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An Introduction to Problem Solving

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To successfully solve any problem, the most important issue to get actively involved. Levine [Lev94] calls this “The Principle of Intimate Engagement.” Writers on problem solving often use terms like “roll up your sleeves” and “get your hands dirty.” It means actively engaging with the problem, and doing some work to get it done. For easier problems, you will “see” an answer fairly quickly once you actively engage, and the issue then is to work through to completion.

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Educators, researchers, and policy makers have advocated student involvement for some time as an essential aspect of meaningful learning. In the past twenty years engineering educators have implemented several means of better engaging their undergraduate students, including active and cooperative learning, learning communities, service learning, cooperative education, inquiry and problem-based learning, and team projects. This paper focuses on classroom-based pedagogies of engagement, particularly cooperative and problem-based learning. It includes a brief history, theoretical roots, research support, summary of practices, and suggestions for redesigning engineering classes and programs to include more student engagement. The paper also lays out the research ahead for advancing pedagogies aimed at more fully enhancing students' involvement in their learning.

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There must be discussion and agreement on the meaning of engaged learning in specific educational contexts for institutions implementing these practices because the potential meaning is vast. It is only in this way those directly involved in implementing, assessing and applying engaged learning can ensure they are targeting the same goals and objectives. For some, it refers to local community engagement in education, for others it is more global in scale. It can have to do with local collaboration, local community-university engagement, global viewpoints and equity in education, transformative learning, sparking the desire to learn, vigor and energy, active or applied learning, application and integration of knowledge, creation of knowledge, or involvement and ownership in decision making. This conceptual paper provides an analysis of literature on the definitions of engagement in learning to examine the similarities and differences in meaning with the intent to expand and enhance the concept of engaged learning and its employment in practice in educational contexts.

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Introduction to Problem Solving Class 11 Notes | CBSE Computer Science

Latest Problem Solving Class 11 Notes includes Problem Solving, steps, algorithm and its need, flow chart, pseudo code with lots of examples.

  • 1 What is Problem Solving?
  • 2 Steps for problem solving
  • 3 What is Algorithm?
  • 4 Why do we need Algorithm?
  • 5.1 Flow chart
  • 5.2 Flow Chart Examples
  • 5.3 Pseudo code
  • 5.4 Pseudo Code Example
  • 6.1 Selection
  • 6.2 Algorithm, Pseudocode, Flowchart with Selection ( Using if ) Examples
  • 6.3 Repetition
  • 6.4 Algorithm, Pseudocode, Flowchart with Repetition ( Loop ) Examples
  • 7 Decomposition

What is Problem Solving?

Problem solving is the process of identifying a problem, analyze the problem, developing an algorithm for the identified problem and finally implementing the algorithm to develop program.

Steps for problem solving

There are 4 basic steps involved in problem solving

Analyze the problem

  • Developing an algorithm
  • Testing and debugging

Analyzing the problem is basically understanding a problem very clearly before finding its solution. Analyzing a problem involves

  • List the principal components of the problem
  • List the core functionality of the problem
  • Figure out inputs to be accepted and output to be produced

Developing an Algorithm

  • A set of precise and sequential steps written to solve a problem
  • The algorithm can be written in natural language
  • There can be more than one algorithm for a problem among which we can select the most suitable solution.

Algorithm written in natural language is not understood by computer and hence it has to be converted in machine language. And to do so program based on that algorithm is written using high level programming language for the computer to get the desired solution.

Testing and Debugging

After writing program it has to be tested on various parameters to ensure that program is producing correct output within expected time and meeting the user requirement.

There are many standard software testing methods used in IT industry such as

  • Component testing
  • Integration testing
  • System testing
  • Acceptance testing

What is Algorithm?

  • A set of precise, finite and sequential set of steps written to solve a problem and get the desired output.
  • Algorithm has definite beginning and definite end.
  • It lead to desired result in finite amount of time of followed correctly.

Why do we need Algorithm?

