L12 Searching Techniques (Student)

8/2/2019 L12 Searching Techniques (Student)

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Temasek Polytechnic School of Informatics & IT

L12 Searching Techniques

CGE2C10 Data Structures and Algorithms


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Temasek Polytechnic School of Informatics & IT 2

Quote of the day

Actions lie louder than words.Carolyn Wells


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Learning Objectives

At the end of this lesson, you should beable to

describe the steps of a sequential search

do a simulation by hand of a sequential search

describe the steps of a binary search

do a simulation by hand of a binary search


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Sequential Search

Also known aslinear searchorserialsearch.

How does it perform the search?

Step through the elements one at a timelooking for the desired element.

Stop

when the element is found or

when the search has examined all elements andcould not find the desired element


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Sequential Search Example

Search for the value 5 in the array, num:

Start the search at the first elementnum[0]:

4 8 3 5 9 10

0 1 2 3 4 5

num

4 8 3 5 9 10

0 1 2 3 4 5

num


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Sequential Search Example

Continue with the next element, num[1]:

4 8 3 5 9 10

0 1 2 3 4 5

num

4 8 3 5 9 10

0 1 2 3 4 5

num

4 8 3 5 9 10num

0 1 2 3 4 5

5 found!


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Sequential Search - Algorithm

What do we need to step through eachelement in the array?

What should the search method take asinput?

A loop (for, while, or do-while)

(1) The array, (2) item to be search


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Binary Search

Method: The elements are stored in a sorted array.

Divide and Conquer.

Algorithm:look at the middle element in the array

if it matches n, then finished

else

if n is less than the middle element,

search on the elements left to the middle

if n is greater than the middle element,

search on the elements right to the middle


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Binary Search Example I

Looking for the value 3 in the following array. Weuse high and low to mark the extreme ends ofthe array and mid to designate the middleelement.

1 3 4 6 7 10 13 15 16 190 1 2 3 4 5 6 7 8 9

low mid high

Is 3 ==num[mid](7) ?

num

(mid = (low + high) / 2)


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3 is not equal to 7, 3 is less than 7, move high to mid -1

1 3 4 6 7 10 13 15 16 19

0 1 2 3 4 5 6 7 8 9

low highmid

num Is 3 ==num[mid](3) ?


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3 is equal to 3, found it!

1 3 4 6 7 10 13 15 16 19

0 1 2 3 4 5 6 7 8 9

lowhighmid

Found 3!

num


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Binary Search Example II

Looking for the value 5 in the following array. Weuse high and low to mark the extreme ends of thearray and mid to designate the middle element.

1 3 4 6 7 10 13 15 16 190 1 2 3 4 5 6 7 8 9

low mid high


(mid = (low + high) / 2)


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5 is not equal to 7, 5 is less than 7, move high tomid-1

1 3 4 6 7 10 13 15 16 19

0 1 2 3 4 5 6 7 8 9

low highmid

numIs 5 ==num[mid](3) ?


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5 is not equal to 3, 5 is greater than 3, move low tomid+1

1 3 4 6 7 10 13 15 16 19

0 1 2 3 4 5 6 7 8 9

low mid high



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5 is not equal to 4, 5 is greater than 4, move low to

mid+1

1 3 4 6 7 10 13 15 16 19

0 1 2 3 4 5 6 7 8 9

mid

low high



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5 is not equal to 6, 5 is less than 4, move high tomid-1, high is less than mid, terminate search.

1 3 4 6 7 10 13 15 16 19

0 1 2 3 4 5 6 7 8 9

mid

lowhigh

num

Not found!


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Quiz

What are the 2 search techniquesintroduced?

What programming construct is used toimplement sequential search?

When is sequential search inefficient?


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References

[Lafore 2002] Robert Lafore, Data Structures and Algorithms inJava

Documents

L12 Searching Techniques (Student)