Introduction to Problem Solving

Introduction to Problem Solving

Dr. Alok Pawar



 1.1    Problem Solving :

A problem obstructs and hinders the progress or movement in achieving an objective. In our daily life, some problems are well understood and one might develop solutions to such problems but there are few which will pose challenges.

For example, we have to make tea for three people of which one is a diabetic person. In that case, we make tea initially without sugar, once we serve that tea to the diabetic person then we add sugar into the tea and again boil. The nature of the problem depends on the situation.

Is Problem-solving an Art or a Science?

Problem Solving as a Science -  

Problem Solving could be referred to as a science as it includes the essentials of science. Now problem-solving is a well-organized body of knowledge. There are underlying principles and theories available which can be used as guidelines for various tasks. Problem-solving includes special knowledge of the field to which the problem is related. Even the principles of problem-solving have evolved over some time after lots of practical experiences and research.

 If we consider our previous example, making tea follows a certain procedure in which we add only water, milk, sugar, and tea power in prescribed quantities, we cannot add oil, spices, etc. and hence it follows science.

Problem Solving as an Art - 

Art entails the practical implementation of personal skills and knowledge to achieve tangible outcomes. It is the way of doing specific things. The function of art is to achieve change and attain desired results.

Art represents the know-how to do work. It is a personalized process and every artist or human being has his own style.

Art is essentially creative and the success of an artist is measured by the results he achieves. As we know art is practice-based. For perfection, it has to be practiced continuously e.g. Music, dancing, and painting are also arts.

Major elements of art are:

1.       Personal skills,

2.       Practical experience,

3.       Result- orientation,

4.       Creativity,

5.       Constant practice aimed at perfection.

In problem-solving, each individual may have his or her own unique way. Considering our example, if one adds ginger to tea for taste, one person can make special tea without water (Only milk) and hence it follows art.

 Software development is a sequentially interrelated process. Multiple steps are performed before developing new software. The first step is to determine the information needs of the proposed software.

 Problem definition is the most important step in this direction. Among some of the general characteristics like the speed of processing, the volume of work, reliability, and accuracy some other functions are expected from the software and they vary from application to application.

Problem definition is the first and most important step in determining information needs. Information needs of software can be determined by:

1.       Studying the existing system

2.       Using questionnaires

3.       Stating the tentative information needs

4.       Suggesting interpretation of information needs with users.

First of all, using any of these steps, the requirements are determined. Analysis of the problem produces a clear and accurate problem definition.

For solving a problem there are many techniques available some of the popular techniques are discussed here:

1.     Trial and Error method

2.     Brain Storming

3.     Divide and Conquer

1.3.1  Trial and Error:

The name of this method ‘Trial and Error’ itself suggests first trying/ process/perform/generate for the process and then thinking about the error (s).

This is an iterative method, based on the idea of successive approximation i.e. starting with initial approximations to the root. As a technique of solving equations trial and error is very general. It is, however, disliked by humans as a method for problem-solving.

The alternative names of trial and error are ‘Generate and Test’ (in computer science) and ‘Guess and Check’ (in elementary algebra).

For a computer, on the other hand. It is the most natural technique because in trial and error method of solving a sequence of steps is repeated over and over again.

For example; Science students perform titration in chemistry, wherein they add the soluble liquid from the burette into the flask. The addition is done till the liquid in the flask changes colour. So these become trials. Normally three to four times repetitions are undertaken till correct titration is achieved. 



Consider another simple example, when we cook vegetables we add salt to them, initially we add some salt, and then taste the vegetable, if we think that the amount of salt is less, we add more salt to it.

Some people take extra salt in the eating plate itself to add to their food. This example suggests the repetitions of the same process of trials until we get desired output. The chef uses the word – ‘namak swadanusar’.

Basically, the trial and error method is used to generate solutions for simple problems as well as games.

Application of the trial and error in basic games wherein the player of the game tries something if he does something right then he wins otherwise he gets an error. In general, this method approaches the knowledge gained for the situation within the game.

Features of Trial and Error  

There are lots of features of the trial and error method by which our knowledge of the problem increases. Some of these features are as follows;

·                Specific Problem Based: Trial and error are useful for certain types of problems, when we apply the trials to certain problems then we specifically find the way to arrive at a solution for that problem only and not any other problem. All those alternatives do not apply to any other problem. So, we can say that it is specific problem based or customized and cannot be generalized.     

·                Solution Based: After various trials and various errors we arrive at a certain solution. For example, if we consider the game in which the king wants to find the road to reach the queen, while the road is riddled with lots of problems and misleading notifications, the solution or victory of the game is when the king finally meets the queen.

·                Knowledge Based: If we consider the above game, then the user may want to know how to play the game. After having learned that he can possibly think of playing.