  • Algorithm helps programmer to visualize the instructions to be written clearly.
  • Algorithm enhances the reliability, accuracy and efficiency of obtaining solution.
  • Algorithm is the easiest way to describe problem without going into too much details.
  • Algorithm lets programmer understand flow of problem concisely.

Characteristics of a good algorithm

  • Precision — the steps are precisely stated or defined.
  • Uniqueness — results of each step are uniquely defined and only depend on the input and the result of the preceding steps.
  • Finiteness — the algorithm always stops after a finite number of steps.
  • Input — the algorithm receives some input.
  • Output — the algorithm produces some output.

What are the points that should be clearly identified while writing Algorithm?

  • The input to be taken from the user
  • Processing or computation to be performed to get the desired result
  • The output desired by the user

Representation of Algorithm

An algorithm can be represented in two ways:

Pseudo code

  • Flow chart is visual representation of an algorithm.
  • It’s a diagram made up of boxes, diamonds and other shapes, connected by arrows.
  • Each step represents a step of solution process.
  • Arrows in the follow chart represents the flow and link among the steps.

introduction to problem solving notes pdf

Flow Chart Examples

Example 1: Write an algorithm to divide a number by another and display the quotient.

Input: Two Numbers to be divided Process: Divide number1 by number2 to get the quotient Output: Quotient of division

Step 1: Input a two numbers and store them in num1 and num2 Step 2: Compute num1/num2 and store its quotient in num3 Step 3: Print num3

introduction to problem solving notes pdf

  • Pseudo code means ‘not real code’.
  • A pseudo code is another way to represent an algorithm.  It is an informal language used by programmer to write algorithms.
  • It does not require strict syntax and technological support.
  • It is a detailed description of what algorithm would do.
  • It is intended for human reading and cannot be executed directly by computer.
  • There is no specific standard for writing a pseudo code exists.

Keywords used in writing pseudo code

Pseudo Code Example

Example:  write an algorithm to display the square of a given number.

Input, Process and Output Identification

Input: Number whose square is required Process: Multiply the number by itself to get its square Output: Square of the number

Step 1: Input a number and store it to num. Step 2: Compute num * num and store it in square. Step 3: Print square.

INPUT num COMPUTE  square = num*num PRINT square

introduction to problem solving notes pdf

Example: Write an algorithm to calculate area and perimeter of a rectangle, using both pseudo code and flowchart.

INPUT L INPUT B COMPUTER Area = L * B PRINT Area COMPUTE Perimeter = 2 * ( L + B ) PRINT Perimeter

introduction to problem solving notes pdf

Flow of Control

An algorithm is considered as finite set of steps that are executed in a sequence. But sometimes the algorithm may require executing some steps conditionally or repeatedly. In such situations algorithm can be written using

Selection in algorithm refers to Conditionals which means performing operations (sequence of steps) depending on True or False value of given conditions. Conditionals are written in the algorithm as follows:

If <condition> then                 Steps to be taken when condition is true Otherwise                 Steps to be taken when condition is false

Algorithm, Pseudocode, Flowchart with Selection ( Using if ) Examples

Example: write an algorithm, pseudocode and flowchart to display larger between two numbers

INPUT: Two numbers to be compared PROCESS: compare two numbers and depending upon True and False value of comparison display result OUTPUT: display larger no

STEP1: read two numbers in num1, num2 STEP 2: if num1 > num2 then STEP 3: display num1 STEP 4: else STEP 5: display num2

INPUT num1 , num2 IF num1 > num2 THEN                 PRINT “num1 is largest” ELSE                 PRINT “num2 is largest” ENDIF

introduction to problem solving notes pdf

Example: write pseudocode and flowchart to display largest among three numbers

INPUT: Three numbers to be compared PROCESS: compare three numbers and depending upon True and False value of comparison display result OUTPUT: display largest number

