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Now maybe you understand why if you can solve only one problem in polynomial time, you can do all of them.
Decision problems are those that can be answered with yes/no. For example, is it possible to reach from A to B in 10 seconds? Optimization problem minimizes or maximizes the answer. For example, how many seconds can it take to get from A to B in minimum time? The above categories deal with the decision version of the problem. Any optimization problem can be formulated as a decision problem in a slightly different way, as we did for the Hamiltonian path above.
Now the question is what is the first np-complete problem? If there is not an np-complete problem first, we cannot put the other problem into the np-complete or hard category because we are doing it by converting the problem. Let’s say you have some boolean variables x,y,z etc. You give some conditions like: “If X is true then Y is false”, “Z and X are both false” etc. Now you need to assign true/false values to x,y,z so that all relations are true.
This is called Boolean satisfiability problem or SAT problem for short. A 2-sat problem if there are 2 variables in the relation, 3-sat if there are 3, such as “if X and Y are false then Z is true” if the relation is 3-sat, generalized it is called k-sat. 2-SAT can be solved in polynomial time, no polynomial solution is obtained if k>2. Using the formal definition of NP categories, Cook–Levin proved that k-sat is an NP complete problem. That was the first evidence. Cook later received the highest Turing Prize in Computer Science for his work. If you can solve the k-sat problem in polynomial time you will be equivalent to an Einstein-Newton type person in no time.
One of Turing’s famous NP-hard problems is the Halting problem. “Given a computer program, will it ever end or will it continue indefinitely”. Nothing can be solved or verified in polynomial time.
NP problems are often seen in programming contests where the size of the input is greatly reduced or a special condition is added so that it can be solved in 3-10 seconds by backtracking. Since many real-life problems do not have polynomial solutions, scientists are trying to improve exponential solutions as much as possible. With the help of branch and bound technique, backtracking can reduce the search space and find the solution fairly quickly. Sometimes heuristics are used. There are many modern algorithms for solving traveling salesman, graph coloring etc., these are still being researched, if you are interested, you can download some research papers and study yourself.
Computer Science
The breadwinner of the book “The Alchemist” dreams of becoming a tourist. But to make that dream come true, he suppressed his dream by not traveling abroad as a shepherd boy because in the eyes of people, the life of a breadwinner is more honorable than that of a shepherd boy. So his dream of pleasing the society was not fulfilled. Most of us are breadwinners, instead of fulfilling our dreams, we think about what will get us a job with more money if we study. Without knowing the “B” of a subject, I suddenly enrolled in the university in the hope of getting a job, then at some point disappointment surrounded me.
Computer Science is a very popular subject. There are many misconceptions among people about this subject, not everyone has a good idea about what is taught in this subject. The saddest thing is that many students get admitted without knowing what is taught in this subject because of the good job market, this is true not only for computer science but for any subject in Bangladesh. What happens next is that many people get frustrated when they can’t adapt.
I’m fortunate that even though I don’t know much about computer science, I already liked programming and had a lot of interest in computers since childhood, so I’m having a great time now, but not everyone is so lucky, and it’s not only the system’s fault, but also our own ignorance to a large extent. I have seen many friends who have scored well in the entrance exam and are now disappointed after looking at the job market and choosing the subject.
We are told from childhood onwards that everything we want to do is impossible. We grow up with this idea, and as the years accumulate, so too do the layers of prejudice, fear and guilt. There comes a time when our personal calling is so deeply buried in our soul as to be invisible. But it’s still there” – The alchemist, Paulo Coelho”
The purpose of my writing is to inform everyone about what is taught in computer science, especially the younger ones who have not yet chosen any subject and their parents. While there are many guidelines regarding the admission test, there is a lack of guidelines regarding the subject. And in those that are there, creativity is needed in computer science, memorization has to be reduced by just writing down these talks, not actually writing down what is taught.
A part of the people of Bangladesh think that Word, Power Point are taught in computer science, and since even the neighborhood shopkeeper can do them well, there is no point in studying computer science. Again, the idea of people who know well about computers, know a little bit of programming, here only teaches how to make a website in HTML, PHP, which can be learned even if you don’t study computer science, this idea works more among freelancers.
Now let’s see one by one what topics to study in computer science. We will know briefly about the topics. Then you can decide yourself how true the above ideas are. Knowing about the topics will be a task for you to think whether this subject is really your choice or you will study electrical, mechanical, physics or any other subject.
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