·                Non-Optimal: Trial and error generate lots of solutions for the problem from which some are suitable or optimal while some are not. Trial and error provide some solutions which are absolutely not optimal for the problem.      


1.3.2  Brain Storming:

Brainstorming is a group activity designed to increase the quality of fresh ideas.

Getting other people involved can help increase knowledge and understanding of the problem and help participants reframe the problem.

OR

Brainstorming is a group method for obtaining new ideas and business solutions, the group is organized by sitting together and stimulating greater creativity by exchange of mutual experiences and participating in discussions.

The brainstorming ideas are canalized to a particular segment of product line or services.

 


  Fig. 1.1 Brainstorming

Method of conducting brainstorming sessions:

  1. The group should be informed of the broad areas of the subject or area of discussion.
  2. The group should consist of people drawn from the same as well as different streams of knowledge such as marketing, production, quality control, planning, finance, costing, stores, taxation, and the like the group also should consist of different levels of officers, and supervisors from the organization.
  3. The brainstorming sessions should be held in a good place with ambiance. So, that the group comes open with their ideas.
  4. The member should have no inhibitions about their status in the organization and department where they serve. The session should be frank and fun. Brainstorming sessions are held where no individual or group dominates the discussions and there is no boss-subordinate relationship.
  5. Daydreaming and wild ideas to be encouraged.
  6. There should not be any negative comments or criticisms against any particular individuals or groups or departments.
  7. The ideas of one can be improved by another but no repetition of ideas. Each individual may be given a chance to three ideas being recorded on a flip chart or blackboard. All ideas are recorded on the flip chart even if one idea is not practical or ill-logical.


1.3.3  Divide and Conquer:

The divide and conquer algorithm consists of the following major phases :

1.       Breaking the problem into several sub-problems that are similar to the original problem but smaller in size.

2.       Solve the sub-problem recursively (successively and independently).

3.       Combine these solutions with sub-problems to create a solution to the original problem.


 

                           Fig 1.2: Divide and Conquer

Steps in Divide and Conquer Algorithm:

In general divide and conquer paradigm consist of the following steps:

                1.    Divide the step

                2.    Conquer step

                3.    Combine step

 

1.     Divide step :

·               In this step of the algorithm, the input is partitioned into p ³ 1 parts. Each size is strictly less than n, the size of the original instance.

·               The most common value of p is 2, although other small constants greater than 2 are not uncommon.

·               We can say this is a splitting step in which we split the problems into several smaller units for further action. 

·               Many of the situations in which we have to make a queue. Some situations are designed as there are two queues, one is for ladies and the other is for gents. This is more for comfort.  

2.     Conquer step:

·               This step consists of performing p recursive call (s) if the problem size is greater than some pre-defined threshold number.

·               This threshold is divided by mathematical analysis of the algorithm.

·               Once it is found, it can be increased by any constant amount without affecting the time complexity of the algorithm.

3.     Combine step:

·               In this step, the solution to the p-recursive call (s) is combined to obtain the desired output.

·               The combining step in a divide and conquer algorithm may consist of merging sorting searching finding the maximum or minimum, matrix addition, etc.

·               In general we can say that this is a merging step.


Fig. 1.3 Divide and Conquer

 

Comments

Post a Comment

Popular posts from this blog

Image
 Algorithm Meaning and Definition: The word “Algorithm, is a distortion of “al-khwauizmi”, a Persian mathematician who wrote an influential treatise about algebraic methods. But the algorithm is a Latin word called “algouismus” which means “calculation methods” An algorithm is a sequence of finite instructions often used for calculations and data processing.  It is a type of effective method in which a list of well-defined instructions for completing a task will, when given an initial state, proceed through a well-defined series of successive states, eventually terminating in an end state. When the user is telling the computer what to do, he also gets to choose how it is going to be done. To make a computer do anything, we have to write a computer program. To write a computer program, we must tell the computer, step by step, exactly what we want it to do. The computer then “exceeds the program, following each step mechanically, to accomplish the end goal”. An algor...
Read more

Steps in Problem Solving

Image
  Steps in Problem Solving Dr. Alok Pawar A logical computation firstly requires defining the problem, secondly, as per the end user requirement, it needs analyzing and designing the output format. After this one can start the actual coding that is followed by testing and maintenance the next section explains all these phases. Definition of the Problem: When a problem is to be solved, two questions arise, first, what to do, and second, how to do it? This phase answers the first question, here the programmer has to define the task precisely and check for completeness, there should not be any ambiguity. The imprecisely or arbitrary defined problem may result in the wrong analysis and design. For example: “Solve the quadratic equation” this problem itself is not complete because it is not specified whether to find the value of roots of the quadratic equation or to find the nature of roots of the quadratic equation or both. The different programmers may program this problem...
Read more