INPUT num1, num2, num3 PRINT “Enter three numbers” IF num1 > num2 THEN                 IF num1 > num3 THEN                                 PRINT “num1 is largest”                 ELSE                                 PRINT “num3 is largest”                 END IF ELSE                 IF num2 > num3 THEN                                 PRINT “num2 is largest”                 ELSE                                 PRINT “num3 is largest”                 END IF END IF

introduction to problem solving notes pdf

  • Repetition in algorithm refers to performing operations (Set of steps) repeatedly for a given number of times (till the given condition is true).
  • Repetition is also known as Iteration or Loop

Repetitions are written in algorithm is as follows:

While <condition>, repeat step numbers                 Steps to be taken when condition is true End while

Algorithm, Pseudocode, Flowchart with Repetition ( Loop ) Examples

Example: write an algorithm, pseudocode and flow chart to display “Techtipnow” 10 times

Step1: Set count = 0 Step2: while count is less than 10, repeat step 3,4 Step 3:                  print “techtipnow” Step 4:                  count = count + 1 Step 5: End while

SET count = 0 WHILE count<10                 PRINT “Techtipnow”                 Count = count + 1 END WHILE

introduction to problem solving notes pdf

Example: Write pseudocode and flow chart to calculate total of 10 numbers

Step 1: SET count = 0, total = 0 Step 2: WHILE count < 10, REPEAT steps 3 to 5 Step 3:                  INPUT a number in var Step 4:                  COMPUTE total = total + var Step 5:                  count = count + 1 Step 6: END WHILE Step 7: PRINT total

Example: Write pseudo code and flow chart to find factorial of a given number

Step 1: SET fact = 1 Step 2: INPUT a number in num Step 3: WHILE num >=1 REPEAT step 4, 5 Step 4:                  fact = fact * num Step 5:                  num = num – 1 Step 6: END WHILE Step 7: PRINT fact

introduction to problem solving notes pdf

Decomposition

  • Decomposition means breaking down a complex problem into smaller sub problems to solve them conveniently and easily.
  • Breaking down complex problem into sub problem also means analyzing each sub problem in detail.
  • Decomposition also helps in reducing time and effort as different subprograms can be assigned to different experts in solving such problems.
  • To get the complete solution, it is necessary to integrate the solution of all the sub problems once done.

Following image depicts the decomposition of a problem

introduction to problem solving notes pdf

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Introduction to Problem Solving – Notes

Introduction to problem solving.

  • Steps for problem solving ( analysing the problem, developing an algorithm, coding, testing and debugging).
  • flow chart and
  • pseudo code,

Decomposition

Introduction

Computers is machine that not only use to develop the software. It is also used for solving various day-to-day problems.

Computers cannot solve a problem by themselves. It solve the problem on basic of the step-by-step instructions given by us.

Thus, the success of a computer in solving a problem depends on how correctly and precisely we –

  • Identifying (define) the problem
  • Designing & developing an algorithm and
  • Implementing the algorithm (solution) do develop a program using any programming language.

Thus problem solving is an essential skill that a computer science student should know.

Steps for Problem Solving-

1. Analysing the problem

Analysing the problems means understand a problem clearly before we begin to find the solution for it. Analysing a problem helps to figure out what are the inputs that our program should accept and the outputs that it should produce.

2. Developing an Algorithm

It is essential to device a solution before writing a program code for a given problem. The solution is represented in natural language and is called an algorithm.

Algorithm: A set of exact steps which when followed, solve the problem or accomplish the required task.

Coding is the process of converting the algorithm into the program which can be understood by the computer to generate the desired solution.

You can use any high level programming languages for writing a program.

4. Testing and Debugging

The program created should be tested on various parameters.

  • The program should meet the requirements of the user.
  • It must respond within the expected time.
  • It should generate correct output for all possible inputs.
  • In the presence of syntactical errors, no output will be obtained.
  • In case the output generated is incorrect, then the program should be checked for logical errors, if any.

