Searching and Sorting
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Binary Search Algorithm Anthony Lin¹* Et Al
WikiJournal of Science, 2019, 2(1):5 doi: 10.15347/wjs/2019.005 Encyclopedic Review Article Binary search algorithm Anthony Lin¹* et al. Abstract In In computer science, binary search, also known as half-interval search,[1] logarithmic search,[2] or binary chop,[3] is a search algorithm that finds a position of a target value within a sorted array.[4] Binary search compares the target value to an element in the middle of the array. If they are not equal, the half in which the target cannot lie is eliminated and the search continues on the remaining half, again taking the middle element to compare to the target value, and repeating this until the target value is found. If the search ends with the remaining half being empty, the target is not in the array. Binary search runs in logarithmic time in the worst case, making 푂(log 푛) comparisons, where 푛 is the number of elements in the array, the 푂 is ‘Big O’ notation, and 푙표푔 is the logarithm.[5] Binary search is faster than linear search except for small arrays. However, the array must be sorted first to be able to apply binary search. There are spe- cialized data structures designed for fast searching, such as hash tables, that can be searched more efficiently than binary search. However, binary search can be used to solve a wider range of problems, such as finding the next- smallest or next-largest element in the array relative to the target even if it is absent from the array. There are numerous variations of binary search. -
Unit 5 Searching and Sorting Algorithms
Sri vidya college of engineering and technology course material UNIT 5 SEARCHING AND SORTING ALGORITHMS INTRODUCTION TO SEARCHING ALGORITHMS Searching is an operation or a technique that helps finds the place of a given element or value in the list. Any search is said to be successful or unsuccessful depending upon whether the element that is being searched is found or not. Some of the standard searching technique that is being followed in data structure is listed below: 1. Linear Search 2. Binary Search LINEAR SEARCH Linear search is a very basic and simple search algorithm. In Linear search, we search an element or value in a given array by traversing the array from the starting, till the desired element or value is found. It compares the element to be searched with all the elements present in the array and when the element is matched successfully, it returns the index of the element in the array, else it return -1. Linear Search is applied on unsorted or unordered lists, when there are fewer elements in a list. For Example, Linear Search 10 14 19 26 27 31 33 35 42 44 = 33 Algorithm Linear Search ( Array A, Value x) Step 1: Set i to 1 Step 2: if i > n then go to step 7 Step 3: if A[i] = x then go to step 6 Step 4: Set i to i + 1 Step 5: Go to Step 2 EC 8393/Fundamentals of data structures in C unit 5 Step 6: Print Element x Found at index i and go to step 8 Step 7: Print element not found Step 8: Exit Pseudocode procedure linear_search (list, value) for each item in the list if match item == value return the item‟s location end if end for end procedure Features of Linear Search Algorithm 1. -
Performance Enhancements in Large Scale Storage Systems
This document is downloaded from DR‑NTU (https://dr.ntu.edu.sg) Nanyang Technological University, Singapore. Performance enhancements in large scale storage systems Rajesh Vellore Arumugam 2015 Rajesh Vellore Arumugam. (2015). Performance enhancements in large scale storage systems. Doctoral thesis, Nanyang Technological University, Singapore. https://hdl.handle.net/10356/65630 https://doi.org/10.32657/10356/65630 Downloaded on 28 Sep 2021 07:25:14 SGT PERFORMANCE PERFORMANCE ENHANCEMENTS IN LARGE LARGE SCALE STORAGE SYSTEMS PERFORMANCE ENHANCEMENTS IN LARGE SCALE STORAGE SYSTEMS RAJESH ARUMUGAM RAJESH RAJESH VELLORE ARUMUGAM SCHOOL OF COMPUTER ENGINEERING 2015 2015 PERFORMANCE ENHANCEMENTS IN LARGE SCALE STORAGE SYSTEMS RAJESH VELLORE ARUMUGAM School Of Computer Engineering A thesis submitted to the Nanyang Technological University in partial fulfilment of the requirement for the degree of Doctor of Philosophy 2015 Acknowledgements I would like to thank my supervisors Asst. Prof. Wen Yonggang, Assoc. Prof. Dusit Niyato and Asst. Prof. Foh Chuan Heng for their guidance, valuable and critical feedback throughout the course of my investigations and research work. I am also grateful to Prof. Wen Yongang for guiding me in writing this thesis and some of the conference papers which were outcome of this research work. His valuable inputs have improved the quality of the writing and technical content significantly. The major part of the thesis are the outcome of the Future Data Center Technologies thematic research program (FDCT TSRP) funded by the A*STAR Science and Engineering Research Council. I am grateful to all my friends/colleagues in A*STAR Data Storage Institute who provided me the guidance and support in executing the project (titled ‘Large Scale Hybrid Storage System’) to a successful completion. -
