This document discusses problem solving techniques in computer science. It begins by explaining that flow charts and pseudo code are intermediate languages that sit between natural languages and computer languages. It then provides examples of flow charts and pseudo code to solve problems like finding the sum and maximum of two numbers, estimating the volume of a box, writing a number between 0-3 in words, and more. The document discusses the different components of flow charts and pseudo code like sequencing, branching, iteration, and walks through checking the correctness of a pseudo code or flow chart. Finally, it discusses approaches for creating computer programs like the top-down approach and structured programming.
This document provides an overview of linear equations in one variable. It defines a linear equation as one that can be written in the form ax = b, where a and b are real numbers and a ≠ 0. Parts of a linear equation like the variable, coefficient, constants, and left and right hand sides are explained. It also discusses how to solve linear equations by finding the value of the variable that makes the left and right sides equal. Several examples are provided of how to translate word problems into linear equations and solve them. Real-world applications of linear equations discussed include comparing rates of pay from different jobs and calculating cab fares.
Applied Artificial Intelligence Unit 2 Semester 3 MSc IT Part 2 Mumbai Univer...Madhav Mishra
This document covers probability theory and fuzzy sets and fuzzy logic, which are topics for an applied artificial intelligence unit. It discusses key concepts for probability theory including joint probability, conditional probability, and Bayes' theorem. It also covers fuzzy sets and fuzzy logic, including fuzzy set operations, types of membership functions, linguistic variables, and fuzzy propositions and inference rules. Examples are provided throughout to illustrate probability and fuzzy set concepts. The document is presented as a slideshow with explanatory text and diagrams on each slide.
Detailed discussion about the types of statistics form Measures of Central Tendency, Measures of Dispersion, Skewness, Kurtosis, Probability Distributions and much more with their uses cases
The document provides an overview of Calculus II and discusses some of the challenges students face in the course. It notes that Calculus II requires a strong foundation in Calculus I concepts. Students must learn to think critically and identify which solution techniques can be applied to problems that may have multiple approaches. The series convergence/divergence section introduces key concepts around infinite series and defines convergent and divergent series. It presents examples to illustrate determining if a series converges or diverges and establishes the important result that if the limit of a series' terms is zero, the series may converge, but the converse is not necessarily true.
The document discusses different scales of measurement used in research. There are four main scales: nominal, ordinal, interval, and ratio. Nominal scales use numbers to replace categories or names and assume no quantitative relationship between numbers. Ordinal scales represent relative quantities of attributes but intervals between numbers are not equal. Interval and ratio scales both assume equal intervals but ratio scales have a true zero point.
This document provides an introduction to algorithms and data structures. It defines algorithms and describes their key properties including being finite, definite, and executable sequences of steps. It also discusses structured programming using sequences, selections, and iterations. The document presents two common algorithm description methods - flow diagrams and pseudocode - and provides examples of each. It then classifies algorithms into four types based on their inputs and outputs and provides example algorithms for each type. The document also discusses special algorithms like recursive and backtracking algorithms, and provides examples of each. Finally, it introduces analysis of algorithms and some common data structures like arrays, linked lists, stacks, queues, binary search trees, and graphs.
This document discusses counting techniques used in probability and statistics. It introduces the fundamental principle of counting and the multiplication rule for determining the total number of possible outcomes of multi-step processes. Specific counting techniques covered include the tree diagram, permutations, and combinations. Examples are provided to demonstrate how to apply these techniques to problems involving determining the number of arrangements of different objects.
This document summarizes a computer science lesson on algorithms and flowcharts. It discusses defining sequential, selective, and repetitive constructs to represent program flow. Sequential constructs execute steps strictly in order. Selection constructs execute code conditionally. Iterative constructs allow statements to repeat until a condition is met. Examples are given of algorithms and flowcharts for calculating averages, finding the largest of two numbers, and counting from 1 to 10. Students are asked to complete homework on algorithm characteristics, summing 10 numbers, and the Fibonacci series.
This document provides an overview of linear equations in one variable. It defines a linear equation as one that can be written in the form ax = b, where a and b are real numbers and a ≠ 0. Parts of a linear equation like the variable, coefficient, constants, and left and right hand sides are explained. It also discusses how to solve linear equations by finding the value of the variable that makes the left and right sides equal. Several examples are provided of how to translate word problems into linear equations and solve them. Real-world applications of linear equations discussed include comparing rates of pay from different jobs and calculating cab fares.
Applied Artificial Intelligence Unit 2 Semester 3 MSc IT Part 2 Mumbai Univer...Madhav Mishra
This document covers probability theory and fuzzy sets and fuzzy logic, which are topics for an applied artificial intelligence unit. It discusses key concepts for probability theory including joint probability, conditional probability, and Bayes' theorem. It also covers fuzzy sets and fuzzy logic, including fuzzy set operations, types of membership functions, linguistic variables, and fuzzy propositions and inference rules. Examples are provided throughout to illustrate probability and fuzzy set concepts. The document is presented as a slideshow with explanatory text and diagrams on each slide.
