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Problem Solving Through Programming in C

In this lesson, we are going to learn Problem Solving Through Programming in C. This is the first lesson while we start learning the C language.

So let’s start learning the C language.

Table of Contents

Introduction to Problem Solving Through Programming in C

Regardless of the area of the study, computer science is all about solving problems with computers. The problem that we want to solve can come from any real-world problem or perhaps even from the abstract world. We need to have a standard systematic approach to problem solving through programming in c.

computer programmers are problem solvers. In order to solve a problem on a computer, we must know how to represent the information describing the problem and determine the steps to transform the information from one representation into another.

In this chapter, we will learn problem-solving and steps in problem-solving, basic tools for designing solution as an algorithm, flowchart , pseudo code etc.

A computer is a very powerful and versatile machine capable of performing a multitude of different tasks, yet it has no intelligence or thinking power.

The Computer performs many tasks exactly in the same manner as it is told to do. This places responsibility on the user to instruct the computer in a correct and precise manner so that the machine is able to perform the required job in a proper way. A wrong or ambiguous instruction may sometimes prove dangerous.

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

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

Problem-solving is a sequential process of analyzing information related to a given situation and generating appropriate response options.

In order to solve a problem with the computer, one has to pass through certain stages or steps. They are as follows:

Steps to Solve a Problem With the Computer

problem solving through programming in c

Step 1: Understanding the Problem:

Here we try to understand the problem to be solved in totally. Before with the next stage or step, we should be absolutely sure about the objectives of the given problem.

Step 2: Analyzing the Problem:

After understanding thoroughly the problem to be solved, we look at different ways of solving the problem and evaluate each of these methods.

The idea here is to search for an appropriate solution to the problem under consideration. The end result of this stage is a broad overview of the sequence of operations that are to be carried out to solve the given problem.

Step 3: Developing the solution:

Here, the overview of the sequence of operations that was the result of the analysis stage is expanded to form a detailed step by step solution to the problem under consideration.

Step 4: Coding and Implementation:

The last stage of problem-solving is the conversion of the detailed sequence of operations into a language that the computer can understand. Here, each step is converted to its equivalent instruction or instructions in the computer language that has been chosen for the implantation.

The vehicle for the computer solution to a problem is a set of explicit and unambiguous instructions expressed in a programming language. This set of instruction is called a program with problem solving through programming in C .

A program may also be thought of as an algorithm expressed in a programming language. an algorithm, therefore, corresponds to a solution to a problem that is independent of any programming language .

To obtain the computer solution to a problem once we have the program we usually have to supply the program with input or data. The program then takes this input and manipulates it according to its instructions. Eventually produces an output which represents the computer solution to the problem.

The problem solving is a skill and there are no universal approaches one can take to solving problems. Basically one must explore possible avenues to a solution one by one until she/he comes across the right path to a solution.

In general, as one gains experience in solving problems, one develops one’s own techniques and strategies, though they are often intangible. Problem-solving skills are recognized as an integral component of computer programming.

Note: Practice C Programs for problem solving through programming in C.

Problem Solving Steps

Problem-solving is a creative process which defines systematization and mechanization. There are a number of steps that can be taken to raise the level of one’s performance in 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:

1. Problem Definition Phase:

The success in solving any problem is possible only after the problem has been fully understood. That is, we cannot hope to solve a problem, which we do not understand. So, the problem understanding is the first step towards the solution of the problem.

In the problem definition phase, we must emphasize what must be done rather than how is it to be done. That is, we try to extract the precisely defined set of tasks from the problem statement.

Inexperienced problem solvers too often gallop ahead with the task of the problem – solving only to find that they are either solving the wrong problem or solving the wrong problem or solving just one particular problem.

2. Getting Started on a Problem:

There are many ways of solving a problem and there may be several solutions. So, it is difficult to recognize immediately which path could be more productive. Problem solving through programming in C.

Sometimes you do not have any idea where to begin solving a problem, even if the problem has been defined. Such block sometimes occurs because you are overly concerned with the details of the implementation even before you have completely understood or worked out a solution.

The best advice is not to get concerned with the details. Those can come later when the intricacies of the problem have been understood.

