# Linear Search And Binary Search In Data Structure Pdf

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- 10 Major Difference Between Linear Search And Binary Search (With Comparison Table)
- 10 Major Difference Between Linear Search And Binary Search (With Comparison Table)
- Difference Between Linear Search and Binary Search
- Searching in Data Structure

Linear search and binary search are the two methods which are used in arrays for searching the elements. Searching is a process of finding an element within the list of elements stored in any order or randomly. The major difference between linear search and binary search is that binary search takes less time to search an element from the sorted list of elements. So it is inferred that efficiency of binary search method is greater than linear search. Another difference between the two is that there is a prerequisite for the binary search, i.

## 10 Major Difference Between Linear Search And Binary Search (With Comparison Table)

In computer science, a binary search tree is an ordered data structure that is logically visualized as a tree with a single root node and has two children, one on its right side and the other on its left. These are known as the left child and right child. These children further make subtrees until they reach leaf nodes.

It is also often referred to as an ordered binary tree or a sorted binary tree. Similarly, the value of the left child is still lesser than the value of the parent node. In short, nodes in the left subtree have lesser values than the parent node, and nodes in the right subtree have costs higher than the parent node. The programmers can quickly implement a binary search tree because it has an extremely organized structure and has lesser complexity.

Moreover, the users can perform the following operations using BST:. After building a BST, a search operation can be performed using a binary search algorithm. The above mentioned is a sample node of BST.

Inserting into BST is a simple process in which the function compares every new node value with the root node. If there does not exist any root node, the inserted key itself becomes the root node.

If there is already a root node present, the newly entered value is compared with the root and placed as the right or left child.

The insert function implementation of BST is as follows:. Search in BST can be implemented used both recursive and iterative methods. The function takes the key in both of these methods, which it needs to find and compare it with the root node. The deletion function works by finding the specified matching node in the tree to remove it later. After removing the desired node, it sorts the BST to avoid any dispositioning occurring in the tree.

There are the following scenarios considered while removing from a BST:. Here Min is the function that finds the minimum node from the tree. This algorithm removes any desired node from the tree while maintaining the balance in it. Unlike linear data structures such as an array, list, queue, stack, which the users can traverse only in one way, the BST can be traversed in many ways.

The most commonly used traversal methods are:. The binary search tree elements are divided into two portions, making the search operation relatively easy. Suppose the value that the user wants to search is located somewhere in the tree. In that case, the algorithm discards the half side of the tree, where the possibility of finding those particular elements is negligible. In addition to this, BST has the following advantages:.

Searching becomes much faster when it comes to working with BST. It does not need to traverse the whole tree and go through every element to find the desired solution. BST takes log2 n time complexity for a search in the worst-case scenario. In the above expression, n is the number of elements in the given sorted array. Insertion, deletion, searching, and updating operations are much faster in binary search trees than others because of their efficient way of storing values inside the nodes.

The coding of the binary search tree is relatively less complicated than other data structures in terms of implementation. The code is easily understandable, and debugging takes less time to find bugs in the implemented code. Ordered statistics are applicable in the BST. Basic operations are relative to the height of a tree. If the user searches for a particular value, the number of operations the user has to do is halved on each step. In the algorithm, this is called O log n.

The user starts with an input size of some sort, and over time that size gets smaller. A straight linear search denotes as O n. As the input size grows, it takes more time to run operations. O n abstractly is a degree line starting at starting point zero on a chart and moves right. The constant time is O 1. It does not matter how significant or small the input size is.

The operation takes place at the same time. For example, pop and push off of an array operate in continuous time. It implies that the user can start at values, the user in the tree, and get tree sub-heights. If the user passes it, the user recursively moves down the tree and adds the function calls to the performance stack other articles.

When the user gets to the bottom, the stack gets filled. The calls get executed as it compares the heights of the left and the right and increments by one. For searching element 1, the user has to navigate all elements in order 3, 2, 1. Thus, searching in a binary search tree has a worst-case complexity of O n. In general, the time complexity is O h , where h is the height of BST.

For inserting element 0, it must insert as the left child of 1. Therefore, the user needs to traverse all elements in order 3, 2, 1 to insert 0, which has the worst-case complexity of O n. In general, the time complexity is O h. For deletion of element 1, the user have to traverse all elements to find 1 in order 3, 2, 1. Therefore, deletion in a binary tree has the worst-case complexity of O n. The disadvantage is that the user should consistently implement a balanced binary search tree — AVL tree, Red-Black tree, Splay tree.

