3. Greedy Method - Introduction
Summary
TLDRThe script introduces the greedy method, a strategy for solving optimization problems that seek either a minimum or maximum result. It explains the concept of feasible and optimal solutions, emphasizing that while there can be multiple feasible solutions, there is typically only one optimal solution. The greedy method involves solving a problem in stages, selecting the most beneficial option at each step, and building towards an optimal solution. Examples given include choosing the best car based on features and hiring the best candidate through a series of tests, illustrating how the greedy approach can save time and resources by not examining every possible option.
Takeaways
- đ The greedy method is a problem-solving strategy used for optimization problems, similar to divide and conquer.
- đŻ Optimization problems are those that require either a minimum or maximum result, such as minimizing cost or maximizing efficiency.
- đ The greedy method involves solving a problem in stages, selecting the most optimal choice at each step based on the current state, hoping to find a global optimum.
- đ Feasible solutions are those that meet the constraints of the problem, while an optimal solution is the best feasible solution that achieves the problem's objective.
- đŠ The method assumes that by making the locally optimal choice at each stage, the globally optimal solution will be reached, which is not always the case.
- đ An example given is choosing the best car based on features without necessarily comparing every car model available, demonstrating a greedy approach to decision-making.
- đą Another example is hiring the best candidate from a large pool by filtering through stages of interviews, which is a time-efficient but potentially greedy method.
- đ The script explains that the greedy method can be faster and more practical than exhaustive methods but may not always guarantee the best solution.
- đ The greedy approach is contrasted with other strategies like dynamic programming and divide and conquer, which may be more suitable for certain types of optimization problems.
- đ The script emphasizes understanding the greedy method's approach and application through various examples to recognize when it can be effectively used.
Q & A
What is the greedy method?
-The greedy method is a strategy for solving optimization problems by making a sequence of choices, each of which seems to be the best at that moment. It involves solving a problem in stages, selecting the most optimal choice at each step, and hoping that these local optimizations lead to a global optimization.
What are optimization problems?
-Optimization problems are those that require either a minimum or maximum result. They demand an optimal solution, which is the best possible outcome in terms of either minimizing or maximizing a certain objective.
What is the difference between a feasible solution and an optimal solution?
-A feasible solution is one that satisfies the constraints of a problem. An optimal solution, on the other hand, is not only feasible but also provides the best result, either the minimum or maximum, according to the problem's objective.
Why is the greedy method considered 'greedy'?
-The greedy method is called 'greedy' because it makes the locally optimal choice at each stage with the hope that these local optimizations will lead to a global optimum. It does not consider all possible options at each step but rather chooses the most promising one immediately.
How does the greedy method approach problem-solving?
-The greedy method approaches problem-solving by breaking it down into stages. At each stage, it selects the most optimal choice based on the current state and the problem's constraints, aiming to construct a solution that meets the overall objective.
What is an example of a greedy method in action?
-An example of the greedy method in action is when choosing the best car based on features without examining every car model available. Instead, one might first select a preferred brand, then a top model from that brand, and finally, the latest or most reliable model from the selected options.
How does the hiring process illustrate the greedy method?
-In the hiring process, the greedy method can be seen when a company filters candidates through a series of tests and interviews, selecting the best candidate according to their criteria at each stage, rather than evaluating every candidate through all stages.
What are the potential drawbacks of using the greedy method?
-The greedy method may not always lead to the optimal solution for every problem. It can be efficient but is not guaranteed to find the best solution in cases where the optimal choice at each step does not combine to form an optimal final solution.
Why is it important to understand the constraints of a problem when using the greedy method?
-Understanding the constraints of a problem is crucial when using the greedy method because these constraints determine what solutions are feasible. Without considering constraints, the method might select choices that seem optimal in isolation but are not viable within the context of the problem.
Can the greedy method be applied to all types of optimization problems?
-The greedy method is not universally applicable to all optimization problems. It is most effective for problems where the greedy choice property holds, meaning that the locally optimal choice at each step leads to a globally optimal solution.
Outlines
đ Introduction to the Greedy Method
The first paragraph introduces the greedy method as a strategy for solving optimization problems, similar to divide and conquer. It explains that the greedy method is used for problems requiring either a minimum or maximum result. The paragraph uses the example of traveling from location A to B within 12 hours to illustrate feasible and infeasible solutions. It further clarifies that from the feasible solutions, the one that provides the minimum cost is considered the optimal solution. The concept of optimization problems is also briefly touched upon, defining them as problems that require either a minimum or maximum result.
