3. Greedy Method - Introduction

Summary

The 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

• 😀 The greedy method is a problem-solving strategy used for optimization problems, similar to divide and conquer.
• 🎯 Optimization problems are those that require either a minimum or maximum result, such as minimizing cost or maximizing efficiency.
• 🚀 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.
• 🔍 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.
• 🚦 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.
• 🛒 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.
• 🏢 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.
• 📉 The script explains that the greedy method can be faster and more practical than exhaustive methods but may not always guarantee the best solution.
• 📚 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.
• 🔑 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

00:00

🚀 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.

05:02

🛠️ 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.

10:02

🏢 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.

Keywords

💡Greedy Method

The Greedy Method is a strategy for solving problems by making the most optimal choice at each stage with the hope of finding a global optimum. It is one of the core algorithms discussed in the video. The method is iterative, where at each step, the algorithm chooses the best option available at that moment. The video uses the analogy of choosing the best car based on features without necessarily checking all available options, illustrating how the Greedy Method works by making locally optimal choices.

💡Optimization Problem

An Optimization Problem is a type of problem where the goal is to find the best solution among many possible solutions, often aiming for either a minimum or maximum result. The video explains that optimization problems are central to the application of the Greedy Method, as it is particularly useful for finding optimal solutions efficiently. An example given is traveling from point A to B in the minimum cost, which is a minimization problem.

💡Feasible Solution

A Feasible Solution is a solution that satisfies the constraints of a given problem. The video emphasizes that not all solutions are feasible, and the Greedy Method involves selecting inputs that are both feasible and optimal. For instance, if the constraint is to travel within 12 hours, only solutions like taking a train or flight would be considered feasible.

💡Optimal Solution

An Optimal Solution is a feasible solution that provides the best outcome in terms of the problem's objective, which could be either minimizing or maximizing a certain parameter. The video clarifies that while there can be multiple feasible solutions, there is typically only one optimal solution. It uses the example of choosing the best car in terms of features, which is deemed optimal without necessarily being the cheapest.

💡Divide and Conquer

Divide and Conquer is a problem-solving strategy that involves breaking down a complex problem into smaller, more manageable sub-problems, solving each sub-problem, and then combining their solutions to solve the original problem. The video mentions this strategy in comparison to the Greedy Method, highlighting that both are approaches for solving problems but differ in their methodology.

💡Algorithm

An Algorithm is a set of rules or steps used to solve a problem. In the context of the video, the Greedy Method is described as an algorithmic approach where the problem is solved in stages, and at each stage, the algorithm makes a choice that seems to be the best at that moment. The video provides a general method of the Greedy Algorithm, explaining how it processes inputs and selects feasible options.

💡Constraints

Constraints are the limitations or conditions that must be satisfied by a solution to be considered valid for a problem. The video discusses how constraints play a crucial role in determining feasible solutions. An example used is the time constraint of 12 hours for travel, which filters out walking or driving as feasible solutions.

💡Minimization Problem

A Minimization Problem is a type of optimization problem where the goal is to find a solution that minimizes a certain quantity or cost. The video explains that when a problem requires a minimum result, it is classified as a minimization problem, using the example of wanting to travel with the least cost.

💡Selection Procedure

A Selection Procedure refers to the process of choosing from a set of options based on certain criteria. The video uses the example of hiring employees, where a company might use a multi-stage selection process to filter candidates and ultimately choose the best candidate according to their criteria, illustrating a greedy approach to decision-making.

💡Global Optimum

The Global Optimum refers to the best possible solution to a problem, considering all possible solutions. While the Greedy Method aims to find a local optimum at each step, the video implies that it may not always lead to a global optimum. This concept is important for understanding the limitations of the Greedy Method and when it is most effective.

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