3. Use of Specific Examples:

To get started on a problem, we can make use of heuristics i.e the rule of thumb. This approach will allow us to start on the problem by picking a specific problem we wish to solve and try to work out the mechanism that will allow solving this particular problem.

It is usually much easier to work out the details of a solution to a specific problem because the relationship between the mechanism and the problem is more clearly defined.

This approach of focusing on a particular problem can give us the foothold we need for making a start on the solution to the general problem.

4. Similarities Among Problems:

One way to make a start is by considering a specific example. Another approach is to bring the experience to bear on the current problems. So, it is important to see if there are any similarities between the current problem and the past problems which we have solved.

The more experience one has the more tools and techniques one can bring to bear in tackling the given problem. But sometimes, it blocks us from discovering a desirable or better solution to the problem.

A skill that is important to try to develop in problem-solving is the ability to view a problem from a variety of angles.

One must be able to metaphorically turn a problem upside down, inside out, sideways, backwards, forwards and so on. Once one has developed this skill it should be possible to get started on any problem.

5. Working Backwards from the Solution:

In some cases, we can assume that we already have the solution to the problem and then try to work backwards to the starting point. Even a guess at the solution to the problem may be enough to give us a foothold to start on the problem.

We can systematize the investigations and avoid duplicate efforts by writing down the various steps taken and explorations made.

Another practice that helps to develop the problem-solving skills, once we have solved a problem, to consciously reflect back on the way we went about discovering the solution.

General Problem Solving Strategies:

problem solving through programming in c

There are a number of general and powerful computational strategies that are repeatedly used in various guises in computer science.

Often it is possible to phrase a problem in terms of one of these strategies and achieve considerable gains in computational efficiency.

1. Divide and Conquer:

The most widely known and used strategy, where the basic idea is to break down the original problem into two or more sub-problems, which is presumably easier or more efficient to solve.

The Splitting can be carried on further so that eventually we have many sub-problems, so small that further splitting is no necessary to solve them. We shall see many examples of this strategy and discuss the gain in efficiency due to its application.

2. Binary Doubling:

This is the reverse of the divide and conquers strategy i.e build-up the solution for a larger problem from solutions and smaller sub-problems.

3. Dynamic Programming:

Another general strategy for problem-solving which is useful when we can build-up the solution as a sequence of the intermediate steps. Problem Solving through programming in C.

The travelling salesman problem falls into this category. The idea here is that a good or optimal solution to a problem can be built-up from good or optimal solutions of the sub-problems.

4. General Search, Back Tracking and Branch-and-Bound:

All of these are variants of the basic dynamic programming strategy but are equally important.

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problem solving and programming in c

Complete C Programming Course from Dr. Chuck

Beau Carnes

We just released a comprehensive C course on the freeCodeCamp.org YouTube channel. This course, developed by Dr. Charles Severance (aka Dr. Chuck), is designed to help you understand computer architecture and low-level programming using the classic C programming language.

About the Course

In this comprehensive course, Dr. Chuck uses the classic book "The C Programming Language" by Brian Kernighan and Dennis Ritchie, often referred to as K&R, to guide you through the fundamentals of C. This book, first published in 1978, has been instrumental in shaping modern programming languages and provides a solid foundation for learning C.

Here are the sections in this course:

K&R 0: Historical Context: Understand the historical significance of C and its impact on computing.

From Python to C: Transition smoothly from Python to C, comparing and contrasting the two languages.

K&R 1: A Tutorial Introduction: Get an introduction to the basics of C programming.

K&R 2: Types, Operators, and Expressions: Learn about data types, operators, and expressions in C.

K&R 3: Control Flow: Explore control flow constructs like loops and conditionals.

K&R 4: Functions and Program Structure: Understand how to structure programs and write functions.

K&R 5: Pointers and Arrays: Dive deep into pointers and arrays, key concepts in C.

K&R 6: Structures: Learn about structures and their uses in C programming.

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In the Epilogue of this course, Dr. Chuck interviews Guido van Rossum, the creator of Python, providing unique insights into the development of modern programming languages and their relationship with C.