đ ïž The Greedy Method Approach
The second paragraph delves into the approach of the greedy method, emphasizing that it involves solving a problem in stages. At each stage, one feasible input is selected from the given problem, and if it meets the criteria, it is included in the solution. The paragraph uses the analogy of buying a car with the best features as an example of applying the greedy method. It contrasts the exhaustive approach of checking every car with the more efficient greedy approach of narrowing down the selection based on certain criteria, such as brand and model, to find the best car without examining every option.
đą Practical Examples of the Greedy Method
The third paragraph provides practical examples to further illustrate the greedy method. It discusses a scenario where a company is hiring and has to select the best candidate from a large pool of applicants. The paragraph explains how the company applies a series of tests to filter candidates, ultimately choosing one as the best, which is a greedy approach. It contrasts this with the impracticality of giving every applicant a chance at every stage of the interview process. The paragraph concludes by reinforcing the concept that the greedy method is about following known, efficient methods to quickly solve problems, even if it might not always yield the absolute best result in every case.
Mindmap
Keywords
đĄGreedy Method
đĄOptimization Problem
đĄFeasible Solution
đĄOptimal Solution
đĄDivide and Conquer
đĄAlgorithm
đĄConstraints
đĄMinimization Problem
đĄSelection Procedure
đĄGlobal Optimum
Highlights
Greedy method is one of the strategies for solving problems, similar to divide and conquer.
The greedy method is suitable for optimization problems that require either a minimum or maximum result.
Optimization problems are those that demand a minimum or maximum outcome.
An example is given where the problem is to travel from location A to B within 12 hours.
Feasible solutions are those that satisfy the constraints of a problem.
An optimal solution is a feasible solution that also provides the best result, either minimum or maximum.
The greedy method involves solving a problem in stages, selecting inputs one by one if they are feasible.
The method ensures that by including all feasible inputs, an optimal solution is obtained.
The general method of the greedy algorithm is outlined, where inputs are evaluated for feasibility.
The greedy method is applied to the example of choosing the best car based on features.
The approach of the greedy method is to make selections based on certain criteria without checking all possibilities.
Another example is hiring the best candidate from a large pool of applicants using a series of tests and filters.
The selection process in hiring is an example of the greedy approach, where candidates are filtered based on specific criteria.
The greedy method is a quick problem-solving approach that follows known methods to achieve an optimal result.
The greedy method is contrasted with a more exhaustive approach that checks all possibilities, which is time-consuming and costly.
The transcript concludes with an introduction to the greedy method and its application in solving optimization problems.
Transcripts
hi next topic is greedy
method this is one of the strategy for
solving
problems just like divide and conquer
and the other strategies greedy method
is also one of the
approach for solving a problem or a
design which you can adopt for solving
similar problem the problems which fits
into this one you can solve all of them
let us understand what this method says
what is this method about
this method is used for solving
optimization
problem what are optimization problems
are problems which demands or which
requires either minimum result or
maximum result so for this let us know
few terms I'll explain it through an
example suppose there's a problem p and
that problem is I want to travel from
one location a to location
B I have to cover this journey that is
my problem for any problem I'm taking
one example it can be any problem
similar type now for this problem there
may be more than one Solutions let us
say I can travel this by walk Solution
One or I can take a bike solution two I
can take a car solution three I can go
by train solution four and I can go by
flight solution five and there may be
more
solutions it can give me more
solutions so my problem is to travel
from location a to location B and there
are many solution you go like this or
take this take this and go there but
there is a constraint in a problem I say
that I have to cover this journey within
12
hours this is a condition
constrain so suppose I cannot cover it
if I go by walk or by car and so I can
cover it only if I go by train or
flight now for a problem there are many
solutions but these Solutions which are
satisfying the condition given in the
problem then these type of solution
becomes feasible
[Music]
Solutions that's the meaning of feasible
solution a solution which is satisfying
the condition given in the problem is
feasible solution though for a given
problem there may be many
solutions this is feasible solution
satisfying the constraint commonly we
use the term Is it feasible or not
feasible in the sense what satisfying
our constraints or not limitations or
not next if I say that I want to cover
this journey in minimum
cost minimum cost I want to spend as
much as less possible then this becomes
a minimization problem so now as the
problem Demands a result should be
minimum then it is a minimization
problem right then out of these two
solution one of the solution may be
taking minimum cost suppose by train if
I go this is minimum cost then this is
called as
optimal
solution a solution which is already
feasible and also giving me minimum cost
that is best results that is best for me
minimum is best for me then that
solution is called as optimal solution
and definitely for any problem there can
be only one optimal solution there
cannot be multiple Optimal
Solutions that means there can be only
one minim minum cost minimum can be only
one there can be more than one Solutions
there can be more than one feasible
solution but there will be definitely
only one optimal solution this problem
requires minimum result some other
problems may require maximum result so
if a problem requires either minimum or
maximum results then we call that type
of problem as
