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Sudoku for Beginners: How to Improve Your Problem-Solving Skills
Are you a beginner when it comes to solving Sudoku puzzles? Do you find yourself frustrated and unsure of where to start? Fear not, as we have compiled a comprehensive guide on how to improve your problem-solving skills through Sudoku.
Understanding the Basics of Sudoku
Before we dive into the strategies and techniques, let’s first understand the basics of Sudoku. A Sudoku puzzle is a 9×9 grid that is divided into nine smaller 3×3 grids. The objective is to fill in each row, column, and smaller grid with numbers 1-9 without repeating any numbers.
Starting Strategies for Beginners
As a beginner, it can be overwhelming to look at an empty Sudoku grid. But don’t worry. There are simple starting strategies that can help you get started. First, look for any rows or columns that only have one missing number. Fill in that number and move on to the next row or column with only one missing number. Another strategy is looking for any smaller grids with only one missing number and filling in that number.
Advanced Strategies for Beginner/Intermediate Level
Once you’ve mastered the starting strategies, it’s time to move on to more advanced techniques. One technique is called “pencil marking.” This involves writing down all possible numbers in each empty square before making any moves. Then use logic and elimination techniques to cross off impossible numbers until you are left with the correct answer.
Another advanced technique is “hidden pairs.” Look for two squares within a row or column that only have two possible numbers left. If those two possible numbers exist in both squares, then those two squares must contain those specific numbers.
Benefits of Solving Sudoku Puzzles
Not only is solving Sudoku puzzles fun and challenging, but it also has many benefits for your brain health. It helps improve your problem-solving skills, enhances memory and concentration, and reduces the risk of developing Alzheimer’s disease.
In conclusion, Sudoku is a great way to improve your problem-solving skills while also providing entertainment. With these starting and advanced strategies, you’ll be able to solve even the toughest Sudoku puzzles. So grab a pencil and paper and start sharpening those brain muscles.
This text was generated using a large language model, and select text has been reviewed and moderated for purposes such as readability.
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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 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
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:
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 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
Note: This exam date is subjected to change based on seat availability. You can check final exam date on your hall ticket.
Course layout, books and references, instructor bio.
Prof. Anupam Basu
- Assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course.
- ( All assignments in a particular week will be counted towards final scoring - quizzes and programming assignments).
- Unproctored programming exam score = 25% of the average scores obtained as part of Unproctored programming exam - out of 100
- Proctored Exam score =50% of the proctored certification exam score out of 100
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CBSE Class 11 | Problem Solving Methodologies
Problem solving process.
The process of problem-solving is an activity which has its ingredients as the specification of the program and the served dish is a correct program. This activity comprises of four steps : 1. Understanding the problem: To solve any problem it is very crucial to understand the problem first. What is the desired output of the code and how that output can be generated? The obvious and essential need to generate the output is an input. The input may be singular or it may be a set of inputs. A proper relationship between the input and output must be drawn in order to solve the problem efficiently. The input set should be complete and sufficient enough to draw the output. It means all the necessary inputs required to compute the output should be present at the time of computation. However, it should be kept in mind that the programmer should ensure that the minimum number of inputs should be there. Any irrelevant input only increases the size of and memory overhead of the program. Thus Identifying the minimum number of inputs required for output is a crucial element for understanding the problem.
2. Devising the plan: Once a problem has been understood, a proper action plan has to be devised to solve it. This is called devising the plan. This step usually involves computing the result from the given set of inputs. It uses the relationship drawn between inputs and outputs in the previous step. The complexity of this step depends upon the complexity of the problem at hand.
3. Executing the plan: Once the plan has been defined, it should follow the trajectory of action while ensuring the plan’s integrity at various checkpoints. If any inconsistency is found in between, the plan needs to be revised.
4. Evaluation: The final result so obtained must be evaluated and verified to see if the problem has been solved satisfactorily.
Problem Solving Methodology(The solution for the problem)
The methodology to solve a problem is defined as the most efficient solution to the problem. Although, there can be multiple ways to crack a nut, but a methodology is one where the nut is cracked in the shortest time and with minimum effort. Clearly, a sledgehammer can never be used to crack a nut. Under problem-solving methodology, we will see a step by step solution for a problem. These steps closely resemble the software life cycle . A software life cycle involves several stages in a program’s life cycle. These steps can be used by any tyro programmer to solve a problem in the most efficient way ever. The several steps of this cycle are as follows :
Step by step solution for a problem (Software Life Cycle) 1. Problem Definition/Specification: A computer program is basically a machine language solution to a real-life problem. Because programs are generally made to solve the pragmatic problems of the outside world. In order to solve the problem, it is very necessary to define the problem to get its proper understanding. For example, suppose we are asked to write a code for “ Compute the average of three numbers”. In this case, a proper definition of the problem will include questions like : “What exactly does average mean?” “How to calculate the average?”
Once, questions like these are raised, it helps to formulate the solution of the problem in a better way. Once a problem has been defined, the program’s specifications are then listed. Problem specifications describe what the program for the problem must do. It should definitely include :
what is the input set of the program
What is the desired output of the program and in what form the output is desired?
2. Problem Analysis (Breaking down the solution into simple steps): This step of solving the problem follows a modular approach to crack the nut. The problem is divided into subproblems so that designing a solution to these subproblems gets easier. The solutions to all these individual parts are then merged to get the final solution of the original problem. It is like divide and merge approach.