Software Testing methods are

  • unit or component testing,
  • integration testing,
  • system testing, and
  • acceptance testing

Debugging – The errors or defects found in the testing phases are debugged or rectified and the program is again tested. This continues till all the errors are removed from the program.

Algorithm is a set of sequence which followed to solve a problem.

Algorithm for an activity ‘riding a bicycle’: 1) remove the bicycle from the stand, 2) sit on the seat of the bicycle, 3) start peddling, 4) use breaks whenever needed and 5) stop on reaching the destination.

Algorithm for Computing GCD of two numbers:

Step 1: Find the numbers (divisors) which can divide the given numbers.

Step 2: Then find the largest common number from these two lists.

A finite sequence of steps required to get the desired output is called an algorithm. Algorithm has a definite beginning and a definite end, and consists of a finite number of steps.

Characteristics of a good algorithm

  • Precision — the steps are precisely stated or defined.
  • Uniqueness — results of each step are uniquely defined and only depend on the input and the result of the preceding steps.
  • Finiteness — the algorithm always stops after a finite number of steps.
  • Input — the algorithm receives some input.
  • Output — the algorithm produces some output.

While writing an algorithm, it is required to clearly identify the following:

  • The input to be taken from the user.
  • Processing or computation to be performed to get the desired result.
  • The output desired by the user.

Representation of Algorithms

There are two common methods of representing an algorithm —

Flowchart — Visual Representation of Algorithms

A flowchart is a visual representation of an algorithm. A flowchart is a diagram made up of boxes, diamonds and other shapes, connected by arrows. Each shape represents a step of the solution process and the arrow represents the order or link among the steps. There are standardised symbols to draw flowcharts.

Start/End – Also called “Terminator” symbol. It indicates where the flow starts and ends.

Process – Also called “Action Symbol,” it represents a process, action, or a single step. Decision – A decision or branching point, usually a yes/no or true/ false question is asked, and based on the answer, the path gets split into two branches.

Input / Output – Also called data symbol, this parallelogram shape is used to input or output data.

Arrow – Connector to show order of flow between shapes.

Question: Write an algorithm to find the square of a number. Algorithm to find square of a number. Step 1: Input a number and store it to num Step 2: Compute num * num and store it in square Step 3: Print square

The algorithm to find square of a number can be represented pictorially using flowchart

introduction to problem solving notes pdf

A pseudocode (pronounced Soo-doh-kohd) is another way of representing an algorithm. It is considered as a non-formal language that helps programmers to write algorithm. It is a detailed description of instructions that a computer must follow in a particular order.

  • It is intended for human reading and cannot be executed directly by the computer.
  • No specific standard for writing a pseudocode exists.
  • The word “pseudo” means “not real,” so “pseudocode” means “not real code”.

Keywords are used in pseudocode:

Question : Write an algorithm to calculate area and perimeter of a rectangle, using both pseudocode and flowchart.

Pseudocode for calculating area and perimeter of a rectangle.

INPUT length INPUT breadth COMPUTE Area = length * breadth PRINT Area COMPUTE Perim = 2 * (length + breadth) PRINT Perim The flowchart for this algorithm

introduction to problem solving notes pdf

Benefits of Pseudocode

  • A pseudocode of a program helps in representing the basic functionality of the intended program.
  • By writing the code first in a human readable language, the programmer safeguards against leaving out any important step.
  • For non-programmers, actual programs are difficult to read and understand, but pseudocode helps them to review the steps to confirm that the proposed implementation is going to achieve the desire output.

Flow of Control :

The flow of control depicts the flow of process as represented in the flow chart. The process can flow in

In a sequence steps of algorithms (i.e. statements) are executed one after the other.

In a selection, steps of algorithm is depend upon the conditions i.e. any one of the alternatives statement is selected based on the outcome of a condition.

Conditionals are used to check possibilities. The program checks one or more conditions and perform operations (sequence of actions) depending on true or false value of the condition.