Detailed discussion about the types of statistics form Measures of Central Tendency, Measures of Dispersion, Skewness, Kurtosis, Probability Distributions and much more with their uses cases
The document provides an overview of Calculus II and discusses some of the challenges students face in the course. It notes that Calculus II requires a strong foundation in Calculus I concepts. Students must learn to think critically and identify which solution techniques can be applied to problems that may have multiple approaches. The series convergence/divergence section introduces key concepts around infinite series and defines convergent and divergent series. It presents examples to illustrate determining if a series converges or diverges and establishes the important result that if the limit of a series' terms is zero, the series may converge, but the converse is not necessarily true.
The document discusses different scales of measurement used in research. There are four main scales: nominal, ordinal, interval, and ratio. Nominal scales use numbers to replace categories or names and assume no quantitative relationship between numbers. Ordinal scales represent relative quantities of attributes but intervals between numbers are not equal. Interval and ratio scales both assume equal intervals but ratio scales have a true zero point.
This document provides an introduction to algorithms and data structures. It defines algorithms and describes their key properties including being finite, definite, and executable sequences of steps. It also discusses structured programming using sequences, selections, and iterations. The document presents two common algorithm description methods - flow diagrams and pseudocode - and provides examples of each. It then classifies algorithms into four types based on their inputs and outputs and provides example algorithms for each type. The document also discusses special algorithms like recursive and backtracking algorithms, and provides examples of each. Finally, it introduces analysis of algorithms and some common data structures like arrays, linked lists, stacks, queues, binary search trees, and graphs.
This document discusses counting techniques used in probability and statistics. It introduces the fundamental principle of counting and the multiplication rule for determining the total number of possible outcomes of multi-step processes. Specific counting techniques covered include the tree diagram, permutations, and combinations. Examples are provided to demonstrate how to apply these techniques to problems involving determining the number of arrangements of different objects.
This document summarizes a computer science lesson on algorithms and flowcharts. It discusses defining sequential, selective, and repetitive constructs to represent program flow. Sequential constructs execute steps strictly in order. Selection constructs execute code conditionally. Iterative constructs allow statements to repeat until a condition is met. Examples are given of algorithms and flowcharts for calculating averages, finding the largest of two numbers, and counting from 1 to 10. Students are asked to complete homework on algorithm characteristics, summing 10 numbers, and the Fibonacci series.
The document provides an overview of a lecture on proving a lower time bound of Ω(n log n) for the element distinctness problem in the decision tree model. It begins by defining the element distinctness problem and stating the lower bound that will be proved. It then discusses interpreting the input sequence as coordinates of an n-dimensional point and restricting points to the unit n-cube. The key claims are that each leaf region is connected, and distinct input points must reach distinct leaves, implying there are at least n! leaves and a time lower bound of n log n.
This document provides an overview of linear and logistic regression models. It discusses that linear regression is used for numeric prediction problems while logistic regression is used for classification problems with categorical outputs. It then covers the key aspects of each model, including defining the hypothesis function, cost function, and using gradient descent to minimize the cost function and fit the model parameters. For linear regression, it discusses calculating the regression line to best fit the data. For logistic regression, it discusses modeling the probability of class membership using a sigmoid function and interpreting the odds ratios from the model coefficients.
This document introduces exponents and explains what they are. Exponents tell us to take a number called the base and multiply it by itself a certain number of times, represented by the exponent. The base is written normally sized and the exponent is written smaller above the base. Exponents show repeated multiplication, with the exponent indicating how many times the base is multiplied. Examples are provided to illustrate exponents and their notation.
Std 10 computer chapter 9 Problems and Problem SolvingNuzhat Memon
Std 10 computer chapter 9 Problems and Problem Solving
Problem and Types of problem
Problem solving
Flowchart
Symbols of flowchart
Flowchart to calculate area of rectangle
Flowchart to calculate area and perimeter of circle
Flowchart to compute simple interest
Flowchart to find youngest student amongst two students
Flowchart to find youngest student amongst three students
Flowchart to find youngest student amongst any number of students
Flowchart to find sum of first 50 odd numbers
Flowchart to interchange or swap values of two variables with extra variable
Flowchart to interchange or swap values of two variables without extra variable
Advantage and disadvantage of flowchart
Algorithm
Advantage of flowchart
disadvantage of flowchart
Algorithm
Algorithm to find sum of numbers divisible by 11 in the range of 1 to 100
Algorithm to compute interest
Algorithm to find total weekly pay of employee
This document contains examples of using for loops and while loops in MATLAB. It begins with examples of summing prime numbers, duplicating vector elements, and converting a for loop to a while loop. It then provides more examples of using loops to calculate interest, convert a matrix to a vector, print patterns of stars, and find twin prime numbers. It discusses the importance of efficiency in MATLAB and compares loop-based approaches to vectorized solutions.