Modular Approach for Programming :
The process of breaking a large problem into subproblems and then treating these individual parts as different functions is called modular programming. Each function behaves independent of another and there is minimal inter-functional communication. There are two methods to implement modular programming :
- Top Down Design : In this method, the original problem is divided into subparts. These subparts are further divided. The chain continues till we get the very fundamental subpart of the problem which can’t be further divided. Then we draw a solution for each of these fundamental parts.
- Bottom Up Design : In this style of programming, an application is written by using the pre-existing primitives of programming language. These primitives are then amalgamated with more complicated features, till the application is written. This style is just the reverse of the top-down design style.
3. Problem Designing: The design of a problem can be represented in either of the two forms :
The ways to execute any program are of three categories:
- Sequence Statements Here, all the instructions are executed in a sequence, that is, one after the another, till the program is executed.
- Selection Statements As it is self-clear from the name, in these type of statements the whole set of instructions is not executed. A selection has to be made. A selected number of instructions are executed based on some condition. If the condition holds true then some part of the instruction set is executed, otherwise, another part of the set is executed. Since this selection out of the instruction set has to be made, thus these type of instructions are called Selection Statements.
Identification of arithmetic and logical operations required for the solution : While writing the algorithm for a problem, the arithmetic and logical operations required for the solution are also usually identified. They help to write the code in an easier manner because the proper ordering of the arithmetic and logical symbols is necessary to determine the correct output. And when all this has been done in the algorithm writing step, it just makes the coding task a smoother one.
- Flow Chart : Flow charts are diagrammatic representation of the algorithm. It uses some symbols to illustrate the starting and ending of a program along with the flow of instructions involved in the program.
4. Coding: Once an algorithm is formed, it can’t be executed on the computer. Thus in this step, this algorithm has to be translated into the syntax of a particular programming language. This process is often termed as ‘coding’. Coding is one of the most important steps of the software life cycle. It is not only challenging to find a solution to a problem but to write optimized code for a solution is far more challenging.
Writing code for optimizing execution time and memory storage : A programmer writes code on his local computer. Now, suppose he writes a code which takes 5 hours to get executed. Now, this 5 hours of time is actually the idle time for the programmer. Not only it takes longer time, but it also uses the resources during that time. One of the most precious computing resources is memory. A large program is expected to utilize more memory. However, memory utilization is not a fault, but if a program is utilizing unnecessary time or memory, then it is a fault of coding. The optimized code can save both time and memory. For example, as has been discussed earlier, by using the minimum number of inputs to compute the output , one can save unnecessary memory utilization. All such techniques are very necessary to be deployed to write optimized code. The pragmatic world gives reverence not only to the solution of the problem but to the optimized solution. This art of writing the optimized code also called ‘competitive programming’.
5. Program Testing and Debugging: Program testing involves running each and every instruction of the code and check the validity of the output by a sample input. By testing a program one can also check if there’s an error in the program. If an error is detected, then program debugging is done. It is a process to locate the instruction which is causing an error in the program and then rectifying it. There are different types of error in a program : (i) Syntax Error Every programming language has its own set of rules and constructs which need to be followed to form a valid program in that particular language. If at any place in the entire code, this set of rule is violated, it results in a syntax error. Take an example in C Language
In the above program, the syntax error is in the first printf statement since the printf statement doesn’t end with a ‘;’. Now, until and unless this error is not rectified, the program will not get executed.
Once the error is rectified, one gets the desired output. Suppose the input is ‘good’ then the output is : Output:
(ii) Logical Error An error caused due to the implementation of a wrong logic in the program is called logical error. They are usually detected during the runtime. Take an example in C Language:
In the above code, the ‘for’ loop won’t get executed since n has been initialized with the value of 11 while ‘for’ loop can only print values smaller than or equal to 10. Such a code will result in incorrect output and thus errors like these are called logical errors. Once the error is rectified, one gets the desired output. Suppose n is initialised with the value ‘5’ then the output is : Output:
(iii) Runtime Error Any error which causes the unusual termination of the program is called runtime error. They are detected at the run time. Some common examples of runtime errors are : Example 1 :
If during the runtime, the user gives the input value for B as 0 then the program terminates abruptly resulting in a runtime error. The output thus appears is : Output:
Example 2 : If while executing a program, one attempts for opening an unexisting file, that is, a file which is not present in the hard disk, it also results in a runtime error.
6. Documentation : The program documentation involves :
- Problem Definition
- Problem Design
- Documentation of test perform
- History of program development
7. Program Maintenance: Once a program has been formed, to ensure its longevity, maintenance is a must. The maintenance of a program has its own costs associated with it, which may also exceed the development cost of the program in some cases. The maintenance of a program involves the following :
- Detection and Elimination of undetected errors in the existing program.
- Modification of current program to enhance its performance and adaptability.
- Enhancement of user interface
- Enriching the program with new capabilities.
- Updation of the documentation.
Control Structure- Conditional control and looping (finite and infinite)
There are codes which usually involve looping statements. Looping statements are statements in which instruction or a set of instructions is executed multiple times until a particular condition is satisfied. The while loop, for loop, do while loop, etc. form the basis of such looping structure. These statements are also called control structure because they determine or control the flow of instructions in a program. These looping structures are of two kinds :
In the above program, the ‘for’ loop gets executed only until the value of i is less than or equal to 10. As soon as the value of i becomes greater than 10, the while loop is terminated. Output:
In the above code, one can easily see that the value of n is not getting incremented. In such a case, the value of n will always remain 1 and hence the while loop will never get executed. Such loop is called an infinite loop. Output:
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