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Dr. Charles Severance is a clinical associate professor at the University of Michigan School of Information. Known for his engaging teaching style and deep expertise in programming, Dr. Chuck has made significant contributions to online education. He is the instructor of the popular "Python for Everybody" course series and has authored several influential textbooks.

Why Learn C in 2024?

Learning C in 2024 can be incredibly beneficial for several reasons:

Foundational Knowledge:

Understanding Low-Level Programming: C provides a deep understanding of how computers work at a low level, including memory management, pointers, and system calls. This knowledge is crucial for grasping how software interacts with hardware.

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Performance and Efficiency:

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Resource Management: C allows fine-grained control over system resources, which is essential for writing efficient and optimized code.

System-Level Programming:

Operating Systems and Kernels: C is the language of choice for developing operating systems and kernels. Learning C is essential if you are interested in systems programming or contributing to open-source projects like Linux.

Embedded Systems: C is widely used in embedded systems programming. If you are interested in developing firmware or working with microcontrollers, C is a must-know language.

Career Opportunities:

Job Market Demand: C remains in demand in various industries, including systems programming, embedded systems, telecommunications, and game development.

Versatility: Knowledge of C can open doors to various career paths, from software development to cybersecurity and beyond.

Legacy Systems:

Maintenance of Existing Codebases: Many legacy systems and critical software are written in C. Understanding C can be crucial for maintaining and updating these systems.

Interoperability: C code is often integrated with other languages and systems. Knowing C can help you work on projects that require interfacing with existing C codebases.

Educational Value:

Algorithm and Data Structure Implementation: C is excellent for learning and implementing fundamental algorithms and data structures. This experience can enhance your problem-solving skills and algorithmic thinking.

Understanding Computer Science Concepts: C is often used in academic settings to teach core computer science concepts, such as operating systems, compilers, and networking.

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I'm a teacher and developer with freeCodeCamp.org. I run the freeCodeCamp.org YouTube channel.

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Home » C programming language

C Programs with Solutions

This section contains popular C programs with solution. Learn and practice these programs to test and enhance your C skills. Last updated : April 01, 2023

The best way to learn C programming is by practicing and solving the C programs (C problems). We have 1000+ C programs with solutions which are categorized below. Practice these C programs to learn and enhance your C problem-solving skills.

List of C programs

Practice the C programs based on the categories, library functions, advanced, top searched, and latest.

C programs by categories

  • C Basic and Conditional Programs 90
  • C switch case programs 06
  • C 'goto' programs 10
  • Bitwise related Programs 32
  • Looping (for, while, do while) Programs 18
  • C String Manipulation programs 10
  • C String programs 50
  • String User Define Functions Programs 11
  • Recursion Programs 13
  • Number (Digits Manipulation) Programs 10
  • Number System Conversion Programs 15
  • Star/Pyramid Programs 17
  • Sum of Series Programs (set 1) 05
  • Sum of Series Programs (set 2) 13
  • Pattern printing programs 01
  • User Define Function Programs (1) 05
  • User Define Function Programs (2) 13
  • One Dimensional Array Programs 58
  • Two Dimensional Array (Matrix) Programs 21
  • File Handling Programs 32
  • Structure & Union Programs 12
  • Pointer Programs 13
  • Dynamic Memory Allocation Programs 05
  • Command Line Arguments Programs 06
  • Common C program Errors 22
  • C scanf() programs 11
  • C preprocessor programs 24
  • C typedef programs 03
  • C SQLite programs 11
  • C MySQL programs 09
  • C Tricky Programs 07
  • Misc Problems & Solutions 05

C programs on standard library functions

  • ctype.h Library Functions (Set 1)
  • ctype.h Library Functions (Set 2)
  • string.h Library Functions
  • conio.h Library Functions
  • dos.h Library Functions
  • math.h Library Functions
  • graphics.h Library Functions
  • assert.h Library Functions
  • stdio.h Library Functions

Advance C programs

  • C program to create your own header file/ Create your your own header file in C
  • gotoxy(),clrscr(),getch(),getche() for GCC, Linux.
  • fork() function explanation and examples in Linux C
  • C program to print character without using format specifiers.
  • C program to find Binary Addition and Binary Subtraction.
  • C program to print weekday of given date.
  • C program to format/extract ip address octets
  • C program to check given string is a valid IPv4 address or not.
  • C program to extract bytes from an integer (Hexadecimal) value
  • C program to store date in an integer variable

Top searched C programs

Here is the list of most important/useful programs searched on the web .

