greedy method report nhoel resos

7/26/2019 Greedy Method Report NHOEL RESOS

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Greedy Method

Reported by: NHOEL C. RESOS


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The Greedy MethodTechnique

The greedy methodis a general algorithmdesign paradigm, built on the following elements: confgurations: dierent choices, collections, or values

to nd

objective unction: a score assigned to congurations,which we want to either maximie or minimie

!t wor"s best when applied to problems with thegreedy-choiceproperty:

a globally#optimal solution can always be found by aseries of local improvements from a startingconguration$

The Greedy Method 2


3/20

%hat is a greedy algorithm&

Greedy algorithm: 'an algorithm alwaysma"es the choice that loo"s best at themoment(

)uman beings use greedy algorithms alot

)ow to maximie your nal grade of thisclass&

)ow to become a rich man&

)ow does a casher minimie the number ofcoins to ma"e a change&


4/20

%hat is a greedy algorithm&

To guarantee that a greedy algorithm iscorrect,

* things have to be proved:

Greedy-choice property: 'we canassemble a globally optimal solution byma"ing locally greedy+optimal choices$(

i$e$ The greedy choice is always part of certainoptimal solution

Optimal substructure: 'an optimal solutionto the problem contains within it optimalsolutions to subproblems$(

i$e$ global optimal solution is constructed fromlocal optimal solutions


5/20

%hat is Greedy -lgorithm&

!n the hard words: - greedy algorithmisan algorithm that follows theproblem solving heuristics of ma"ing the

locally optimal choice at each stagewiththe hope of nding a global optimum$

+src: http://en$wi"ipedia$org/wi"i/Greedy0algorithm

1implify: 2hoose the best choice that3reachable4 at current state


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CHARACTERISTICS AND

FEATURES To construct the solution in an optimal way. Algorithm

aintains two sets!

"#ne contains chosen items an$"The other contains re%ecte$ items.

&ree$y algorithms ma'e good local choices in the hope that

They result in!

"An optimal solution.

"Feasi(le solutions.

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C#NTINUED)

The gree$y algorithm consists o* *our +,- *unction.

A *unction that chec's whether chosen set o* items proi$e a

solution. A *unction that chec's the *easi(ility o* a set.

The selection *unction tells which o* the items is the most

promising.

An o(%ectie *unction! which $oes not appear e/plicitly! giesthe alue o* a solution.

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#0TII1ATI#N 0R#23ES

An optimi4ation pro(lem5

&ien a pro(lem instance! a set o* constraintsan$ anobjective function.

Fin$ a feasiblesolution *or the gien instance *or which theo(%ectie *unction has an optimal alue.

Either ma/imum or minimum $epen$ing on the pro(lem (eingsole$.A *easi(le solution that $oes this is calle$ optimalsolution.

8


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Continue$)

Feasible5A *easi(le solution satis*ies the pro(lem6s constraints

Constraints5The constraintsspeci*y the limitations on the re7uire$solutions.

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1ample 5sage of Greedy

6or better explanation we use oldsimple problem: Travelling 1alesman7roblem:


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T17

The 7roblem is how to travel from city -and visit all city on the map, then bac" tocity - again$

The rules: you only visit each city once andyou can4t pass through any traversed path$


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1olution:

6ind the shortest path from city -+start toany other city$

8ecause the nearest city is 8, so we go to 8

8-


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6rom 8, we nd any other city but

-+because - has been visited that hasnearest path$ 1o we choose 2:

9eep tuning on

8-

2


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6rom 2, we loo" to nearest city again,

but don4t loo" for - and 8, becauseboth has been visited$ 1o we choose ;$

1oon end

8-

2 ;


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-t this node+;, we can4t go to any city,because all neighbor of ; has beenvisited$ %e go bac" to rst city+-$

-nd that was how to solve T17 problem$

8-

2 ;


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1ample 5sage of Greedy


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The knapsack problemor rucksack problemis a problem in combinatorial optimiation: Given a set of items,each with a weight and a value, determine the number of each item to include in a collection so that the total

weight is less than or equal to a given limit and the total value is as large as possible$ !t derives its name from theproblem faced by someone who is constrained by a xed#sie "napsac"and must ll it with the most valuableitems$The problem often arises in resource allocationwhere there are nancial constraints and is studied in elds suchas combinatorics, computer science, complexity theory, cryptography, applied mathematics, anddaily fantasy sports$The "napsac" problem has been studied for more than a century, with early wor"s dating as far bac" as ?$@


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-dvantage of Greedy

Greedy is easy to be implemented$ust search the best choice from thecurrent state that 3reachable4 +has

any paths or any connections$

!n simple case, greedy often give youthe best solution$


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;rawbac" of Greedy

!n large and complex case, greedydoesn4t always give you the bestsolution, because it4s Hust search and

ta"e the best choice that you canreach from the current state$

!t ta"es longer time than any other

algorithms for big case of problem


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0R#S AND C#NS

0R#S5 They are easier to implement! they re7uire much less computing resources! they are much *aster to e/ecute.

&ree$y algorithms are use$ to sole optimi4ation pro(lems

C#NS5 Their only $isa$antage (eing that they not always reach the

glo(al optimum solution8 on the other han$! een when the glo(al optimum solution isnot reache$! most o* the times the reache$ su("optimalsolution is a ery goo$ solution.

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greedy method report nhoel resos

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