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Design and Analysis of Algorithm

Br u t e Fo r ce A l go r i t hm

D esign Tech n iq u e 

c Definition of Brute Force algorithm designtechnique

c Importance of Brute Force algorithm designtechnique

c Application of Brute Force algorithm designtechnique in the following:

 

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q Bubble sort

q Sequential search

q String matching

q Exhaustive search

c Sample problem using the application of

Exhaustive search

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Design and Analysis of Algorithm

Wh at i s B r u t e Fo r ce

A l go r i t h m D esi gnTechn ique?

c a straight forward approach to solving a problem,usually directly based on the problem statement

anddefinition of theconcepts involved. [LEV07]

c a simple algorithm design technique which worksthrough every possible answer until the correctone is found

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Design and Analysis of Algorithm

Wh at i s B r u t e Fo r ce

A l go r i t h m D esi gnTechn ique?

c Sample Application Problem:

q Finding all of the factors for number 625

c Possible Solut ion to the Problem:

q Divide every number up to 624 into 625

q For each number without remainders, the

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  .

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Design and Analysis of Algorithm

Wh at i s B r u t e Fo r ce

A l go r i t h m D esi gnTechn ique?

c Importance of using Brute Force algorithmdesign technique

q Always return the correct result

q Useful for testing the accuracy of fasteralgorithms

q Sometimes a particular problem can be solvedso quickly with a brute force method that it

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oesn ma e sense o was e me evs ng amore elegant solution.

q Applicable to a very wide variety of problems

• sorting, searching, string matching.

q It yields reasonable algorithms of at leastsome practical value with no limitation on

instance size.

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Design and Analysis of Algorithm

B r u t e Fo r ce A l go r i t h m

i n Sel ect i o n So r t  

c Sorting

q data are arranged in according to their values

c Selection sort:

q the smallest value in the unsorted portion of alist is selected and placed at the end of thesorted portion of the list

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Design and Analysis of Algorithm

B r u t e Fo r ce A l go r i t h m

i n Sel ect i o n So r t  

c Pseudo code for Selection sort algorithm

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Design and Analysis of Algorithm

B r u t e Fo r ce A l go r i t h m

i n Sel ect i o n So r t  

c Example of Selection sort algorithm

q Given the original unsorted list:

q Solution:

24 79 46 9 33 57

 

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 After Pass 1After Pass 1 

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Design and Analysis of Algorithm

B r u t e Fo r ce A l go r i t h m

i n Sel ect i o n So r t  

c Analysis of algorithm of Selection sort using theBrute Force approach

q the algorithm’s basic operation is the keycomparison List [ j] < List [min ]

q the number of times it is executed dependsonly on the array’s size

2  

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q the number of key swaps is only O(n) or, moreprecisely,n -1

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Design and Analysis of Algorithm

B r u t e Fo r ce A l go r i t h m

i n Bu b b l e So r t  

c Bubble Sort

q compares the adjacent elements of the list

and swap if elements are out of order

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Design and Analysis of Algorithm

c Pseudo code for Bubble sort algorithm

B r u t e Fo r ce A l go r i t h m

i n Bu b b l e So r t  

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Design and Analysis of Algorithm

c Example of Bubble sort algorithm

q Given the original unsorted list:

q Solution:

B r u t e Fo r ce A l go r i t h m

i n Bu b b l e So r t  

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After Pass 1 

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Design and Analysis of Algorithm

c Analysis of algorithm of Bubble sort using theBrute Force approach

q the outer loop runs n times and the onlycomplexity in this analysis in the inner loop

q the number of key comparisons for the bubblesort version given above is the same for allarra s of size n 

B r u t e Fo r ce A l go r i t h m

i n Bu b b l e So r t  

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Design and Analysis of Algorithm

c Analysis of algorithm of Bubble sort using theBrute Force approach

q  The number of key swaps depends on theinput.

B r u t e Fo r ce A l go r i t h m

i n Bu b b l e So r t  

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q For the worst case of decreasing arrays, it isthe same as the number of key comparisons.

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Design and Analysis of Algorithm

B r u t e Fo r ce A l go r i t h m

i n Seq u en t i a l Sear ch 

c Sequential search

q compares successive elements of a given list

with a given search key until either a match isencountered or the list is exhausted withoutfinding a match

c Pseudo code for Sequential search algorithm

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Design and Analysis of Algorithm

B r u t e Fo r ce A l go r i t h m

i n Seq u en t i a l Sear ch 

c Example of Sequential search algorithm

q Given the original unsorted list:

q Solution:

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Design and Analysis of Algorithm

B r u t e Fo r ce A l go r i t h m

i n St r i n g M at ch i n g  

c String matching

q process of finding the exact copy of pattern(s)

in the given text

c Pseudo code for Pattern matching algorithm

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Design and Analysis of Algorithm

B r u t e Fo r ce A l go r i t h m

i n St r i n g M at ch i n g  

c Example of Pattern matching algorithm

q Given a string of n characters, find a substring

of the text that matches the pattern, that is tofind i—the index of the leftmost character ofthe first matching substring in the text—suchthat:

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Solution:

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Design and Analysis of Algorithm

B r u t e Fo r ce A l go r i t h m

i n St r i n g M at ch i n g  

c Analysis of algorithm of Pattern matching usingthe Brute Force approach

q the algorithm shifts the pattern almost alwaysafter a single character comparison

q the algorithm may have to make all mcomparisons before shifting the pattern, andthis can ha en for each of the n -m + 1 tries

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Design and Analysis of Algorithm

B r u t e Fo r ce A l go r i t h m

i n Exh au st i ve sear ch 

c Exhaustive search:

q is a brute-force approach to combinatorial

problem

c Example of Exhaustive search

q  Traveling Salesman Problem

• find the shortest tour through a given set of n

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 returning to the city where it started

• in what order should he visit them to minimizethe distance travelled?

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Design and Analysis of Algorithm

B r u t e Fo r ce A l go r i t h mi n Exh au st i ve Sear ch 

c Determining the tour and the total cost asillustrated in the table below:

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