The document discusses the power of recursion and induction in mathematics, modeling, and technology. It provides examples of how recursion appears in definitions of natural numbers and functions. Recursion can also be used to solve complex problems by breaking them down into simpler subproblems. Spreadsheets are an example of how recursion naturally occurs in technology. Teaching recursion enhances modeling skills and helps move from complex to simple problems.
Here are the algorithms in pseudocode:
1. Find largest number of unknown set:
- Read first number and assign to largest
- Read next number
- If number is greater than largest, assign it to largest
- Repeat step 2 until no more numbers
- Output largest
2. Find average of numbers:
- Read number of elements n
- Initialize sum = 0
- Initialize i = 0
- Repeat while i < n
- Read element at array[i]
- Add element to sum
- Increment i
- Calculate average = sum / n
- Output average
Here are the algorithms in pseudocode:
1. Find largest number of unknown set:
- Read first number and assign to largest
- Read next number
- If number is greater than largest, assign it to largest
- Repeat step 2 until no more numbers
- Output largest
2. Find average of numbers:
- Read number of elements n
- Initialize sum = 0
- Initialize i = 0
- Repeat while i < n
- Read element at array[i]
- Add element to sum
- Increment i
- Calculate average = sum / n
- Output average
The document discusses the characteristics of algorithms and the concept of mathematical expectation in average case analysis. It then provides the pseudocode for the MaxMin algorithm and discusses the greedy knapsack algorithm and the travelling salesman problem. Finally, it explains the sum of subsets problem, describing two formulations and how the solution space can be organized into trees.
Rational numbers can be represented as fractions or decimals. Fractions in the form of p/q where p and q are integers and q is not equal to 0 are called rational numbers. Some key rational number concepts discussed include:
- Natural numbers are counting numbers and whole numbers include zero. Integers include both positive and negative whole numbers.
- Rational numbers can be added, subtracted, multiplied, and divided using the same rules as fractions.
- Two fractions are equal if their numerator to denominator ratios are equal.
- Rational numbers that terminate are called terminating decimals, while those that repeat infinitely are non-terminating or recurring decimals.
This guide provides a refresher on basic computer programming concepts without using a specific programming language. It defines key terms like variables, which represent values that can change throughout a program, and statements, which are the smallest standalone elements a computer can understand. It also explains functions and methods as named sets of instructions that can be reused, and parameters as values passed into functions. Finally, it outlines different data types like integers, doubles, strings, and booleans that variables can take on to store different kinds of values.
This document provides notes for a Calculus I course taught by Paul Dawkins at Lamar University. The notes cover topics such as functions, inverse functions, trigonometric functions, exponential and logarithmic functions. The notes are intended to be a complete resource for learning Calculus I, though the author warns students that not everything covered in the notes is discussed in class. Students are advised to supplement the notes with attendance and their own class notes. The document contains examples and explanations to accompany the course material.
Learning with Technology in the Mathematics ClassroomColleen Young
This document contains slides from a presentation on using technology in the mathematics classroom. It discusses using various websites, online tools like Desmos and WolframAlpha, and different types of activities for starters, homework, and feedback. It also provides examples of rich tasks and ideas for ending lessons well. The final slides discuss organizing resources and the importance of reading.
Decimals are commonly used in measurements and commerce. They allow numbers to be represented on the number line through repeated subdivision into tenths. A decimal number locates a point on the number line through the place value of its digits. Decimals extend the place value concept for whole numbers to include tenths, hundredths, thousandths, and so on. While widely used today, decimals were not commonly adopted until the early 17th century. Decimals can represent both rational and some irrational numbers and are useful for approximations and measurements recorded to a given accuracy.
This document provides an overview of solving linear inequalities. It introduces inequality notation and properties, discusses multiplying and dividing by negative numbers, and provides examples of solving different types of linear inequalities. It also covers interval notation, graphing solutions to inequalities on number lines, and using interactive tools like Gizmos for additional practice with inequalities.
This document provides an overview and review of key concepts in precalculus that are important for success in Calculus I, including:
- Functions and function notation. Key points are that a function assigns a single output to each input, and function notation (e.g. f(x)) represents the output of a function given a specific input.
- Finding roots of functions by setting the function equal to zero and solving.
- Composition of functions, where the output of one function becomes the input of another. The order of functions in composition matters.
- Other topics like inverse functions, trigonometric functions, exponentials and logarithms are also reviewed at a high level.
The document
Amatyc improving reading for developmental mathematics2014Linda Russell
The document discusses the challenges of reading in mathematics and strategies to improve mathematical literacy. It notes that mathematical reading requires precision and an understanding of domain-specific terminology, symbols, and concepts. Some key habits for successful mathematical reading include carefully reading all words and representations, valuing accuracy, thinking systematically, and persisting when concepts are unclear. The document provides examples of linguistic elements that are precisely defined in mathematics versus more casual meanings and recommends techniques for teachers to support students' mathematical reading abilities.
