# Binary And Linear Search Pdf

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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.

## Introduction to Searching Algorithms

Search operation is involved in day to day life. Computers are used to process bulk amount of data and searching information from these large database is crucial operation. Almost all computing applications involve searching. Two widely used and the most fundamental searching techniques are linear search and binary search. Before thinking about any searching techniques it is necessary to determine the organization of data which is termed as data structure.

How the data structure is organized is also the responsible for what kind of operations can be performed on data structure. Linear search can be applied to both types of arrays static and dynamic as well as linked list, but binary search can not be directly applied to linked list. Here an effort is made to implement binary search for linked list. Also comparison of array and linked list, comparison of static and dynamic array and comparison of linear search and binary search is described.

Various search algorithms are developed to deal with various data structures. It is not possible to directly implement binary search on linked list. So the solution is developed to apply binary search on linked list. That means compilers must aware about the information needed for memory allocation. Whereas linked linear list is dynamic in nature.

Following is the detailed comparison between array and linked list. This implies the size of array must be given prior to compilation whereas size of linked list is changed during the life-span of it.

For this reason array can be used only when the number of elements are known otherwise linked list is the best choice. Insertion and deletion operation of an element requiresshifting of elements which is the time consuming process whereas the same operations can be efficiently implemented using linked list. If an element is found then index, flag signal or value can be returned or processed, otherwise special index as -1 or flag signal can be returned.

It is called linear or sequential because this algorithm scans the elements in a list in linear manner or in sequence by scanning one by one element in a list.. The best case time is O 1 which is constant and element is found at the first position. In general time required by linear search is O N as Big-O notation is simply determines the highest order terms and ignores the coefficients and lower order terms.

Due to its simplest implementation it can be applied to array list as well as all types of linked lists. So it is easy to implement but it is not useful when the size of the list is too large. Because the time require is proportional to total number of elements N. So it is useful when we have small size of an array or a linked list but require more time when an array becomes large.

The algorithm of linear search technique is listed below which finds the location of the search term if found otherwise the message of element not found is displayed.

Exit Above algorithm searches vector starting from the first element upto the last element in linear manner for the search element X. Each time an index variable I is increment to search next element.

If an element does not exist in the vector then entire vector is scanned and then result in element not found. The same algorithm can be applied to linked list whose typical node structure contains information field s and one pointer field that points to the next node. The last node's pointer field contains NULL means there are no more elements and which is the last node in the list. Following algorithm is again the linear search algorithm which search the linked list..

This algorithm searches the linked list for a given value of X. If X is found in linked list then it displays the message that element is found otherwise it displays the message that element is not found. The pointer SAVE is updated each time to point to the next node in the linked list. The time required by both of the above algorithms is O N that is linearly proportional to total number of elements in the list.

In such situation binary search algorithm is quite useful. The binary search algorithm can be applied to an array whose elements are to be required in sorted form [1] [2]. Each iteration of binary search narrows the search interval by half of the search interval of its previous iteration. The time required by binary search is O log 2 N [1] [5]. Variation of binary search can be possible by selecting a random element between lower and upper bound.

Above algorithm searches an element X by first examining the center element of the vector K. If it is found then search process is completed otherwise it will check for the element whether exist in first half or the second half by testing the condition.

More [6] Both the algorithms are quite useful depending on the application. If array is the data structure and elements are organized in sorted order then binary search is preferred for fast searching. If linked list is the data structure no matter how the elements are arranged, linear search is preferred due to unavailability of direct implementation of binary search algorithm.

We require other data structure to obtain the effect of binary search or we require to design the variation of binary search algorithm that can work on linked list too because binary search is faster in execution than a linear search [6]. The original Binary search algorithm can not be applied to linked list because linked list by nature is dynamic and it is not known where the middle element is actually allocated.

So, some of the efforts are required to apply binary search over a linked list to obtain the advantages. If the size is only a matter then the solution is to implement dynamic array. The size of dynamic array can be determined during execution time. The both types of arrays are discussed with different view point. Static arrays are compile-time array declaration and size is known at compilation time while dynamic arrays are determined during run time and its size is determined when the program is actually run.

Dynamic array is varying and size is determined during execution of a program. Further, the size of dynamic array can be altered during execution time with some more efforts and processing is taken. If we loss the pointer pointing to the dynamically allocated array resulting in to garbage array to which we have no access at all. Processing of both the static and dynamic arrays are different but both the searching algorithms that is linear and binary search can be implemented by using of either type of array.

For dynamic array, total number of elements must be kept up to date which is not necessary in static array because the size of the array is already known. But in dynamic array it must be updated when an element is inserted or deleted. This algorithm can not be directly implemented to linked list [2]. Although we can obtain the benefits of binary search by organizing the same array elements in non linear data structure tree [8].

Binary search tree is a non-linear data structure which searches an element in equal amount of time as binary search requires O log 2 N [1] [5]. But it is difficult to maintain and manipulate binary search tree. The second option to implement binary search on linked list is to copy all the elements of linked list into either sorted array or a binary search tree. This option is again not practical for maintenance of the data as each time searching will be faster but require more processing of creating and copy elements.

