Lecture 3 (Stud Copy) - Searching

8/3/2019 Lecture 3 (Stud Copy) - Searching

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Data Structures andAlgorithm Analysis

Searching

Part 1Prepared by : Harprith Kaur Randhawa

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Searching

Searching is the process of findingthe location of a target among a listof objects.

There are two basic searching

methods: sequential and binary

search.

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Searching

Sequential Search

The sequential search is normally used

when an array is not sorted. It starts atthe beginning of the array and searchesuntil it finds the data or hits the end ofthe list.

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Sequential Search Algorithm

Algorithm seqsearch(val list

val last

val target )

Locate the target in an ordered list of elements

Pre List must contain at least one element

last represents the last index

target contains the data to be located

Post if found assign found to true

if not found assign found to false

1. looker = 0

2. loop ( looker


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Variations on sequentialsearches

Sentinel Search

Probability Search

Ordered Search

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Sentinel Search

Algorithm sentinelsearch( val list val last val target )

1. list[last + 1] = target2. looker = 0

3. loop (target not equal list[looker] )looker = looker + 14 if ( looker


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Probability Search

Algorithm probabilitylsearch( val list val last val target )

looker = 0loop ( looker 0)

temp = list[looker 1]list[looker 1] = list[looker]list[looker] = templooker = looker - 1else

found = falsereturn foundend probabilitysearch

What is thedifferencebetween

probability searchand generalsequential search???

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Ordered SearchAlgorithm orderedsearch(val list

val last

val target )

if ( target < = list[last])

looker = 0

loop ( target > list[looker])

looker = looker + 1

2. else

looker = last

3. if ( target equal list[looker])

found = true4. else

found = false

return found

end of orderedsearch

What is thedifferencebetween orderedsearch andgeneral sequentialsearch ???

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Exercise:

Convert the sequential searchalgorithm into a program code.

You may use C++ or JAVA asthe programming language.

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Solutionimport javax.swing.JOptionPane;

public class Seq

{

public static void main(String args[])

{ int list[] = {7,8,5,4,3,2,1,9,6,10};

int last = 9;

int target;

target =

Integer.parseInt(JOptionPane.showInputDialog("Enter target value"));

if (seqsearch(list,last,target) )

JOptionPane.showMessageDialog(null, "The valuewas found in list ");

else

JOptionPane.showMessageDialog(null, "The valueis not in the list");

}

static boolean seqsearch(int list[], intlast, int target)

{int looker = 0;

boolean found;

while ( looker


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Binary Search

The sequential search algorithm is very slow. If wehave an array of 1000 elements, we must do 1000comparisons in the worst case. If the array is notsorted, the sequential search is the only solution. If

the array is sorted, we can use a more efficientalgorithm called the binary search.

The binary search starts by testing the data in the

element at the middle of the array to determine ifthe target is in the first or second half of thelist. If it is in the first half of the list, we do notneed to check the second half.

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Binary Search AlgorithmAlgorithm binarysearch ( val list

val end val target )

Search an ordered list using Binary Search

Pre list is ordered, it must contain at least one elementend is index to the largest element in the list

target is the value of element being sought

Post FOUND :Found set trueNOT FOUND :Found is set to false

Return found

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Binary Search Algorithm

first = 0

last = end

loop ( first list[mid] )first = mid + 1

3. else if ( target < list[mid] )

last = mid 1

4. elsefirst = last + 1

5.end if

4 end loop

5. if ( target equal list [mid] )

found = true

6. else

found = false

7. end if

8. return found

end binarysearch

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ALGORITHM EFFICIENCY

Conclusion :

Which searching technique ismore efficient ????

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Analyzing Search Algorithms

The basic loop for the sequential search is

shown as below:

while ( looker < last && target != list[looker]

++looker;

This is a linear algorithm. This search is known

as a linear search because the algorithm islinear, so its efficiency isO(n).

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Analyzing Search Algorithms

The binary search locates an item by repeatedlydividing the list in half. Its loop is

while ( first list[mid] )

first = mid + 1

else if ( target < list[mid])last = mid 1;

else

first = last + 1;

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This loops divides and it is thereforea logarithmic loop. So, the efficiency

is thus

O( log 2n)

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Exercise

Write a complete program that willimplement binary search to search anelement stored in an array.

You may write your program in C++ orJAVA code.

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Lecture 3 (Stud Copy) - Searching

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