Internet Connections and Its Protocols - R D SivakumarSivakumar R D .
This document discusses internet connections and protocols. It explains that an internet connection requires a computer, telephone line, modem, and internet service provider (ISP). The ISP maintains the user's account using a unique username and password. Common web browsers like Chrome, Firefox, and Internet Explorer are used to access websites by entering URLs. Protocols like TCP/IP, HTTP, HTTPS, FTP, Telnet, and SMTP allow devices to communicate over the internet and transfer files and emails. TCP/IP breaks data into packets and ensures intact delivery. HTTP is used for communication between web servers and clients, while HTTPS provides security. FTP transfers files, Telnet enables remote login, and SMTP transfers emails between systems.
The document discusses the internet and its uses. It defines the internet as a network of networks and lists some common users as students, faculty, scientists, and executives. It also explains that the Internet Society and ICANN help govern and administer the internet by overseeing domain names. Additionally, it outlines email and how it is used to exchange messages and files between users. The document also briefly discusses the future of the internet and popular tools on the internet like the world wide web, which is a collection of web pages used for research, chatting, job searches and more.
More Related Content
Similar to Problem Solving Techniques - R.D.Sivakumar
The document provides an overview of a lecture on proving a lower time bound of Ω(n log n) for the element distinctness problem in the decision tree model. It begins by defining the element distinctness problem and stating the lower bound that will be proved. It then discusses interpreting the input sequence as coordinates of an n-dimensional point and restricting points to the unit n-cube. The key claims are that each leaf region is connected, and distinct input points must reach distinct leaves, implying there are at least n! leaves and a time lower bound of n log n.
This document provides an overview of linear and logistic regression models. It discusses that linear regression is used for numeric prediction problems while logistic regression is used for classification problems with categorical outputs. It then covers the key aspects of each model, including defining the hypothesis function, cost function, and using gradient descent to minimize the cost function and fit the model parameters. For linear regression, it discusses calculating the regression line to best fit the data. For logistic regression, it discusses modeling the probability of class membership using a sigmoid function and interpreting the odds ratios from the model coefficients.
This document introduces exponents and explains what they are. Exponents tell us to take a number called the base and multiply it by itself a certain number of times, represented by the exponent. The base is written normally sized and the exponent is written smaller above the base. Exponents show repeated multiplication, with the exponent indicating how many times the base is multiplied. Examples are provided to illustrate exponents and their notation.
Std 10 computer chapter 9 Problems and Problem SolvingNuzhat Memon
Std 10 computer chapter 9 Problems and Problem Solving
Problem and Types of problem
Problem solving
Flowchart
Symbols of flowchart
Flowchart to calculate area of rectangle
Flowchart to calculate area and perimeter of circle
Flowchart to compute simple interest
Flowchart to find youngest student amongst two students
Flowchart to find youngest student amongst three students
Flowchart to find youngest student amongst any number of students
Flowchart to find sum of first 50 odd numbers
Flowchart to interchange or swap values of two variables with extra variable
Flowchart to interchange or swap values of two variables without extra variable
Advantage and disadvantage of flowchart
Algorithm
Advantage of flowchart
disadvantage of flowchart
Algorithm
Algorithm to find sum of numbers divisible by 11 in the range of 1 to 100
Algorithm to compute interest
Algorithm to find total weekly pay of employee
This document contains examples of using for loops and while loops in MATLAB. It begins with examples of summing prime numbers, duplicating vector elements, and converting a for loop to a while loop. It then provides more examples of using loops to calculate interest, convert a matrix to a vector, print patterns of stars, and find twin prime numbers. It discusses the importance of efficiency in MATLAB and compares loop-based approaches to vectorized solutions.
The document discusses the power of recursion and induction in mathematics, modeling, and technology. It provides examples of how recursion appears in definitions of natural numbers and functions. Recursion can also be used to solve complex problems by breaking them down into simpler subproblems. Spreadsheets are an example of how recursion naturally occurs in technology. Teaching recursion enhances modeling skills and helps move from complex to simple problems.
Here are the algorithms in pseudocode:
1. Find largest number of unknown set:
- Read first number and assign to largest
- Read next number
- If number is greater than largest, assign it to largest
- Repeat step 2 until no more numbers
- Output largest
2. Find average of numbers:
- Read number of elements n
- Initialize sum = 0
- Initialize i = 0
- Repeat while i < n
- Read element at array[i]
- Add element to sum
- Increment i
- Calculate average = sum / n
- Output average
Here are the algorithms in pseudocode:
1. Find largest number of unknown set:
- Read first number and assign to largest
- Read next number
- If number is greater than largest, assign it to largest
- Repeat step 2 until no more numbers
- Output largest
2. Find average of numbers:
- Read number of elements n
- Initialize sum = 0
- Initialize i = 0
- Repeat while i < n
- Read element at array[i]
- Add element to sum
- Increment i
- Calculate average = sum / n
- Output average
The document discusses the characteristics of algorithms and the concept of mathematical expectation in average case analysis. It then provides the pseudocode for the MaxMin algorithm and discusses the greedy knapsack algorithm and the travelling salesman problem. Finally, it explains the sum of subsets problem, describing two formulations and how the solution space can be organized into trees.