optimization
problem optimization problem is one
which requires either minimum result or
maximum
result so let us briefly look at the
terms once again feasible solution means
a solution which is satisfying some
constraint optimal solution means which
is achieving the objective of a problem
satisfying the objective of a problem
that is either minimum result or maximum
result a problem which requires a
minimum or maximum result is a
optimization
problem so greedy method is used for
solving optimization
problems these are the strategies used
for solving optimization problems
[Music]
these three methods are for solving
optimization problem the approach is
different and every problem whichever
requires optimal results some may be
suitable here some may be suitable here
this strategy can apply on it or some
this strategy can be applied or some for
some problems all three strategies can
be applied on them so we will learn all
these strategies through problems one by
one now we are going to cover this
greedy method so we will start with
greedy method we will understand what
greedy method says what is the approach
so next I will tell you about greedy
method what is its
approach here is the general method of
greedy I have written an algorithm now
see greedy method says that a problem
should be solved in
stages in each stage we will consider
one input from a given problem and if
that input is feasible then we will
include it in the solution so by
including all those feasible in inputs
we will get a optimal solution so in
stages we will each time we'll pick up
our input and we consider it and if it
is feasible we will include it and like
this if we follow this procedure we will
get the optimal
solution so here uh method is given if a
problem is given and that problem is
having a input of some size and N is the
size and it is having some data some
values input values now it will go
through all those input values from 1 to
n and each time it will select something
from a and call it as X if that X is
feasible that is one input one by one it
will pick up the input and that input if
it is feasible it will include in the
solution if it is feasible it is
included in solution so this comes under
if this is the general method now I will
explain you through example the approach
of gritty method is
that suppose if you have to buy a best
car best car best car in the sense in
terms of features you want a best car
optimal optimal okay the cost will be
maximum definitely so but you optimal
optimal in the sense for in terms of
features now how do you choose a best
car how do you choose a best car so one
method is you should look at all the
brands and all the models of cars
available in the world or at least in
your city then you can say that I have
checked all the cars then I have
selected the best
car this is one approach for solving a
problem the problem is to buy a
car this one method this will be very
much time consuming you have to check
each and every brand and every model see
the cost may not be a thing sometimes a
car may be better than costlier car so
checking with the features and you are
deciding that this is the best car so
but actually what is the method we
follow we first of all sort out the
brands and we say that we don't want in
this this we want let us say you are
selecting a brand that is Toyota or
Hyundai right okay you are saying that
these are the best brands for you and in
these Brands then again you will select
the top
models right so you are you are not
looking at the lower models so again you
have sort out then again you say that in
this Top Model the latest release car or
the well-known car well tested car
you're picking up that one and you're
saying that is the best one is it really
the best one out of all the cars in the
market for you it's the best one so what
is the approach you adopted you have
adopted a greedy approach so you have
your own method of selection and based
on that selection method you got some
result and you are seeing that is the
best result that's how it is greedy and
definitely when you do this you will be
pick up a best car so you don't have to
waste time in checking all the cars in
the available in the city available in
the market so that's it so without
checking all of them you say that you
select few and say this is the best car
no doubt that's the best car but the
approach you adopted is
greedy I'll give you one more example
suppose you are running a company and
you want to hire some people so when you
have given an ad some thousand people
came to for the interview now you'll
conduct some type of test like you first
you conduct return return test and then
you have a technical test or group
discussion like that you will have
various phases of test and you'll filter
the people and finally you select one
person and you say that this is the best
person on out of those thousand is he
really a best person yes according to
your procedures it's a best person what
was your selection procedure based on
the selection procedure he is the best
person and yes you have got the optimal
solution so the approach is greedy many
student complain that I was better than
him and he got selected they think like
that but really the person who got
selected is the best one definitely so
the approach that you're are adopting
now I'll tell you if you selecting one
person out of thousand then for all you
should give a chance for return return
test for all you should give a chance
for group discussion for all you should
you should give a chance for technical
interview and HR interview then pick up
the best one this will be very timec
consuming and costly process we don't do
that we simply filter the people and
select the best one this approach is
called as greedy approach so we have our
own methods of selection and we follow
blindly we follow those methods because
those are the known methods when you
follow known methods of solving a
problem and you quickly solve it that
approach is called as grey so I have
given you enough idea about the greedy
method now you will come across through
the problems one by one I will pick up
and I will solve them so in while
discussing the problem also I'll show
you what the approach GD is following so
that if you type find any similar type
of problem you can follow the same
approach and solve
it that's it the introduction for gy
method
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