searching (dastal)

8/14/2019 Searching (DASTAL)

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Searching


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Searching algorithm is an algorithm that takes a problem as input

and returns a solution to the problem, usuallyafter evaluating a number of possible solutions


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Sample searching algorithm Sequential Search Algorithm

Binary Search Algorithm


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Sequential Search It operates by checking every element of a list

one at a time in sequence until a match is found

a.k.a Linear Search

Two Types of Sequential Seach Sequential Search of an unordered file

Sequential Search of an ordered file


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Sequential Search of an unordered file Basic algorithm:

Getthe search criterion (key)Get the first record from the file

While ( (record != key) and (still more records) )

Get the next record

End while


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Sequential Search of an ordered file

Basic algorithm:

Getthe search criterion (key)Get the first record from the file

While ( (record < key) and (still more records) )

Getthe next record

End while

If( record = key )

Then success

Else there is no match in the file

End else


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Sequential Search algorithm1. Set found = false

2. Set loc = 03. While loc


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Binary Search Search a sorted arrayby repeatedly dividing the

search interval in half. Begin with an intervalcovering the whole array. If the value of the

search keyis less than the item in the middle of

the interval, narrow the interval to the lower half.

Otherwise narrow it to the upper half.

Repeatedly check until the value is found or theinterval is empty.


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Specification for Binary Search Purpose: Perform a binary search of an ordered

list

Precondition: the list elements are ascending

order and are stored in array. The list has n

elements, where n is a positive integer. Item isthe value to be found and has the same type as

the array elements.

Postcondition: found is true and mid is theposition of item if the search is successful;

otherwise found false


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How a Binary Search Works

Always look at the centervalue. Each time you get to

discard half of the remaininglist.


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How Fast is a Binary Search?

11 items in the list took 4 tries 1st try - list has 16 items 2nd try - list has 8 items

3rd try - list has 4 items

4th try - list has 2 items

5th try - list has 1 item


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How Fast is a Binary Search? (cont)

List has 250 items 1st try - 125 items 2nd try - 63 items 3rd try - 32 items 4th try - 16 items

5th try - 8 items 6th try - 4 items 7th try - 2 items 8th try - 1 item

List has 512 items 1st try - 256 items 2nd try - 128 items 3rd try - 64 items 4th try - 32 items 5th try - 16 items 6th try - 8 items 7th try - 4 items 8th try - 2 items 9th try - 1 item


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Whats the Pattern?

List of 11 took 4 tries




32 = 25 and 512 = 29

8 < 11 < 16 23 < 11 < 24

128 < 250 < 256 27 < 250 < 28


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A Very Fast Algorithm!

How long will it take to find an item in a list 30,000items long?

210 = 1024 213 = 8192

211 = 2048 214 = 16384

212

= 4096 215

= 32768

So, it will take only 15 tries!


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End

searching (dastal)

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