Searching & Sorting
Searching & Sorting Dr. Chris Bourke Department of Computer Science & Engineering University of Nebraska|Lincoln Lincoln, NE 68588, USA http://cse.unl.edu/~cbourke [email protected] 2015/04/29 12:14:51 These are lecture notes used in CSCE 155 and CSCE 156 (Computer Science I & II) at the University of Nebraska|Lincoln. Contents 1. Overview5 1.1. CSCE 155E Outline..............................5 1.2. CSCE 156 Outline..............................5 I. Searching6 2. Introduction6 3. Linear Search6 3.1. Pseudocode..................................7 3.2. Example....................................7 3.3. Analysis....................................7 4. Binary Search7 4.1. Pseudocode: Recursive............................8 4.2. Pseudocode: Iterative.............................9 4.3. Example....................................9 4.4. Analysis....................................9 1 5. Searching in Java 11 5.1. Linear Search................................. 11 5.2. Binary Search................................. 11 5.2.1. Preventing Arithmetic Errors.................... 12 5.3. Searching in Java: Doing It Right...................... 13 5.4. Examples................................... 13 6. Searching in C 14 6.1. Linear Search................................. 14 6.2. Binary Search................................. 15 6.3. Searching in C: Doing it Right........................ 16 6.3.1. Linear Search............................. 16 6.3.2. Binary Search............................. 16 6.4. Examples................................... 17 II. Sorting -
Modified Binary Search Algorithm
International Journal of Applied Information Systems (IJAIS) – ISSN : 2249-0868 Foundation of Computer Science FCS, New York, USA Volume 7– No. 2, April 2014 – www.ijais.org Modified Binary Search Algorithm Ankit R. Chadha Rishikesh Misal Tanaya Mokashi Dept. of Electronics & Department of Computer Department of Computer Telecommunication Engg. Engineering. Engineering. Vidyalankar Institute of Vidyalankar Institute of Vidyalankar Institute of Technology Technology Technology Mumbai, India Mumbai, India Mumbai, India st ABSTRACT present in the 1 and last position of the intermediate array at This paper proposes a modification to the traditional binary every iteration. Modified binary search is also optimized for search algorithm in which it checks the presence of the input the case when the input element does not exist which is out of range amongst the range present in the array that is, if the element with the middle element of the given set of elements st at each iteration. Modified binary search algorithm optimizes input number is less the 1 element or it is greater than the last the worst case of the binary search algorithm by comparing element it certainly does not exist the given set of elements. the input element with the first & last element of the data set Since it checks the lower index and higher index element in along with the middle element and also checks the input the same pass, it takes less number of passes to take a decision number belongs to the range of numbers present in the given whether the element is present or not. data set at each iteration there by reducing the time taken by the worst cases of binary search algorithm. -
A Survey on Different Searching Algorithms
International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 07 Issue: 01 | Jan 2020 www.irjet.net p-ISSN: 2395-0072 A Survey on Different Searching Algorithms Ahmad Shoaib Zia1 1M.Tech scholar at the Department of Computer Science, Sharda University Greater Noida, India ---------------------------------------------------------------------***--------------------------------------------------------------------- Abstract - This paper presents the review of certain b) Internal searching: [3] Internal searching is that important and well discussed traditional search algorithms type of searching technique in which there is fewer with respect to their time complexity, space Complexity , amounts of data which entirely resides within the with the help of their realize applications. This paper also computer’s main memory. In this technique data highlights their working principles. There are different resides within the main memory on. types of algorithms and techniques for performing different tasks and as well as same tasks, with each having its own advantages and disadvantages depending on the 2. Exiting Search Algorithms type of data structure. An analysis is being carried out on 2.1 Binary Search different searching techniques on parameters like space and time complexity. Dependent upon the analysis, a It is a fast search algorithm [9] as the run-time complexity is comparative study is being made so that the user can Ο (log n). Using Divide and conquer Principle for it search choose the type of technique used based on the algorithm. This algorithm performs better for sorted data requirement. collection. In binary search, we first compare the key with the item in the middle position of the data collection. If there is a match, we can return immediately. -
