Difference Between Binary Tree and Binary Search Tree

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In computer science, the Tree is the most popular and most efficient non-linear data structure that is commonly used for the representation of the hierarchical organization of data. As one goes through different types of trees, it’s also important to work on a large dataset. In computer science binary trees and binary search trees, also known as BSTs, are the two major categories of trees that are basic data structures. Both of them are critical factors for the efficient handling of databases.

Binary trees and binary search trees are both node-based. Despite using the term “binary,” they have various functions and have different structural guidelines and modes of operation. They’re useful in situations with data relationships since, in contrast to linear structures, they let data be arranged hierarchically. In this article, we will compare both Binary Trees and Binary Search Trees (BST), and learn about their implementation, operations, and some code examples.

What is a Binary Tree?

Binary Tree is one type of data structure that is non-linear and forms a middle center known as a root and nodes on the edges. Binary Tree is a tree structure wherein every parent has only up to two children, this has led to the use of words ‘Left Child’ and ‘Right Child’ in defining the two children. This type of non-linear data structure can have 0, 1, or 2 nodes for each non-terminal element. The nodes are the elements which have data in them and construct a tree-like structure with the root at the top.

In this tree, each node functions as a parent node or a child node. The root node is the highest in a binary tree. There can only be two child nodes for each parent node (root node). The appearance of binary trees can vary. A well-proportioned binary tree, referred to as an AVL tree, has a minimal variation in height between the left and right halves of each node. Users can have faster searches and more structured data possible by the balanced structure of an AVL tree in a data structure. Every node is made up of three components:

Data: The node’s stored value or data.

Left Child: A reference or pointer to the node’s left child.

Right Child: A reference or pointer to the node’s right child.

What is a Binary Search Tree (BST)?

A binary search tree or BST carries a special feature of various data structures as it is a form of the binary tree but follows a particular order of nodes, thus it is named as a binary search tree. Because the nodes are arranged in the BST in a particular sequence, this order allows easy retrieval from the node where a search request has been placed.

In this tree, a node’s left child has values that are less than the root or parent node, while its right child has values that are more than the root or parent node. BST makes insertion, deletion, and searching more efficient, and is a preferred option for implementing dynamic sets and lookup tables in databases.

A BST has the following properties:

A root node can have at most two children.

Both the right and left subtree must also be a binary search tree.

A node’s left subtree must contain node values smaller than the node, and the right subtree must contain node values larger than the node.

A Binary Search Tree does not allow duplicate nodes.

Operations in Binary Tree and Binary Search Tree

Operations in Binary Tree

A binary tree consists of three different operations in computer science, and are as follows:

Insertion: Nodes can be inserted at any available position. No property constraints are placed on where a node can be inserted.

Deletion: Nodes are removed randomly and there are no properties constrained in the BST’s deletion process.

Traversal:

Preorder Traversal (Root-> Left-> Right)- A preorder traversal starts at the root and traverses to the left child node followed by the right child node.

Inorder Traversal (Left -> Root ->Right )- In this type of traversal, which is called in order, we begin from the left child, backward to the root followed by the child that is located to the right.

Postorder Traversal (Left-> Right-> Root)- A postorder traversal starts at the leaf node and traverses left followed by the right child and then the root.

Breadth First Search (BFS) or Level-order Traversal- BFS involves the traversal of the tree by the children starting from the root to each one of the children on the same level.

Operations in Binary Search Tree

A BST consists of three different operations in computer science, and are as follows:

Insertion: During this operation, nodes are added in such a manner that the properties of the BST are not violated. For instance, the values of the child node to the left side of the parent node are expected to be lesser in value than the latter while the values of the child node to the right of the parent node are expected to be greater in value than the latter.

Deletion: Nodes are removed from the BST without violating the properties of the BST. In a more complicated way than deleting a binary tree, the structure of the tree is required to be maintained and sorted.

Traversal: In this operation, the whole tree is traversed in search of a target element. The properties of a BST must be satisfied while traversing a binary search tree.

Applications of Binary Tree and Binary Search Tree

Understanding the differences between a binary tree and a binary search tree will help you to learn about their different applications in every different field and domain:

Binary Tree

Binary trees are used as decision trees in machine learning for tasks involving regression and classification.

Binary trees, such as the Huffman coding tree, are used in data compression techniques.

In priority queues, heaps are a unique type of binary tree that is used to quickly access the largest or smallest member.

Compilers utilize binary trees, to parse and assess mathematical expressions.

A priority queue is another binary tree application that looks for the maximum or minimum in O(log n) time complexity.

They are used in Microsoft Excel editing programs and spreadsheets.

Many popular computer compilers, such as GCC and AOCL, use syntax trees to carry out arithmetic operations.

Binary trees are used for cache storage in the system and indexing segmentation at the database level.

File directories, organization charts, and other systems are modeled using hierarchical data representation.

Binary trees are used in computers to allocate memory rapidly by locating stuff more quickly.

Binary Search Tree

The primary uses of BST trees are efficient data retrieval and searching. The ability to search in O(log n) time is ensured in part by the binary search property.

