Trees are one of the most fundamental data structures. They are used to store and organize data.

A binary tree is a tree data structure composed of nodes, each of which has at most, two children, referred to as left and right nodes. The tree starts off with a single node known as the root.

A Binary Search Tree is a binary tree where each node contains a key and an optional associated value. It allows particularly fast lookup, addition, and removal of items.

The nodes are arranged in a binary search tree according to the following properties:

The left subtree of a particular node will always contain nodes with keys less than that node’s key.

The right subtree of a particular node will always contain nodes with keys greater than that node’s key.

The left and the right subtree of a particular node will also, in turn, be binary search trees.

Introduction to Binary Tree vs Binary Search Tree

A tree data structure where we have different nodes which are commonly referred to as child nodes that can be used for computational programming is called a Binary tree. We can access the nodes based on some value or any label. Also, this can be used as the representation of data for a bifurcating structure. Binary search tree is a sorted binary tree where binary searches can be done for faster results or in computational terms, for a faster lookup. We have different variants in the binary search tree and each has different orders to be sorted.

Key Differences of Binary Tree vs Binary Search Tree

The structure of both Binary tree and Binary search tree is the same but Binary tree is not ordered like Binary search tree. The data can be any type, be it numbers or strings in Binary tree. Also, if the node is on the left side, it is called the left child and if it is on the right side, it is called right child. The left child and right child of Binary search tree have conditions. Left child value should be less than parent node and right child value should be greater than the parent node. These conditions are not applicable in Binary tree.

In parallel tree, the subtrees can be moved from left to right or the other way around with no estimations or requesting. This is impossible in double pursuit tree. Regardless of whether we work out the information in the hubs, it won't be right to move left to right because of the limitations. Paired inquiry tree is the ideal rendition of information tree to do queries in information and to sort information in an effective way. Inclusion and cancellation of information likewise happen quicker than a double tree.

Binary search is used in algorithms where we search a specific item in the entire tree where the arrays are sorted. The search can happen only on sorted arrays. Binary search tree is otherwise called a sorted or ordered tree because the search can happen easily over here for any values. This binary search cannot be done on binary trees as it is not ordered.

Ordered operations are efficiently supported in both binary and binary search trees with search, insert, and traversal operations. It is not restricted that binary tree must be unordered always and thus any kind of operations can be done in binary tree. If the operation is ordered, then it can be done on the subtrees of binary search trees.

At the point when we do the crossing procedure on a double tree and on the off chance that it is in unordered structure, we get a twofold inquiry tree. The crossing procedure on parallel tree need not be in any request as it takes all types of crossing.

Double pursuit tree, amazing parallel tree, full paired tree, and so on are framed from the foundation of a twofold tree structure. Adjusted twofold inquiry trees like 2-3 trees, red-dark trees, and so forth are framed from paired pursuit trees. A large portion of these trees are stature adjusted.

Double pursuit trees design is to improve and deal with the hunt activity while doing the query action and this succeeds significantly in that reason. Double trees shaped the base and presently the upsides of parallel hunt trees and adjusted trees are shocking in the programming scene.

Head to Head Comparison Between Binary Tree vs Binary Search Tree (Infographics)

As it does not have any specific condition for its child nodes, it is useful in representing a hierarchical structure and not an ordered structure. Ancestral family hierarchy is an example of binary tree.

Since there is no ordering of data in Binary tree, duplicate values are allowed here.

We can perform operations on Binary tree but it takes longer time than binary search tree as the nodes are not in an ordered manner. The operations can be search, update, insert or delete.

The top node is called the root node which has left and right pointer. Left pointer has an address of the left subtree and right pointer has right subtree.

We can edit the values in nodes as per our need and still, it remains as a binary tree.

Rooted trees, full binary tree, degenerate tree, perfect and complete binary trees are the types of binary trees. If the height of binary tree ‘h’ has ‘2h-1’ nodes, it is called perfect binary tree.

We cannot say all Binary trees are binary search trees. Some may follow the condition but some may not.

The only condition for a binary tree is that the child nodes must be of number two. 

Binary search tree can be used to represent both hierarchical structure and an ordered structure based on its child node conditions.