Extra overload will be faced by processor in obtaining the benefits of binary search. The third alternative is to derive new algorithm that can equally perform binary search on linked list by making alternative changes in original binary search algorithm. Directly it is not possible to implement binary search over linked list due to dynamic memory allocation and searching center element through address calculation.

So we keep track of all the addresses of each node in a separate array of pointer. FIRST is the pointer to the first node of the linked list. Linked list is organized in order of INFO field in increasing order of value.

PTR is an array of pointer whose first element pointing to first node of linked list, second element pointing to second node of the linked list and so on.

N is the total number of element in the list. This algorithm searches the linked list structure for a given element whose value is given by X. Further it is also possible to apply binary search on linked list by making necessary modifications to original binary search algorithm.

The selectiom of searching algorithm can be based on the data structure on to which it is applied and which operations are required more. Balance is required between search and maintanance of a data structure.

It is also possible to combine two searching algorithms and obtaining benefits of both. For example binary search algorithm applied for linked list say primary linked list in which each node may represent another linked list say secondary linked list which can be searched using linear search. Hashing technique is another alternate for direct searching an element from a table without concerning where the element is actually allocated.

Different applications require different searching techniques base on the insertion, deletion, searching and maintenance operations. Time required to search an element if exist or to determine that element is not found depends on the total number of elements in the list. So the time complexity of linear search isO N [1][9]. Worst case requires N comparison if an element is found at the last position N or an element does not exist in the list. Table : 1:Comparison of Linear search and Binary searchSr.

The function returns the index of the linked list element if the search is successful and returns 0 otherwise. Related Papers. By Jay karavadra.

## Binary Search Data Structure Using C Book

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. Although both the searching methods use different techniques which are discussed below.

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

In computer science , a linear search or sequential search is a method for finding an element within a list. It sequentially checks each element of the list until a match is found or the whole list has been searched. A linear search runs in at worst linear time and makes at most n comparisons, where n is the length of the list. Linear search is rarely practical because other search algorithms and schemes, such as the binary search algorithm and hash tables , allow significantly faster searching for all but short lists. A linear search sequentially checks each element of the list until it finds an element that matches the target value.

### Difference Between Linear Search and Binary Search

Binary search tree is a data structure that quickly allows us to maintain a sorted list of numbers. It is called a binary tree because each tree node has a maximum of two children. Basic concepts: Introduction to data structures, classification of data structures, operations on data structures, abstract data type, algorithms, different approaches to design an algorithm, recursive algorithms; Searching techniques: Linear search, binary search and Fibonacci. Binary Search is a searching algorithm for finding an element's position in a sorted array. In this approach, the element is always searched in the middle of a portion of an array.

// Search for a matching String val in the array vals. // If found, return index. If not found, return int eSearch(String val, String[] vals) {. // Loop over all items in the​.

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.

Пустой номер. Наверное, уплыли на уик-энд с друзьями на яхте. Беккер заметил, что на ней дорогие вещи. - И у тебя нет кредитной карточки. - Есть, но отец ее заблокировал.

Прихожане могли понять нетерпение этого человека, стремившегося получить благословение, но ведь существуют строгие правила протокола: подходить к причастию нужно, выстроившись в две линии. Халохот продолжал двигаться. Расстояние между ним и Беккером быстро сокращалось. Он нащупал в кармане пиджака пистолет. До сих пор Дэвиду Беккеру необыкновенно везло, и не следует и дальше искушать судьбу. Пиджак защитного цвета от него отделяли теперь уже только десять человек. Беккер шел, низко опустив голову.

Все повернули головы к Сьюзан Флетчер, которая выпрямилась и поднялась со стула. Лицо ее побелело, глаза не отрываясь смотрели на застывший кадр, демонстрировавший неподвижное тело Дэвида Беккера, залитое кровью, брошенное на пол мини-автобуса. - Вы его убили! - крикнула .

То, что там происходит, серьезно, очень серьезно. Мои данные еще никогда меня не подводили и не подведут.  - Она собиралась уже положить трубку, но, вспомнив, добавила: - Да, Джабба… ты говоришь, никаких сюрпризов, так вот: Стратмор обошел систему Сквозь строй.

И что. Хейл понимал: то, что он сейчас скажет, либо принесет ему свободу, либо станет его смертным приговором. Он набрал в легкие воздуха. - Вы хотите приделать к Цифровой крепости черный ход. Его слова встретило гробовое молчание.

Она оказалась бессмысленной, потому что он ввел задание в неверной последовательности, но ведь Следопыт работал. Но Сьюзан тут же сообразила, что могла быть еще одна причина отключения Следопыта. Внутренние ошибки программы не являлись единственными причинами сбоя, потому что иногда в действие вступали внешние силы - скачки напряжения, попавшие на платы частички пыли, повреждение проводов. Поскольку за техникой Третьего узла следили самым тщательным образом, она даже не рассматривала такую возможность.

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