Many databases employ binary search trees to search and index dispersed, massive reports.

Indexing is perfect for usage in file systems and databases because it offers effective search, insertion, and deletion operations.

Auto-complete features can be implemented via a binary search tree in a variety of contexts, including search engines. When typing, it can swiftly recommend completions based on the prefix entered.

The binary search technique is used by several modern file systems to store files in directories.

Compilers use symbol tables to store information about variables and functions for easy retrieval.

Priority queues can also be implemented with them. You may quickly extract the element with the highest (or lowest) priority by using the key that corresponds to each element’s priority.

Range queries are also implemented using BST for effective range-based searches, which is beneficial for various applications including big data searches, etc.

Binary search trees are a useful tool for addressing a variety of optimization issues.

It can be used to include decision trees in machine learning and artificial intelligence algorithms to forecast the models’ decisions and results.

It may assist in encrypting private and public keys in cryptography.

Binary Tree Implementation

Example

#include <iostream>
using namespace std;
// Define a tree node structure
struct TreeNode {
int val;
TreeNode* left;
TreeNode* right;
TreeNode(int value) {
val = value;
left = right = nullptr;
}
};
// Insert node in binary tree at first available position
TreeNode* insert(TreeNode* root, int value) {
if (root == nullptr) {
return new TreeNode(value);
}
if (root->left == nullptr) {
root->left = new TreeNode(value);
} else if (root->right == nullptr) {
root->right = new TreeNode(value);
} else {
insert(root->left, value);
}
return root;
}
// Inorder traversal
void inorder(TreeNode* root) {
if (root == nullptr) {
return;
}
inorder(root->left);
cout << root->val << " ";
inorder(root->right);
}
// Preorder traversal
void preorder(TreeNode* root) {
if (root == nullptr) {
return;
}
cout << root->val << " ";
preorder(root->left);
preorder(root->right);
}
// Postorder traversal
void postorder(TreeNode* root) {
if (root == nullptr) {
return;
}
postorder(root->left);
postorder(root->right);
cout << root->val << " ";
}
// Main function
int main() {
TreeNode* root = new TreeNode(40);
insert(root, 50);
insert(root, 60);
insert(root, 70);
cout << "Inorder traversal of Binary Tree: ";
inorder(root);
cout << "nPreorder traversal of Binary Tree: ";
preorder(root);
cout << "nPostorder traversal of Binary Tree: ";
postorder(root);
return 0;
}

Output:

Inorder traversal of Binary Tree: 70 50 40 60
Preorder traversal of Binary Tree: 40 50 70 60
Postorder traversal of Binary Tree: 70 50 60 40

#include <iostream>
using namespace std;
// Define a node structure for the BST
struct TreeNode {
int val;
TreeNode* left;
TreeNode* right;
TreeNode(int value) {
val = value;
left = right = nullptr;
}
};
// Insert a node in BST
TreeNode* insertNode(TreeNode* root, int value) {
if (root == nullptr) {
return new TreeNode(value);
}
if (value < root->val) {
root->left = insertNode(root->left, value);
} else if (value > root->val) {
root->right = insertNode(root->right, value);
}
return root;
}
// Search for a value in BST
TreeNode* searchNode(TreeNode* root, int key) {
if (root == nullptr || root->val == key) {
return root;
}
if (key < root->val) {
return searchNode(root->left, key);
}
return searchNode(root->right, key);
}
// Inorder traversal (for sorted output)
void inorder(TreeNode* root) {
if (root == nullptr) {
return;
}
inorder(root->left);
cout << root->val << " ";
inorder(root->right);
}
// Preorder traversal
void preorder(TreeNode* root) {
if (root == nullptr) {
return;
}
cout << root->val << " ";
preorder(root->left);
preorder(root->right);
}
// Postorder traversal
void postorder(TreeNode* root) {
if (root == nullptr) {
return;
}
postorder(root->left);
postorder(root->right);
cout << root->val << " ";
}
// Main function
int main() {
TreeNode* root = nullptr;
root = insertNode(root, 80);
insertNode(root, 90);
insertNode(root, 120);
insertNode(root, 130);
insertNode(root, 160);
insertNode(root, 180);
insertNode(root, 200);
cout << "Inorder traversal of Binary Search Tree: ";
inorder(root);
cout << "nPreorder traversal of Binary Search Tree: ";
preorder(root);
cout << "nPostorder traversal of Binary Search Tree: ";
postorder(root);
int target = 160;
if (searchNode(root, target)) {
cout << "nThe target value of" << target << "was found in the BST.";
} else {
cout << "nThe target value of" << target << "was not found in the BST.";
}
return 0;
}

Output:

Inorder traversal of Binary Search Tree: 80 90 120 130 160 180 200
Preorder traversal of Binary Search Tree: 80 90 120 130 160 180 200
Postorder traversal of Binary Search Tree: 200 180 160 130 120 90 80
The target value of 160 was found in the BST.

Key Differences Between Binary Tree and Binary Search Tree

The key differences between the two binary trees and binary search trees are as follows:

Basis

Binary Tree

Binary Search Tree

Definition

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

A BST is a non-linear data structure in which there are less than or equal to two children per node, and all left and right subtrees ought to be binary search trees.

