## Linear Search, Binary Search and other Searching Techniques

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Join Stack Overflow to learn, share knowledge, and build your career. A linear search looks down a list, one item at a time, without jumping. In complexity terms this is an O n search - the time taken to search the list gets bigger at the same rate as the list does. A binary search is when you start with the middle of a sorted list, and see whether that's greater than or less than the value you're looking for, which determines whether the value is in the first or second half of the list.

Jump to the half way through the sublist, and compare again etc. This is pretty much how humans typically look up a word in a dictionary although we use better heuristics, obviously - if you're looking for "cat" you don't start off at "M". In complexity terms this is an O log n search - the number of search operations grows more slowly than the list does, because you're halving the "search space" with each operation.

As an example, suppose you were looking for U in an A-Z list serial and binary search in data structure ppt letters index ; we're looking for the value at index Compare list[12] 'M' with 'U': Smaller, look further on.

Think of it as two different ways of finding your way in a phonebook. A linear search is starting at the beginning, reading every name until you find what you're looking for. A binary search, on the other hand, is when you open the book usually in the middlelook at the name on top of the page, and decide if the name you're looking for is bigger or smaller than the one you're looking for.

If the name you're looking for is bigger, then you continue searching the upper part of the book in this very fashion. A linear search works by looking at each element in a list of data until it either finds the target or reaches the end. This results in O n performance on a given list.

A binary search comes with the prerequisite that the data must be sorted. We can leverage this information to decrease the number of items we need to look at to find our target. We know that if we look at a random item in the data let's say the middle item and that item is greater than our target, then all items to the right of that item will also be greater than our target.

This means that we only need to look at the left part of the data. Basically, each time we search for the target and miss, we can eliminate half of the remaining items. This serial and binary search in data structure ppt us a nice O log n time complexity.

So you should never sort data just to perform a single binary search later on. But if you will be performing many searches say at least O log n searchesit may be worthwhile to sort the data so that you can perform binary searches. You serial and binary search in data structure ppt also consider other data structures such as a hash table in such situations.

A linear search starts at the beginning of a list of values, and checks 1 by 1 in order for the result you are looking for. A binary search starts in the middle of a sorted array, and determines which side if any the value you are looking for is on.

That "half" of the array is then searched again in the same fashion, dividing the results in half by two each time. Make sure to deliberate about whether the win of the quicker binary search is worth the cost of keeping the list serial and binary search in data structure ppt to be able to use the binary search.

Open the book at the half way point and look at the page. Ask yourself, should this person be serial and binary search in data structure ppt the left or to the right. Repeat this procedure until you find the page where the entry should be and then either apply the same process to columns, or just search linearly along the names on the page as before.

Linear search also referred to as sequential search looks at each element in sequence from the start to see if the desired element is present in the data structure. When the amount of data is small, this search is fast.

Its easy but work needed is in proportion to the amount of data to be searched. Doubling the number of elements will double the time to search if the desired element is not present. Binary search is efficient for larger array. In this we check the middle element. If the value is bigger that what we are looking for, then look in the first half;otherwise,look in the second half.

Repeat this until the desired item is found. The table must be sorted for binary search. It eliminates half the data at each iteration. If we have elements to search, binary search takes about 10 steps, linear search steps. Binary Search finds serial and binary search in data structure ppt middle element of the array.

Checks that middle value is greater or lower than the search value. If it is smaller, it gets the left side of the array and finds the middle element of that part. If it is greater, gets the right part of the array. It loops the operation until it finds the searched value. Or if there is no value in the array finishes the search. Also you can see visualized information about Linear and Binary Search here: Thank you for your interest in this question. Because it has attracted low-quality or spam answers that had to be removed, posting an answer now requires 10 reputation on this site the association bonus does not count.

Bill the Lizard k Please read the appropriate sections in your course material which, has hopefully, been selected and prepared by your instructor s. Failing that, a general wikipedia, c2 or google search can answer may of these sort of questions.

A linear search would ask: The binary search would ask: Binary search requires the input data to be sorted; linear search doesn't Binary search requires an ordering comparison; linear search only requires equality comparisons Binary search has complexity O log n ; linear search has complexity O n as discussed earlier Binary search requires random access to the data; linear search only requires sequential access this can be very important - it means a linear search can stream data of arbitrary size.

Jon Skeet k A better analogy would be the "guess my number between 1 and game" with responses of "you got it", "too high", or "too low". The dictionary analogy seems fine to me, though it's a better match for interpolation search. Dictionary analogy is better for me Apr 4 '14 at With serial and binary search in data structure ppt approach, the take away is sorting. So the importantly you must make sure the data is sorted before the binary search is started. If not you will be jumping all over the oceans without finding the value: If you do not mark the already tried ones, this can become worse.