Rational numbers can be represented as fractions or decimals. Fractions in the form of p/q where p and q are integers and q is not equal to 0 are called rational numbers. Some key rational number concepts discussed include:
- Natural numbers are counting numbers and whole numbers include zero. Integers include both positive and negative whole numbers.
- Rational numbers can be added, subtracted, multiplied, and divided using the same rules as fractions.
- Two fractions are equal if their numerator to denominator ratios are equal.
- Rational numbers that terminate are called terminating decimals, while those that repeat infinitely are non-terminating or recurring decimals.
This guide provides a refresher on basic computer programming concepts without using a specific programming language. It defines key terms like variables, which represent values that can change throughout a program, and statements, which are the smallest standalone elements a computer can understand. It also explains functions and methods as named sets of instructions that can be reused, and parameters as values passed into functions. Finally, it outlines different data types like integers, doubles, strings, and booleans that variables can take on to store different kinds of values.
This document provides notes for a Calculus I course taught by Paul Dawkins at Lamar University. The notes cover topics such as functions, inverse functions, trigonometric functions, exponential and logarithmic functions. The notes are intended to be a complete resource for learning Calculus I, though the author warns students that not everything covered in the notes is discussed in class. Students are advised to supplement the notes with attendance and their own class notes. The document contains examples and explanations to accompany the course material.
Learning with Technology in the Mathematics ClassroomColleen Young
This document contains slides from a presentation on using technology in the mathematics classroom. It discusses using various websites, online tools like Desmos and WolframAlpha, and different types of activities for starters, homework, and feedback. It also provides examples of rich tasks and ideas for ending lessons well. The final slides discuss organizing resources and the importance of reading.
Decimals are commonly used in measurements and commerce. They allow numbers to be represented on the number line through repeated subdivision into tenths. A decimal number locates a point on the number line through the place value of its digits. Decimals extend the place value concept for whole numbers to include tenths, hundredths, thousandths, and so on. While widely used today, decimals were not commonly adopted until the early 17th century. Decimals can represent both rational and some irrational numbers and are useful for approximations and measurements recorded to a given accuracy.
This document provides an overview of solving linear inequalities. It introduces inequality notation and properties, discusses multiplying and dividing by negative numbers, and provides examples of solving different types of linear inequalities. It also covers interval notation, graphing solutions to inequalities on number lines, and using interactive tools like Gizmos for additional practice with inequalities.
This document provides an overview and review of key concepts in precalculus that are important for success in Calculus I, including:
- Functions and function notation. Key points are that a function assigns a single output to each input, and function notation (e.g. f(x)) represents the output of a function given a specific input.
- Finding roots of functions by setting the function equal to zero and solving.
- Composition of functions, where the output of one function becomes the input of another. The order of functions in composition matters.
- Other topics like inverse functions, trigonometric functions, exponentials and logarithms are also reviewed at a high level.
The document
Amatyc improving reading for developmental mathematics2014Linda Russell
The document discusses the challenges of reading in mathematics and strategies to improve mathematical literacy. It notes that mathematical reading requires precision and an understanding of domain-specific terminology, symbols, and concepts. Some key habits for successful mathematical reading include carefully reading all words and representations, valuing accuracy, thinking systematically, and persisting when concepts are unclear. The document provides examples of linguistic elements that are precisely defined in mathematics versus more casual meanings and recommends techniques for teachers to support students' mathematical reading abilities.
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Tux Paint is a free, simple drawing program designed for young children. It has an easy-to-use interface with basic drawing tools like a paint brush, stamps, shapes, and text. The program supports multiple platforms and languages. It allows children to create drawings and save them to their computer. Tux Paint provides fun sound effects and templates to encourage creativity.
R.D. Sivakumar is an Assistant Professor in the Department of Computer Science at Ayya Nadar Janaki Ammal College in Sivakasi, India. The college is affiliated with Madurai Kamaraj University and has been recognized and accredited by various organizations for its academic excellence. Sivakumar teaches computer science and heads the M.Com.(CA) department. He also trains faculty as a technical trainer at the Centre for Teacher Education and Learning (CTEL). His contact information, including email and websites containing his academic blog, are provided.
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This is part 1 of my Java Learning Journey. This Contains Custom methods, classes, constructors, packages, multithreading , try- catch block, finally block and more.
