Fundamentals of Computing

IDENTIFICATION OF COMPUTATIONAL PROBLEMS

FUNDAMENTALS OF COMPUTING

1. Introduction

2. Computational Problem

2.1 Types of computational problems

3 Problem Solving Process

3.1 Problem Analysis

3.2 Program Design ‒ Algorithm, Flowchart and Pseudocode

3.3 Coding

3.4 Compilation and Execution

3.5 Debugging and Testing

3.6 Program Documentation

4. Identification of Computational Problems

4.1 Problem Solving with Computers

5. Problem analysis charts (PACS)

5.1 Components of a Problem Analysis Chart 

5.2 When to use Problem Analysis Charts 

5.3 Creating a Problem Analysis Chart

5.4 Relationship with other problem‒solving tools

1. INTRODUCTION

In computer science, computational problem is a problem that a computer might be able to solve or a question that a computer may be able to answer.

A computational problem can be viewed as a set of instances or cases together with a, possibly empty, set of solutions for every instance/case.

What is computation?: It is any type of calculation that includes both arithmetical and non‒arithmetical steps and follows a well‒defined model Eg: Algorithm.

The first step in the problem solving and decision making process is to identify and define the problem. Therefore, before a program is written for solving a problem, it is important to define the problem clearly. For most software projects, systems analysts approach the user requirements and define the problem that a system aims to solve. They typically look at the following issues:

• What is the problem?

• What is the input required for supporting the solution process?

• What is the expected output of the solution?

• How do people solve the problem currently?

• Can the problem or part of the problem be more effectively solved by a software solution?

2. COMPUTATIONAL PROBLEM

 In computer science, a computational problem is a mathematical object representing a collection of questions that computers might be able to solve. For example, the problem of factorial "Given a positive integer n, find a factorial of n.” is a computational problem.

Computational problems are one of the main objects of study in computer science. The field of algorithms studies methods of solving computational problems efficiently.

Types of computational problems

A Decision Problem is a computational problem where the answer for every instance is either yes or no.

In a Search Problem, the answers can be arbitrary strings.

A Counting Problem asks for the number of solutions to a given search problem.

An Optimization Problem asks for finding a "best possible" solution among the set of all possible solutions to a search problem.

In a Function Problem a single output (of a total function) is expected for every input, but the output is more complex than that of a decision problem, that is, it isn't just "yes" or "no".

Decision Problem :

Where the answer for every instance is either Yes or No

Decision whether a given number is even ?

Searching and Sorting:

Searching an element from a given list or sort them in order

Finding an employee name using empid and sort names in alphabetical order

Counting Problem:

Counting a number of ban occurrences an element in a list

Count how many type of books available in store

Optimization Problem:

Finding best solution out of number of feasible solutions

Finding best combination of products for promotional campaign

3. PROBLEM SOLVING PROCESS

A computer cannot solve a problem on its own. One has to provide step by step solutions of the problem to the computer. In fact, the task of problem solving is not that of the computer.

It is the programmer who has to write down the solution to the problem in terms of simple operations which the computer can understand and execute.

The following are six steps that must be followed to solve a problem using computer

1. Problem Analysis

2. Program Design ‒ Algorithm, Flowchart and Pseudocode

3. Coding

4. Compilation and Execution

5. Debugging and Testing

6. Program Documentation

1. Problem Analysis

A Problem Analysis investigates a situation/problem in order to allow the researcher to understand more fully the problem, in order to recommend practical solutions for solving it. Thus, the problem analysis would report that the lighting was not the cause of the problem, saving the company time and money. The following are steps involves in problem analysis.

a. Understand your problem

b. Break the problem

c. Define problem goals

d. Decide how to measure progress towards goals.

Understand Your Problem: You must understand the issue or problem you are experiencing before you can realistically try to figure out what to do about it. As a first step towards self‒help, take steps to understand the nature of your problem.

Break the Problem Down Into Small Parts: Even when you understand what your problem is, it may be too big and too well established for you to figure out how to fix all at once. Instead of trying to tackle the entire problem all at once, break it down into manageable parts. Then, make a plan for how you will fix or address each part separately.

Define Problem Goals: For each of your small manageable problem parts, figure out what your goals are; where you want to end up at the end of the self‒help process for each part of your problem. If you don't know what you are working towards, you will never know when you've arrived there.

