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Binary trees and binary search trees are fundamental hierarchical data structures used in computer science. Unlike linear structures, they allow data to be organized hierarchically, making them valuable in scenarios where data relationships exist.

Binary trees can have up to two child nodes per parent, providing flexibility in structuring data. Binary search trees, a specialized form, arrange nodes so that values to the left are smaller and those to the right are larger, facilitating efficient searching and sorting.

A Binary Tree is a Data Structure having a root node and at most two children nodes. Each of these children forms the left subtree and the right subtree. The end nodes or the leaf nodes have no children and the left and right children of a leaf node are pointed by a NULLpointer.

You can think of using binary trees in a database, like organizing your files into folders. Each folder (node) represents a record, and this setup makes it easy to find specific records quickly, even if you have a lot of data. It's like having a well-organized filing system for your information.

For example,

In the above example, each node has either 0,1 or 2 children. Therefore, this tree is a binary tree.

Node: A fundamental unit of a binary tree containing data and references to its left and right children

Root: The topmost node, serving as the tree's starting point

Parent Node: A node that has child nodes connected to it

Child Node: Nodes linked below a parent node

Leaf Node: A node with no children

Depth: The level or distance of a node from the root

Height: The maximum depth of the tree, i.e., the longest path from root to leaf

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What is a Binary Search Tree?

A binary search treeis a type of treedata structure where for every node, all the nodes to the left of this node have a value lesser than the current node’s value. All the nodes to the right of this node have a value greater than the current node’s value, along with the fact that both the left subtree and the right subtree are Binary Search Trees. Both the left and the right subtrees are also BSTs.

For example,

Above is an example of the binary search tree. You can observe that each node has less than or equal to two children. And theleft child’s value is always lesser than the node’s value, and the right child’s value is always greater than the node’s value.

Characteristics of Binary Search Tree

A binary search tree (BST) is a node-based binary tree data structure which has the following properties:

Each node contains a data element and two pointers, left and right, which point to its left and right child nodes, respectively

The left subtree of a node contains only nodes with keys lesser than the node's key

The right subtree of a node contains only nodes with keys greater than the node's key

The left and right subtree each must also be a binary search tree

Binary Tree vs Binary Search Tree

The following table highlights Differences between Binary tree and Binary search tree

Basis of comparison

Binary Tree

Binary search tree

Defination

It is a non-linear data structure in which each node has less than or equal to two children, and each of the left and right subtrees should also be a binary tree.

It is a non-linear data structure in which each node has less than or equal to two children, and each of the left and right subtrees should also be a binary search tree.

Order of Elements

Elements are stored without any specific order.

Elements are arranged in ascending order (left < parent < right)

Add its basis here

Elements in this tree are in any random order.

Elements in this tree are in a fixed order. The order is that for each node, its left child should have a value less than its value, and the right child should have a value greater than the node’s value.

Operations

The elements in a binary tree are not ordered, and therefore, operations like searching, inserting, and deletion takes longer time, i.e., O(n) time to execute.

The elements in a binary search tree are ordered, and therefore, operations like searching, inserting, and deletion takes a shorter time, i.e., O(logn) time to execute.

Types

There are four types of binary trees. These are Full Binary Tree, Complete Binary Tree, Perfect Binary Tree, and Extended Binary Tree.

There are three types of binary search trees. These are AVL trees, splay trees, and Tango trees.

Structure

Hierarchical structure with nodes having at most two children.

Hierarchical structure with nodes having at most two children.

Data Representation

Elements stored without any specific order.

Elements stored in an ordered manner.

Duplicate Values

Can accommodate duplicate values.

Typically does not accommodate duplicate values.

Time Efficiency

Operations may be slower due to lack of ordering.

Operations are faster due to ordered structure.

Complexity

Complexities can vary, especially for unbalanced trees.

Balanced BSTs maintain O(log n) complexities.

Speed

Slower for search and retrieval.

Faster for search and retrieval.

Hierarchy

No inherent hierarchy in terms of values.

Hierarchy based on values, facilitating ordered operations.

Usage

Used when order is not a concern, and hierarchy is sufficient.

Ideal for scenarios requiring ordered data and efficient operations.

What are the advantages of binary search tree over binary tree?

A binary search tree (BST) offers the advantage of efficient searching, insertion, and deletion operations due to its organized structure. It maintains elements in sorted order, enabling faster retrieval and updates compared to a standard binary tree.

Which searching technique is best?

The best searching technique depends on the specific context and requirements. Binary search is optimal for sorted data, offering O(log n) time complexity. For unsorted data or dynamic datasets, hashing or linear search may be more suitable, depending on the use case.

Why is binary search faster?

Binary search is faster because it systematically eliminates half of the remaining elements at each step. This logarithmic time complexity (O(log n)) reduces the number of comparisons significantly in large datasets, making it faster than linear search (O(n)) for sorted data.

Conclusion

In this article, we’ve discussed the differences between binary trees and binary search trees in detail and then we have discussed each of the one in details like Basic terminologies and characteristics. Finally some of the FAQs has been discussed.

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