Lecture Notes on Binary Search Trees
Lecture Notes on Binary Search Trees 15-122: Principles of Imperative Computation Frank Pfenning Andre´ Platzer Lecture 16 June 11, 2014 1 Introduction In this lecture, we will continue considering associative arrays as we did in the hash table lecture. This time, we will follow a different implementation principle, however. With binary search trees we try to obtain efficient insert and search times for associative arrays dictionaries, which we have pre- viously implemented as hash tables. We will eventually be able to achieve O(log(n)) worst-case asymptotic complexity for insert and search. This also extends to delete, although we won’t discuss that operation in lecture. In particular, the worst-case complexity of associative array operations im- plemented as binary search trees is better than the worst-case complexity when implemented as hash tables. 2 Ordered Associative Arrays Hashtables are associative arrays that organize the data in an array at an index that is determined from the key using a hash function. If the hash function is good, this means that the element will be placed at a reasonably random position spread out across the whole array. If it is bad, linear search is needed to locate the element. There are many alternative ways of implementing associative arrays. For example, we could have stored the elements in an array, sorted by key. Then lookup by binary search would have been O(log(n)), but insertion would be O(n), because it takes O(log n) steps to find the right place, but LECTURE NOTES JUNE 11, 2014 Binary Search Trees L16.2 then O(n) steps to make room for that new element by shifting all bigger elements over. -
Exponential Search
4. Searching Linear Search, Binary Search, Interpolation Search, Lower Bounds [Ottman/Widmayer, Kap. 3.2, Cormen et al, Kap. 2: Problems 2.1-3,2.2-3,2.3-5] 119 The Search Problem Provided A set of data sets examples telephone book, dictionary, symbol table Each dataset has a key k. Keys are comparable: unique answer to the question k1 ≤ k2 for keys k1, k2. Task: find data set by key k. 120 The Selection Problem Provided Set of data sets with comparable keys k. Wanted: data set with smallest, largest, middle key value. Generally: find a data set with i-smallest key. 121 Search in Array Provided Array A with n elements (A[1];:::;A[n]). Key b Wanted: index k, 1 ≤ k ≤ n with A[k] = b or ”not found”. 22 20 32 10 35 24 42 38 28 41 1 2 3 4 5 6 7 8 9 10 122 Linear Search Traverse the array from A[1] to A[n]. Best case: 1 comparison. Worst case: n comparisons. Assumption: each permutation of the n keys with same probability. Expected number of comparisons: n 1 X n + 1 i = : n 2 i=1 123 Search in a Sorted Array Provided Sorted array A with n elements (A[1];:::;A[n]) with A[1] ≤ A[2] ≤ · · · ≤ A[n]. Key b Wanted: index k, 1 ≤ k ≤ n with A[k] = b or ”not found”. 10 20 22 24 28 32 35 38 41 42 1 2 3 4 5 6 7 8 9 10 124 Divide and Conquer! Search b = 23. -
Data Structures and Algorithms
Lecture Notes for Data Structures and Algorithms Revised each year by John Bullinaria School of Computer Science University of Birmingham Birmingham, UK Version of 27 March 2019 These notes are currently revised each year by John Bullinaria. They include sections based on notes originally written by Mart´ınEscard´oand revised by Manfred Kerber. All are members of the School of Computer Science, University of Birmingham, UK. c School of Computer Science, University of Birmingham, UK, 2018 1 Contents 1 Introduction 5 1.1 Algorithms as opposed to programs . 5 1.2 Fundamental questions about algorithms . 6 1.3 Data structures, abstract data types, design patterns . 7 1.4 Textbooks and web-resources . 7 1.5 Overview . 8 2 Arrays, Iteration, Invariants 9 2.1 Arrays . 9 2.2 Loops and Iteration . 10 2.3 Invariants . 10 3 Lists, Recursion, Stacks, Queues 12 3.1 Linked Lists . 12 3.2 Recursion . 15 3.3 Stacks . 16 3.4 Queues . 17 3.5 Doubly Linked Lists . 18 3.6 Advantage of Abstract Data Types . 20 4 Searching 21 4.1 Requirements for searching . 21 4.2 Specification of the search problem . 22 4.3 A simple algorithm: Linear Search . 22 4.4 A more efficient algorithm: Binary Search . 23 5 Efficiency and Complexity 25 5.1 Time versus space complexity . 25 5.2 Worst versus average complexity . 25 5.3 Concrete measures for performance . 26 5.4 Big-O notation for complexity class . 26 5.5 Formal definition of complexity classes . 29 6 Trees 31 6.1 General specification of trees . 31 6.2 Quad-trees . -
Evaluating the Time Efficiency of the Modified Linear Search Algorithm