Decide How To Measure Progress Towards Goals: Find ways to measure progress you make towards accomplishing each of your problem goals, so that you will always know:

i. What your problem starting point looked like.

ii. How far you've come towards meeting your goals at any given moment.

iii. How you wil know when when you have met yours goals and are done.

2. Program Design ‒ Algorithm, Flowchart and Pseudocode

Algorithm: A set of sequential steps usually written in Ordinary Language to solve a given problem is called Algorithm.

A flowchart is a type of diagram that represents a workflow or process. A flowchart can also be defined as a diagrammatic representation of an algorithm, a step‒by‒step approach to solving a task.

In computer science, pseudocode is a plain language description of the steps in an algorithm or another system. Pseudocode often uses structural conventions of a normal programming language, but is intended for human reading rather than machine reading.

3. Coding

Coding or computer programming is the process of designing and building an executable computer program to perform a specific task.

4. Compilation and Execution

Compilation is the process the computer takes to convert a high‒ level programming language into a machine language that the computer can understand. The software which performs this conversion is called a compiler.

Execution in computer and software engineering is the process by which a computer reads and acts on the instructions of a computer program. Each instruction of a program is a description of a particular action which must be carried out, in order for a specific problem to be solved.

5. Debugging and Testing

In computer programming and software development, debugging is the process of finding and resolving bugs within computer programs, software, or systems. Debugging tactics can involve interactive debugging, control flow analysis, unit testing, integration testing, log file analysis, monitoring at the application or system level, memory dumps, and profiling. Many programming languages and software development tools also offer programs to aid in debugging, known as debuggers.

Software testing is an investigation conducted to provide stakeholders with information about the quality of the software product or service under test. Test techniques include the process of executing a program or application with the intent of finding failures, and verifying that the software product is fit for use.

6. Program Documentation

Software documentation is written text or illustration that accompanies computer software or is embedded in the source code. The documentation either explains how the software operates or how to use it, or may mean different things to people in different roles.saheb od ode de in

4. IDENTIFICATION OF COMPUTATIONAL PROBLEMS

Problem: Problem is a thing that requires logical thought and /or mathematics

Problem Solving: Problem solving is the systematic approach to define the problem and creating number of solutions. The problem solving process starts with the problem specifications and ends with a Correct program.

Problem Solving with Computers

• Computers are built to solve problems with algorithmic solutions, which are often difficult or very time consuming when input is large.

• Solving a complicated calculus problem or alphabetizing 10,000 names is an easy task for the computer.

• So the basis for solving any problem through computers is by developing an algorithm.

• Field of computers that deals with heuristic types of problems is called Artificial Intelligence (AI)

• Artificial intelligence enables a computer to do things like human by building its own knowledge bank

• As a result, the computer's problem‒solving abilities are similar to those of a human being.

• Artificial intelligence is an expanding computer field, especially with the increased use of Robotics.

5. PROBLEM ANALYSIS CHARTS (PACS)

Problem analysus charts are structured visual tools that help in breaking down complex problems into manageable components to better understand, analyze, and address them. They are often used as an initial step in problem‒solving, particularly in the context of designing algorithms and flowcharts, to organize information and develop a structured approach to a solution.

1. Components of a Problem Analysis Chart

A typical Problem Analysis Chart might involve these key sections:

• Given Data (Inputs): Information or data provided or available to address the problem.

• Required Results (Outputs): The desired outcome or solution expected after processing the given data.

• Processing Required: The steps, calculations, or logic needed to transform the inputs into the desired outputs.

• Solution Alternatives: A list of different ideas or approaches that could be used to solve the problem.

2. When to use Problem Analysis Charts

Problem Analysis Charts are particularly useful in various situations:

• Complex Problems: Breaking down multifaceted issues with multiple steps or variables into manageable parts.

• Team Collaboration: Providing a shared understanding of a problem and potential solutions among team members.

• Analyzing Processes: Mapping out a process to understand its intricacies and identify areas for improvement or bottlenecks.

• Decision Making: Visualizing various paths or decisions and their potential outcomes to aid in informed choices.

• Identifying Root Causes: Facilitating a systematic approach to identify the underlying causes of a problem.

3. Creating a Problem Analysis Chart

Here's a general approach to creating a problem analyses charts.

• Define the Problem: Start by clearly and concisely articulating the problem or task you want to solve.

• Identify Inputs and Outputs: Determine the necessary inputs (data, information, resources) and desired outputs or outcomes.