Conditionals are written in the algorithm as follows: If is true then steps to be taken when the condition is true/fulfilled otherwise steps to be taken when the condition is false/not fulfilled

Question : Write an algorithm to check whether a number is odd or even. • Input: Any number • Process: Check whether the number is even or not • Output: Message “Even” or “Odd” Pseudocode of the algorithm can be written as follows: PRINT “Enter the Number” INPUT number IF number MOD 2 == 0 THEN PRINT “Number is Even” ELSE PRINT “Number is Odd”

The flowchart representation of the algorithm

flow_chart_if_else

Repetitions are used, when we want to do something repeatedly, for a given number of times.

Question : Write pseudocode and draw flowchart to accept numbers till the user enters 0 and then find their average. Pseudocode is as follows:

Step 1: Set count = 0, sum = 0 Step 2: Input num Step 3: While num is not equal to 0, repeat Steps 4 to 6 Step 4: sum = sum + num Step 5: count = count + 1 Step 6: Input num Step 7: Compute average = sum/count Step 8: Print average The flowchart representation is

flow_chart_repetition

Once an algorithm is finalised, it should be coded in a high-level programming language as selected by the programmer. The ordered set of instructions are written in that programming language by following its syntax.

The syntax is the set of rules or grammar that governs the formulation of the statements in the language, such as spelling, order of words, punctuation, etc.

Source Code: A program written in a high-level language is called source code.

We need to translate the source code into machine language using a compiler or an interpreter so that it can be understood by the computer.

Decomposition is a process to ‘decompose’ or break down a complex problem into smaller subproblems. It is helpful when we have to solve any big or complex problem.

  • Breaking down a complex problem into sub problems also means that each subproblem can be examined in detail.
  • Each subproblem can be solved independently and by different persons (or teams).
  • Having different teams working on different sub-problems can also be advantageous because specific sub-problems can be assigned to teams who are experts in solving such problems.

Once the individual sub-problems are solved, it is necessary to test them for their correctness and integrate them to get the complete solution.

Computer Science Answer Key Term 2 Board Examination

  • Input Output in Python

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Introduction to Optimization with Genetic Algorithm

Optimization is the process of finding the best solution after evaluating all possible combinations. When dealing with complex problems, finding the optimal solution becomes crucial. One powerful tool in machine learning for solving such optimization problems is the genetic algorithm . Inspired by the theory of natural selection, this algorithm mimics the process of evolution to identify the most optimal solution.

In this article, we will explore the concept of genetic algorithms, their key components, how they work, a simple example, their advantages and disadvantages, and various applications across different fields.

Table of Content

What is a Genetic Algorithm?

Key concepts of genetic algorithms, how does a genetic algorithm work, solving a simple problem with a genetic algorithm, implementation: optimizing a neural network using a genetic algorithm in python, advantages of genetic algorithms, disadvantages of genetic algorithms, applications of genetic algorithms.

A genetic algorithm (GA) is a problem-solving technique inspired by Charles Darwin’s theory of natural evolution. It operates on the principle of natural selection, where the fittest individuals are chosen for reproduction to produce the next generation’s offspring. Think of it as solving a puzzle with multiple potential solutions. By iteratively selecting, combining, and mutating these solutions, a genetic algorithm gets closer to the optimal solution with each step, much like assembling a puzzle piece by piece.

Understanding the fundamental components of a genetic algorithm is essential for grasping how it works. Here are the key concepts:

  • Population: A population is a group of potential solutions that evolve over time. It represents different guesses at the answer to the problem.
  • Chromosome: A chromosome is the blueprint of a solution. It is a single solution represented in a form that the algorithm can manipulate.
  • Gene: A gene is a part of a chromosome that represents a piece of the solution. Each gene holds a value that contributes to the overall solution.
  • Fitness Function: The fitness function evaluates how good a solution is. The higher the fitness score, the better the solution. It guides the selection process by favoring better solutions.
  • Selection: Selection is the process of choosing the best solutions from the population to create the next generation. The fittest solutions have a higher chance of being selected.
  • Crossover: Crossover is the process of combining two solutions to produce a new one. It mimics biological reproduction, where two parents produce offspring that inherit traits from both.
  • Mutation: Mutation introduces small changes in a solution to explore new possibilities. It ensures diversity within the population and prevents premature convergence to suboptimal solutions.