Otherwise, the cost of the operation may not be logarithmic and perverted into a linear search on an array. Sign Up Now. Zapier Plugin. Integromat Plugin. UiPath Plugin. Explore All Integrations.. API Documentation. Postman Collection.. On-Premise Version.

What is a Binary Search Tree? Following is a visual representation of a sample Binary Search Tree: Operations performed using Binary Search Trees The programmers can quickly implement a binary search tree because it has an extremely organized structure and has lesser complexity.

Traversal of the BST Unlike linear data structures such as an array, list, queue, stack, which the users can traverse only in one way, the BST can be traversed in many ways. The most commonly used traversal methods are: Breadth-first traversal: This type of traversal is also called level-order traversal.

In this traversal method, the function traverses all nodes at the same level first and then moves to the next level. In doing so, it traverses bottom level nodes at the end. The breadth-first traversal of the above BST gives 50, 40, 60, 35, 45, 55, and Depth-first traversal: The depth-first traversal methods are of three types: In-order traversal: This traversal method follows the pattern of the left, root, and then right.

Post-order traversal: The traversal pattern of the post-order method is left, right, and then root. Fast Operations Insertion, deletion, searching, and updating operations are much faster in binary search trees than others because of their efficient way of storing values inside the nodes. Easy Implementation The coding of the binary search tree is relatively less complicated than other data structures in terms of implementation.

Time Complexity Searching For searching element 1, the user has to navigate all elements in order 3, 2, 1. Insertion For inserting element 0, it must insert as the left child of 1. Deletion For deletion of element 1, the user have to traverse all elements to find 1 in order 3, 2, 1.

It employs a recursive approach, which requires more space in the stack adapter. Programming binary search algorithm is error-prone and arduous. The interface of binary search with memory hierarchy as caching is poor. Related Posts:. Python Dictionaries: Complete Tutorial A dictionary in Python is a collection of data that is unordered, indexed, and can be changed A dictionary contains [ Terms Of Use — Privacy Policy.

## 10 Major Difference Between Linear Search And Binary Search (With Comparison Table)

In computer science, a binary search tree is an ordered data structure that is logically visualized as a tree with a single root node and has two children, one on its right side and the other on its left. These are known as the left child and right child. These children further make subtrees until they reach leaf nodes. It is also often referred to as an ordered binary tree or a sorted binary tree. Similarly, the value of the left child is still lesser than the value of the parent node. In short, nodes in the left subtree have lesser values than the parent node, and nodes in the right subtree have costs higher than the parent node.

Linear search also referred to as sequential search is the simplest searching algorithm that searches for an element in a list in sequential order. It relies on the technique of traversing a list from start to end by exploring properties of all the elements that are found on the way. Linear sear is mostly very simple to implement and is practical when the list has only a few elements or when performing a single search in an un-ordered list list which the items are not sorted. Step 4- if both are not matched, then compare search element with the next element in the list. Step 5- Repeat steps 3 and 4 until search element is compared with last element in the list.

Also Read- Linear Search. Binary Search Algorithm searches an element by comparing it with the middle most element of the array. This time complexity of binary search remains unchanged irrespective of the element position even if it is not present in the array. Watch this Video Lecture. Next Article- Selection Sort. Get more notes and other study material of Design and Analysis of Algorithms.

## Difference Between Linear Search and Binary Search

Our Data Structure tutorial is designed for beginners and professionals. The data structure name indicates itself that organizing the data in memory. There are many ways of organizing the data in the memory as we have already seen one of the data structures, i. Array is a collection of memory elements in which data is stored sequentially, i. In other words, we can say that array stores the elements in a continuous manner.

In computer science , a binary search tree BST , also called an ordered or sorted binary tree , is a rooted binary tree whose internal nodes each store a key greater than all the keys in the node's left subtree and less than those in its right subtree. A binary tree is a type of data structure for storing data such as numbers in an organized way. Binary search trees allow binary search for fast lookup, addition and removal of data items, and can be used to implement dynamic sets and lookup tables.

### Searching in Data Structure

This chapter explores various searching techniques. The process of identifying or finding a particular record is called Searching. You often spend time in searching for any desired item. If the data is kept properly in sorted order, then searching becomes very easy and efficient. In this chapter, you will get to know the basic concepts of searching that are used in the data structure and case of programming also. Searching is an operation or a technique that helps finds the place of a given element or value in the list.

Not even a single day pass, when we do not have to search for something in our day to day life, car keys, books, pen, mobile charger and what not. Same is the life of a computer, there is so much data stored in it, that whenever a user asks for some data, computer has to search it's memory to look for the data and make it available to the user. And the computer has it's own techniques to search through it's memory fast, which you can learn more about in our Operating System tutorial series.

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#### Searching Techniques

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