. Analyzing such vast volumes of data is practically impossible, but sorting can help systematically arrange the data for practical analysis. When you identify a particular record, the process is known as searching, which allows simplified data sorting and analysis. In this article, we will learn about non-linear data structure trees. We will also discuss binary tree vs binary search tree and related aspects.Â

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The main purpose of using trees is to represent data by presenting a hierarchical relationship between different elements. For instance, the table of content and family tree. Technically, you can define a tree as a finite set â€˜Tâ€™, which consists of one or more nodes in a manner that a node is assigned as the treeâ€™s root, and the other nodes are divided into n>=0 disjoint sets T1, T2, T3, T4â€¦..Tn. These are known as subtrees or children of the root node.Â

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## What is a Binary Tree?

A Binary Tree is a non-linear hierarchical data structure represented in a top-down way (there is random allocation of memory). The top node is known as the root, a collection of nodes and is a non-ordered data structure.

Each node in the Binary Tree can have two children (0, 1, or 2), called the left and the right child. The nodes which have child nodes are called Parent nodes, and the ones that donâ€™t are known as Leaf nodes.

Every node in memory will have the following attributes:

• Data (it can be any type).
• Left Pointer with reference for Left Child.
• Right Pointer with reference for Right Child.

For instance,Â

source

This is an example of a binary tree. It is clear from the image that this tree is not ordered. Node 1 is the root node of this tree. Two arrows go down from the root node as a left arrow and a right arrow. These indicate the left and right child, respectively. Left nodes are the nodes present at the last level. Therefore, in this particular binary tree, Nodes 1, 2, and 3 are parent nodes. Node 1 and Node 2 have two children each. Thus, they are called internal nodes.Â

### Some common terminologies used in a Binary Tree

Mentioned below are some common terminologies used to understand b tree vs binary tree:

• Node – Node is the fundamental representation of a treeâ€™s termination point.Â
• Root Node – The root node is the top node in a tree.
• Parent Node – The parent node connects two other nodes through edges. In the case of a Binary Tree, there can be a maximum of 2 child nodes that a parent node can have.Â
• Leaf Node – A node that doesnâ€™t have any child node is known as a lead node.Â
• Child Node -If a node has a predecessor, it is the child node.Â
• Height of the Tree – The tree’s height can be measured as the longest distance from the treeâ€™s root node to the leaf node.Â
• Depth of a Node – The depth of a node is the distance from the root node to the specific node whose depth you need to measure.Â

### Operations on Binary Trees with Complexities

There are three attributes in this:

• Search -Traverse all the nodes in the Binary Tree to search for an element in the tree. For example, you can use â€˜Level Order Traversalâ€™ to search time complexity for implementing search is O(n) for n numbers of nodes in a Tree.Â
• Insert – If there is a Skewed Binary Tree and you want to insert an element, traverse to the last node of the tree for action. The overall complexity will be O(n).Â
• Delete – If you want to delete a node, first search it in the tree. Once you have found it, you can deallocate the memory. Like the search operation, it also needs O(n) time.Â

## What is a Binary Search Tree?

A Binary Search Tree, also known as BST, is a special kind of node-based binary tree data structure. The specialty is its nodes are arranged in a specific manner and order carrying the same structure as a binary tree but in a different arrangement. A Binary Search Tree is an ordered tree that follows certain conditions:

• The left child of the node will have data or value less than the parent node.
• The right child of the node will have data or values greater than the parent node.Â
• The left subtrees have nodes with lesser values than the tree’s root, and the right subtrees will have nodes with greater values than the tree’s root.
• If each node’s right and left subtrees exist, there will be a binary search tree. The data of each node should be lesser than or greater than that parent node. Therefore, no nodes with duplicate values or keys are permitted.Â

Mentioned below is a typical Binary Search Tree:

source

Node 7 is the root node in the tree mentioned above, and Node 2 is its left child with a value less than the root node. Again node 9 is node 7â€™s right child, and the value is greater than node 7. Every subtree of a node is a binary search tree itself.Â

### Operations on Binary Search Tree with Complexities

The concept of using a Binary Search Tree is optimizing the search operation for every lookup. While searching a node in a Binary Search Tree, removing half the sub-tree at almost every step is possible as it follows an orderly structure.Â

• Search – When you want to search for an element in a Binary Search Tree, it will generally take O(log n) time or O(h). Here â€˜hâ€™ is the treeâ€™s height.Â
• Insert – The time is identical to the search operation O(h) or O(log n). However, it might take O(n) time in the worst cases.Â
• Delete – Overall complexity of deallocating and searching memory is the same as O(log n).

## Understanding the difference between Binary Tree and Binary Search Tree

The binary tree vs. binary search tree comparison chart will help you glance at the major differences.

 Binary Tree Binary Search Tree A binary tree is a non-linear data structure where every node has two child nodes at the maximum. This is a specialized form of Tree data structure.Â A binary Search Tree is a node-based binary tree. Each node has two children maximum. Trees present on the right half and left half of each node are a Binary Search Tree itself. It is useful for data representation in a hierarchical format.Â You can represent data in an ordered format in Binary Search Tree. There is no particular data ordering while arranging nodes in a Binary Tree. A Binary Search Tree is an ordered tree. The left childâ€™s value is smaller than the parent node, and the right childâ€™s value is greater than the parent node. This structure is followed in all the subtrees. Nodes with duplicate values are permitted. There is no permission for duplicate nodes. A binary tree acts as a base for implementing Perfect Binary Tree, Full Binary Tree, Binary Search Tree, etc.Â Binary Search Tree is used in implementing Balanced Binary Search Trees like Red-Black Trees, AVL Trees, etc.Â It takes a longer time to carry out operations on a Binary Tree. Therefore, the Search, Insert, and Delete operation takes O(n) time.Â Since Binary Search Trees are sorted and ordered, operations like Search, Insert and Delete take O(log n) time. For lookups, using Binary Search Tree is a great option as the keys are in sorted order.Â

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## Conclusion

Binary Search Tree vs Binary Tree come with a common hierarchical structure and a collection of nodes. But there are some differences between the b tree vs binary tree when it comes to application.

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## What is the purpose of a Binary Tree?

Binary trees are mainly used in computing for sorting and searching data. These trees are a means of storing data hierarchically.

## What do you mean by Binary Search Tree?

A Binary Search Tree, also known as BST commonly, is a special kind of binary tree. This binary tree data structure is node-based, where nodes are arranged orderly.

## Can a binary tree be a binary search tree (BST)?

A binary search tree is also referred to as a sorted or ordered binary tree in computer science. BST is a rooted binary tree data structure.