There is an ordering of data. The value of the left node must be smaller than the parent node and the value of the right node must be higher than the parent node. This applies to subtrees as well. Hence, duplicate values are not allowed here.

The operations done on Binary search tree is done in a faster manner be it delete, update, insert or search because of the ordering of nodes. Lookups are done easily in binary search trees.

This itself is a subtree of binary tree. Only difference is in the ordering of right and left nodes. The organization is the same as binary tree with a root node, left, and right nodes.

If we edit the values of the binary search tree, it is important to check whether the values still meet the condition of left and right nodes. If not, it will be reduced to a binary tree.

The types of binary search tree are Red-black trees, T-trees, Splay trees, and AVL trees. All these trees have a relative order in the arrangement of nodes.

All Binary search trees are binary trees as it is the subset of binary trees and whether the condition is met, it is a binary tree always.

There are two main conditions in a binary search tree. The child nodes must be two and the left node should have values less than parent. Right nodes should have values greater than parent node.

In this blog, we will discuss the difference between Binary tree and binary search tree.

Binary Tree vs Binary Search Tree

A binary search tree in C++ is defined as a data shape that consists of the node-primarily based binary tree where each node consists of at most 2 nodes that are called infant nodes. This tree is also called an ordered or sorted tree. The usage of this idea, you may store numbers in an organized way and a binary tree helps in a quick search, upload, and/or delete operations to be executed on the dataset. Using the idea you possibly can implement dynamic sets and research tables. The shape of the binary tree permits skipping of half of the final tree accordingly leading to higher time complexity with the average being o(log n) for seek, upload, and/or delete operations. This technique is higher than the linear search due to its improved time complexity. In this newsletter, we will examine all of the standards of addition, seek and delete in the first-rate element.

Retrieve the value of root in a Binary Search tree:

Point to the left of the root in a Binary Search tree:

Point to the right of the root in a Binary Search tree:

How does the Binary search tree work in C++?

By now we understand that the Binary Search tree (BST) has a root node and at max 2 child nodes either on to left or right or both. The algorithm in a BST undergoes operations by comparison of values in the root node, and subsequently, it is lesser or more, the navigation in the tree takes place accordingly. In the working of Binary search tree, 3 operations are performed, namely:

Insert: In this operation, if the tree is empty, the first value that is inserted is always the root node, now when the next value is inserted, it compares if the value is greater than the root node or not. If greater it gets inserted to the right-hand side and if not, it moves to the left. If there is already a left side existing while inserting, it checks till the last node is hit and subsequently based on it being more or less, gets inserted into the corresponding location of the node.

Search: This is fairly an easy operation, where the number which needs to be searched is compared against the node values that are present. If the value that needs to be searched is more than the node value, the right side of the tree is searched and vice versa. In this way, we can avoid the other half of the tree which need not be searched as the binary tree is an ordered one. Till the end, if the node is NULL, we return that the value is not found.

Delete: Finally coming to the delete, which is one of the toughest amongst the three, but here we are to simplify it for you. When we delete, we might have 3 possibilities that we will discuss below one by one:

Case 1: The leaf node is to be deleted. When the number which needs to be deleted lies in the leaf, which means that there are no other values as a branch, we simply navigate to that location and delete the leaf node.

Case 2: One leaf node is attached to the root node. Here we navigate to the node which contains one leaf node, delete the node and assign that leaf node as the root node.

Case 3: The node that desires to be deleted has 2 leaf nodes connected to it. Right here we discover the in-order successor of the node, then replica all of the contents of the in-order successor observed using replacing the deleted node with the so as successor and pasting the contents of the in-order successor on the node which changed the deleted node. The in-order successor is the maximum value on the proper aspect of the tree from the node where the value is deleted from.

With the understanding of the above 3 processes, it will be easier to now look at some examples, to get the practical experience of the theory we just learned.

Here are the following examples mentioned below:

nodeBST* nodeBST ::insertFunc(nodeBST* root, int value)

root->rgt = insertFunc(root->rgt, value);

root->lft = insertFunc(root->lft, value);

void nodeBST ::traverseInOrder(nodeBST* root)

cout<<"\nThe sorted binary search tree is  "<< endl;

In this blog, we will discuss Binary search tree C++ & how it works?

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