Top visited programs on IncludeHelp

  • Pattern Programs in C
  • C program to design calculator with basic operations using switch
  • C program to find factorial of a number
  • C program to check whether number is Perfect Square or not
  • C program to find SUM and AVERAGE of two numbers
  • C program to convert temperature from Fahrenheit to Celsius and Celsius to Fahrenheit
  • C program to read and print an employee's detail using structure
  • Dynamic Memory Allocation programs
  • C program to convert number from Decimal to Binary
  • C program to check whether number is Palindrome or not

Top searched programs on the web

  • First C program to print "Hello World".
  • C program to find factorial of a number.
  • C program to swap two numbers without using third variable.
  • C program to check whether a number if Armstrong or not.
  • C program to check whether a number if Even or Odd.
  • C program to print all leap years from 1 to N.
  • C program to calculate employee gross salary.
  • C Program to print tables of numbers from 1 to 20.
  • C program to print star/pyramid series.
  • C program to convert temperature from Celsius to Fahrenheit and vice versa.
  • C program to convert number from Decimal to Binary.
  • C program to convert number from Binary to Decimal.
  • C program to print ASCII Table.
  • C program to get and set current system date and time.
  • C program to run dos command.

Latest C programs

  • C program to generate random numbers within a range
  • C program to compare strings using strcmp() function
  • Interchange the two adjacent nodes in a given circular linked list | C program
  • Find the largest element in a doubly linked list | C program
  • Convert a given singly linked list to a circular list | C program
  • Implement Circular Doubly Linked List | C program
  • Print the Alternate Nodes in a Linked List without using Recursion
  • Print the Alternate Nodes in a Linked List using Recursion
  • Find the length of a linked list without using recursion
  • Find the length of a linked list using recursion
  • Count the number of occurrences of an element in a linked list without using recursion
  • Count the number of occurrences of an element in a linked list using recursion
  • C program to convert a Binary Tree into a Singly Linked List by Traversing Level by Level
  • C program to Check if nth Bit in a 32-bit Integer is set or not
  • C program to swap two Integers using Bitwise Operators
  • C program to replace bit in an integer at a specified position from another integer
  • C program to find odd or even number using bitmasking
  • C program to check whether a given number is palindrome or not using Bitwise Operator
  • C program to count number of bits set to 1 in an Integer
  • C program to check if all the bits of a given integer is one (1)
  • C program to find the Highest Bit Set for any given Integer
  • C program to Count the Number of Trailing Zeroes in an Integer
  • C Program to find the Biggest Number in an Array of Numbers using Recursion
  • C program to accept Sorted Array and do Search using Binary Search
  • C Program to Cyclically Permute the Elements of an Array
  • C program to find two smallest elements in a one dimensional array
  • Write your own memset() function in C
  • memset() function in C with Example
  • Write your own memcpy() function in C
  • memcpy() function in C with Example

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Problem Solving with Computer

By Bipin Tiwari

Problem Solving is a scientific technique to discover and implement the answer to a problem. The computer is the symbol manipulating device that follows the set of commands known as program.

Program is the set of instructions which is run by the computer to perform specific task. The task of developing program is called programming.

Problem Solving Technique:

Sometimes it is not sufficient just to cope with problems. We have to solve that problems. Most people are involving to solve the problem. These problem are occur while performing small task or making small decision. So, Here are the some basic steps to solve the problems

Step 1: Identify and Define Problem

Explain you problem clearly as possible as you can.

Step 2: Generate Possible Solutions

  • List out all the solution that you find. Don’t focus on the quality of the solution
  • Generate the maximum number of solution as you can without considering the quality of the solution

Step 3: Evaluate Alternatives

After generating the maximum solution, Remove the undesired solutions.

