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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

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

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

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

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.

• Input Output in Python

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• Computer Science and Engineering
• NOC:Problem Solving through Programming in C (Video) 
• Co-ordinated by : IIT Kharagpur
• Available from : 2017-12-21
• Intro Video
• Lecture 1 : Introduction
• Lecture 2 : Idea of Algorithms
• Lecture 3 : Flow Chart and Pseudocode
• Lecture 4 : Introduction to Programming Language Concepts
• Lecture 5 : Variables and Memory
• Lecture 6 : Types of Software and Compilers
• Lecture 7 : Introduction to C Programming Language
• Lecture 8 : Variables and Variable Types in C
• Lecture 9 : Introducing Functions
• Lecture 10 : Address and Content of Variables and Types
• Lecture 11 : Assignment Statement and Operators in C
• Lecture 12 : Arithmetic Expressions and Relational Expressions
• Lecture 13 : Logical Operators and Change in Control Flow
• Lecture 14 : Use of Logical Operaotrs in Branching
• Lecture 15 : Branching : IF - ELSE Statement
• Lecture 16 : IF-ELSE Statement (Contd.)
• Lecture 17 : Switch statement
• Lecture 18 : Switch Statement (Contd.) and Introduction to Loops
• Lecture 19 : Implementing Repetitions (Loops)
• Lecture 20 : Implementation of Loops with for Statement (Contd.)
• Lecture 21 : For Statement (Contd.)
• Lecture 22 : Example of If-Else
• Lecture 23 : Example of Loops
• Lecture 24 : Example of Loops (Contd.)
• Lecture 25: Example of Loops (Contd.), Use of FOR Loops
• Lecture 26 : Introduction to Arrays
• Lecture 27 : Arrays (Contd.)
• Lecture 28 : Arrays (Contd.)
• Lecture 29 : Program using Arrays
• Lecture 30 : Array Problem
• Lecture 31 : Linear Search
• Lecture 32 : Character Array and Strings
• Lecture 33 : String Operations
• Lecture 34 : 2-D Array Operation
• Lecture 35 : Introducing Functions
• Lecture 36 : More on Functions
• Lecture 37 : Function (Contd.)
• Lecture 38 : Scanf and Printf Functions; Function Prototype
• Lecture 39 : Parameter Passing in Function Revision
• Lecture 40 : Parameter Passing in Function Revision (Contd.)
• Lecture 41: Substitution of # include and Macro
• Lecture 42: "search" as a function
• Lecture 43: Binary Search
• Lecture 44: Binary Search (Contd.)
• Lecture 45: Sorting Methods
• Lecture 46 : Bubble Sort (Contd.)
• Lecture 47 : Use of Pointer in Function : Context Bubble Sort
• Lecture 48 : Arrays at Strings
• Lecture 49 : Data Representation
• Lecture 50 : Bisection Method
• Lecture 51 : Interpolation
• Lecture 52 : Trapezoidal Rule and Runge-Kutta Method
• Lecture 53 : Recursion
• Lecture 54 : Recursion(Contd.)
• Lecture 55 : Structure
• Lecture 56 : Structure (Contd.)
• Lecture 57 : Structure with typedef
• Lecture 58 : Pointer
• Lecture 59 : Pointer (Contd.)
• Lecture 60 : Pointer in Structures
• Lecture 61 : Dynamic Allocation and File
• Week 2 - PMRF Live Session
• Week 3 - PMRF Live Session
• Watch on YouTube
• Assignments
• Download Videos
• Transcripts
• Handouts (3)

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.

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

• 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

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

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

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

• 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

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

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

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