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Chapter wise All Notes of First year Basic Civil Engineering.pptxDenish Jangid
Chapter wise All Notes of First year Basic Civil Engineering
Syllabus
Chapter-1
Introduction to objective, scope and outcome the subject
Chapter 2
Introduction: Scope and Specialization of Civil Engineering, Role of civil Engineer in Society, Impact of infrastructural development on economy of country.
Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
Linear Measurements: Instruments used. Linear Measurement by Tape, Ranging out Survey Lines and overcoming Obstructions; Measurements on sloping ground; Tape corrections, conventional symbols. Angular Measurements: Instruments used; Introduction to Compass Surveying, Bearings and Longitude & Latitude of a Line, Introduction to total station.
Levelling: Instrument used Object of levelling, Methods of levelling in brief, and Contour maps.
Chapter 4
Buildings: Selection of site for Buildings, Layout of Building Plan, Types of buildings, Plinth area, carpet area, floor space index, Introduction to building byelaws, concept of sun light & ventilation. Components of Buildings & their functions, Basic concept of R.C.C., Introduction to types of foundation
Chapter 5
Transportation: Introduction to Transportation Engineering; Traffic and Road Safety: Types and Characteristics of Various Modes of Transportation; Various Road Traffic Signs, Causes of Accidents and Road Safety Measures.
Chapter 6
Environmental Engineering: Environmental Pollution, Environmental Acts and Regulations, Functional Concepts of Ecology, Basics of Species, Biodiversity, Ecosystem, Hydrological Cycle; Chemical Cycles: Carbon, Nitrogen & Phosphorus; Energy Flow in Ecosystems.
Water Pollution: Water Quality standards, Introduction to Treatment & Disposal of Waste Water. Reuse and Saving of Water, Rain Water Harvesting. Solid Waste Management: Classification of Solid Waste, Collection, Transportation and Disposal of Solid. Recycling of Solid Waste: Energy Recovery, Sanitary Landfill, On-Site Sanitation. Air & Noise Pollution: Primary and Secondary air pollutants, Harmful effects of Air Pollution, Control of Air Pollution. . Noise Pollution Harmful Effects of noise pollution, control of noise pollution, Global warming & Climate Change, Ozone depletion, Greenhouse effect
Text Books:
1. Palancharmy, Basic Civil Engineering, McGraw Hill publishers.
2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
3. Ketki Rangwala Dalal, Essentials of Civil Engineering, Charotar Publishing House.
4. BCP, Surveying volume 1
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Answers about how you can do more with Walmart!"
This presentation includes basic of PCOS their pathology and treatment and also Ayurveda correlation of PCOS and Ayurvedic line of treatment mentioned in classics.
A review of the growth of the Israel Genealogy Research Association Database Collection for the last 12 months. Our collection is now passed the 3 million mark and still growing. See which archives have contributed the most. See the different types of records we have, and which years have had records added. You can also see what we have for the future.
1. Mr. R.D.SIVAKUMAR, M.Sc.,M.Phil.,M.Tech.,
Assistant Professor of Computer Science &
Assistant Professor and Head, Department of M.Com.(CA),
Ayya Nadar Janaki Ammal College,
Sivakasi – 626 124.
Mobile: 099440-42243
e-mail : sivamsccsit@gmail.com
website: www.rdsivakumar.blogspot.in
PROBLEM SOLVING TECHNIQUES
2. PROBLEM SOLVING TECHNIQUES
In the computer languages every statement must be written precisely, including commas
and semicolons. One has to be very careful while writing these lines.
In the natural languages the sentences may be long. Sometimes they may be vague. So, to
understand things clearly without any ambiguity, we write it in an intermediary language.
This will be easy to write and understand, and also without any ambiguity. These
intermediate languages are in between the natural languages and the computer languages.
We shall study two such intermediate languages, namely, the flow chart and the pseudo
code
3. PROBLEM SOLVING TECHNIQUES
First let us consider the flow chart. Since the flows of computational paths are
depicted as a picture, it is called a flow chart.
Let us start with an example. Suppose we have to find the sum and also the
maximum of two numbers. To achieve this, first the two numbers have to be received
and kept in two places, under two names. Then the sum of them is to be found and
printed. Then depending on which one is bigger, a number is to be printed.
The flow chart for this is given in flow chart 4.1.
4. PROBLEM SOLVING TECHNIQUES
In the flow chart, each shape has a particular meaning.
They are given in flow chart 4.2.
In the flow chart mentioned above, there is a special meaning in writing C = A + B.
Though we use the familiar equal to sign, it is not used in the sense as in an equation.
This statement means — Add the current values available for the names A and B, which
are on the RHS, and put the sum as the new value of the name C, which is in the LHS.
For example, under this explanation, A = A + 1 is a valid statement. The value of A is
taken, incremented by one and the new value is stored as A. That is, the value of A gets
incremented by 1. Note that we can write A = A + B, but not A + B = A. On the LHS
there must be only a name of a place for storing.