Proceedings of the World Congress on Engineering and Computer Science 2017 Vol I WCECS 2017, October 25-27, 2017, San Francisco, USA Evaluating the Time Efficiency of the Modified Linear Search Algorithm G. B. Balogun Abstract: In this study, a comparative analysis of three search it is inefficient when the array being searched contains large algorithms is carried out. Two of the algorithms; the linear and number of elements. binary are popular search methods, while the third, ‘The Bilinear Search Algorithm’ is a newly introduced one; A The algorithm will have to look through all the elements in modified linear search algorithm that combines some features order to find a value in the last element. The average in linear and binary search algorithms to produce a better probability of finding an item at the beginning of the array is performing one. These three algorithms are simulated using almost the same as finding it at the end. (Thomas and Devin, seventeen randomly generated data sets to compare their time 2017). efficiency. A c_Sharp (C#) code is used to achieve this by Nell, Daniel and Chip,(2016), tried to improve on the generating some random numbers and implementing their performance of the linear search by stopping a search when working algorithms. The internal clock of the computer is set an element larger than the target element is encountered, to monitor the time durations of their computations. The result but this is based on the condition that the elements in the shows that the linear search performs better than the binary search. This agrees with the existing assertion that when a data array be sorted in ascending order. -
Comparative Analysis on Sorting and Searching Algorithms
International Journal of Civil Engineering and Technology (IJCIET) Volume 8, Issue 8, August 2017, pp. 955–978, Article ID: IJCIET_08_08_101 Available online at http://http://iaeme.com/Home/issue/IJCIET?Volume=8&Issue=8 ISSN Print: 0976-6308 and ISSN Online: 0976-6316 © IAEME Publication Scopus Indexed COMPARATIVE ANALYSIS ON SORTING AND SEARCHING ALGORITHMS B Subbarayudu Dept. of ECE, Institute of Aeronautical Engineering, Hyderabad, India L Lalitha Gayatri Dept. of CSE, Stanley College of Engineering & Tech. Hyderabad, India P Sai Nidhi Dept. of CSE, Stanley College of Engineering & Tech. Hyderabad, India P. Ramesh Dept. of ECE, MLR Institute of Technology, Hyderabad, India R Gangadhar Reddy Dept. of ECE, Institute of Aeronautical Engineering, Hyderabad, India Kishor Kumar Reddy C Dept. of CSE Stanley College of Engineering & Tech. Hyderabad, India ABSTRACT Various algorithms on sorting and searching algorithms are presented. The analysis shows the advantages and disadvantages of various sorting and searching algorithms along with examples. Various sorting techniques are analysed based on time complexity and space complexity. On analysis, it is found that quick sort is productive for large data items and insertion sort is efficient for small list. Also, it is found that binary search is suitable for mid-sized data items and is applicable in arrays and in linked list, whereas hash search is best for large data items, exponential search can be used for infinite set of elements. Key word: Algorithm, Searching, Sorting, Space Complexity, Time Complexity Cite this Article: B Subbarayudu, L Lalitha Gayatri, P Sai Nidhi, P. Ramesh, R Gangadhar Reddy and Kishor Kumar Reddy C, Comparative Analysis on Sorting and Searching Algorithms. -
ANALYSIS on SEARCHING ALGORITHMS JASC: Journal Of
JASC: Journal of Applied Science and Computations ISSN NO: 1076-5131 ANALYSIS ON SEARCHING ALGORITHMS N.Pavani, M.Sree Vyshnavi, K. Sindhu Reddy, Mr. C Kishor Kumar Reddy and Dr.B V Ramana Murthy. Stanley College of Engineering and Technology for Women, Hyderabad [email protected], [email protected], [email protected], [email protected], [email protected] ABSTRACT Searching algorithms are designed to check form an element and retrieve an element from array from any of data structure where it is stored. Various searching techniques are analyzed based on the time a space complexity. There are two types of searching, internal searching and external searching. The analysis shows the advantages and disadvantages of various searching algorithms. On analysis it is found out that binary search is suitable for mid-sized data items in arrays and linked list whereas hash search is best for the larger data items. Keywords: Algorithm, Searching, Internal and External Searching, Time complexity. 1. INTRODUCTION Searching is a technique which programmers are always passively solving. Not even asingle day pass by, when we do not have to search for something in our daily life. Whenever a user asks for some data, computer has to search its memory to look for that data and should make it available to the user. And the computer has its own techniques to search through its memory very fast. To search an element in a given array, there are few algorithms available here: ⦁ Linear Search ⦁ Exponential Search ⦁ Ternary Search ⦁ Binary Search ⦁ Interpolation Search ⦁ Hash Search Volume VI, Issue I, January/2019 Page No:654 JASC: Journal of Applied Science and Computations ISSN NO: 1076-5131 1.1.