Step 4: Decide a Solution

After filtering all the solution, you have the best solution only. Then choose on of the best solution and make a decision to make it as a perfect solution.

Step 5: Implement a Solution:

After getting the best solution, Implement that solution to solve a problem.

Step 6: Evaluate the result

After implementing a best solution, Evaluate how much you solution solve the problem. If your solution will not solve the problem then you can again start with Step 2 .

Algorithm is the set of rules that define how particular problem can be solved in finite number of steps. Any good algorithm must have following characteristics

  • Input: Specify and require input
  • Output:  Solution of any problem
  • Definite:  Solution must be clearly defined
  • Finite: Steps must be finite
  • Correct:  Correct output must be generated

Advantages of Algorithms:

  • It is the way to sole a problem step-wise so it is easy to understand.
  • It uses definite procedure.
  • It is not dependent with any programming language.
  • Each step has it own meaning so it is easy to debug

Disadvantage of Algorithms:

  • It is time consuming
  • Difficult to show branching and looping statement
  • Large problems are difficult to implement

The solution of any problem in picture form is called flowchart. It is the one of the most important technique to depict an algorithm.

Advantage of Flowchart:

  • Easier to understand
  • Helps to understand logic of problem
  • Easy to draw flowchart in any software like MS-Word
  • Complex problem can be represent using less symbols
  • It is the way to documenting any problem
  • Helps in debugging process

Disadvantage of Flowchart:

  • For any change, Flowchart have to redrawn
  • Showing many looping and branching become complex
  • Modification of flowchart is time consuming

Symbol Used in Flowchart:

Example: Algorithm and Flowchart to check odd or even

Coding, Compiling and Execution

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Problem Solving and Programming In C Notes and Study Material PDF Free Download

Problem Solving and Programming in C Notes: C is one of the popular programming languages that are simple and flexible. It is a general-purpose programming language that is widely used in different kinds of applications. Operating Systems like Windows and many others are written in C language. Git, Python Interpreter, and Oracle Database are also written in C. This language is often called the base knowledge of programming. If you know this language, it becomes easier for you to learn any other programming language. This is a simple language which can provide faster execution. The demand for C developers is very high in the job market. This programming language can extend itself. It contains various kinds of functions that are part of the library. In this article, you will find complete details about problem-solving and programming of C language Lecture Notes .

Problem Solving And Programming In C Notes and Study Material PDF Free Download

Problem solving and programming in c reference books, problem solving and programming in c curriculum, list of problem solving and programming in c important questions.

  • FAQs on Problem Solving And Programming In C Notes

Introduction to Problem Solving And Programming In C

Ritchie first developed this language in 1972. It is a structured language that is widely used in the software development field. For every software developer, it is important to know the C language. This language can handle low-level activities and can be compiled easily. This language is primarily used in UNIX. This language is the successor of the B language. C language is used in databases, utilities, text editors, assemblers, operating systems, and language compilers. In C programming course, you will learn this programming language from scratch. You will find all the study materials of this widely used language from this article.

Anyone interested in making a career in software development should learn C programming. It is because this language is considered as the base language of every other programming language. If you plan to do a course on C programming, you can find the right study material through this article. We have made a list of some important study materials on C programming. You can check out computer programming terminologies once before starting C programming course.

It is a relatively small language, but it is very useful. You need to learn some simple things in C programming. This language was mainly discovered so that programmers can interact with the machines efficiently. To learn this language, you must read the right set of books. We have made a list of some important books on C language.

  • C Programming Absolute Beginner’s Guide.
  • C Programming Language.
  • The C Programming Language 2nd Edition.
  • C Programming: A Modern Approach.
  • Expert C Programming: Deep Secrets.
  • C: The Complete Reference.
  • Head First C: A Brain-Friendly Guide.
  • Computer Fundamentals and Programming in C.
  • Low-Level Programming by Igor Zhirkov
  • C in a Nutshell by Peter Prinz & Tony Crawford

Before starting the course on C programming, you must know the syllabus. It is crucial to understand the syllabus. The syllabus of C programming varies depending on the type of course and institution. However, the basic structure of the C programming’s syllabus remains the same. In this article, you will get to know about the necessary details taught in C programming.