5. PROBLEM SOLVING TECHNIQUES
For big problems, the flow chart will also be big. But our paper sizes are limited.
We may need many pages for one flow chart. But how to go from one page to
another?
This is solved by using small circles, called connectors. In this circle, we put some
symbol. All connectors having the same symbol represent the same point, wherever
they are, whether they are in the same page or on different pages. Flow chart 4.3
gives an example.
The advantages of the flow charts are:
• They are precise. They represent our thoughts exactly.
• It is easy to understand small flow charts.
The disadvantage is that real life flow charts can occupy many pages, and hence very difficult
to understand. So no one uses flow charts in such situations.
6. PROBLEM SOLVING TECHNIQUES
Consider the small flow charts given for the following problems. See whether they will
solve the problems. Do not memorize them. Try to understand them. Note how much we
have to think before writing a program.
Flow chart 4.4 estimates the volume of a box using its length, breadth and height.
12. PROBLEM SOLVING TECHNIQUES
Flow chart finds the smallest integer n such that, 1+ 2+ 3+...+n is equal to or
just greater than 1000.
13. FUNDAMENTAL CONDITION AND CONTROL
STRUCTURES
In a computer pseudo code, we have to instruct the computer regarding each and
every step. Only if we can decide all these things by ourselves, we can write a
computer pseudo code. The computer will simply do what we say. And exactly as we
say. It won’t do anything on its own. We can even say that the computer is the fifth
disciple of Paramaartha guru. Do you wonder why?
We shall see one episode in a sequence of such episodes. Paramaartha guru’s
disciples are named (in Tamil) as Matti, Madayan, Moodan and Muttaal, all different
forms of the word ‘fool’. They buy an old horse for their guru. The guru sits on the
horse and the disciples come by walking. The guru’s turban hits a branch of a tree
and falls down. After some time the guru asks for the turban. The disciples say that it
fallen down. When he asks why they had not brought it, they say that he had not told
them so. The guru says that they should take and bring anything that falls down.
One disciple goes back and brings the turban. The guru is annoyed to see the horse
dung in his turban. When the guru asks why he had put the dung in the turban, the
disciple answers “You only asked us to bring whatever has fallen down. How do we
know which one to take and which one to leave? Better give us a list of things to take,
so that there won’t be any confusion.” The guru dictates a long list and then they
proceed.
14. FUNDAMENTAL CONDITION AND CONTROL
STRUCTURES
After some time, the old horse trips and falls down. Then one disciple starts reading
from the list. Things like turban, dhoti, towel etc. are taken one by one. The guru lies
there only with the loincloth. He asks them to take him and put on the horse. For this
comes the prompt reply “ You are not in the list, guru.” When his pleadings fall on
deaf ears, the guru asks tem to revise the list, and include his name in the list. Then
he asks them to check the list again. Now he was helped to get up.
A computer pseudo code is like that list. The computer is like one of these disciples.
It is not much different. It is our responsibility to instruct the computer properly and
elaborately. We should get trained in thinking in such elaborate manner.
In all these, they are only three techniques, which occur again and again. All the
computing is done using only these techniques. Understanding them is just as
necessary as the fisherman learning to swim.
Sequencing
Usually the calculations are done one after another, in a sequence. This is one of the
fundamental control structures
15. BRANCHING
Two-way branching
Ask a question. Get the answer as ‘Yes’ or ‘No’. Depending on the answer,
branch to one of the two available paths. This is depicted by a diagonal shaped
box. You can see this box in many flow charts. Also many times in the same flow
chart. Branching is also a fundamental control structure.
For example, if A > B, then print A, otherwise print B.
This is called the “If ...Then ...Else” structure. If no action is to be taken in one
path, then we can use the “If...Then” structure. In this, if the
answer is ‘No’, then it means that the execution goes to the next
statement without doing anything.
For example, If you find anyone there then say hello
16. BRANCHING
Multi-way branching
For some questions there may not be just a Yes or No answer.
For example -” What is the age of this boy?” the answer can be one of many
integers. Depending on the answer, we may have to make different set of
computations, by going through different paths. This is called multi-way
branching. This can be depicted as in the flow chart
For example, if n is 0 then print ‘zero’
1 then print ‘one’
2 then print ‘two’
3 then print ‘three’
17. ITERATION
The third fundamental technique is iteration. That is, repeating a set of actions again
and again. Of course, we do not repeat the same actions for the same data, as this will be
just a waste of time. The action will be the same, but the data will change every time.
For example, reading 100 numbers, or, finding the interest payable for 1000
customers. In both these examples, we know how many times we are going to repeat the
same action. Hence the name definite iteration. In this method we have to keep track of
the count of the number of times the actions are performed. For this we use a variable
called the index variable or control variable.
There are 4 basic steps involved in using an index variable.
• The index variable should be given an integer as the initial value to start with.