So always do the sorting. Some Java based binary search implementation is found here digizol. Yes, the serial and binary search in data structure ppt that the input data is sorted is my first bullet point Mia Clarke 6, 3 41 I would like to add one difference- For linear search values need not to be sorted. But for binary search the values must be in sorted order. Pick a random name "Lastname, Firstname" and look it up in your phonebook.

Time both methods and report back! Prabu - Incorrect - Best case would be 1, worstwith an average of May 4 '09 at Linear Search looks through items until it finds the searched value. O n Example Python Code: O logn Example Python Code: Stack Overflow works best with JavaScript enabled.

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Search engine indexing collects, parses, and stores data to facilitate fast and accurate information retrieval. Index design incorporates interdisciplinary concepts from linguistics, cognitive psychology, mathematics, informatics , and computer science. An alternate name for the process in the context of search engines designed to find web pages on the Internet is web indexing.

Popular engines focus on the full-text indexing of online, natural language documents. Meta search engines reuse the indices of other services and do not store a local index, whereas cache-based search engines permanently store the index along with the corpus. Unlike full-text indices, partial-text services restrict the depth indexed to reduce index size. Larger services typically perform indexing at a predetermined time interval due to the required time and processing costs, while agent -based search engines index in real time.

The purpose of storing an index is to optimize speed and performance in finding relevant documents for a search query. Without an index, the search engine would scan every document in the corpus, which would require considerable time and computing power.

For example, while an index of 10, documents can be queried within milliseconds, a sequential scan of every word in 10, large documents could take hours. The additional computer storage required to store the index, as well as the considerable increase in the time required for an update to take place, are traded off for the time saved during information retrieval.

Search engine architectures vary in the way indexing is performed and in methods of index storage to meet the various design factors. A major challenge in the design of search engines is the management of serial computing processes. There are many opportunities for race conditions and coherent faults. For example, a new document is added to the corpus and the index must be updated, but the index simultaneously needs to continue responding to search queries.

This is a collision between two competing tasks. Consider that authors are producers of information, and a web crawler is the consumer of this information, grabbing the text and storing it in a cache or corpus. The forward index is the consumer of the information produced by the corpus, and the inverted index is the consumer of information produced by the forward index. This is commonly referred to as a producer-consumer model.

The indexer is the producer of searchable information and users are the consumers that need to search. The challenge is magnified when working with distributed storage and distributed processing. In an effort to scale with larger amounts of indexed information, the search engine's architecture may involve distributed computing , where the search engine consists of several machines operating in unison.

This increases the possibilities for incoherency and makes it more difficult to maintain a fully synchronized, distributed, parallel architecture. Many search engines incorporate an inverted index when evaluating a search query to quickly locate documents containing the words in a query and then rank these documents by relevance. Because the inverted index stores a list of the documents containing each word, the search engine can use direct access to find the documents associated with each word in the query in order to retrieve the matching documents quickly.

The following is a simplified illustration of an inverted index:. This index can only determine whether a word exists within a particular document, since it stores no information regarding the frequency and position of the word; it is therefore considered to be a boolean index.

Such an index determines which documents match a query but does not rank matched documents. In some designs the index includes additional information such as the frequency of each word in each document or the positions of a word in each document.

Such topics are the central research focus of information retrieval. The inverted index is a sparse matrix , since not all words are present in each document. To reduce computer storage memory requirements, it is stored differently from a two dimensional array. The index is similar to the term document matrices employed by latent semantic analysis.

The inverted index can be considered a form of a hash table. In some cases the index is a form of a binary tree , which requires additional storage but may reduce the lookup time. In larger indices the architecture is typically a distributed hash table.

The inverted index is filled via a merge or rebuild. A rebuild is similar to a merge but first deletes the contents of the inverted index. The architecture may be designed to support incremental indexing, [17] where a merge identifies the document or documents to be added or updated and then parses each document into words. For technical accuracy, a merge conflates newly indexed documents, typically residing in virtual memory, with the index cache residing on one or more computer hard drives.

After parsing, the indexer adds the referenced document to the document list for the appropriate words. In a larger search engine, the process of finding each word in the inverted index in order to report that it occurred within a document may be too time consuming, and so this process is commonly split up into two parts, the development of a forward index and a process which sorts the contents of the forward index into the inverted index.

The inverted index is so named because it is an inversion of the forward index. The forward index stores a list of words for each document. The following is a simplified form of the forward index:. The rationale behind developing a forward index is that as documents are parsed, it is better to immediately store the words per document.