Now, we are going to see how the genetic algorithm works step wise. We will break down in very simple steps:

  • Initialization: It start by creating a random population of possible solutions. Each created solution is like a guess at the answer.
  • Selection: Now it evaluate each solution using the fitness function. The better solution have more possibility in getting selected for creating the next generation.
  • Crossover: Now, it combine parts of two selected solutions to create a new solution. We hope that the newly created solution is more better and contain traits of both the combined solution. It is same as two parents produce a child.
  • Mutation: Sometimes, we make small changes in solution to introduce new diversity. This method help us to explore new possibilities that have not been considered yet.
  • Evaluation: Now it check how good the new solutions are using the fitness function.
  • Replacement: In this step, we replace the old population with the new one and repeat the process until we find the best solution or until we have run the algorithm for a certain number of generations.
  • Termination: The process stops when the solution is good enough. The solution may also terminate after a number of generations.

A genetic algorithm (GA) is a search heuristic that mimics the process of natural selection. It’s used to find optimal or near-optimal solutions to problems by iteratively improving a set of candidate solutions according to the rules of evolution and natural genetics.

For the specific problem of finding the maximum value of the function f(x)=x where x ranges from 0 to 31, you would use a genetic algorithm as follows:

  • Representation: Each solution, x, is represented as a 5-bit binary string.
  • Initial Population: Start with a randomly generated group of these binary strings.
  • Fitness Function: Calculate the fitness of each string by converting it from binary to an integer, plugging it into f(x)=x, and using the result as the fitness score.
  • Selection: Choose the best-performing strings from the population.
  • Crossover: Mix the binary strings of selected pairs to create new strings.
  • Mutation: Occasionally flip some bits in the strings to introduce variability.
  • New Generation: Replace the old generation with the new one and repeat the process until the string that represents the maximum value of f(x) is found.

This genetic algorithm evolves solutions over generations, increasingly moving towards an optimal solution by mimicking the evolutionary process of natural selection.

Here’s an example of how a genetic algorithm can optimize a neural network using Python. The algorithm runs for 50 generations, evaluating the fitness of each neural network in the population. The best fitness value shows the highest accuracy achieved by any individual in that generation.

Step 1: Import Libraries

We start by importing all necessary libraries for data manipulation, machine learning, and plotting.

Step 2: Create the Dataset

Using scikit-learn, we generate a synthetic classification dataset. This dataset will be used to train and validate the neural network.

Step 3: Define Neural Network Structure

We define the structure of our simple neural network, which includes the size of the input layer, hidden layer, and output layer.

Step 4: Helper Functions

Define the sigmoid activation function and the forward pass function, which are essential for the neural network’s operation. The sigmoid function provides a non-linear transformation, and the forward_pass performs the neural computation.

Step 5: Define Fitness Function

This function computes the fitness of a neural network configuration. It uses the forward pass function to make predictions and then evaluates these predictions using the accuracy score.

Step 6: Initialize Population

Set up the initial population of neural networks with random weights. Each individual in the population represents a potential solution.

Step 7: Genetic Algorithm Loop

Run the genetic algorithm, which includes fitness evaluation, selection, crossover, and mutation across multiple generations.

Step 8: Evaluation on Validation Set

After training, evaluate the best performing model on the validation set to see how well it generalizes.

Step 9: Plot Fitness History

Finally, plot the fitness history to visualize the genetic algorithm’s performance over the generations.