C Programming Language Syllabus

Fundamentals of C Language

About C tutorial

Important points about C

Applications of C

C Language and English Language

Features of C

C, C++ and Java

Overview of C Language

History of C

First Program in C Hello World

Basic Structure of C Programming

Tokens in C

Keywords in C

Identifiers in C

Format Specifiers

Format Specifiers Examples

Data Types in C Language

Introduction to Data Types in C

int Data Type in C

float Data Type in C

double Data Type in C

char Data Type in C

Variable in C Language

Variable Introduction in C

Variable Declaration and Initialization

Variable types and Scope in C

Local Variable in C

static Variable in C

Global variables in C

Storage Class in C

Constant in C Language

Constants in C

Operators and Enums in C Language

Introduction to Operator

Arithmetic Operators in C

Relational Operators in C

Bit-wise Operators in C

Logical Operators in C

Assignment Operators in C

Conditional Operator in C

size of() Operator in C

Operator Precedence

Decision Making of C Language

Decision Making in C Introduction

if Statement

if-else Statement

Nested if Statement

if- else if Ladder

switch case

Loop control in C Language

Loop Introduction in C

while loop in C

do-while Loop In C

for Loop in C

Control Flow in C Programming

break Statement in C

continue Statement in C

goto statement in C

Array in C Language

Single Dimensional Array

Multi-Dimensional Array in C

String in C Language

Introduction to String

Function in C Language

Function in C

Function Calling in C

return type in Function

Call by Value in C

User Define Function

Predefined Functions

String functions in C

All String Functions

strcat() function

strncat() function

strcpy() function

strncpy() function

strlen() function

strcmp() function

strcmpi() function

strchr() function

strrchr() function

strstr() function

strrstr() function

strdup() function

strlwr() function

strupr() function

strrev() function

strset() function

strnset() function

strtok() function

Recursion in c

Introduction to Recursion

Direct and Indirect Recursion

Pointer in C Language

Pointer in C

types of pointer

NULL pointer

Dangling Pointer

Void/Generic Pointers

Wild Pointer

Near, Far and Huge Pointer

Pointer Expressions and Arithmetic

Pointer and Array

Strings as pointers

Pointer to Function

Call by Reference in C

Structure in C Language

Structure in C

Nested Structure in C

The array of Structures in C

Pointer to Structure

Structure to Function in C

typedef in C

typedef vs #define in C

Union in C Language

File Input/Output

Introduction to File

File Operation in c

Dynamic Memory Allocation

Introduction to DMA

calloc() and free() function

realloc() and free() function

C Pre-processor

Introduction about Pre-processor

  • What is the difference between ++i and i++?
  • Give a brief note on the volatile keyword.
  • What are the basic data types related to C?
  • Explain syntax errors.
  • How can you create a decrement and increment statement in C?
  • Explain dangling pointer in C.
  • What is called the prototype function in C?
  • What is a header file? Explain its usage in C programming.
  • Explain pointer on a pointer in C language.
  • How can you save data in a stack data structure type?

FAQs on Problem Solving and Programming in C Notes

Question 1. What is called the C language?

Answer: C is one of the popular programming languages that are simple and flexible. It is a general-purpose programming language that is widely used in different kinds of applications.

Question 2. What kind of software is written in the C language?

Answer: Operating Systems like Windows and many others are written in C language. Git, Python Interpreter, and Oracle Database are also written in C.

Question 3. When was C language developed?

Ritchie first developed the C language in 1972. It is a structured language that is widely used in the software development field.

Question 4. Is it tough to learn the C language?

Answer: It is not that difficult to learn the C language. C language is often called the base language in programming. After learning the C language, it becomes easier to learn other programming languages like C++, Java, C# etc.

The information provided above regarding the syllabus and study materials for C programming will help in your study. If you have any other questions regarding C programming study materials, please let us know in the comment section.