The delineation enables Asynchronous system processing, which partially circumvents the inverted index update bottleneck.

The forward index is essentially a list of pairs consisting of a document and a word, collated by the document. Converting the forward index to an inverted index is only a matter of sorting the pairs by the words.

In this regard, the inverted index is a word-sorted forward index. Generating or maintaining a large-scale search engine index represents a significant storage and processing challenge. Many search engines utilize a form of compression to reduce the size of the indices on disk. Given this scenario, an uncompressed index assuming a non- conflated , simple, index for 2 billion web pages would need to store billion word entries. At 1 byte per character, or 5 bytes per word, this would require gigabytes of storage space alone.

This space requirement may be even larger for a fault-tolerant distributed storage architecture. Depending on the compression technique chosen, the index can be reduced to a fraction of this size. The tradeoff is the time and processing power required to perform compression and decompression. Notably, large scale search engine designs incorporate the cost of storage as well as the costs of electricity to power the storage.

Thus compression is a measure of cost. Document parsing breaks apart the components words of a document or other form of media for insertion into the forward and inverted indices. The words found are called tokens , and so, in the context of search engine indexing and natural language processing , parsing is more commonly referred to as tokenization. It is also sometimes called word boundary disambiguation , tagging , text segmentation , content analysis , text analysis, text mining , concordance generation, speech segmentation , lexing , or lexical analysis.

The terms 'indexing', 'parsing', and 'tokenization' are used interchangeably in corporate slang. Natural language processing is the subject of continuous research and technological improvement. Tokenization presents many challenges in extracting the necessary information from documents for indexing to support quality searching. Tokenization for indexing involves multiple technologies, the implementation of which are commonly kept as corporate secrets.

Unlike literate humans, computers do not understand the structure of a natural language document and cannot automatically recognize words and sentences. To a computer, a document is only a sequence of bytes. Computers do not 'know' that a space character separates words in a document. Instead, humans must program the computer to identify what constitutes an individual or distinct word referred to as a token.

Such a program is commonly called a tokenizer or parser or lexer. Many search engines, as well as other natural language processing software, incorporate specialized programs for parsing, such as YACC or Lex. During tokenization, the parser identifies sequences of characters which represent words and other elements, such as punctuation, which are represented by numeric codes, some of which are non-printing control characters. The parser can also identify entities such as email addresses, phone numbers, and URLs.

When identifying each token, several characteristics may be stored, such as the token's case upper, lower, mixed, proper , language or encoding, lexical category part of speech, like 'noun' or 'verb' , position, sentence number, sentence position, length, and line number.

If the search engine supports multiple languages, a common initial step during tokenization is to identify each document's language; many of the subsequent steps are language dependent such as stemming and part of speech tagging. Language recognition is the process by which a computer program attempts to automatically identify, or categorize, the language of a document. Other names for language recognition include language classification, language analysis, language identification, and language tagging.

Automated language recognition is the subject of ongoing research in natural language processing. Finding which language the words belongs to may involve the use of a language recognition chart.

If the search engine supports multiple document formats , documents must be prepared for tokenization. The challenge is that many document formats contain formatting information in addition to textual content. If the search engine were to ignore the difference between content and 'markup', extraneous information would be included in the index, leading to poor search results.

Format analysis is the identification and handling of the formatting content embedded within documents which controls the way the document is rendered on a computer screen or interpreted by a software program. Format analysis is also referred to as structure analysis, format parsing, tag stripping, format stripping, text normalization, text cleaning and text preparation. The challenge of format analysis is further complicated by the intricacies of various file formats.

Certain file formats are proprietary with very little information disclosed, while others are well documented. Common, well-documented file formats that many search engines support include:. Options for dealing with various formats include using a publicly available commercial parsing tool that is offered by the organization which developed, maintains, or owns the format, and writing a custom parser.

Some search engines support inspection of files that are stored in a compressed or encrypted file format. When working with a compressed format, the indexer first decompresses the document; this step may result in one or more files, each of which must be indexed separately. Commonly supported compressed file formats include:. Format analysis can involve quality improvement methods to avoid including 'bad information' in the index.

Content can manipulate the formatting information to include additional content. Examples of abusing document formatting for spamdexing:. Some search engines incorporate section recognition, the identification of major parts of a document, prior to tokenization. Not all the documents in a corpus read like a well-written book, divided into organized chapters and pages.

Many documents on the web , such as newsletters and corporate reports, contain erroneous content and side-sections which do not contain primary material that which the document is about. For example, this article displays a side menu with links to other web pages.