Complete Code

generation-vs-fitness

  • Flexible: This algorithm can be applied to various domain it is not only limited to mathematics and computer science domain.
  • Global Search: This algorithm is good at finding a global optimum in a large search space.
  • Simple and Parallelizable: This process is easy to understand and can be run on multiple processors at single time.
  • Expensive: Genetic algorithms requires a lot of resources and time for very complex problems.
  • No Optimal Solution: After applying this approach we cannot guarantee the most optimal solution. We cannot say that we evaluated the best solution.

There are different applications of genetic algorithms in various fields. Some of them are:

  • Engineering Design: It is used in engineering for optimizing structures, electronic circuits, and systems.
  • Artificial Intelligence: It is used in the domain of AI to evolve neural networks, decision trees, and other AI models.
  • Finance: It is used in finances for portfolio optimization and algorithmic trading strategies.
  • Robotics: This algorithm is used for evolving control strategies and optimizing the movement of robots.

We can find the optimal problem of a solution using genetic algorithms. This is used to solve optimization problems by the same as the theory of natural selection works. This algorithm is generally used when the problem is complex has a large search space. We can understand the gentic algorithm and apply its basic concepts in various complex problems and see how they works.

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  1. 9.1 Introduction to problem solving class

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  6. Problem Solving: Mastering a Key Skill in English

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  1. PDF Introduction to Problem Solving

    finding the solution to a problem might consist of multiple steps. When problems are straightforward and easy, we can easily find the solution. But a complex problem requires a methodical approach to find the right solution. In other words, we have to apply problem solving techniques. Problem solving begins with the precise identification of

  2. PDF CS2104: Introduction to Problem Solving

    1. Problem solving is a skill (it can be learned). It is not an innate ability. 2. Problem solving is fundamentally about attitude and effort (the "problem-solving stance"). 3. The problem-solving stance isn't something that you can just "turn on" when you need it for a test, etc. You have to live it - and successful

  3. PDF An Introduction to Computer Science and Problem Solving

    COMP1405/1005 - An Introduction to Computer Science and Problem Solving Fall 2011 - 4- There are also other types of programming languages such as functional programming languages and logic programming languages. According to the Tiobe index (i.e., a good site for ranking the popularity of programming languages), as of February 2011 the 10 most

  4. PDF Introduction to Problem-Solving Strategies

    Write the problem on one side of the card. On the other side, write the solution or solutions, the strategy or strategies used to solve the problem, the correct answer, and wher. the problem may fit into your curric. As a means of introducing a topic. As a means of reviewing a topic taught earlier.

  5. PDF An Introduction to Problem Solving

    a history of success with problem solving. Dismissers have a history of failure. Of course, you might be an engager for one type of problem, and a dismisser for another. Many students do significant problem solving for recreation - Sodoku puzzles, computer games with meaningful problem solving tasks, and all sorts of "puzzles."

  6. PDF Chapter 0 Introduction to Problem-Solving

    Computer Science can be summarized with two simple words: problem solving. Computer Science is the study of problems, problem-solving, and the solutions that come out of this problem-solving process. Given a problem, the goal is to develop an algorithm to solve the problem. An algorithm is a step-by-step list of instructions to solve the problem.

  7. PDF SECTION 1.1 Introduction to Problem Solving

    gSECTION 1.1Introduction iPROBLEM OPENERProblem solving is the hallmark of mathematical activity and a major. means of developing mat. 00, p. 116.Figure 1.1to Problem Solving iThere is no more significant privilege than to rel. International Business Machines CorporationAlice counted 7 cycle ride.

  8. PDF Introduction to problem solving

    Specify the problem requirements. Describe the problem completely and unambiguously. Analyze the problem requirements. Identify (a) inputs, (b) the data to work with, (c) outputs (i.e. desired results). Design the algorithm to solve the problem. Write the step-by-step procedures required to solve the problem.

  9. PDF CSC 101 LectureNotes Week 1 Introduction to the Course Introduction to

    1. Statingclearlywhat the problem is 2. Defininghow the problem can be solved in a logical sequence of steps 3. Verifying that the solution really does solve the stated problem B. Whenhumans solveproblems by themselves, theyuse a vast array of knowledge and understanding to per-form these problem solving steps.