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Problem solving through Programming In C

  • Formulate simple algorithms for arithmetic and logical problems
  • Translate the algorithms to programs (in C language)
  • Test and execute the programs and  correct syntax and logical errors
  • Implement conditional branching, iteration and recursion
  • Decompose a problem into functions and synthesize a complete program using divide and conquer approach
  • Use arrays, pointers and structures to formulate algorithms and programs
  • Apply programming to solve matrix addition and multiplication problems and searching and sorting problems 
  • Apply programming to solve simple numerical method problems, namely rot finding of function, differentiation of function and simple integration

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Welcome to the daily solving of our PROBLEM OF THE DAY with Yash Dwivedi . We will discuss the entire problem step-by-step and work towards developing an optimized solution. This will not only help you brush up on your concepts of Bit Manipulation but also build up problem-solving skills. Given a number n , Your task is to swap the two nibbles and find the resulting number. 

A nibble is a four-bit aggregation, or half an octet. There are two nibbles in a byte. For example, the decimal number 150 is represented as 10010110 in an 8-bit byte. This byte can be divided into two nibbles: 1001 and 0110.

Input: n = 100 Output: 70 Explanation: 100 in binary is 01100100, two nibbles are (0110) and (0100). If we swap the two nibbles, we get 01000110 which is 70 in decimal.

Give the problem a try before going through the video. All the best!!! Problem Link: https://practice.geeksforgeeks.org/problems/swap-two-nibbles-in-a-byte0446/1

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The Algebra Problem: How Middle School Math Became a National Flashpoint

Top students can benefit greatly by being offered the subject early. But many districts offer few Black and Latino eighth graders a chance to study it.

The arms of a student are seen leaning on a desk. One hand holds a pencil and works on algebra equations.

By Troy Closson

From suburbs in the Northeast to major cities on the West Coast, a surprising subject is prompting ballot measures, lawsuits and bitter fights among parents: algebra.

Students have been required for decades to learn to solve for the variable x, and to find the slope of a line. Most complete the course in their first year of high school. But top-achievers are sometimes allowed to enroll earlier, typically in eighth grade.

The dual pathways inspire some of the most fiery debates over equity and academic opportunity in American education.

Do bias and inequality keep Black and Latino children off the fast track? Should middle schools eliminate algebra to level the playing field? What if standout pupils lose the chance to challenge themselves?

The questions are so fraught because algebra functions as a crucial crossroads in the education system. Students who fail it are far less likely to graduate. Those who take it early can take calculus by 12th grade, giving them a potential edge when applying to elite universities and lifting them toward society’s most high-status and lucrative professions.

But racial and economic gaps in math achievement are wide in the United States, and grew wider during the pandemic. In some states, nearly four in five poor children do not meet math standards.

To close those gaps, New York City’s previous mayor, Bill de Blasio, adopted a goal embraced by many districts elsewhere. Every middle school would offer algebra, and principals could opt to enroll all of their eighth graders in the class. San Francisco took an opposite approach: If some children could not reach algebra by middle school, no one would be allowed to take it.

The central mission in both cities was to help disadvantaged students. But solving the algebra dilemma can be more complex than solving the quadratic formula.

New York’s dream of “algebra for all” was never fully realized, and Mayor Eric Adams’s administration changed the goal to improving outcomes for ninth graders taking algebra. In San Francisco, dismantling middle-school algebra did little to end racial inequities among students in advanced math classes. After a huge public outcry, the district decided to reverse course.

“You wouldn’t think that there could be a more boring topic in the world,” said Thurston Domina, a professor at the University of North Carolina. “And yet, it’s this place of incredibly high passions.”

“Things run hot,” he said.

In some cities, disputes over algebra have been so intense that parents have sued school districts, protested outside mayors’ offices and campaigned for the ouster of school board members.

Teaching math in middle school is a challenge for educators in part because that is when the material becomes more complex, with students moving from multiplication tables to equations and abstract concepts. Students who have not mastered the basic skills can quickly become lost, and it can be difficult for them to catch up.

Many school districts have traditionally responded to divergent achievement levels by simply separating children into distinct pathways, placing some in general math classes while offering others algebra as an accelerated option. Such sorting, known as tracking, appeals to parents who want their children to reach advanced math as quickly as possible.

But tracking has cast an uncomfortable spotlight on inequality. Around a quarter of all students in the United States take algebra in middle school. But only about 12 percent of Black and Latino eighth graders do, compared with roughly 24 percent of white pupils, a federal report found .