• The current value in the index variable v should be compared with the final value to
decide whether more iteration is required.
• If the answer is Yes, then
Do the required actions once.
Then increment the index v by 1.
Go to step 2 and do the checking again.
• If the answer is No, then
The iterations are over.
Go to the next action in the sequence.
18. ITERATION
The flow chart explains about definite iteration. In this case, the iteration is shown
by the presence of a loop formed by the directed lines.
In some situations, we may not know exactly how many times the iteration is to be
performed, as a number, in the beginning. For example, suppose we have to find the smallest
number n such that 1 + 2 + 3 + ... + n gives at least 100. Suppose we add numbers one by one
and test whether 100 has been reached. We will stop when 100 has been reached.
Here we do not know when we are going to stop as a number. A count is not going to work
here. Only a condition is to be checked for this. Such iteration is called an indefinite
iteration. Using sequencing, branching and iteration, all the computation can be carried out.
Definite Iteration
19. PSEUDO CODE
Instead of using flow chart, pseudo code can be used to represent a procedure for
doing something. Pseudo code is in-between English and the high-level computer
languages. In English the sentences may be long and may not be precise. In the
computer languages the syntax has to be followed meticulously. If these two irritants are
removed then we have the pseudo code.
There are only a few basic sentence types in this. They are also small in their size. But
they have the power to specify any procedure. We have one more felicity. We can use the
usual brackets in the usual sense of combining many things together. By indentation also
we can club statements together. It is easy to understand things written in pseudo code.
The flow chart fundamental control structures for branching and iteration correspond
to the following pseudo code.
• If .... then .... else ....
• If .... then ....
• For ..... to .... do ......
• While .... do .....
20. PSEUDO CODE
A few examples for these are as follows.
• If a > b then print a else print b
• If a < 10 then b = c + d
• For i = 1 to 20 do
n = n + i
• While sum < 100 do
sum = sum + i
i = i + 1
Note that in the while .. do example, the two lines with indentation are to be clubbed
together and treated as one unit for execution. The corresponding flow charts for the
above examples are given below:
21. PSEUDO CODE
Note that all these control structures have only one entry point and only one exit
point. That is after executing the things mentioned in these statements, the control is
transferred to the next statement. That is, after this statement computer takes up the
next statement for execution. This is one of the strong points of these control
structures.
This makes the understanding and debugging (finding and removing errors) easier.
22. PSEUDO CODE
The pseudo codes corresponding to the problem we have worked out in an
earlier section are given below. Compare the flow charts and the pseudo codes,
and ascertain their equivalence
• Finding the volume.
start
read length, breadth and height.
volume = length x breadth x height
print volume
End
Only sequence is used in the above example.
• Write in words.
start
read n
if n is
0 then write ‘zero’
1 then write ‘one’
2 then write ‘two’
3 then write ‘three’
End
24. PSEUDO CODE
There are a few points to be noted.
• Within one ‘if then else’ statement, there is another ‘if then else’ statement. To show this
clearly indentation is used.
• Only the inner statement is written with extra indentation. All the statements in a
sequence have the same indentation.
• Just as we use brackets in Mathematics, here also we use brackets for bunching.
• Since the procedures written in the pseudo code look similar to a program, it is very
easy to convert it into a high-level language computer program
25. WALKTHROUGH
As a first step in writing a program, a flow chart or pseudo code is created, to
represent the solution method. This comes under the designing a solution for the
problem. From this, the program is written with the specific syntax rules of a
particular language. Before writing the program, one must be sure of the correctness
of the method used.
Hence it is necessary to check the correctness of the flow charts and pseudo codes.
First we shall see what an algorithm (solution method) is. Then we shall see a
method, called walkthrough, of checking the pseudo code or flow chart.
An algorithm is a procedure with the following properties.
• There should be a finite number of steps.
• Each step is executable without any ambiguity.
• Each step is executable within a finite amount of time, using a finite amount of
memory space.
• The entire program should be executed within a finite amount of time.
26. CREATING A PROGRAM
Writing a small program is easy. A flow chart or pseudo code can be drawn for
this first. Then from this the program can be written easily. But this method does
not work in the case of real life programs, which are big. A systematic approach
is very much essential in this case.
To create a program, the problem should be divided into many smaller
problems. We should know the method of putting together the results of these
sub problems to get the result for the bigger problem. This is one step in creating
a program. This step is repeatedly used, until the problem becomes small enough
to write a flow chart or pseudo code.
This method of approach is called the ‘Top Down Approach’. In each step we
concentrate on a single thing, find how to get the solution by combining the
results of smaller problems. In the case of computer programs, when this method
was used first, more importance was given to the procedures, that is, the method
of executing things, and not for the data. It is called ‘Structured Programming’.
When dividing a problem into smaller parts, if both the procedure and the data
are taken into account, then we have what is called the ‘Object Oriented
Approach’.