Structure

It doesn’t need the nodes in a tree to have an ordered structure.

It is structured in an orderly manner. The left subtree’s value should be smaller than the node, while the right subtree’s value should be larger.

Data Organization

A binary tree can store any data without any restrictions.

A binary search tree stores the data in the sorted form because it is its property to ensure efficient searching.

Operations

A binary tree has three operations searching, inserting, and deletion.

A binary search tree has three operations searching, inserting, and deletion.

Types

A binary tree is of multiple types such as a Full Binary Tree, Complete Binary Tree, and Extended Binary Tree.

A binary search tree is of multiple types such as AVL Trees, T-trees, etc.

Duplicate values

A binary tree can have duplicate values.

A binary search tree cannot have duplicate values.

Balance

It can be balanced or unbalanced.

A binary search tree is known for optimal performance therefore, trees like AVL, or red-black trees are used.

Speed

The Binary Tree has slower performance in searching, insertion, or deletion as it is unordered.

The Binary Search Tree searches, inserts, and deletes components more quickly due to its ordered properties.

Hierarchical structure

A binary tree is a hierarchical data structure. It exists as a group of components called nodes.

The nodes are placed in a relative order, making it a variant of a Binary Tree.

Insertion operation

In this the nodes are inserted in any order, there is no rule or constraint for this.

Here, nodes are inserted according to their values, keeping in mind the BST property.

Search operation

In a binary tree, there is no particular order for searching a node as it requires a whole tree traversal.

Here, the search space is cut into half to be efficient while searching for a node in a BST.

Traversal

A binary tree provides various traversals such as Preorder, Inorder, Postorder, and Level-order traversal.

A binary search tree provides various traversals similar to BT but mostly the inorder traversal is used as it provides an ordered output.

Time complexity

In an unordered binary tree, the time complexity in cases: Insertion: O(N) in worst case Deletion: O(N) in worst case Search: O(N) in worst case

In a binary search tree, the time complexity in cases: Insertion: O(log N), when the tree is balanced. Deletion: O(log N), when the tree is balanced. Searching: O(log N), when the tree is balanced.

Space complexity

The space complexity of a binary tree is O(N).

The space complexity of a binary search tree is O(N).

Use cases

Binary tree has various use cases including decision trees, Huffman coding, priority queues or heaps, etc.

Binary search tree has various use cases including priority queues or heaps, file systems, autocomplete, features, etc.

Advantages and Disadvantages of Binary Tree and Binary Search Tree

The advantages of the binary tree are as follows:

Flexibility: It can represent many other hierarchical structures, not just based on the constraint of the node values.

Variety of Traversal: Flexibility provided by multiple traversals helps in processing data smartly using a binary tree.The disadvantages of the binary tree are as follows:

No Structure: In most structures, placing nodes in any order tends to make operations inefficient.

Highly Unbalanced: If not, it can also turn out to be heavily skewed, leading to degraded performance.

Efficient Searching: Search operations are very fast because of the ordering of keys, especially in a balanced BST.

Traversal: The In-order traversal of a BST requires sorted data, which is useful in many applications.The disadvantages of Binary Search Tree:

Unbalanced Trees: In the worst case, a BST can degenerate into a linked list, making operations inefficient, e.g., inserting data in ascending order. Requires

Balancing: More complex to implement compared to BSTs; AVL or Red-Black trees are necessary for maintaining efficiency.

Conclusion

The differences between binary trees and binary search trees have been covered in this article. Binary Trees and BSTs remain core data structures designed to meet different objectives, although each has different attributes. While a Binary Tree gives a flexible way of representing hierarchical data, the Binary Search Tree does this by introducing a specific ordering that facilitates efficient searching, insertion, and deletion operations.

These two structures have brought into perspective the possibility of a great number of computational problems to be addressed and are important in learning data structures for algorithms. These two structures play a large role in the possibility of solving a wide range of computational problems and are the basis of studying data structures and algorithms.

FAQs

What is the difference between a binary tree and a binary search tree?

A binary tree is a data structure where each node has at most two children. A binary search tree is a binary tree where the left child's value is less than the parent's, and the right child's value is greater.

How is a binary search tree faster?

Binary search trees are faster for search, insertion, and deletion operations because they are organized in a way that allows efficient searching.

Which traversal algorithms are employed on a binary search tree?

Traversing a binary search tree can be done using three possible ways: inorder traversal, preorder traversal, and postorder traversal.

What is a complete binary tree and a full binary tree, and how does it differ? Explain.

Any tree is said to be a full binary tree in which each of the nodes has children ranging from 0-2. A complete binary tree on the other hand is one whose all the nodes are filled to the maximum level.

What are the rules for BST?

There are several rules for a binary search tree (BST), but the one that is most important in data structure is the arrangement of the order of the nodes. The elements of a binary search tree are placed in a predetermined order. According to this rule, a right node’s value must exceed that of its parent node, and a left node’s value must be less than that of its parent node.

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