“That’s why middle school math is this flashpoint,” said Joshua Goodman, an associate professor of education and economics at Boston University. “It’s the first moment where you potentially make it very obvious and explicit that there are knowledge gaps opening up.”

In the decades-long war over math, San Francisco has emerged as a prominent battleground.

California once required that all eighth graders take algebra. But lower-performing middle school students often struggle when forced to enroll in the class, research shows. San Francisco later stopped offering the class in eighth grade. But the ban did little to close achievement gaps in more advanced math classes, recent research has found.

As the pendulum swung, the only constant was anger. Leading Bay Area academics disparaged one another’s research . A group of parents even sued the district last spring. “Denying students the opportunity to skip ahead in math when their intellectual ability clearly allows for it greatly harms their potential for future achievement,” their lawsuit said.

The city is now back to where it began: Middle school algebra — for some, not necessarily for all — will return in August. The experience underscored how every approach carries risks.

“Schools really don’t know what to do,” said Jon R. Star, an educational psychologist at Harvard who has studied algebra education. “And it’s just leading to a lot of tension.”

In Cambridge, Mass., the school district phased out middle school algebra before the pandemic. But some argued that the move had backfired: Families who could afford to simply paid for their children to take accelerated math outside of school.

“It’s the worst of all possible worlds for equity,” Jacob Barandes, a Cambridge parent, said at a school board meeting.

Elsewhere, many students lack options to take the class early: One of Philadelphia’s most prestigious high schools requires students to pass algebra before enrolling, preventing many low-income children from applying because they attend middle schools that do not offer the class.

In New York, Mr. de Blasio sought to tackle the disparities when he announced a plan in 2015 to offer algebra — but not require it — in all of the city’s middle schools. More than 15,000 eighth graders did not have the class at their schools at the time.

Since then, the number of middle schools that offer algebra has risen to about 80 percent from 60 percent. But white and Asian American students still pass state algebra tests at higher rates than their peers.

The city’s current schools chancellor, David Banks, also shifted the system’s algebra focus to high schools, requiring the same ninth-grade curriculum at many schools in a move that has won both support and backlash from educators.

And some New York City families are still worried about middle school. A group of parent leaders in Manhattan recently asked the district to create more accelerated math options before high school, saying that many young students must seek out higher-level instruction outside the public school system.

In a vast district like New York — where some schools are filled with children from well-off families and others mainly educate homeless children — the challenge in math education can be that “incredible diversity,” said Pedro A. Noguera, the dean of the University of Southern California’s Rossier School of Education.

“You have some kids who are ready for algebra in fourth grade, and they should not be denied it,” Mr. Noguera said. “Others are still struggling with arithmetic in high school, and they need support.”

Many schools are unequipped to teach children with disparate math skills in a single classroom. Some educators lack the training they need to help students who have fallen behind, while also challenging those working at grade level or beyond.

Some schools have tried to find ways to tackle the issue on their own. KIPP charter schools in New York have added an additional half-hour of math time to many students’ schedules, to give children more time for practice and support so they can be ready for algebra by eighth grade.

At Middle School 50 in Brooklyn, where all eighth graders take algebra, teachers rewrote lesson plans for sixth- and seventh-grade students to lay the groundwork for the class.

The school’s principal, Ben Honoroff, said he expected that some students would have to retake the class in high school. But after starting a small algebra pilot program a few years ago, he came to believe that exposing children early could benefit everyone — as long as students came into it well prepared.

Looking around at the students who were not enrolling in the class, Mr. Honoroff said, “we asked, ‘Are there other kids that would excel in this?’”

“The answer was 100 percent, yes,” he added. “That was not something that I could live with.”

Troy Closson reports on K-12 schools in New York City for The Times. More about Troy Closson

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    Course abstract. This course is aimed at enabling the students to • formulate simple algorithms for arithmetic and logical problems • translate the algorithms to programs (in C language) • test and execute the programs and correct syntax and logical errors • implement conditional branching, iteration and recursion • decompose a problem into functions and synthesize a complete program ...

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