  10. (PDF) An Introduction to Problem Solving

    An Introduction to Problem Solving. To successfully solve any problem, the most important issue to get actively involved. Levine [Lev94] calls this "The Principle of Intimate Engagement.". Writers on problem solving often use terms like "roll up your sleeves" and "get your hands dirty.". It means actively engaging with the problem ...

  11. PDF Problem Solving Basics and Computer Programming

    We can do this in four steps. 1. Identify all of the nouns in the sentence. Given the 3 dimensions of a box (length, width, and height), calculate the volume. The nouns in the problem specification identify descriptions of information that you will need to either identify or keep track of.

  12. 1.1: Introduction to Problem Solving

    The very first Mathematical Practice is: Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of ...

  13. PDF Problem-solving strategies

    Problem-solving strategies From Problems and Solutions in Introductory Mechanics (Draft version, August 2014) David Morin, [email protected] TO THE READER: This book is available as both a paperback and an eBook. I have made a few chapters available on the web, but it is possible (based on past experience) that a pirated

  14. Introduction to Problem Solving Class 11 Notes

    Steps for problem solving. There are 4 basic steps involved in problem solving. Analyze the problem. Developing an algorithm. Coding. Testing and debugging. Analyze the problem. Analyzing the problem is basically understanding a problem very clearly before finding its solution. Analyzing a problem involves.

  15. Problem Solving: Lecture Notes: Part I. Types of Problems

    Problem Solving_ Lecture Notes - Free download as PDF File (.pdf), Text File (.txt) or read online for free. The document discusses problem solving and different types of problems. It describes the problem solving cycle which includes problem identification, definition, developing a strategy, organizing information, allocating resources, monitoring progress, and evaluating the solution.

  16. UNIT 1

    Introduction to Problem Solving: Problem-solving strategies, Problem identification, Problem understanding, Algorithm development, Solution planning (flowcharts ... Problem solving - Lecture notes 1. Problem Solving and Programming. Lecture notes. 100% (9) ... This pdf contains the basics of Thermodynamics and Statistical mechanics to;

  17. CSC 102 Introduction To Problem Solving PDF

    CSC 102 INTRODUCTION TO PROBLEM SOLVING.pdf - Free download as PDF File (.pdf), Text File (.txt) or read online for free.

  18. PDF Introduction to Problem Solving

    that problem by using our knowledge of the problem domain and by relying on our ability to select and use appropriate problem-solving Strategies, Techniques and Tools. Problem solving (with in the context of developing programs) refers to analyzing a problem with the intention of deriving a solution for the problem

  19. Introduction to Problem Solving

    Step 1: Find the numbers (divisors) which can divide the given numbers. Step 2: Then find the largest common number from these two lists. A finite sequence of steps required to get the desired output is called an algorithm. Algorithm has a definite beginning and a definite end, and consists of a finite number of steps.

  20. PDF Problem Solving UNIT 1 PROBLEM SOLVING

    one's performance in problem solving. 1.2.1 Steps for Problem - Solving A problem-solving technique follows certain steps in finding the solution to a problem. Let us look into the steps one by one: Problem definition phase The success in solving any problem is possible only after the problem has been fully understood.

  21. PDF Chapter 1 What Is Critical Thinking?

    Here are three definitions of critical thinking by leading researchers. First, Robert Ennis's classic definition:1. Critical thinking is reasonable, reflective thinking that is focused on decid-ing what to believe or do. 1. Even before you start reading this text, begin by examining your own con-cept of critical thinking.

  22. Introduction to Optimization with Genetic Algorithm

    A genetic algorithm (GA) is a problem-solving technique inspired by Charles Darwin's theory of natural evolution. It operates on the principle of natural selection, where the fittest individuals are chosen for reproduction to produce the next generation's offspring. Think of it as solving a puzzle with multiple potential solutions.

  23. 5.1: Introduction to Problem Solving

    Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway ...