## Serial Search of an Array, and Binary Search

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You want to find Samuel Jones in the local telephone book. Would you start at page 1 and then go on from there, page by page? You don't do this because you know an important fact about telephone books - the entries are in alphabetic order. So what you do is make a guess - J is about halfway down the alphabet and so you open the telephone book around half way. The page you see has names starting with N.

So you know J will be in the first serial and binary search of the book. Next you open a page about halfway down the first half - the page has 'H'.

So now Jones must be in the upper half of this section. You are carrying out a 'Binary search' algorithm. Serial and binary search that after only two guesses you are getting much closer to the answer.

Serial and binary search you were carrying out a serial search, you would still be at page 2. If the list is large and changing often, with items constantly being added or deleted, then the time it takes to constantly re-order the list to allow for a binary search might be longer than a simple serial search in the first place. If the list is large and static e. If the list is small then it might be simpler to just use a linear search 4.

If the list is random, then linear is the only way 5. If the list is skewed so that the most often searched items are placed at the beginning, then on average, a linear search might be better. Challenge see if you can find out one extra fact on this topic that we haven't already told you.

Click on this link: Revision resources include exam question practice and coursework guides. Topics include network systems, database, data communications, legal issues such as the Data Protection Act, measurement and control, the OSI model along with serial and binary search ethics and social effects of ICT at work and home. Sometimes, you may be doing a binary search without realising it. Example You want to find Samuel Jones in the local telephone book. No Is item less than criteria?

Is Binary searching better than serial searching? Challenge see if you can find out one extra fact on this topic that we haven't already told you Click on this link:

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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 of 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 middle , look 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 gives 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 searches , it may be worthwhile to sort the data so that you can perform binary searches.

You might 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 sorted 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 to 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 the 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.

Would you like to answer one of these unanswered questions instead? Email Sign Up or sign in with Google. What is the difference between Linear search and Binary search? 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 dictionary 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 requirement 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, worst , with 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.